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Analysis of the heat of hydration in mass concrete structures

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Title:
Analysis of the heat of hydration in mass concrete structures
Creator:
Petersen, Kelsey Jo
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English

Thesis/Dissertation Information

Degree:
Master's ( Master of science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Civil Engineering, CU Denver
Degree Disciplines:
Civil engineering
Committee Chair:
Rutz, Frederick
Committee Members:
Li, Chengyu
Rens, Kevin

Notes

Abstract:
This thesis analyzes the temperature development and distribution in mass concrete structures, specifically a steam turbine generator pedestal, by comparing field data with a simulated finite element model in Ansys. A stress analysis was also performed to determine how the thermal loading impacts different areas of the structure. The chemical reactions that occur as a result of combining cement and water cause significant heat generation in the concrete mixture. For mass concrete structures, the heat that is generated is dissipated quickly at the surface, but is retained at the center of the structure, achieving large maximum temperatures. The maximum temperature and temperature differential pose a risk to the structural integrity of the structure as excessive temperatures can induce tensile stresses in the structure, resulting in cracking. The temperatures, and therefore stresses, that are developed are time dependent and most commonly occur during the first few days after casting. Temperature data was recorded for each of the concrete pours associated with the steam turbine generator pedestal, including the basemat, columns (8), and tabletop, with the use of thermocouples at select locations in the structure. The data was analyzed for the time history of the temperatures and the differentials. A model was created in Ansys with a variety of input parameters to perform a thermal analysis by simulating the temperature results as seen in the field. The model reasonably represented the field results for each structure and proved to be a powerful tool to analyze scenarios for future pedestal structures. Using the same model, a parametric study was completed to understand the impacts of a variety of variables. The thermal analysis was then applied to a structural analysis of the same model. The temperatures were applied as thermal loads at each nodal location of the structure. The model simulated how the stresses are developed over time and where they occur. Large stresses were seen at the surface and corners as a result of self-stress; other large stresses were seen towards the bottom of the structure as a result of restraint-stress.

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University of Colorado Denver
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Auraria Library
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Copyright Kelsey Jo Petersen. Permission granted to University of Colorado Denver to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

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ANALYSIS OF THE HEAT OF HYDRATION IN MASS CONCRETE STRUCTURE S b y KELSEY JO PETERSEN B.S., University of Colorado, 2013 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment Of the requirements for the degree of Master of Science Civil Engineering Program 2018

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ii © 2018 KELSEY JO PETERSEN ALL RIGHTS RESERVED

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iii This thesis for the Master of Science degree by Kelsey Jo Petersen h as been approved for the Civil Engineering Program By Fred erick Rutz, Chair Chengy u Li Kevin Rens Date: May 12, 2018

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iv Petersen, Kelsey Jo (M.S., Civil Engineering Program) Analysis of the Heat of Hydration in Mass Concrete Structures Thes is directed by Professor Chengy u Li ABSTRACT This thesis analyzes the te mperature development and distribution in mass concrete structures, specifically a steam turbine generator pedestal, by comparing field data with a simulated finite element model in Ansys. A stress analysis was also performed to determine how the thermal loading i m p a c t s different areas of the structure. The chemical reactions that occur as a result of combining cement and water cause significant heat generation in the concrete mixture. For mass concrete structures, the heat that is generated is dissip ated quickly at the surface, but is retained at the center of the structure , achieving large maximum temperatures . The maximum temperature and temperature differential pose a risk to the structural integrity of the structure as excessive temperatures can induce tensile stresses in the st ructure , resulting in cracking. The temperatures, and therefore stresses, that are developed are time dependent and most commonly occur during the first few days after c a s t i n g . Temperature data was recorded for each of the concrete pours associated with the steam turbine generator pedestal, including the basemat, columns (8), and tabletop, with the use of thermocouples at select locations in the structure. The data was analyzed for the time history of the temperatures a nd the differentials.

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v A model was created in Ansys with a variety of input parameters to perform a thermal analysis by simulating the temperature results as seen in the field. The model reasonably represented the field results for each structure and pr oved to be a powerful tool to analyze scenarios for future pedestal str uctures. Using the same model, a parametric study was completed to understand the impacts of a variety of variables. The thermal analysis was then applied to a structural analysis of the same model. The temperatures were applied as thermal loads at each nodal location of the structure. The model simulated how the stresses are developed over time and where they occur. Large stresses were seen at the surface and corners as a result of self stress; other large stresses were seen towards the bottom of the structure as a result of restraint stress. The form and content of this abstract are approved. I recommend its publication. Approved: Chengy u Li

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vi TABLE OF CONTENTS CHAPTER I . I NTRODUCTION ................................ ................................ ................................ ....................... 1 Background ................................ ................................ ................................ ............................ 1 Research Approach ................................ ................................ ................................ ............... 2 II . LITERATURE REVIEW ................................ ................................ ................................ .............. 4 History of Concrete and Cement ................................ ................................ ........................... 4 Material Properties of Concrete ................................ ................................ ........................... 5 Portland Cement ................................ ................................ ................................ ............... 6 Aggregate ................................ ................................ ................................ .......................... 8 Water ................................ ................................ ................................ .............................. 10 Thermal Properties of Concrete ................................ ................................ .......................... 10 Thermal Conductivity ................................ ................................ ................................ ..... 11 Specific Heat ................................ ................................ ................................ ................... 11 Density ................................ ................................ ................................ ............................ 12 Diffusivity ................................ ................................ ................................ ........................ 12 Hydration ................................ ................................ ................................ ............................. 12 Hydration of Calcium Silicates ................................ ................................ ........................ 14 Hydration of Tricalcium Aluminate ................................ ................................ ................ 15 Hydration Products ................................ ................................ ................................ ......... 16 Delayed Ettringite Formation (DEF) ................................ ................................ ............... 16 Heat of Hydration ................................ ................................ ................................ ........... 17

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vii Mass Concrete ................................ ................................ ................................ ..................... 17 Thermal Stresses in Concrete ................................ ................................ ......................... 19 Cracking in Concrete ................................ ................................ ................................ ....... 22 Maximu m Concrete Temperature ................................ ................................ .................. 23 Maximum Concrete Temperature Differential ................................ .............................. 23 III . HISTORIC FIELD DATA ANALYSIS ................................ ................................ ......................... 25 Project Background ................................ ................................ ................................ ............. 25 Mass Concrete Temperature Results ................................ ................................ .................. 29 Steam Turbine Generator P edestal Basemat ................................ .............................. 29 Steam Turbine Generator Pedestal Columns ................................ .............................. 33 Steam Turbine Generator Pedestal Tabletop ................................ .............................. 43 IV . TRANSIENT THERMAL AN ALYSIS SIMULATION ................................ ................................ .. 47 Introduction ................................ ................................ ................................ ......................... 47 Ansys APDL Therm al Simulation ................................ ................................ .......................... 50 Material and Element Properties of Model ................................ ................................ ... 50 Initial and Boundary Conditions ................................ ................................ ..................... 52 Ansys APDL STG Thermal Simulation Results ................................ ................................ ...... 57 Ansys APDL Dependent Variable Study ................................ ................................ ............... 82 Initial Temp erature of Concrete ................................ ................................ ..................... 83 Ambient Temperature ................................ ................................ ................................ .... 85 Structure Insulation ................................ ................................ ................................ ........ 87 Cement Concentrations ................................ ................................ ................................ .. 89

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viii Size of Structure ................................ ................................ ................................ ............. 91 V . THERMAL STRESS ANALY SIS SIMULATION ................................ ................................ ........... 94 Introduction ................................ ................................ ................................ ......................... 94 Theory ................................ ................................ ................................ ................................ .. 95 Ansys APDL Structural Simulation ................................ ................................ ....................... 97 Material and Element Properties of Model ................................ ................................ ... 97 Boundary Conditions and Loads ................................ ................................ ................... 101 Ansys APDL STG Structur al Simulation Results ................................ ................................ . 101 VI . CONCLUSION ................................ ................................ ................................ ..................... 115 LIST OF REFERENCES ................................ ................................ ................................ .............. 117 APPENDIX A . THERMAL ANALYSIS ANS YS COMMAND DATA ................................ ................................ .. 120 B . STRUCTURAL ANALYSIS ANSYS COMMAND DATA ................................ ............................. 129

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ix LIST OF TABLES TABLE 1 . Typical Concrete Mix Design Proportions ................................ ................................ .............. 5 2 . Portland Cement Compounds ................................ ................................ ................................ 6 3 . Portland Cement Compound % by Weight ................................ ................................ ............ 6 4 . Concrete Quantities and Dimensions for Steam Turbind Generator ................................ .. 26 5 . Concrete Mix Design Requirements ................................ ................................ .................... 27 6 . Standard I AA Base Concrete Mix Design ................................ ................................ ............ 28 7 . Standard I AA + Superplasticizer Base Concrete Mix Design ................................ ............... 28 8 . Basemat Temperature Sensor Summary ................................ ................................ ............. 31 9 . Column Temperature Sensor Summary ................................ ................................ ............... 35 10 . Colum n Maximum Temperature Differential Comparison ................................ ................ 42 11 . Tabletop Temperature Sensor Summary ................................ ................................ ........... 44 12 . Ansys Thermal Input Parameters ................................ ................................ ....................... 52 13 . Initial Conditions for each STG Component in Fahrenheit and Celsius ............................. 52 1 4 . Input Parameters for Dependent Variable Study ................................ .............................. 82

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x LIST OF FIGURES FIGURE 1 . Adiabatic Temperature Rise vs. Time for each Cement Type ................................ ................ 8 2 . Relations hip between Aggregate Size, Cement Content, and Concrete Compressive Strength ................................ ................................ ................................ ................................ . 9 3 . Aggregate Gradation by Sieve Size ................................ ................................ ...................... 10 4 . Rate of Cement Hydration vs. Time ................................ ................................ ..................... 13 5 . Plot of Concrete Temperature, Modulus of Elasticity, and Stress with Respect to Time .... 19 6. Concrete Stress Diagram ................................ ................................ ................................ ...... 21 7. Steam Turbine Generator Pedestal Model ................................ ................................ ......... 26 8. Snapshot of the Concrete Pour Procedure ................................ ................................ .......... 30 9 . Thermocouple Location for Basemat ................................ ................................ ................... 31 1 0 . Basemat Foundation Temperature Data vs. Time ................................ ............................. 32 11 . Basemat Concrete Temperature Differential from Middle and Top Sensors .................... 33 1 2 . Thermocouple Location for Columns ................................ ................................ ................. 34 13 . Column 1 Temperature Data vs. Time ................................ ................................ ............... 36 14 . Column 2 Temperature Data vs. Time ................................ ................................ ............... 36 15 . Column 3 Temperature Data v s. Time ................................ ................................ ............... 37 16 . Column 4 Temperature Data vs. Time ................................ ................................ ............... 37 17 . Column 5 Temperature Data vs. Time ................................ ................................ ............... 38 18 . Column 6 Temperature Data vs. Time ................................ ................................ ............... 38 19 . Column 7 Temperature Data vs. Time ................................ ................................ ............... 39

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xi 2 0 . Column 8 Temperature Data vs. Time ................................ ................................ ............... 39 21 . Middle Temperature Comparison for Columns ................................ ................................ . 41 22 . Surface Temperature Comparison for Columns ................................ ................................ 41 23 . Column Temperature Differential vs. Time ................................ ................................ ..... 42 3 2 4 . Thermocouple Locations for Tabletop ................................ ................................ ............... 44 25 . Tabletop Temperature Data vs. Time ................................ ................................ ................ 45 26 . Tabletop Temperature Differentia l vs. Time ................................ ................................ ...... 46 27 . SOLID70 Ansys Element ................................ ................................ ................................ ..... 51 28 . Ambient Temperature vs. Time for Basemat, Column, and Tabletop ............................... 54 29 . Coefficient Charts for Adiabatic Temperature Rise ................................ ........................... 55 30 . Heat Generation Rate for Ansys Simulation ................................ ................................ ...... 56 31 . Temperature vs Time for West Basemat Simulation ................................ ......................... 57 32 . Temperature vs Time for East Basemat Simulation ................................ ........................... 58 33 . Basemat Temperature Field at Hour 1 in YZ Cross Section ................................ ............... 59 34 . Basemat Temperature Field at Hour 1 in XZ Cross Section ................................ .............. 59 35 . Basemat Temperature Field at Hour 12 in YZ Cross Section ................................ ............. 60 36 . Basemat Temperature Field at Hour 12 in XZ Cross Section ................................ ............. 60 37 . Basemat Temperature Field at Hour 24 in YZ Cross Section ................................ ............. 61 38 . Basemat Temperature Field at Hour 24 in XZ Cross Section ................................ ............. 61 39 . Basemat Temperature Field at Hour 48 in YZ Cross Section ................................ ............. 62 40 . Basemat Temperature Field at Hour 48 in XZ Cross Section ................................ ........... 62 41 . Basemat Temperature Field at Hour 60 in YZ Cross Section ................................ ............. 63

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xii 42 . Basemat Temperature Field at Hour 60 in XZ Cross Section ................................ ............. 63 43 . Basemat Temperature Field at Hour 120 in YZ Cross Section ................................ ........... 64 44 . Basemat Temperature Field at Hour 120 in XZ Cross Section ................................ ........... 64 45 . Basemat Temperature Field at Hour 500 in YZ Cross Section ................................ ........... 65 46 . Basemat Temperature Field at Hour 500 in XZ Cross Section ................................ .......... 65 47 . Temperature vs Time for Column Simulation ................................ ................................ .... 66 48 . Column Temperature Field at Hour 1 in XZ Cross Section ................................ ................ 67 49 . Column Temperature Field at Hour 1 in XY Cross Section ................................ ................ 67 50 . Column Temperature Field at Hour 12 in XZ Cross Section ................................ .............. 68 51 . Column Temperature Field at Hour 12 in XY Cross Section ................................ .............. 68 52 . Column Temperature Field at Hour 24 in XZ Cross Section ................................ .............. 69 53 . Column Temperature Field at Hour 24 in XY Cross Section ................................ .............. 69 54 . Column Temperature Field at Hour 48 in XZ Cross Section ................................ .............. 70 55 . Column Temperature Field at Hour 48 in XY Cross Section ................................ .............. 70 56 . Column Temperature Field at Hour 60 in XZ Cross Section ................................ .............. 71 57 . Column Temperature Field at Hour 60 in XY Cross Section ................................ .............. 71 58 . Column Temperature Field at Hour 120 in XZ Cross Section ................................ ............ 72 59 . Column Temperature Field at Hour 120 in XY Cross Section ................................ ............ 72 60 . Column Temperature Field at Hour 500 in XZ Cross Section ................................ ............ 73 61 . Column Temperature Field at Hour 500 in XY Cross Section ................................ ............ 73 62 . Temperature vs Time for Tabletop Simulation ................................ ................................ .. 74 63 . Tabletop Temperature Field at Hour 1 in YZ Cross Section ................................ ............... 75

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xiii 6 4 . Tabletop Temperature Field at Hour 1 in XZ Cross Section ................................ ............... 75 65 . Tabletop Temperature Field at Hour 12 in YZ Cross Section ................................ ............. 76 66 . Tabletop Temperature Field at Hour 12 in XZ Cross Section ................................ ............. 76 67 . Tabletop Temperature Field at Hour 24 in YZ Cross Section ................................ ............. 77 68 . Tabletop Temperature Field at Hour 24 in XZ Cross Section ................................ ............. 77 69 . Tabletop Temperature Field at Hour 48 in YZ Cross Section ................................ ............. 78 70 . Tabletop Temperature Field at Hour 48 in XZ Cross Section ................................ ............. 78 71 . Tabletop Temperature Field at Hour 60 in YZ Cross Section ................................ ............. 79 72 . Tabletop Temperature Field at Hour 60 in XZ Cross Section ................................ ............. 79 73 . Tabletop Temperature Field at Hour 120 in YZ Cross Section ................................ ........... 80 74 . Tabletop Temperature Field at Hour 120 in XZ Cross Section ................................ ........... 80 75 . Tabletop Temperature Field at Hour 500 in YZ Cross Section ................................ ........... 81 76 . Tabletop Temperature Field at Hour 500 in XZ Cross Section ................................ .......... 81 77 . Temperature vs. Time at Column Surface for Various Initial Temperatures ..................... 83 78 . Temperature vs. Time at Column Center for Various Initial Temperatures ...................... 84 79 . Temperature Difference vs. Time for Column at Various Initial Temperatures ................ 84 80 . Temperature vs. Time at Column Surface for Var ious Ambient Temperatures ................ 85 81 . Temperature vs. Time at Column Center for Various Ambient Temperatures ................. 86 82 . Temperature Dif ference vs. Time for Column for Various Ambient Temperatures .......... 86 83 . Temperature vs. Time at Column Surface for Various Insulation Methods ...................... 88 84 . Temperature vs. Time at Column Center for Various Insulation Methods ....................... 88 85 . Temperature Difference vs. Time for Column for Various Insulation Methods ................ 89

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xiv 86 . Temperature vs. Time at Column Surface for Various Cement Dosages ........................... 90 87 . Temperature vs. Time at Column Center for Various Cement Dosages ............................ 90 88 . Temperature Difference vs. Time for Column for Various Cement Dosages .................... 91 8 9 . Temperature vs. Time at Column Surface for Variou s Structure Sizes .............................. 92 90 . Temperature vs. Time at Column Center for Various Structure Sizes ............................... 92 91 . Temperature Difference vs. Tim e for Column for Various Structure Sizes ....................... 93 92 . SOLID45 Ansys Element ................................ ................................ ................................ ..... 98 93 . Maturity Index Curve ................................ ................................ ................................ ....... 100 94 . Stress Diagram in Y Direction for Basemat at Different Time Steps ............................... 104 95 . Location of Basemat Vertical Stress Diagram ................................ ................................ . 104 96 . Locations of Stress Analysis in Basemat ................................ ................................ ........... 105 97 . Stress vs. Time at Various Basemat Locations ................................ ................................ . 105 98 . Stress Diagram in X Direction for Column at Various Time Steps ................................ ... 107 99 . Location of Column Horizontal Stress Diagram ................................ ............................... 1 07 100 . Stress Diagram in Y Direction for Column at Various Time Steps ................................ . 108 101 . Location of Column Vertical Stress Diagram ................................ ................................ .. 108 102 . Locations of Stress Analysis for the Column ................................ ................................ .. 109 103 . Stress vs. Time at Various Column Locations ................................ ................................ . 109 104 . Stress Diagram in Z Direction for Tabletop at Various Time Steps ................................ 111 105 . Location of Tabletop Z Direction Stress Diagram ................................ .......................... 111 106 . Stress Diagr am in Y Direction for Tabletop at Various Time Steps ................................ 112 107 . Location of Tabletop Y Direction Stress Diagram ................................ .......................... 112

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xv 1 08 . Locations of Stress Analysis for the Tabletop ................................ ................................ 113 109. Stress vs. Time at Various Tabletop Locations ................................ ............................... 113

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1 CHAPTER I INTRODUCTION Background Portland cement is the key component that makes concrete a versatile material in many forms of construction. Cement allows concrete to be in a fluid initial state and harden over time to dramatically increase its strength. The hardening of concrete is a result of the hydration reaction which occurs between cement and water. This is an exothermic reaction generating heat within the structure . risk to the structural integrity as the heat is dissipated quickly from the surface. However, for large concrete structures, the heat is released from the surface, but the heat generated in the middle is unable to dissipate due to the low thermal conductivity of concrete. The maximum temperatures and the temperature differe ntial of the structure must be properly managed through the design and construction phases. If the temperatures exceed the allowable amounts, several issues can occur, however the most common issue is concrete cracking. The cracking is a result of therma l expansion and contraction between the middle and surface of the concrete and ultimately create tensile stresses which exceed Understanding the behavior of concrete under extreme thermal conditions is essential in developing a ther mal control plan which begins at the design phase . The thermal plan includes the concrete mix design, pre cooling techniques, and post cooling techniques. Several preventative measures can be set in place to manage these temperatures and the negative eff ects.

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2 Research Approach The purpose of this thesis is to a ssess how large concrete structures , classified as mass concrete, behave when a significa nt amount of heat is generated through hydration reactions . Field data from over 2,1 00 cubic yards of concr ete from a power plant project have been analyzed to demonstrate the temperature patterns of the system and the resulting stresses that are developed . The data provides concrete pours under different initial conditions, concrete mix designs, and geomet ry. This allows observation of the thermal behavior and to determine how the above parameters impact the temperature results. In general, the concrete associated with mass concrete pours had a large increase in temperature during the first twelve hours. Fr om there, the rate of temperature increase tapered, until the maximum was achieved. For the remaining hours that data was logged, the temperature of the structure gradually cooled at a steady rate. The temperature data was analyzed to determine the maxim um temperature, as well as the temperature differential throughout the system. The results provided in the field data are then simulated in the program, Ansys. Ansys can simulate the temperature and stresses within a system. Understanding the simulatio n capabilities, as it relates to field data, will provide valuable information to develop a thermal plan in future projects. The thesis is presented in f ive different chapters Introduction, Literature Review, Historic Field Data Analysis, Transient Th ermal Analysis Simulation, and Thermal Stress Simulation.

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3 Chapter II provides a brief history of concrete and how Portland cement evolved. This section also provides a summary of the material and thermal properties associated with concrete. These prope rties and the materials used play a large role in the chemical reactions that occur in concrete. These reactions are discussed further in Chapter II, as well. Chapter III analyzes the temperature data from several mass concrete pours for a power plant p roject. The data assesses the concrete for the basemat, columns, and the tabletop. Several plots to illustrate the temperature curves and thermal differentials are provided. Chapter IV simulates the temperature results from Chapter III through a finite element transient thermal analysis. These results are compared back to the actual field data for accuracy. Additionally, other simulations are run to consider different construction methods its impact on the thermal behavior of the structure. Chapter V builds on the temperature analysis from Chapter IV and analyzes the thermal stresses that are developed as a result of the temperatures in the system. These stresses are simulated to determine where tensil e stresses develop in the structure and how they c hange with respect to time.

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4 CHAPTER II LITERATURE REVIEW History of Concrete and Cement Every region of the world has its own history of how concrete and cement were developed and utilized. The invention of concrete dramatically changed the type of bui lding and infrastructure that could be constructed. Concrete could provide strength and versatility to construction industry and i s continuing to evolve and exp and its potential. The first uses of concrete date back to 300 0 BC in Egypt . Their concrete was blocks composed of straw and straw in combination with gypsum and lime to create adherence of blocks . This combination of materials made the Egyptian Pyrami ds, at 455 feet high, a possibility. (Con crete and Cement History Timeline, 2017). New and innovative findings continued to develop throughout the years. The Greeks utilized a natural pozzolan that developed hydraulic properties when mixed with lime. A lthough the Greeks made this finding, the Romans mastered this form of construction by 200 BC. The Romans found great success in utilizing b rick to serve as forms to the large limestone rocks secure d with mortar . As the Roman construction became more imm ense, the need for a more durable material arose. Romans discovered a volcanic sand, pozzuolana that reacted with lime and water. The reaction caused hydration resulting in a durable, water resistant, and solid material. This material and methodology wa s used to create well known structures, such as the Colosseum , Roman Baths, and the Pantheon (Gromicko & Vangeem).

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5 p ortland cement was invented by J oseph Aspdin. The creati on of p ortland cement is a major testament to the strength and durability of modern concrete (Concrete and Cement History Timeline, 2017). Material Properties of Concrete Despite the various forms of concrete in the early development phases, the concrete mix designs have become more standardized. Co ncrete is primarily made up of p ortland cement, aggregate, and water. Depending on the application, pozzo lans and admixtures can be used to alter the concrete properties . Concrete forms as a result of the ce ment paste, formed by cement and water, surrounding the aggregate creat ing a matrix. A h ydration reaction occurs within the cement paste which allows the paste and aggregate to harden and gain strength to ultimately form concrete. Table 1 below provides the proportions of each material by weight for a typical concrete mix design. Table 1 Typical Concrete Mix Design Proportions Material Percent by Weight Water 8.1 Portland Cement 14.7 Coarse Aggregate 46.5 Fine Aggregate 30.7 Concrete is considered economical due to the fact that the most expensive and energy intensive material, Portland cement, only makes up 15% of concrete by weight. A single pound of cement can yield five to ten pounds of concret e (Thomas & Jennings ).

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6 Portland Cement Portland cement is the combination of several compounds , as tabulated in Table 2 . Table 2 Portland Cement Compounds Compound Formula Calcium Oxide (lime) Silicon dioxide (silica) Aluminum oxide (alum ina) Iron Oxide Water Sulfate In order to form Portland cement, t he calcium, silicon , aluminum, and iron are chemically combined and heated to a high temperature (approximately 2,600 F ) . The combination of the co mpounds and the heat forms hard, rock like pellets, known as clinker . In order to achieve the fi ne powder of cement, the clinker is ground extremely fine (How Cement is Made, 2017). The combination of the compounds tabulated above form the composition an d proportions shown in Table 3 . Table 3 Portland Cement Compound % by Weight Compound Shorthand Formula % by Weight Tricalcium aluminate 10 Tetracalcium aluminoferrite 8 Dicalcium silicate 20 Tricalcium s ilicate 55 Sodium oxide Up to 2 Potassium oxide Gypsum 5 The compounds above have a direct impact on the properties the concrete will exhibit and how the hydration reaction will occur . Optimizing the compounds will create differen t

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7 results that can be more applicable for a variety of environments. The tricalcium aluminate ( ), does not provide a lot of strength, but will begin hydrating rapidly (if not impacted by gypsum) and generate significant heat in the structure. Trica lcium s ilicate ( ) and dicalcium silicate ( hydrates quickly in the process and provides the initial strength gain; the dicalcium silicate hydrates much slower e strength until the first week (Hydration of Portland Cement). There are 5 categories of Portland cement as recognized in ASTM C 150 , known as Ordinary Portland Cements (ACI Committee 207, 1996). Type I : This cement is used for typical construction which does not require special properties. Type I is not used for mass concrete as it does not manage the heat generated by hydration sufficiently. However, with certain admixtures, it could possibly be applied. Type II : Type II cement li mits the amount of tricalcium aluminate used in the heat generated in the concrete. Because there is limited tricalcium aluminate used in Type II cement the concrete w ill only generate moderate heat thus making it ideal in mass concrete applications. Type III : Type III cement is also known as High Early cement. This cement obtains a high strength very quickly. Generally, type III cement is not used for mass concrete s tructures. The typical application is for cold weather or to reduce the time of curing.

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8 Type IV : This cement, commonly known as, the low heat cement, which monitors the maximum , , and used in the mixture. Because the compounds are lim ited, very little heat is generated. Under the consideration of low heat, it would make sense that Type IV is commonly used for mass concrete structures. However, this is not the case, Type IV is not commonly used as it is difficult to maintain and alter native methods have been developed to control the large temperature increases . Type V : Type V cement is applied when high s ulfate resistance is necessary. The following chart in Figure 1 provides the adiabatic temperature rise for each cement type. Fi gure 1 Adiabatic Te mperature Rise vs. Time for each Cement Type Aggregate Aggregate can vary significantly depending upon the purpose and application of the concrete. The aggregate can be a s oft sand to large, coarse rocks , or a gradation of each . Coarse aggregate, sized between No. 4 and 6 in ch es , must be hard and dense for the mass

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9 concrete application. The size of the aggregate is largely dependent on the structure. For heavily reinforced structures, the aggregate will likely be smaller to ensure it can flow through the reinforcement throughout the structure. When limitations, such as reinforcement, are not a factor, the coarse aggregate size is essentially unlimited thus reducing the cementitious material . However, economics , feasibility , and quality do play a large factor. Figure 2 optimizes the maximum aggregate size with the cement to achieve a given compressive strength level . Figure 2 Relationship between Aggregate Size, Cement Content, and Co ncrete Compressive Strength F ine aggregate is also used in mass concrete structures. The fine aggregates are crucial to ensure a workable mixture (ACI Committee 207, 1996) . While the gradations can be modified as needed , it must be within the parameter s provided in Figure 3 below :

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10 Figure 3 Aggregate Gradation by Sieve Size Water Water is the third major ingredient in concrete. When applying water to the mix, it should not contain any particles that would facilitate hydrati on reactions. A common rule of thumb is that drinking water is acceptable (ACI Committee 207, 1996). Water , when combined with cement, acts as a binder of the aggregate. The water creates the hydration process which ul timately hardens the concrete (Scie ntific Principals). Thermal Properties of Concrete The thermal properties of concrete are determined by the four parameters, thermal conductivity, specific heat, density, and diffusivity . Each of these properties are affected by the heat associated with h ydration of the cement and can provide a model for the effects of temperature and volume changes.

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11 The equation below, as defined by the ASTM, expresse s the relationship between the thermal properties (ACI Committee 207, 2007 ) . Wh ere, = Thermal Diffusivity K = Thermal Conductivity = Specific Heat = Density Thermal Conductivity Conductivity is the ratio between the heat flux density of the structure to the temperature gradient. Rather, the measure of how well heat fl ows through a given material . Thermal conductivity of concrete is not a constant and changes with external temperature, degree of saturation, and the concrete mix composition ( Chini & Parham, 2005). T ypical values range from 1.0 to 2.05 , spe cifically determined by the aggregate type. ( ACI Committee 207, 1996 ). Specific Heat The specific heat of concrete is defined as it is a measure of how the concrete can undergo temperature changes due to the type of m aterial, rather than the mass (Faruq, 2013 ) . Typical values for concrete are approximately 0. 179 to 0.25

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12 . The specific heat values for concrete are generally independent of the external conditions and materials ( ACI Committee 207, 1996 ) . Density Density is the ratio from mass to unit volume. This value is dependent on the various constituents o f the concrete mix. Typical values for the density of concrete range from 140 to 150 lb/ . Diffusivity Diffusivity is the measure of the concretes ability to experience temperature change. This value is an index ranging from 0.032 to 0.058 , as determined by aggregate type. The higher the index, the easier heat will flow through the system . Typically, diffusivity and conductivity correspond, meaning a highly conductive structure will likely have a higher diffusivity index ( ACI Committee 20 7, 1996 ) . Hydration Hydration of cement is the reaction of cement with water, which forms the binding material. This occurs under a two step process; 1) dissolution; 2) precipitation. When the water is mixed with the cement, the highly soluble materials in cement, gypsum ( ), the silicates ( and ), and the aluminate s ( and ) dissolve in the water to create the pore solution. As the materials continue to dissolve, the water contributes hydroxyl ions which allows the ionic s pecies to increase rapidly until the pore solution is supersaturated. This will allow the ions to combine to create new solid phases, known as hydration products (C S H and ) . The continuous dissolution of the cement materials is a result of th e precipitation of

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13 the supersaturated pore solution. There is a steady development of strength and hardening as this occurs. Although the true hydration process is a result of all cement minerals dissoluting into the same pore solution, each reaction is a nalyzed separately to approximate the overall behaviors. The overall proc ess of cement hydration can be broken down into four phases as demonstrated in Figure 4 . Figure 4 Rate of Cement Hydration vs. Time The f irst phase of hyd ration begins rapidly and lasts about one minute . This is due to the rapid creation of the hydration products and the heat output from the dissolving cement . The products that are created surround the cement particles limiting further reaction from occur ring, thus initiating phase 2. Phase 2 , known as the induction period shows the rate of hydration plummeting and ultimately reaching a rate of zero reaction . This one to two hour time frame is important as it allows the concrete to be mixed and pour ed in the field without reaching an unworkable level of hardness and/or strength. The reaction of the tricalcium

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14 silicate ini ti ates phase 3 with a rapid , but short increase in hydration. This typically begins less than 24 hours after the initial dissolution, but is highly dependent on the temperature and particle size of the cement. The rate of hydration will eventually reach its peak in this phase and begin to taper as the hydration products increase. The end of this phase generally marks the 30% completion of cement hydration. At stage 4 , almost all of the hydration has occurred and the hydration products are remaining, primarily in the form of C S H gel and CH. This sta ge, known as the diffusion limited reaction period , only hydrates further if water dif fuses to areas where a reaction can occur. Due to the creation of hydration prod ucts, this occurs less and less (Thomas & Jennings). Hydration of Calcium Silicates As demonstrated in Table 3, the calcium silicates make up the majority of the p ortland ceme nt composition . While the reactions for both silicates are similar, there are some significant differences. Tricalcium silicate is more soluble than dicalcium silcate and will therefore have a quicker rate of hydration and produce more hydration product. Additionally, tricalcium silicate is a key contributor to the early strength development in concrete while dicalcium silicate provides strength later in the phases. The reaction equations are as follows: Where x is t he amount of wate r associated with the C S H gel (Thomas & Jennings).

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15 Hydration of Tricalcium Aluminate Gypsum is a key mineral in the tricalcium aluminate reaction as it slows down the initial reaction. Without gypsum present, the cement paste would rapi dly hard en and would lose workability in an unreasonable timeframe. The reaction is as follows: On most occasions, the ettringite is converted into monosulfoaluminate within the first few days of the hydration reaction. This is a result of the e ttringite becoming unstable due to the decrease in sulfate ions. This issue is seen when the gypsum is reacted entirely before the tricalcium aluminte ( Thomas & Jennings) . The reaction is a s follows: T he tetracalcium aluminoferrite creates a similar hydration product as it also has two reactions as a result of the gypsum. The first reaction the ettringite from the tricalcium aluminate reacti on reacts with the gypsum and water followed by the newly created ettringite reacting with the ferrite to create garnets (Composition of Cement) . The reaction s are as follows :

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16 Hydration Products Calcium Silicate Hydrate (C S H) Gel As stated in previous sections, the largest percentage of cement is the calci um silicates. Similarly, its reaction produce s , Calcium Silicate Hydra te (C S H) gel attributes to approximately 50% of the total cement paste. The C S H gel helps the concrete gain its initial firmness due to gel binding to the cement particles. As the hydration process continues and more C S H is created, the gel grows outward with interconnected layers continuously built on itself. Concrete gains most of its strength from the increase in layers of the solid phases (Thomas & Jennings) . Calcium Hydroxi de While the C S H gel creates interconnected layers, the calcium hydroxide forms crystals. Calcium hydroxide is key to avoiding shrinkage of the concrete. The amount of shrinkage is reduced with the presence of calcium hydroxide because its crystalline structure remains intact as water is dried from the system, unlike C S H which collapses. Because the structure is unaffected, it acts as a restraint and reduces the shrinkage (Thomas & Jennings). Delayed Ettringite Formation (DEF) Ettringite was previous ly discusses as part of the hydration reactions. Ettrinigite is created early in the mixing process with the reaction between sulfate compounds, which are commonly added, and calcium aluminate from the cement. The ettringite is very important as it makes up the stiffness of the concrete. However, if the hydration process creates excessive temperatures, this ettringite can be destroyed (Ettringite Formation and the Performance of Concrete, 2001 ) . This damage typically will occur afte r the concrete has ex ceeded 158 F at

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17 which point the ettringite melts. The combination of the cooling concrete , which occurs later, and water can allow the ettringite to reform and cause internal volumetric expansion (Bartojay, 2012). Heat of Hydration All of the reactions pr eviously discussed are exothermic reactions, meaning the hydration process creates and emits heat. This ultimately increases the internal temperature of the concrete. Depending upon the concrete application, this may or may not pose a risk to the concret e properties. Small concrete pours will not see the impact of the heat because it will dissipate into the environment. Mass concrete, however, can see a distinguished increase in internal temperatures because concrete has a low conductivity and the heat that is generated cannot be quickly dissipated from the center of the structure . This causes temperatures to exceed the allowable maximum and large temperature differentials throughout the structure. If the temperatures are not monitored, cracking is i mminent (Portland Cement, Concrete, and Heat of Hydration, 1997) . Mass Concrete Additional challenges arise for projects including concrete dams, power plants, and l arge foundations as these are categorized as mass concrete which requires additional provisions. Mass concrete, as defined by The American Concrete Institute (ACI) with dimensions large enough to require that measures be taken to cope with generation of heat from hydration of the cement and attendant volume change to minimize cracking The heat from hydration that is generated by the reaction of cement and water will occur in all

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18 concrete settings. However, in large scale co ncrete projects, this heat is unable to dissipate from the surface uniformly. The dramatic temperatures observed, specifically in mass concrete structures can create tensile stresses within the structure. If not properly managed, the maximum heat and/or the temperature differential can cause cracks in the structure. While some cracks are minor, severe cracks can develop from within the structure and have negative impacts to the integrity and durability of the structure. Management of mass concrete occu rs both at the design and construction phase. In design, the concrete mix design can dictate that amount of heat generated. The type and specifications. These mix designs will commonly require low heat pozzolans in place of cement , which help maintain workability of the mixture . Examples of low heat pozzolans are slag or fly ash which can significantly reduce the amount of heat generated without compromising the st rength. A dditionally, while the aggregate specified may not have an impact on the temperatures, there are certain types that are more conducive in mass concrete as they have limited expansion when exposed to heat. At the time of construction, there are s everal methods that can be used in an effort to maintain the temperatures of the concrete. Prior to placing the concrete, the concrete mix temperature, as well as the ambient temperature should be considered. If the mi x is too hot, ice is commonly added in place of mixing water to pre cool the mixture . The concrete pour schedule must also be detailed to ensure that the pour sizes will not generate an unmanageable amount of heat. Some considerations must be the lift height, seasonal pour schedule, and pl acement schedule. Once the concrete is poured, the structure can be

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19 insulated. This will prevent the surface temperatures from dissipating and reduce the temperature differential of the structure. Another method, which was implement ed on the Hoover Dam, is to embed small piping through the structure to run cold water through. This helps regulate the temperatures throughout the structure in its entirety (Gajda & Vangeem, 2002). Thermal Stresses in Concrete The thermal stresses in concrete differ drastica lly in comparison to steel, as the thermal stresses are not proportional to the temperature change. The differences in behavior are a result of a varying modulus of elasticity , concrete creep , temperature differentials, coefficient of thermal expansion, a n d the degree of restraint (ACI Committee 207, 1996 ) . As discussed previously, the temperature of the concrete increases rapidly early on in its lifecycle due to hydration. The concrete will eventually reach its peak temperature and will gradually cool o ver time. While the concrete is experiencing these temperature changes, the stresses and modulus of elasticity are also varying, but are minimal early on, as shown in Figure 5. Figure 5 Plot of Concrete Temperature, Modulu s of Elasticity, and Stress with Respect to Time

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20 The plot shows a peak in tempera ture while the hydration reaction occurs . During the initial temperature rise , the modulus of elasticity and relaxation coefficient, (K(t, ), are at its lowest and st resses are near zero . Over time, the temperatures reach a maximum and decrease to a steady temperature, while increasing strength and stiffness . During the cooling process , the compressive stresses are reduced at the surface and instead, thermal tensile stresses develop. This is a result of the concrete internal and external temperature changes , increase in modulus of elasticity, and the restraint of the system . The tensile stresses that develop are significant . When these stresses are larger than the t ensile strength of the structure, cracks will inevitably occur. These cracks can have a signifi cant impact to the strength, integrity , and lifespan of the structure (Zhu, 2014) . Thermal Stress Self Stress Self stress is developed as a result of the stru cture itself. This will occur when the temperature is non linearly distributed throughout the structure. The non linear temperature is typically cooler at the surface and warmer in the center. As the heat is dissipated from the surface, shrinkage occurs , but is restrained by the wa r mer, i nner surface of the structure which does not incur corresponding volumetric changes . The inner surface goes into compression, while the outer is in tension (Zhu, 2014) . To maintain equilibrium, the overall self stress requires that tension stress and compression stress are equal , as shown in Figure 6.

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21 Figure 6 Concrete Stress Diagram The thermal stresses related to self stress are generally negligible when considering restraint stresses. Th is is because the temperature differentials between the surface, center, and ambient are managed reasonably with the insulation of the forms. However, self stresses can become a greater issue when thermal shock is experienced. Thermal shock, as previous ly discussed, occurs as a result of extreme ambient temperatures, improper insulation of the form s, and removing the form s early (ACI Committee 207, 1996 ). Thermal Stress Restraint Stress There are instances when the limits of a structure are partially o r fully restrained, such as a solid rock foundation. As the temperature in the structure changes, it tends to deform slightly and incur volumetric changes . The dimensions, strength, and modulus of elasticity of the concrete and neighboring material will largely determine the degree of restraint, however, volumetric restraints are likely, even if minor. These restraints will also be greater in the concrete which is closer to the physical restraint. In the instance of a foundation, the bottom surface of the structure is retrained and will likely develop stress that exceeds the tensile strength of the structure. This will result in cracking at the base of the structure and propagate

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22 upward and outward towards a lower stress section. Once a crack is initi ated, the structure will have a lower threshold for tensile stress in the given area. These cracks can create a compounding issue and jeopardize the integrity of the structure (ACI Committee 207, 1996). Cracking in Concrete The thermal stresses discussed previously can create large tensile stresses in a concrete structure. The tensile stresses are developed due to temperature differentials in the structure and boundary constraints. If the tensile stresses developed exceed the tensile strength of the give n structure, then cracking will occur. In consideration of the boundary constraints, the following equation can be used to determine the thermal stress: Where , The value of the thermal stress provided in the equation above must remain lower than the allowable tensile stress (with the safety factor) , otherwise cracks are inevitable. Once a mass concrete structure has cracked, the structural integrity in its entirety is jeopardized. In an effort to keep the thermal stresses manageable, engineers can take certain precautions t o

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23 prevent cracking, including limiting the temperature differential in concrete, allowing movement of the structure by reducing the re straint coefficient, and increasing the tensile strength capacity of the structure (Zhu, 2014) . Maximum Concrete Temperature In an effort to properly manage the quality of mass concrete, the temperature during the hydration process can be tracked. If t he temperatures exceed values of 155 to 165 , then the ettringite formation may be delayed. If delayed, DEF occurs, and internal expansion and cracking may occur; sometimes years after concrete placement (Gajda & Vangeem, 2002). Additionally, if the co ncrete reaches temperatures that greatly exceed the steady state temperatures, drastic volume changes are to be expected. (ACI Committee 207, 1996 ) Maximum Concrete Temperature Differential A temperature differential will occur in a structure when a given point of the structure is different than that of the surface. The temperature changes induce volumetric changes, specifically contraction at the surface during cooling. This differential of temperature and volume can create tensile stresses that typicall y exceed the strength of the concrete, resulting in cracking (Gajda & Vangeem, 2002 ) . During construction, the temperature differential is commonly managed by removing the forms at an opportune time. The form s are typically left on the structure, and some times insulated, to target surface temperatures that correspond to those at the center. When forms are removed prematurely, specifically on a cold day, the structure will experie ly result in cracking. (ACI Committee 207 , 2007 ). Not only is this differential experienced during the curing phase, known as mass gradient, it can also be an issue throughout the life of the structure due to ambient

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24 temperature variations , known as surface gradient . Climates with temperatures that varies throughout seasons impact concrete surfaces. The concrete surface react s to these temperature changes through contraction and expansion, however the center of the structures is much slower to react. The movement at the surface is being restra ined by the center and causing tensile stresses (ie cracking) at the surface. These cracks, however, are relatively shallow as the temperature differential is dissipated rapidly (ACI Committee 207, 1996 ) . The temperature differential in mass concrete str uctures will occur and is commonly limited to a maximum of 35 F difference between the hottest and coldest point at any given time.

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25 CHAPTER III HISTORIC FIELD DATA ANALYSIS Project Background A Combined Cycle Power Plant was constructed in 2015. In order to maintain compliance with the Clean Air Clean Jobs Act the existing coal fired units had to be retired and replace d with natural gas fired units . The newly constructed power plant now provides a cleaner source of energy while still producing approximately 580 megawatts of energy . Combined Cycle Power Plants are densely populated with structures in order for it to properly perform with efficiency. Specifically analyzed in this study was the Steam Turbine Generator Pedestal (STG) . This turbine generator is structurally composed the base mat, columns, and the table top, each constructed primarily of structural concrete. Figure 7 provides the model of the STG. It is important to note that the STG is considered mass reinforced concrete, which differs from the mass concrete associated with dam construction. Mas s reinforced concrete typically differs in the aggregate size, amount of water, and type of cement which ultimately attribute to less temperature control of the structure (ACI 207 Committee, 1996 ).

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26 Figure 7 Steam Turbine Genera tor Pedestal Model This study analyzes just under 2,200 cubic yards of concrete. Table 4 summarizes the dimensions and quantity of concrete, in cubic yards, required to construct each component; each which are classified as mass concrete. Table 4 Concrete Quantities and Dimensions for Steam Turbind Generator Item Description Quantity (CY) General Dimensions 1 Basem at 928.3 D 2 Columns (8 EA ) 6 44 . 7 3 Tablet op 606.1 The re were two concrete mix design s used to construct all three components listed in Table 5 . The first one, used for the basemat and table top is known as I AA Base Mix and the

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27 second one, used for the columns was used f or all eight of the columns is known as I AA Base Mix + Super Plasticizer (SP). Table 5 below tabulates the required parameters. Table 5 Concrete Mix Design Requirements Item Design Parameter I AA Base Mix I AA Base Mix + SP 1 Strength 4,500 psi 4,500 psi 2 Air Content 6.0% +/ 2.0% 6.0% +/ 2.0% 3 Slump 2 to 4 in. 8 In. Max 4 Water/Cement Ratio 0.43 0.39 The required strength and air content is the same for both mix designs. I AA Base Mix has a higher water/cement ratio than the I AA Base Mix + SP, yet has a significantly smaller slump value. The primary difference in slump, despite the water content, is attributed to the superplasticizer which was added for the column mix. The superplasticizer acts as a lubricant to the cement grains which allows for a hi gher slump, or fluidity, without increasing the amount of water. The slump for I AA Base Mix + SP is considered a plasticizer slump, as opposed to the standard water slump. When optimizing the design for mass concrete, it is important to consider the amo unt of water used in the mix as it is a key component to initiating and further facilitating the hydration reaction. A water slump of 2 to 4 inches, as required by the I AA Base Mix , is typical in an effort to avoid reduced strength and durability (Concre te News, 2008) . The lower water/cement ratio from I AA Base Mix to the I AA Base Mix + SP can also be due to the addition of the superplasticizer. The standard water/cement ratio ranges from 0.4 and 0.6. The required 0.43 is on the low end of the spect rum likely to maintain workability and reduce generating heat as a result of hydration, while achieving a higher strength and reducing

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28 shrinkage cracks. I AA Base Mix + SP requires 0.39 because the superplasticizer is substituted in place of additional wa ter. The mix proportion s are also important to und erstand. Table 6 provides the breakdown of each mix . Table 6 Standard I AA Base Concrete Mix Design Standard I AA Base Mix Item Material Amount Unit 1 Type I II Cement 483 Lb 2 Fly Ash 122 Lb 3 1,743 Lb 4 Sand 1,231 Lb 5 Water 262 Lb 6 Air . 55 Oz/cwt C+P 7 Viscocrete 4 .0 Oz/cwt C+P Table 7 Standard I AA + Superplasticizer Base Concrete Mix Design Standard I AA Base Mix + Superpla sticizer Item Material Amount Unit 1 Type I II Cement 488 Lb 2 Fly Ash 122 Lb 3 1,739 Lb 4 Sand 1,287 Lb 5 Water 241 Lb 6 Air .25 Oz/cwt C+P 7 Viscocrete 5.0 Oz/cwt C+P Both concrete mix designs are similar, just minor difference s in the quantity of each constituent. Each mix requires approximately 485 lbs of cement which is relatively high for mass concrete. The fly ash is used to provide additional strength without drastically increasing the amount of hydration reaction.

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29 Due t o the large quantities of concrete, the concrete temperature needed to be monitored prior to placement and during the cure process. The following temperature parameters were required by the project specifications: Concrete delivered with a temperature bet ween 50 F and 90 F ; Maximum concrete temperature after placement is not to exceed 180 F ; Maximum temperature differential between center and surface is not to exceed 35 F . It is important to note, that while the temperature differential was not to exceed 35 F , it was also performance based. If a larger differential was seen, but the temperature of the structure had achieved a specified temperature, the differential did not pose a risk. In order to verify the temperature results, thermocouple sensors were installe d at various locations in each structure with lead wires connecting to a data logger. Thermocouples are electronic temperature sensors that consist of welded wires of two different alloys. The sensors produce voltage that is dependent on the temperature changes. These voltages are different for each of the alloys, but can be measured and converted to output temperature readings. The next sections will detail each specific operation and its results. The different geometry and quantities of the structure s will impact the placement and temperature results. Mass Concrete Temperature Results Steam Turbine Generator Pedestal Basem at Extensive pre work before pouring the concrete is done to ensure that the temperatures can be managed within specifications. If the temperature s exceed the

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30 budget and sched ule will be incurred. The base mat was performed in ten phases progressing horizontally and four lifts to compl ete in a single eight hour shift. The structure was completed by working east to west in a little over 1 1 foot wide sections and high lifts. Lift 1 was not completed entirely before proceeding to Lift 2. Instead, the concrete was poured in a diago nal progression, working on additional lifts of a given phase, while proceeding to another lift and phase. The diagram below provides a snapshot in time to demonstrate how structure was poured in phases. that have not been poured yet. Figure 8 Snapshot of the Concrete Pour Procedure Four thermocouple sensors were installed into the basemat prior to the initial pour. Two sensors were installed near the top of the s tructure, one on the east side and one on the west. Additionally, two sensors were installed in th e middle, one on the east side and one on the west . weather database.

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31 Figure 9 Thermocouple Location for Basemat Tem perature monitoring of the base mat began on June 23, 2013 just before 11:00 pm and conclude d 107 hours later. Each sensor documented hourly readings of the temperature. The concrete t emperature prior to placing ranged from 59 F to 63 F . A night shift operation was scheduled to avoid the high summer temperatures that could negatively affect the concrete. Table 8 summarizes the temperature readings after the given hours. Table 8 Basemat Temperature Sensor Summary Location 12 Hrs 24 Hrs 48 Hrs 72 Hrs 96 Hrs 107 Hrs Max Temp Max Time Top, East Side 80.6 138.2 149.0 147.2 143.6 138.2 150.8 43 H Top, West Side 91.4 143.6 152.6 149.0 143.6 138.2 152.6 43 H Mid., East Side 80.6 138. 2 152.6 149.0 145.4 143.6 152.6 43 H Mid., West Side 114.8 143.6 152.6 149.0 145.4 143.6 152.6 37 H The chart below in Figure 10 provides a summary of all of the temperature data extracted from the field .

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32 Figure 10 Basemat F oundation Temperature Data vs. Time The basemat foundation temperatures generally reflect the anticipated results. There is a large spike in temperature throughout the structure within the first 24 hours after concrete placement. It can be observed that the west side of the structure was poured first due to the earlier temperature rise due to the hydration reactions. After the first day, t he rate of temperature increase tapered , but the temperature did continue to rise to a maximum of 152 .6 F . Over the next hours, the documented temperatures continued to cool at a similar rate . The temperatures at both the east and west surface fluctuated more apparently in accordance with the ambient temperature. The middle temperatures were not impacted by the surrounding air temperatures as significantly. When analyzing the differential temperature, a difference between the middle sensor and the top sensor, for a given side, is to be expected. This is because the heat on the top edge is able to dispers e the heat generated at the surface. Based on the plot in Figure 11, the 0 20 40 60 80 100 120 140 160 180 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 Internal Temperature ( ) Time Elapsed (Hours) STG Basemat Foundation Temperature Data West Side Middle West Side Top East Side Middle East Side Top Ambient Temperature

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33 differential for both the east and west sides was consistently minor when compared to the 35 F allowable differential . This can be attributed to the proper pour plan that allowed the middle section to emit the heat generated, rather than trap it below the surface . Figure 11 Basemat Concrete Temperature Differential from Middle and Top Sensors Steam Turbine Generator Pedestal Columns The planning work associated with the columns was not nearly as extensive as the basemat , as each column was schedule d to be com pleted in one lift at one column per shift. The pour ra te was planned at approximately 15 CY/hour. Managing the pour rate not only helps monitor the temperatures, but it also allows the concrete to gain enough strength without compromising the integrity of the form. A s discussed in previous sections , this op eration required a special concrete mix design, known as, I A A Base Mix + Super Plasticizer. T he column concrete pours occurred ov er the course of eight days, at one column per day. The pour s took place during day shift on th e last two weeks in July wit h a concrete -5 0 5 10 15 20 25 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 102 105 Internal Temperature ( ) Time Elapsed (Hours) STG Basemat Foundation Temperature Differential Data West Side Differential Between Middle & Top East Side Differential Between Middle & Top

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34 temperature prior to placing ranging from 61 F to 75 F. A temperature sensor was placed at the middle of the column and at the top surface to track hourly temperatures. Figure 12 Thermocouple Location for Columns Table 9 summarizes the temperature read ings at the given hours as well as the maximum temperatures documented.

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35 Table 9 Column Temperature Sensor Summary Location 12 Hrs 24 Hrs 48 Hrs 72 Hrs 96 Hrs 108 Hrs Max Temp Max Time Column 1, Top 136.4 134.6 132.8 122.0 116.6 111.2 138.2 13 H Column 1, Mid 143.6 159.8 165.2 159.8 152.6 149.0 165.2 35 H Column 2, Top 138.2 145.4 134.6 122.0 113.0 113.0 145.4 17 H Column 2, Mid 140.0 158.0 165.2 159.8 149.0 145.4 165.2 36 H Column 3, Top 140.0 141.8 131.0 122.0 111.2 109.4 1 43.6 17 H Column 3, Mid 143.6 159.8 165.2 159.8 149.0 143.6 167.0 37 H Column 4, Top 143.6 145.4 141.8 131.0 123.8 112.0 147.2 25 H Column 4, Mid 141.8 156.2 161.6 158.0 150.8 145.4 161.6 34 H Column 5, Top 140.0 141.8 132.8 125.6 120.2 122.0 143.6 14 H Column 5, Mid 138.2 154.4 163.4 159.8 152.6 149.0 163.4 39 H Column 6, Top 140.0 140.0 132.8 127.4 113.0 114.8 141.8 27 H Column 6, Mid 143.6 159.8 165.2 159.8 152.6 149.0 165.2 34 H Column 7, Top 143.6 149.0 136.4 122.0 114.8 109.4 149.0 20 H Colum n 7, Mid 145.4 161.6 167.0 163.4 152.6 149.0 168.8 42 H Column 8, Top 136.4 140.0 131.0 123.8 114.8 113.0 140.0 20 H Column 8, Mid 145.4 159.8 167.0 159.8 152.6 147.2 167.0 34 H The chart s below in Figure 1 3 through Figure 20 provide a summary of all o f the temperature data extracted from the field for each column.

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36 Column 1 was poured on July 11, 2013 and began tracking temperature data around 10 am. Figure 13 Column 1 Temperature Data vs. Time Column 2 was poured on July 10, 2013 and began tracking temperature data around 9 am. Figure 14 Column 2 Temperature Data vs. Time 0 20 40 60 80 100 120 140 160 180 0 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 Temperature ( ) Time Elapsed (Hour) Steam Turbine Generator Column 1 STG Column 1 Edge STG Column 1 Middle Ambient Temperature 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 Internal Temperature ( ) Time Elapsed (Hour) Steam Turbine Generator Column 2 STG Column 2 Edge STG Column 2 Middle Ambient Temperature

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37 Column 3 was poured on July 12, 2013 and began tracking temperature data around 10 am. Figure 15 Column 3 Temperature Data vs. Time Column 4 was poured on July 13, 2013 and began tracking temperature data around 10 am. Figure 16 Column 4 Temperature Data vs. Time 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 Internal Temperature ( ) Time Elapsed (Hour) Steam Turbine Generator Column 3 STG Column 3 Edge STG Column 3 Middle Ambient Temperature 0 20 40 60 80 100 120 140 160 180 0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 196 203 210 217 Internal Temperature ( ) Time Elapsed (Hour) Steam Turbine Generator Column 4 STG Column 4 Edge STG Column 4 Middle Ambient Temperature

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38 Column 5 was poured on July 18, 2013 and began tracking t emperature data around 9 am. Figure 17 Column 5 Temperature Data vs. Time Column 6 was poured on July 19, 2013 and began tracking temperature data around 1:30 pm. Figure 18 Column 6 Temperature Data vs. Time 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 Internal Temperature ( ) Time Elapsed (Hour) Steam Turbine Generator Column 5 STG Column 5 Edge STG Column 5 Middle Ambient Temperature 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 Internal Temperature ( ) Time Elapsed (Hour) Steam Turbine Generator Column 6 STG Column 6 Edge STG Column 6 Middle Ambient Temperature

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39 Column 7 was poured on July 19, 2013 and began tracking temperature data around 4:00 pm. Figure 19 Column 7 Temperature Data vs. Time Finally, Column 8 was poured on July 24, 2013 and began tracking temperature data a r ound 1:00 pm. Figure 20 Column 8 Temperature Data vs. Time 0 20 40 60 80 100 120 140 160 180 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 124 128 132 136 140 144 Internal Temperature ( ) Time Elapsed (Hour) Steam Turbine Generator Column 7 STG Column 7 Edge STG Column 7 Middle Ambient Temperature 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 Internal Temperature ( Time Elapsed (Hour) Steam Turbine Generator Column 8 STG Column 8 Edge STG Column 8 Middle Ambient Temperature

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40 The temperature results for each column yielded results as expected. Within the first twelve hours, there was an immediate initial peak of temperature for each column. During this time, the readings between the center and surface temperature were generally consistent. However, when the surface of the column reached the maximum, the center temperature of the column continued to increase. As time progressed, the middle and top cooled at a consistent rate , however the middle temperature readings were significantly and consistently higher than the edge of the column . Column 7 yielded the highest maximum temperature at 168.8 F . Column 1 yielded the lowest maximum tempera ture at 138.2 F Having data to analyze for eight similar columns allows patterns to be recognized. In order to see the trends for both the middle temperatures and the top temperatures, they were each plotted in Figure 21 and Figure 22 . For simplicity, th e ambient temperature was averaged over time for all eight columns. The plots indicate that the middle of the columns had consistent temperatures and consistent rate of temperature gain/loss. T he edge of the columns yielded variable results with rate of temperature decrease . Rather than a smooth reduction, the temperatures increased and decreased, but ultimately formed a downward trend in temperature. This is likely a function of the ambient temperatures effecting the surface temperature of the concrete . The average maximum temperature at for the top sensor of each column is 143.6 F with a minimum of 138.2 F in column 1 and a maximum of 149.0 F in column 7. The average maximum temperature at for the middle sensor of each column is 1 65.4 F with a minimu m of 161.6 F in column 4 and a maximum of 1 68.8 F in column 7. Column 7, as a whole, achieved the highest temperatures.

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41 Figure 21 Middle Temperature Comparison for Columns Figure 22 Surface Tempe rature Comparison for Columns The columns yielded signifi cantly larger differentials between the middle and edge sensors as compared to the basemat previously discussed. Table 10 summarizes the largest temperature differential between the surface sensor and the center in each column. 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 Internal Temperature ( ) Time Elapsed (Hours) Middle of Column Temperature Comparison Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8 Ambient Temp 0 20 40 60 80 100 120 140 160 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 Internal Temperature ( ) Time Elapsed (Hours) Surface of Column Temperature Comparison Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8 Ambient Temp

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42 Table 10 Column Maximum Temperature Differential Comparison Location Time at Largest Differential Edge Temperature Middle Temperature Differential Column 1 115 H 104.0 145.4 41.4 Column 2 70 H 122.0 159.8 37.8 Column 3 90 H 109.4 152.6 43.2 Column 4 93 H 123.8 152.6 28.8 Column 5 73 H 123.8 159.8 36.0 Column 6 90 H 113.0 156.2 43.2 Column 7 68 H 122.0 165.2 43.2 Column 8 73 H 122.0 159.8 37.8 The largest temperature differen t ial was 43.2 F which was seen in three columns, column 3, column 6, and column 7. Column 3 and 6 both reached the maximum differential 90 hours after placement. At this time, the rapid heat generation has already occurred and the surface is able to dissi pate heat at a quicker rate than the center. The 90 hour mark for column 3 was at approximately 4:30 am. The cooler ambient temperatures in the early morning may have had an impact on the larger differential. The peak differential for column 7 occurred 68 hours after initial placement. Column 7 also reached the highest maximum temperature among all of the columns. A significant center temperature can cause an increased temperature differential if heat is easily released at the surface. The smallest m aximum temperature differential occurred in Column 4 at 28.8 F which was measured 93 hours after placement. When considering all temperature differentials from the beginning of placement to the completion of data measurements, the average differential was 25.87 F. The plot in Figure 23 provides all of the temperature differentials with respect to time. The temperature difference rapidly increases as the heat is generated through the cement hydration reaction. Over time, a temperature differential exist s between the two sensors,

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43 however the difference remains generally the same. The columns yielded similar results, however column 4 stands out as an outlier. This column was significantly lower in comparison to the other columns. Column 7 also appears t o have a steady increase in the temperature change for a longer period that the other columns. All columns tended to peak around 40 to 48 Figure 23 Column Temperature Differential vs. Time Steam Turbine Generator Pedestal Tabletop The tabletop structure was the last structure analyzed for the Combine d Cycle Power columns. The tabletop, which is 6.5 feet thick, was poured in four lifts at the following heights: L ift ift ift ift . The table top was divided into two sections, the east and west side. Each side had its own concrete pump tr uck and was poured in a coun ter clockwise progression at approximately 80 CY/hour . Three thermocouple s were installed -20 -10 0 10 20 30 40 50 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126 131 136 141 146 151 Temperature ( Time Elapsed (Hour) Temperature Differentials per Column Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8

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44 throughout the structure, one in the middle, one on the top, and one on the edge as shown in Figure 24 . Figure 24 Thermocouple Locations for Tabletop Data was logged beginning at 4:15 am on September 9, 2013, but not all of the concrete was poured until 1:15 pm. The concrete temperature prior to placing ranged from 63 F to 70 F . Table 11 summarizes the temperature data associated with the tabletop. Table 11 Tabletop Temperature Sensor Summary Location 12 Hrs 24 Hrs 48 Hrs 72 Hrs 96 Hrs 108 Hrs Max Temp Max Time Tabletop Top 134 .6 140.0 140.0 132.8 118.4 116.6 141.8 36 H Tabletop Middle 141.8 158.0 163.4 159.8 152.6 147.2 165.2 39 H Tabletop Edge 131.0 132.8 127.4 114.8 105.8 102.2 132.8 13 H The chart below plots all of the data extracted from each thermocouple and also comp ares it against the ambient temperature.

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45 Figure 25 Tabletop Temperature Data vs. Time The concrete temperature data associated with the tabletop also yields expected results. The temperature increases at a steady rate for ap proximately the first 12 hours. At about 18 hours both the top and edge temperatures begin to level out. At that time, t he middle temperature rate increase beg a n slow down, but it continued to increase to a maximum temperature of 165.5 F . The temperatur e at the edge began to decrease around 48 hours, in comparison to the top at 72 hours. The rates of cooling were generally the same for all three locations in the tabletop . For the entire curing process, the edge remained the coolest while the middle was the warmest. The edge of the structure likely has more surface area exposed to the environment allowing it to dissipate heat quicker. Additionally, the differential temperature data is plotted below. 0 20 40 60 80 100 120 140 160 180 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 Internal Temperature (degF) Time Elapsed (Hours) STG Tabletop Temperature Data STG Tabletop Middle STG Tabletop Top STG Tabletop Edge Ambient Temperature

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46 Figure 26 Tabletop Temp erature Differential vs. Time The temperature differential seen within the first eight hours are slightly variable because the entire structure was not poured yet; some of these readings are based on the ambient temperatures rather than the concrete itself . The temperature difference between the middle and edge of the structure remained the largest throughout the data collection. The difference increased early on and leveled out to approximately 40 F difference. The difference between the middle and top sensor peaked at 34.2 F at 87 hours after placement. The difference betwee n the top and edge sensor peaked at 19.8 F at 60 hours after placement. -30 -20 -10 0 10 20 30 40 50 60 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 Temperature degF Time Elapsed (Hours) Temperature Differentials for Tabletop Middle Top Differential Middle Edge Differential Top Edge Differential

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47 CHAPTER IV TRANSIENT THERMAL AN ALYSIS SIMULATIO N Introduction To understand the thermal i n tera c tions of a system, a steady state analysis or a transient analysis can be performed. A steady state thermal analysis calculates the thermal loads on a system which do not vary with time. It determines how these loads impact the thermal properties and the temperature distribution of the system. A transient thermal analysis recognizes the temperature changes, and given thermal properties, with respect to time. Eventually a transient system will reach steady state conditions . Because the curing process of concrete involves significant temperature changes over time, a transient thermal anal ysis will be used. Using a program such as Ansys , allows the thermal analysis of the STG structure to be performed through a fi nite element thermal analysis. Finite element analyses, in general, simplify a given system by breaking it into minuscule sectio ns, known as a discretized model composed of elements. Each of the elements have a given number of nodes that are interconnected to the neighboring nodes or surface. Ansys considers the internal heat generated through cement reactions and the temperature interaction between the surface concrete, air, and formwork to determine the temperature field response . The calculations begin with an initial temperature and is time stepped incrementally measuring the temperature at each nodal element in the system.

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48 T heory The overall thermal analysis is based on the heat diffusion equation. Where, = density T = Temper a ture , T(x,y,z) t = time q = heat generation per unit volume k = thermal conductivity Th e heat diffusion equation defines that the rate of change of stored thermal energy within a given volume must be equal to the rate of energy transfer (conduction) plus the thermal energy generation of the volume. The solution provides the temperature dist ribution at any given time. Understanding the temperature distribution will also help facilitate the understanding of thermal stresses and thermal expansions. In Bofang Zhu defines four different types o f boundary conditions which can be appl ied to accurately determine the temperature distribution of a volume (Zhu, 2014) . 1. The first boundary condition is temperature. A prescribed temperature can be assigned to a given surface. This value can change as a function of time. 2. The second boundary c ondition is heat flux on the surface. This value changes as a function of time and material conductivity. Heat flux is a measure of the heat flow rate intensity.

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49 3. The third boundary condition is the heat transfer between the surface and the surrounding me dium, typically air. This condition considers the temperature of the two materials transferring heat and conductivity , known as convection . Radiation can also be incorporated into this condition. 4. The final boundary condition is the heat transfer between two solids in contact. This is calculated through the measured temperatures of each surface and their conductivities. In this analysis, the boundary condition associated with convection is applicable . The general principal behind natural convection is an increase in temperature of a give fluid reduces the density causing it to rise and forcing the colder molecules downward . The colder molecules will accept heat from the warmer source and rise carrying the heat and energy with it. This creates a consta nt motion of molecules continuing the heat transfer cycle. The heat that is transferred between the structure and air is dependent on the heat transfer coefficient and temperature measurements of each material as defined in the following heat transfer ra te equation. Where, Q = heat transfer rate with respect to time h = heat transfer coefficient A = Area = Ambient Temperature

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50 he ambient air surrounding it and is further impacted by the insulation provided by the winter blankets and formwork. As the heat is generated within the concrete and reaches the surface, the convection through the ambient air will accept heat from the su rface until equilibrium of the system is achieved. The insulation of the structure impacts the heat transfer coefficient value and ultimately the heat flux between the structure and air. Ansys APDL Thermal Simulation Ansys is widely used for finite elem ent analyses in a variety of applications. In Ansys, there are four steps to completing the analysis, Preprocessor, Solution, General Post Processing, and Time History Post Processing. The preprocessor step includes selecting material and element propert ies, drafting a model, developing the mesh, and applying the loads, specifically thermal loads. The solution step provides a selection of analyses and time step options for the analysis. Several time steps can be performed in one analysis, in addition to substeps for inter im calculations between the time steps. The number of substeps should be optimized such that accurate results are provided, but not so many that the analysis time is drastically increased. Once the solution is obtained, the results can be reviewed in the general post processing step. This step depicts the solution on the model for a given time step and can also develop animations. Finally, the time history post processing step provides the results at a given location over time. These steps will be further detailed in the next sections. Material and Element Properties of Model Ansys has a vast selection of element s each with key features that make it suitable for a given analysis. For this specific analysis, SOLID70 was utilized. Th is three dimensional element,

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51 as shown below, is specifically used in thermal analyses due to the single degree of freedom, temperature, at each of the eight nodes (SOLID70 3 D Thermal Solid) . Figure 27 SOLID70 Ansys Element Th e mesh of the model was created to develop the discretized element model. A mapped mesh with hexahedron shapes was used for the columns . This creates a regular pattern of elements with the same shape for each. Due to the irregular shape of the basemat a nd tabletop, a free mesh was used for these component s . When building the model within Ansys, material thermal properties must b e defined. The model was assigned material properties, as shown in Table 12 . The concrete properties were assumed to be const ant with time and temperature of the system. The density value was based off of the mix designs, while the thermal conductivity and specific heat were adopted from industry standards. The concrete, as placed in the field, may have differing parameters, b ut for the interest of the simulation these constants will be used.

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52 Table 12 Ansys Thermal Input Parameters Property Value ( U.S ) Value (SI) Density 143.6 lb/ 2,300 kg/ Thermal Conductivity 1.70 Btu/ft*hr*°F 10.6 kg/m *h*°C Specific Heat 0.179 Btu/lb*°F 0.75 kJ/kg*°C Initial and Boundary Conditions An initial condition for temperature is also required. This val ue is the temperature of the in place concrete, which serves as a baseline for the temperature changes to b e calculated from. This value, as measured on site, is the following. Table 13 Initial Conditions for each STG Component in Fahrenheit and Celsius STG Component Initial Temperature ( ° F ) Initial Temperature ( ° C ) Basemat 61. 7 16 .5 Column (avg) 82.4 28.0 Tabletop 69.8 21.0 The next step in the Ansys analysis is to determine what boundary conditions to apply. Ansys has the capabilities to apply temperature, heat flow, convection, heat flux, heat generation, and radiation loads , which align with the four boun dary conditions discussed above. The two condit ions applied for this analysis are convection and heat generation. The relationship between the concrete, insulation, and ambient air effect the temperature results. The insul ation, including the formwork and a winter insulation physically modeled, but was modeled through the value of the coefficient of convection. The formwork layer against the con crete structure was made of 5/8 inch steel. Due the small thic kness and little impact on the convection, the coefficient of convection value for the

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53 formwork was assumed to be zero. The insulating blankets that were wrapped on all surfaces, including formwork, exposed to the ambient air provide R 2.5 insulation. Th e R value is the measure of the thermal resistance and it s inverse is equivalent to the coefficient of con v ection. After calculating the inverse to be 0.4 Btu/hr* *°F and converting to the applicable input units, a coefficient of convection value of 8.17 kJ/h r * *°C was input into the program for all three components. When the forms were removed, the blankets were put back into place and were assumed to remain for the entire duration of the analysis. The basemat and columns each have one surface of the structure that is not blanketed, but is in contact with the subgrade and concrete respectively. In order to properly account for the heat transfer at these areas, the equation below was applied. For the column surface to the basemat, the coefficie nt of convection was input as 1.36 Btu/hr* *° F ( 7.73 kJ/hr* *°C ) and a value of 0. 425 Btu/hr* *°F ( 2.415 kJ/hr* *°C ) was used for the basemat to subgrade. Where, = thickness of material = thermal conductivity of material As stated before, the convection is a function of the surrounding fluid, which in this analysis is ambient temperature. In order to model the heating and cooling associated with day and night, the ambient temperature is input as a sinusoidal function based on archived temperature data fr om neighboring weather stations. Figure 28 plots the ambient temperature formulas for

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54 eac h STG component to align the temperature at Hour 1 with the initial temperatures as measured in the field. Figure 28 Ambient Temperature vs. Time for Basemat, Column, and Tabletop Next, the heat generation rate must be input in to the analysis. As discussed in previous sections, the hydration rate is time dependent. As the cement hydrates an exothermic reaction occurs to generate heat within the system. In order to accurately model the heat generation, a formula with respect t o time was calculated. Based on research recognized by the American Society of Civil Engineers , the adiabatic temperature rise , as a result of the hydration reaction , is defined by the following equation (Tan abe, 1985) . Where, temperature, °C , T = the age, day, K = constant from Figure 29 0 20 40 60 80 100 120 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 Temperature (degF) Time (Hour) Ambient Temperature vs. Time Basemat Ambient Temp. =88+20*sin((PI/12)*t+3.5) Column Ambient Temp =72+14*sin((PI/12)*t+0.75) Tabletop Ambient Temp =63+12.5*sin((PI/12)*t+4.3)

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55 constant from Figure 29 The figure below determines the K and alpha constants based on the unit cement content of the concrete mix. Figure 29 Coefficient Charts for Adiabatic Temperature Rise Using the adiabatic temperature equation, the amount of heat generated can be calculated from the following equation. Where, temperature, °C , T = the age, day, K = constant from Figure 29 constant from Figure 29 = specific heat capacity of concrete, kJ/kg °C = density of concrete kg/

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56 In Ansys, however, the allowable input parameter is the rate of heat generation, which can be de termined through the derivative of the heat generation with respect to time. Because this analysis is performed hourly, the time unit is converted from days to hours. The heat generation rate can be calculated b y the following equation. The K value was assumed to be 56 °C and alpha was determined to be 1.75. While the values assumed are high on the spectrum, it is in alignment with the temperature rise seen in the field measur e ments . Figure 30 is the Heat Generation Rate for all structures of the STG. Figure 30 Heat Generation Rate for Ansys Simulation The thermal analysis was performed for 1,000 hours with one substep per hour. The next sections provide the thermal results , as processed by t he heat diffusion equation, for the basemat, columns, and tabletop. 1,000.00 2,000.00 3,000.00 4,000.00 5,000.00 6,000.00 7,000.00 8,000.00 0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 Heat Generated Time (Hours) Heat Generation Rate Heat Generation Rate

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57 Ansys APDL STG Thermal Simulation Results Basemat The basemat temperatures generated from the Ansys simulation are compared to the field measured data below. Figure 31 prov ides the west side and Figure 32 provides the east side of the basemat. Figure 31 Temperature vs Time for West Basemat Simulation 0 20 40 60 80 100 120 140 160 180 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 198 Temperature ( ° F ) Time Elapsed (Hour) Basemat West Ansys Simulation West Mid West Top Ansys West Mid Ansys West Top

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58 Figure 32 Temperature vs Time for East Basemat Simulation Both simulations follow similar trends to the actual field measurements. The simulation consistently shows a temperature differential between the center and edge of each side. The field results have similar temperatures until approximately 120 hours elapsed. This reduced diffe rential is likely a result of proper thermal management through the pour schedule in the field . The pour schedule was not implemented in the simulation which is likely why the larger differential is seen. The simulated heat generation rate does not appea r to be as significant as seen in the field, but ultimately yielded a similar maximum temperature after a specific amount of time. Another observation is that the ambient temperature effected the surface temperature in the field more significantly than th e simulation results. This could be a result of improper insulation of the blankets. The following figures show the temperature distribution of the basemat after 1, 12, 24, 48, 60, 120, and 500 hours have elapsed. 0 20 40 60 80 100 120 140 160 180 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 198 Temperature ( ° F ) Time Elapsed (Hour) Basemat East Ansys Simulation East Mid East Top Ansys East Mid Ansys East Top

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59 Figure 33 Base mat Temperature Field at Hour 1 in YZ Cross Section Figure 34 Basemat Temperature Field at Hour 1 in XZ Cross Section

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60 Figure 35 Basemat Temperature Field at Hour 12 in YZ Cross Section Figu re 36 Basemat Temperature Field at Hour 12 in XZ Cross Section

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61 Figure 37 Basemat Temperature Field at Hour 24 in YZ Cross Section Figure 38 Basemat Temperature Field at Ho ur 24 in XZ Cross Section

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62 Figure 39 Basemat Temperature Field at Hour 48 in YZ Cross Section Figure 40 Basemat Temperature Field at Hour 48 in XZ Cross Section

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63 Figure 41 Basemat Temperature Field at Hour 60 in YZ Cross Section Figure 42 Basemat Temperature Field at Hour 60 in XZ Cross Section

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6 4 Figure 43 Basemat Temperature Field at Hour 120 in YZ Cross Section Fi gure 44 Basemat Temperature Field at Hour 120 in XZ Cross Section

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65 Figure 45 Basemat Temperature Field at Hour 500 in YZ Cross Section Figure 46 Basemat Temperature Field at Hour 500 in XZ Cross Section

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66 Columns The column temperatures as measured in the field are compared to the simu lated temperatures in Figure 47 . The simulated results closely match temperatures seen in the field. The concrete cooling trends are very simi lar for both the middle and the surface; even the ambient temperature impacts are accurately modeled. Based on the graph, the heat was generated quicker at the surface than the finite element analysis demonstrated, but similar maximum temperatures were yi elded. The heat generated in the center of the column is accurately modeled. Figure 47 Temperature vs Time for Column Simulation The following figures show the temperature distribution of the column after 1, 12, 24, 48, 60, 12 0, and 500 hours have elapsed. 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 Temperature ( ° F ) Time Elapsed (Hour) Column Ansys Simulation Edge Middle Edge Ansys Mid Ansys

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67 Figure 48 Column Temperature Field at Hour 1 in XZ Cross Section Figure 49 Column Temperature Field at Hour 1 in XY Cross Section

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68 Figure 50 Column Temperature Field at Hour 12 in XZ Cross Section Figure 51 Column Temperature Field at Hour 12 in XY Cross Section

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69 Figure 52 Column Temperature Field at Hour 24 in XZ Cross Section Figur e 53 Column Temperature Field at Hour 24 in XY Cross Section

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70 Figure 54 Column Temperature Field at Hour 48 in XZ Cross Section Figure 55 Column Temperature Field at Hour 4 8 in XY Cross Section

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71 Figure 56 Column Temperature Field at Hour 60 in XZ Cross Section Figure 57 Column Temperature Field at Hour 60 in XY Cross Section

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72 Figure 58 Colum n Temperature Field at Hour 120 in XZ Cross Section Figure 59 Column Temperature Field at Hour 120 in XY Cross Section

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73 Figure 60 Column Temperature Field at Hour 500 in XZ Cross Section Figure 61 Column Temperature Field at Hour 500 in XY Cross Section

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74 Tabletop The three locations in the tabletop that were measured in the field are compared to the simulated results in Figure 62 . Figure 62 Tem perature vs Time for Tabletop Simulation In comparison to the other models, the simulated results of the tabletop differ the most from the field results. However, the trends of the heating and cooling temperatures are similar at all three locations. Whi le the trends are similar, the magnitude of the temperature measured in the field was larger than the analysis due to the heat generation. The maximum temperature in the field was 165.2°F as compared to 157.6°F in the Ansys results. The top and edge resu lts were consistent with the field measurements considering the edge location was always cooler that the surface. The following figures show the temperature distribution of the tabletop after 1, 12, 24, 48, 60, 120, and 500 hours have elapsed. 0 20 40 60 80 100 120 140 160 180 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 Temperature ( ° F ) Time Elapsed (Hour) Tabletop Ansys Simulation Middle Top Edge Middle Ansys Top Ansys Edge Ansys

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75 Figure 63 Tabletop Temperature Field at Hour 1 in YZ Cross Section Figure 64 Tabletop Temperature Field at Hour 1 in XZ Cross Section

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76 Figure 65 Tabletop Temperature Field at Hour 12 in YZ Cross Section Figure 66 Tabletop Temperature Field at Hour 12 in XZ Cross Section

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77 Figure 67 Tabletop Temperature Field at Hour 24 in YZ Cross Section Figure 68 Table top Temperature Field at Hour 24 in XZ Cross Section

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78 Figure 69 Tabletop Temperature Field at Hour 48 in YZ Cross Section Figure 70 Tabletop Temperature Field at Hour 48 in XZ Cross Section

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79 Figure 71 Tabletop Temperature Field at Hour 60 in YZ Cross Section Figure 72 Tabletop Temperature Field at Hour 60 in XZ Cross Section

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80 Figure 73 Tabletop Temperature Field at Hour 12 0 in YZ Cross Section Figure 74 Tabletop Temperature Field at Hour 120 in XZ Cross Section

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81 Figure 75 Tabletop Temperature Field at Hour 500 in YZ Cross Section Figure 76 Ta bletop Temperature Field at Hour 500 in XZ Cross Section

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82 Ansys APDL Dependent Variable Study It is known that m ass concrete temperatures are impacted by environmental factors, constituents of the concrete mix design, construction methods, etc. While the temperatures seen are a cumulation of the factors previously mentioned, the Ansys program makes it feasible to isolate a variable and observe the impact it has on the structure. Because of the reasonably accurate simulation between the actual STG tempera tures and those provided by Ansys, the STG column model will be used to perform an analysis of how different parameters effect the concrete and to what extent. In the following analyses, several trials were run with will all consistent input data , exclu ding the one variable in question. Each variable will be analyzed to recognize the impact it has on the concrete temperature and temperature differential. The concrete data that was input into the analysis is as follows: Table 14 Input Parameters for Dependent Variable Study Item Description Value (English) Value (SI) 1 Density 143.6 lb/ 2,300 kg/ 2 Specific Heat 0.179 Btu/lb* °F 0.75 kJ/kg Btu/hr*°C 3 Thermal Conductivity 1.7 Btu/ft*hr*°F 10.6 kg/m*hr*°C 4 Initial Temperature 82.4°F 28°C 5 Ambient Temperature =72+14*sin((PI/12)*t+0.75) °F =22+8*sin((PI/12)*t+0.75) °C 6 Thermal Convection Coefficient 0.4 Btu/hr* *°F 8.17 kJ/hr* *°C 7 Heat Generation Rate Btu/ kJ/ 8 Model Size 8 x 8 x 34 ft 2.44 x 2.44 x 10.36 m

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83 Initial Temperature of Concrete The column temperature distribution was modeled four times, each with the different initial temperatures of 0°F, 32°F , 64 °F , and 97 °F . As expected, the higher the initial temperature, the higher the temperatures in the concrete at both the surface and the center. The maximum temperature was 180°F with the largest differential at 43 °F . The cooler initial temperatures had a significantly larger increase in temperature. The 0 °F initial temperature rose 82 °F to achieve a maximum temperature of 91 °F . After about 15 days, the surface temperature for all four trials were within a few degrees of each other. The cooler initial temperatures are consistent with chilling the concrete prior to placement. The maximum temperatures are manageable and the temperature differentials are minor. The plot for the surface temperatures, center temperatures, and the differential can be referenced in Figu re 77 , Figure 78, Figure 79 , respectively. Figure 77 Temperature vs. Time at Column Surface for Various Initial Temperatures 0 20 40 60 80 100 120 140 160 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature vs. Time at Column Surface for Various Initial Temperatures Surface 0 degF Surface 32 degF Surface 64 degF Surface 97 degF

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84 Figure 78 Temperature vs. Time at Column Center for Various Initial Tempe ratures Figure 79 Temperature Difference vs. Time for Column at Various Initial Temperatures 0 20 40 60 80 100 120 140 160 180 200 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature vs. Time at Column Center for Various Initial Temperatures Center 0 degF Center 32 degF Center 64 degF Center 97 degF -20 -10 0 10 20 30 40 50 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F) Time (Hour) Temperature Difference vs. Time Between Column Center and Surface for Various Initial Temperatures Difference 0 degF Difference 32 degF Difference 64 degF Difference 97 degF

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85 Ambient Temperature The column was also analyzed for a variety of ambient temperatures. The four ambient temperatures are intended to model the four different seasons seen in Colorado. Each season is modeled by sinusoidal functions with varying amplitudes and vertical shifts. The temperatures in at the surface are almost identical for spring and fall seasons, however the springs se ason did yield a larger gradient. Because of the low temperatures associated with winter, larger temperature differences were seen. If performing a winter concrete pour, proper insulation will be necessary to keep the heat maintained at the surface. Ove rall, the maximum temperature was 167.5 °F for the summer months with a maximum differential of 53 °F in winter. The plot for the surface temperatures, center temperatures, and the differentia l can be referenced in Figure 80, Figure 81, Figure 82 , respectiv ely. Figure 80 Temperature vs. Time at Column Surface for Various Ambient Temperatures 0 20 40 60 80 100 120 140 160 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature vs. Time at Column Surface for Various Ambient Temperatures Surface Spring Surface Summer Surface Winter Surface Fall

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86 Figure 81 Temperature vs. Time at Column Center for Various Ambient Temperatures Figure 82 Temperature Difference vs. Time for Column for Various Ambient Temperatures 0 20 40 60 80 100 120 140 160 180 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature vs. Time at Column Center for Various Ambient Temperatures Center Spring Center Summer Center Winter Center Fall -10 0 10 20 30 40 50 60 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature Difference vs. Time Between Column Center and Surface for Various Ambient Temperatures Difference Spring Difference Summer Difference Winter Difference Fall

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87 Structure Insulation Structure insulation is an important consideration in mass concrete pours as it can minimize the temperature differential and avoid thermal shock. I n this analysis, the convection 2.5 rated winter protection blanket, and one R 5 rated winter protection blanket. The minimal amplitudes indicate that the ambient air has a significantly l ess impact on the temperatures at the surface of the structure when it is more insulated. The insulation did not impact the rate of temperature increase, but it did a ffect the overall maximum temperatures achieved both at the surface and center of the co lumn. The rate of cooling was also dependent on the level of insulation. The structure exposed to ambient air had a dramatic drop in temperature over a short amount of time. The maximum temperature measured was 171 °F for the R 5 rated winter protection blanket and a maximum differential of 75 °F for the column without insulation. After 1 , 000 hours, the heavily insulated column is still cooling at a steady rate while all of the others have reached equilibrium with the ambient air. It is clear that the existing environment must be considered when determining the type of insulation. Excessive insulation may provide temperature that exceeds the allowable amount, yet minimal insulation will undoubtedly cause extreme temperature differentials resulting in c racking. The plot for the surface temperatures, center temperatures, and the differentia l can be referenced in Figure 83 , Figu re 84, Figure 85 , respectively.

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88 Figure 83 Temperature vs. Time at Column Surface for Various Insulati on Methods Figure 84 Temperature vs. Time at Column Center for Various Insulation Methods 0 20 40 60 80 100 120 140 160 180 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature vs. Time at Column Surface for Various Insulation Methods Surface Air Surface Plywood Surface R-2.5 Blanket Surface R-5 Blanket 0 20 40 60 80 100 120 140 160 180 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature vs. Time at Column Center for Various Insulation Methods Center Air Center Plywood Center R-2.5 Blanket Center R-5 Blanket

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89 Figure 85 Temperature Difference vs. Time for Column for Various Insulation Methods Cement Concentrations Because it is the that generates the heat it is expected that the more cement in the concrete mix, the hotter the structure will get. The Ansys results were consistent with this expectation. The mix designs with the larger ce ment dosage generated significantly larger temperatures. The maximum temperature and maximum differential were seen in the column with 400 kg/ of cement with temperatures of 156 °F and 34 °F respectively. This maximum temperature was 55% higher than the column with 100 kg/ of cement. It can also be observed that the higher rate of temperature increase also resulted in a faster rate of cooling at the surface and the center of the column. Under the conditions tested, all four cement dosages yie lded results within standard acceptable ranges. The plot for the surface temperatures, center temperatures, and the differential can be referenced in Figure 86, Figure 87, Figure 88 , respectively. -20 -10 0 10 20 30 40 50 60 70 80 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature Difference vs. Time Between Column Center and Surface for Various Insulation Methods Difference Air Difference Plywood Difference R-2.5 Blanket Difference R-5 Blanket

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90 Figure 86 Temperature vs. Tim e at Column Surface for Various Cement Dosages Figure 87 Temperature vs. Time at Column Center for Various Cement Dosages 0 20 40 60 80 100 120 140 1 30 59 88 117 146 175 204 233 262 291 320 349 378 407 436 465 494 523 552 581 610 639 668 697 726 755 784 813 842 871 900 929 958 987 Temperautre ( ° F ) Time (Hour) Temperature vs. Time at Column Surface for Various Cement Dosages Surface 100 kg/m3 Surface 200 kg/m3 Surface 300 kg/m3 Surface 400 kg/m3 0 20 40 60 80 100 120 140 160 180 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature vs. Time at Column Center for Various Cement Dosages Center 100 kg/m3 Center 200 kg/m3 Center 300 kg/m3 Center 400 kg/m3

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91 Figure 88 Temperature Difference vs. Time for Column for Various Cement Dosa ges Size of Structure The size of the structure significantly affected the temperature results. The cube models with dimensions 13.1 feet and 19.7 feet yielded maximum temperatures within a few degrees. H owever, the rate of cooling was much slower for th e larger specimen. After 1,000 hours, the largest column had not reached ambient temperatures, compared to the smaller cubes whose center reached equilibrium around 500 hours. Another important observation is the extensive time the largest cube endured a temperature differential over 40 °F . This differential existed from hour 82 through 672. Over the course of these 584 hours, or 24 days, significant stresses can occur as a result of the differential and increase in rigidity during this time. The plot for the surface temperatures, center temperatures, and the differential can be referenced in Figure 89 , Figure 90, Figure 91 , respectively. -5 0 5 10 15 20 25 30 35 40 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F) Time (Hour) Temperature Difference vs. Time Between Column Center and Surface for Various Cement Dosages Difference 100 kg/m3 Difference 200 kg/m3 Difference 300 kg/m3 Difference 400 kg/m3

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92 Figure 89 Temperature vs. Time at Column Surface for Various Structure Sizes Figure 90 Temperature vs. Time at Column Center for Various Structure Sizes 0 20 40 60 80 100 120 140 160 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature vs. Time at Column Surface for Various Structures Sizes Surface 3.2 x 3.2 x 3.2' Surface 6.4 x 6.4 x 6.4' Surface 13.1 x 13.1 x 13.1' Surface 19.7 x 19.7 x 19.7' 0 20 40 60 80 100 120 140 160 180 200 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421 449 477 505 533 561 589 617 645 673 701 729 757 785 813 841 869 897 925 953 981 Temperature ( ° F ) Time (Hour) Temperature vs. Time at Column Center for Various Structure Size Center 3.2 x 3.2 x 3.2' Center 6.4 x 6.4 x 6.4' Center 13.1 x 13.1 x 13.1' Center 19.7 x 19.7 x 19.7'

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93 Figure 91 Temperature Difference vs. Time for Column for Various Structure Sizes -10 0 10 20 30 40 50 60 70 1 30 59 88 117 146 175 204 233 262 291 320 349 378 407 436 465 494 523 552 581 610 639 668 697 726 755 784 813 842 871 900 929 958 987 Temperature ( ° F ) Time (Hour) Temperature Difference vs. Time Between Column Center and Surface for Various Structures Size Difference 3.2 x 3.2 x 3.2' Difference 6.4 x 6.4 x 6.4' Difference 13.1 x 13.1 x 13.1' Difference 19.7 x 19.7 x 19.7'

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94 CHAPTER V THERMAL STRESS ANALY SIS SIMULATION I ntroduction Thermal stresses that develop in mass concrete pose a large risk to the integrity of the structure as it can c ause cracking. The stresses in mass concrete occur as a result of the inability to dissipate heat quickly. Large temperatures are seen in the middle of the concrete structure creating a large differential with the surface temperature. The large temperatures at the core of the structure cause material expansion while the s urface is shrinking due to the cooling with the ambient temperature. The exterior tends to resist the movement at the center causing stresses to develop at the surface. The larger temperature differential between the center and the surface, the more extr eme and opposing contraction/expansion behavior will be seen within the structure. Other stresses can develop due to restraining forces. If the structure is restrained and unable to expand and contract with the changing temperatures, high stresses may o ccur and they may result in cracking. While the stresses within the structure are typically self equilibrating, they have the potential to exceed the allowable amount of the structure. The tensile stresses specifically or performance under tension. The development of stresses which lead to cracking is why the thermal control of mass concrete is crucial.

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95 Theory The calculations performed in the structural analysis are based on the stiffness method and the stress stra in relationship. The stiffness method is defined by the following equation. Where, F = Applied forces K = Stiffness Matrix U = Displacement Conversely, the displacement can be determined by the inverse of the stiffness matrix. The stiffness matrix contains the geometric properties and represents the materi als resistance of element under loading. The applied forces for this analysis are the thermal loads from the thermal analysis. The following equation represents the inverse stiffness matrix. Once the displacement it known at all loc ations throug hout the model, the stresses can be determined by the following equation. Where, = Stress Vector D = Elasticity Matrix = Strain Vector ( = )

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96 The elasticity matrix , as well as the strains associated with temperature differentials and displacement , impact the stress concentration of the s tructure. The elasticity matrix is primarily dependent on the material properties. The Ansys analysis calculates the stresses at ever y nodal location of the structure for each applied time step. Coefficient of Thermal Expansion The coefficient of thermal expansion is material property related to how much it expands when exposed to heat, and more specifically, the change in length per un it temperature rise. Where, = original length = final length = initial temperature = Final temperature The coeffi ci ent value is primarily dependent on the coarse aggregate of the concrete. The type of aggregate and quantity will both effect its thermal expansion. However, the most accurate values are based on the concrete mix and the weighted average of each constituent. Typical values range from 5 to 7 x in/in/ °F . Modulus of Elasticity The modulus of elasticity is related to the stiffness or rigidity of the concrete. During the early stages of concrete, the modulus of elasticity is minimal which provides the workability and

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97 fluidity of the concrete a t this time. The modulus quickly increases and eventually reaches a value ranging from 4.1 5.7 x psi. the relative change in lateral dimensions when force is applied longitudina l l y and vice versa. Ultim ately, it is the ratio of the lateral and longitudinal strains within the elastic range . and will slightly increase as the concrete cures. This increase is generally insignificant and will not be considered in this analysis. Ansys APDL Structural Simulation The previous chapter discusses the overview of the Ansys simulation process. The procedure to perform a structural analysis is similar and builds on the thermal results from the simula tion in Chapter IV . The temperatures at each node for a given time was input into the stress analysis as a temperature load. This was done by loading the temperature time file and assigning the time to the given time step in the structural analysis. Ma terial and Element Properties of Model The element used for the thermal model is known as SOLID45 ( SOLID45 3 D Structural Solid ) . The element type was assigned because is optimal for solid 3 D analyses with eight nodes for x, y, and z translations.

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98 Figure 92 SOLID45 Ansys Element The model was meshed identically to the thermal analysis with the same nodes a elements. This allowed identical location s to be referenced in both the thermal and structural models. P rior to run ning the simulation, the material properties, including the density, the the program. The density was input as 143.6 lb/ (2,300 kg/ ) which is base d off of the concrete mix designs and is in line with indust ry standards. The value of 5.889 x / °F (1 .06 x / °C) was adopted for the coefficient of thermal expan sion. While the other values were assumed to be constant, t he modulus of elasticity varied with time throughout this analysis. Premature concrete has a very low modulus of elasti city, but as cement hydrates and hardens, the modulus of elasticity drastically increases. The stresses that are developed are directly The values for modulus of elasticity were obtained through the maturity method as performed and measured in the field. The maturity method, as recognized by ASTM C1074,

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99 provides a method of estimating in field concrete strength, by means other than strength of 7 day and 28 day cylinder breaks. The maturity of t he concrete is a measure of the strength based on the age and temperature of the concrete. The concept assumes that similar concrete maturities will yield similar strengths, despite a different time/temperature combination to achieve a given maturity. Th e Nurse Saul formula can be used to determine the maturity index. Where, M(t) = the maturity index , °C hr = Average Temperature for a time interval , °C = datum temperature, 0 °C = specified time interval , hour In order to correlate a maturity index to the corr esponding strength, cylinders must be tested to generate a strength maturity curve which will serve as the basis for all field testing. The cylinders test the temperature and strength at various ages to establish consistent and accurate results of the str ength and maturity relationship. The plot below represents the strength maturity curve for the mix designs used for the STG concrete pours.

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100 Figure 93 Maturity Index Curve The measured temperature in the field allowed the st rengths to be estimated at any given time. The following relationship between concrete strength and modulus of elasticity was used to determine how the modulus of elasticity developed over time ( ACI Committee 207 , 2007) . Where, E = Modulus of Elasticity, psi = Co mpressive Strength, psi The calculated modulus of elasticity was input into the analysis at the respective time step. 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 2000 4000 6000 8000 10000 12000 Compressive Strength (psI) Maturity Index ( hr) STG Strength vs Maturity Index Curve

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101 Boundary Conditions and Loads In order to isolate the stresses induced by the thermal gradi ents, only temperature loads were applied in this analysis. As previously discussed, the nodal results of the thermal analysis are input into the structural analysis. Because the meshing is identical in both trials, the temperature will be recognized at all nodes for any given time. The analysis only applied a boundary condition restraining the bottom of the structure in the x, y, and z directions. This allowed the concrete to deform with minimal constraint to see how the thermal distribution impacted the deformation and stresses. The analysis was performed at approximately 12 hour intervals to reach the 7 da y results, then continued at 24 hour intervals until the 28 day mark. Each interval represents a time step with several sub steps to ensure accu racy. Ansys APDL STG Structural Simulation Result s After the structural simulation was completed, the results were analyzed. In the following sections, the following is provided for each component: Stress Diagram through vertical section of structure St ress diagram through horizontal section of structure ( excluding the basemat ) Ansys FEM model of stress nodal solution at 48 hours. The cross section corresponds with the vertical section of the stress diagram Ansys FEM model of stress nodal solution at 48 hours. The cross section corresponds with the horizontal section of the stress diagram (excluding the basemat)

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102 Discrete Model identifying locations of stress analysis Stress vs Time plot at a variety of locations of the structure In general, the results of the FEM analysis were consistent with what was expected. The stress at the center of the structure was in compression while the top and bottom surfaces were in tension. These stresses continued to develop and increase overtime. However, by hour 672 (28 days) the internal thermal stresses at most locations neared zero. The stresses seen over time are representative of the self stress of the structures. The center is in compression and attempting to expand. The surface is much cooler and resists th is movement and induces tensile stresses. As shown in the diagrams, these stresses only need to be closely monitored (via temperatures) during the early ages of concrete and eventually level out. The tensile stresses at the bottom of the structure, specif ically in the column and tabletop, remain significant even after 28 days. These stresses represent the restraint stresses. The bottom of each structure has been models with a restraint to prevent any movement or displacement. Since the rest of the struc ture is expanding and contracting with various temperatures, stresses are induced and maintained at the bottom of the surface. As previously discusse d , these stresses pose a greater risk to the structure as the begin towards the bottom and can propagate u pwards. The Stress vs. Time plot for each of the structures indicate where the higher tensile stresses and compression stresses develop overtime. Because corners and edges are typically susceptible to tensile stresses they are analyzed in this model. T he red dotted line represents

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103 the allowable tensile strength. This is calculated from the tensile relationship with compression by the following equation: Where, = te nsile strength of concrete, psi = co mpressive strength of concrete, psi The compressive strength is determined by the maturity index discussed in previous sections. The actual structures constructed in the field contained reinforcement which would dramatically increase the tensile stress cap a city of the structure, however the rebar reinfor cement was not considered in this analysis.

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104 Basemat Figure 94 Stress Diagram in Y Dir ection for Basemat at Different Time Steps Figure 95 Location of Basemat Vertical Stress Diagram 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 -100 -50 0 50 100 150 200 250 Y Direction (ft) Stress (psi) Stress Diagram in Y Direction Basemat Time 24 Time 48 Time 168 Time 672

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105 Figure 96 Locations of Stress Analysis in Basemat Figure 97 Stress vs. Time at Various Basemat Locations -200 -100 0 100 200 300 400 500 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 Stress (psi) Time (Hour) Stress vs. Time Basemat Allowable Stress Corner 1 Corner 2 Center East Center West Top East Top West

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106 In the plot in Figure 97, the four locations of the thermocouples are analyzed in addition to the east side top corners (Corner 1 and Corner 2). T he tensile stresses seen approach the maximum allowable of the structure ; cracking would be likely, specifically at the corners. The jagged results are likely a result of inconsistencies of the free mesh. Refinement of the mesh may provide more accurate results; however, the trends of the stress are in line with the anticipa ted results. The lower tensile stresses seen may be attributable to the minimal temperature differential.

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107 Column Figure 98 Stress Diagram in X Direction for Column at Various Time Steps Figure 99 Location of Column Horizontal Stress Diagram -200 -100 0 100 200 300 400 500 600 0.00 0.27 0.53 0.80 1.07 1.33 1.60 1.87 2.13 2.40 2.67 2.93 3.20 3.47 3.73 4.00 4.27 4.53 4.80 5.07 5.33 5.60 5.87 6.13 6.40 6.67 6.93 7.20 7.47 7.73 8.00 Stress (psi) X Direction (ft) Stress Diagram in X Direction Column Time 12 Time 48 Time 168 Time 672

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108 Figure 100 Stress Diagram in Y Direction for Column at Various Time Steps Figure 101 Location of Column Vertical Stress Diagram 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 -800 -600 -400 -200 0 200 400 600 800 Y Direction (ft) Stress (psi) Stress Diagram in Y Direction Column Time 12 Time 48 Time 168 Time 672

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109 Figure 102 Locations of Stress Analysis for the Column Figure 103 Stress vs. Time at Various Column Locations -200 -100 0 100 200 300 400 500 600 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 Stress (psi) Time (Hour) Stress vs. Time Column Allowable Stress Surface Edge Surface Center Center Surface Corner

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110 The two locations of the thermocouples were analyzed for stresses. As expected, the center of the structure was in compression while the surface was in tension. The center edge of the surface and the surface corner at the top of the column was also considered. The corner yielded the highest tensile stress and is the most likely to crack. The surface edge and surface center had similar development of stresses after casting.

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111 Tabletop Figure 104 Stress Diagram in Z Direction for Tabletop at Various Time Steps Figure 105 Location of Tabletop Z Direction Stress Diagram -500 -400 -300 -200 -100 0 100 200 300 400 Stress (psi) Z Direction (ft) Stress Diagram in Z Direction Tabletop Time 12 Time 48 Time 168 Time 672

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112 Figure 106 Stress Diagram in Y Direction for Tabletop at Various Time Steps Figure 107 Location of Tabletop Y Direction Stress Diagram 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 -600 -400 -200 0 200 400 600 800 Y Direction (ft) Stress (psi) Stress Diagram in Y Direction Tabletop Time 12 Time 48 Time 168 Time 672

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113 Figure 108 Loca tions of Stress Analysis for the Tabletop Figure 109 Stress vs. Time at Various Tabletop Locations -600 -400 -200 0 200 400 600 800 1000 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 Stress (psi) Time (Hour) Stress vs. Time Tabletop Allowable Stress Center Surface Center Edge Surface Edge Corner 1 Corner 2

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114 All three thermocouple locations, as well as two corners were analyzed for stresses. Corner 1 is the furthest x coordi n ate at z=0 and corner 2 is the furthest z coordinate at x=0. When compared to the maximum tensile stress, both corners and the edge are likely to crack. The corners yielded the highest tensile stress, but the edge endured the tensile stresses for a longer dura tion. The tabletop had a significant temperature differential which is facilitating these large stresses.

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115 CHAPTER VI CONCLUSION The objective of this thesis study was to understand the behavior of mass concrete structures under thermal loading due to t he heat generated from hydration. The conclusions based on the findings are as follows: The finite element analysis program, Ansys, and the input parameters of this STG analysis can accurately simulate the temperature field of structures in similar volume and geometry as the basemat, column, and tabletop. The measured temperature data from the STG project are in alignment with those calculated through the Ansys finite element analysis. Initial temperature, ambient temperature, cement dosages, insulation, and structure size all play a significant role in the thermal behavior of a given mass concrete structure. While these can be modeled individually, all parameters must be considered simultaneously to understand the net effect of the temperature distributi on. Large temperature differentials within a given structure combined with the stiffening of the structure develop tensile stresses at the surface. These stresses cannot be ignored as the magnitude can exceed the structures tensile limit and result in cra cking. Ansys is a powerful program with numerous features to analyze structures. In order to expand on the efforts from this thesis and use Ansys to its full potential, a few different scenarios can be implemented in future studies. By doing the follow ing, the results may yield a higher level of accuracy when compared to the field measurements.

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116 The actual pour plan and progression can be incorporated into the analysis using the Kill/Alive elements in Ansys. Although these pours are relatively small, i n comparison to a dam, the thermal results may be improved and different stresses may be developed at the interfaces of the lifts and phases. Additionally, this may optimize pour plans in the field based on the results. A study of the formwork can be perf ormed. The formwork will provide different restraints which will go to zero once the formwork is removed. This may cause a spike in stresses upon removal, or provide larger stresses due to more external restraints and limited movement with thermal expans ion. Elaborate on the stress study to understand and model how the cracks impact the long term behavior of the structure.

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117 LIST OF REFERENCES Institute, Farmington Hills, Mich ., Dec. 2005. Farmington Hills, Mich., Nov. 1996. Concrete (ACI 207.2R 07) te Institute, Farmington Hills, Mich., Sept. 2007. Bartojay, Katie. Thermal Properties of Reinforced Structural Mass Concrete. 2012, Thermal Properties of Reinforced Structural Mass Concrete. e of Mass Concrete in CIP 39 Maturity Methods to Estimate Concrete Strength. National Ready Mixes Concrete Association, 2006, www.nrmca.org/aboutconcrete/cips/39p.pdf. ent, www.engr.psu.edu/ce/courses/ce584/concrete/library/construction/curing/Compos ition%20of%20cement.htm. www.uomisan.edu.iq/eng/ar/admin/pdf/90666947094.pdf. Cement Association, 2001, www.cement.org/docs/default source/fc_concrete_technology/is417 ettringite formation and the performance of concrete.pdf?sfvrsn=2. pecific Heat of Normal Strength Concrete and the Journal of Advanced Structures and Geotechnical Engineering, vol. 02, no. 02, Apr. 2013. 2002. InterNACHI, www.nachi.org/history of concrete.htm.

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118 of hydra tion/. Concrete Network, 28 Apr. 2017, www.concretenetwork.com/concrete history/. How Cement Is Made. Portland Cement Association, 2017, www.cement.org/cement concrete applications/how cement is made. Hydration of Portland Cement. www.engr.psu.edu/ce/courses/ce584/concrete/library/construction/curing/Hydrati on.htm. t ies of Calcium Silicate Hydrate G Concrete. ser. 2, July 1997. 2, www.philadelphia.edu.jo/academics/aalfraihat/uploads/heat%20of%20hydration.pd f. e: Scientific Principles, University of Illinois, matse1.matse.illinois.edu/concrete/prin.html. www.slideshare.net/KhaldoonSlaiai1/heat of hydration in mass concre te 69523510. lmcc.cyberlaunch.net/concrete_news/0801/5 minute classroom slump.asp. ss SOLID45 3 D Structural Solid. www.ansys.stuba.sk/html/elem_55/chapter4/ES4 45.htm.

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119 www.ansys.stuba.sk /html/elem_55/chapter4/ES4 70.htm. Civil Engineers, 1985. Thermal Expansion. ASM I nternational, www.owlnet.rice.edu/~msci301/ThermalExpansion.pdf. Thomas, Jeff, and Hamlin Jennings. The Science of Concrete. Northwestern University, iti.northwestern.edu/cement/aboutTheAuthor.html. www.thermoworks. com/why_use_thermocouples. Zhu, Bofang. Thermal Stresses and Temperature Control of Mass Concrete. Elsevier, 2014, books.google.com/books?id=eY OAwAAQBAJ&lpg=PP1&dq=what%20is%20mass%20concrete&lr&pg=PR3#v=onepag e&q=what%20is%20mass%20concrete&f=true.

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120 APPENDIX A Thermal Analysis Ansys Command Data Basemat Thermal Analysis Command Data /COM,ANSYS RELEASE Release 19.0 BUILD 19.0 UP20171214 15:11:53 /input,start,ans,'C: \ Program Files \ ANSYS Inc \ ANSYS Student \ v190 \ ANSYS \ apdl \ ' !* /REPLO T,RESIZE /FILNAME,BM,0 /CWD,'C: \ Users \ Kelsey.Petersen \ Desktop \ ANSYS REV' *DEL,_FNCNAME *DEL,_FNCMTID *DEL,_FNCCSYS *SET,_FNCNAME,'HGEN' *SET,_FNCCSYS,0 ! /INPUT,D: \ My Folder \ Thesis \ Ansys Tables \ HGEN9.func,,,1 *DIM,%_FNCNAME%,TABLE,6,12,1, ,,,%_FNCCSYS% ! ! Begin of equation: 7043.75*exp( 1.75*{TIME}/24) *SET,%_FNCNAME%(0,0,1), 0.0, 999 *SET,%_FNCNAME%(2,0,1), 0.0 *SET,%_FNCNAME%(3,0,1), 0.0 *SET,%_FNCNAME%(4,0,1), 0.0 *SET,%_FNCNAME%(5,0,1), 0.0 *SET,%_FNCNAME%(6,0,1), 0.0 *SET,%_FNCNAME%(0,1,1), 1.0, 1, 0, 0, 0, 0, 0 *SET,%_FNCNAME%(0,2,1), 0.0, 2, 0, 1, 0, 0, 1 *SET,%_FNCNAME%(0,3,1), 0, 3, 0, 1, 1, 2, 2 *SET,%_FNCNAME%(0,4,1), 0.0, 1, 0, 1.75, 0, 0, 3 *SET,%_FNCNAME%(0,5,1), 0.0, 2, 0, 1, 3, 3, 1 *SET,%_ FNCNAME%(0,6,1), 0.0, 1, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,7,1), 0.0, 2, 0, 24, 0, 0, 1 *SET,%_FNCNAME%(0,8,1), 0.0, 3, 0, 1, 1, 4, 2 *SET,%_FNCNAME%(0,9,1), 0.0, 1, 7, 1, 3, 0, 0 *SET,%_FNCNAME%(0,10,1), 0.0, 2, 0, 7043.75, 0, 0, 1 *SET,%_FNC NAME%(0,11,1), 0.0, 3, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,12,1), 0.0, 99, 0, 1, 3, 0, 0 ! End of equation: 7043.75*exp( 1.75*{TIME}/24) ! -> *DEL,_FNCNAME *DEL,_FNCMTID *DEL,_FNCCSYS *SET,_FNCNAME,'ATEMP' *SET,_FNCCSYS,0 ! /INPUT,D: \ My Fo lder \ Thesis \ Ansys Tables \ Basemat Ambient Temp.func,,,1 *DIM,%_FNCNAME%,TABLE,6,10,1,,,,%_FNCCSYS% ! ! Begin of equation: 31+11*sin(.261799*{TIME}+3.5) *SET,%_FNCNAME%(0,0,1), 0.0, 999 *SET,%_FNCNAME%(2,0,1), 0.0 *SET,%_FNCNAME%(3,0,1), 0.0 *S ET,%_FNCNAME%(4,0,1), 0.0 *SET,%_FNCNAME%(5,0,1), 0.0 *SET,%_FNCNAME%(6,0,1), 0.0 *SET,%_FNCNAME%(0,1,1), 1.0, 1, 0, .261799, 0, 0, 1 *SET,%_FNCNAME%(0,2,1), 0.0, 2, 0, 1, 1, 3, 1 *SET,%_FNCNAME%(0,3,1), 0, 1, 0, 3.5, 0, 0, 2 *SET,%_FNCNAME%( 0,4,1), 0.0, 3, 0, 1, 2, 1, 1 *SET,%_FNCNAME%(0,5,1), 0.0, 1, 9, 1, 3, 0, 0

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121 *SET,%_FNCNAME%(0,6,1), 0.0, 2, 0, 11, 0, 0, 1 *SET,%_FNCNAME%(0,7,1), 0.0, 3, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,8,1), 0.0, 1, 0, 31, 0, 0, 3 *SET,%_FNCNAME%(0,9,1), 0.0 , 2, 0, 1, 1, 1, 3 *SET,%_FNCNAME%(0,10,1), 0.0, 99, 0, 1, 2, 0, 0 ! End of equation: 31+11*sin(.261799*{TIME}+3.5) ! -> /AUX15 !* IOPTN,IGES,SMOOTH IOPTN,MERGE,YES IOPTN,SOLID,YES IOPTN,SMALL,YES IOPTN,GTOLER, DEFA IGESIN,'STG Model Basema t Exploded m reoirented','iges','D: \ My Folder \ Thesis \ KP MODEL \ ' VPLOT !* !* /NOPR KEYW,PR_SET,1 KEYW,PR_STRUC,0 KEYW,PR_THERM,1 KEYW,PR_FLUID,0 KEYW,PR_ELMAG,0 KEYW,MAGNOD,0 KEYW,MAGEDG,0 KEYW,MAGHFE,0 KEYW,MAGELC,0 KEYW,P R_MULTI,0 /GO !* /COM, /COM,Preferences for GUI filtering have been set to display: /COM, Thermal !* FINISH /PREP7 !* ET,1,SOLID70 !* TOFFST,273 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,KXX,1,,10.6 MPTEMP,,,,,,,, MPTEMP,1,0 MPD ATA,C,1,,.75 MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,DENS,1,,2300 SMRT,6 SMRT,7 MSHAPE,1,3D MSHKEY,0 !* CM,_Y,VOLU VSEL, , , , 1 CM,_Y1,VOLU CHKMSH,'VOLU' CMSEL,S,_Y !*

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122 VMESH,_Y1 !* CMDELE,_Y CMDELE,_Y1 CMDELE,_Y2 !* FL ST,5,829,2,ORDE,2 FITEM,5,1 FITEM,5, 829 CM,_Y,ELEM ESEL, , , ,P51X CM,_Y1,ELEM CMSEL,S,_Y CMDELE,_Y !* !* EREF,_Y1, , ,1,0,1,1 CMDELE,_Y1 !* !* ANTYPE,4 /UI,MESH,OFF FLST,2,9,5,ORDE,4 FITEM,2,11 FITEM,2, 15 FITEM,2,17 FITEM, 2, 20 /GO !* !* SFA,P51X,1,CONV,8.17, %ATEMP% FLST,2,1,5,ORDE,1 FITEM,2,16 /GO !* !* SFA,P51X,1,CONV,2.414, %ATEMP% FLST,2,1,6,ORDE,1 FITEM,2,1 /GO !* !* BFV,P51X,HGEN, %HGEN% FLST,2,1796,1,ORDE,2 FITEM,2,1 FITEM,2, 17 96 IC,P51X,TEMP,16.5, FINISH /SOL !* ANTYPE,4 !* TRNOPT,FULL LUMPM,0 !* DELTIM,1,.1,1 OUTRES,ERASE OUTRES,ALL,1 LNSRCH,1 NEQIT,1000 TIME,1000 /STATUS,SOLU SOLVE

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123 FINISH Column Thermal Analysis Command Data /COM,ANSYS RELEASE R elease 19.0 BUILD 19.0 UP20171214 14:42:11 /input,menust,tmp,'' /GRA,POWER /GST,ON /PLO,INFO,3 /GRO,CURL,ON /CPLANE,1 /REPLOT,RESIZE WPSTYLE,,,,,,,,0 /REPLOT,RESIZE /FILNAME,Large Col,0 /CWD,'C: \ Users \ Kelsey.Petersen \ Desktop \ ANSYS RE V' *DEL,_FNCNAME *DEL,_FNCMTID *DEL,_FNCCSYS *SET,_FNCNAME,'ATEMP' *SET,_FNCCSYS,0 ! /INPUT,D: \ My Folder \ Thesis \ Ansys Tables \ Column 3 AmbTemp.func,,,1 *DIM,%_FNCNAME%,TABLE,6,12,1,,,,%_FNCCSYS% ! ! Begin of equation: 22+8*sin((PI*{TIM E}/12)+.75) *SET,%_FNCNAME%(0,0,1), 0.0, 999 *SET,%_FNCNAME%(2,0,1), 0.0 *SET,%_FNCNAME%(3,0,1), 0.0 *SET,%_FNCNAME%(4,0,1), 0.0 *SET,%_FNCNAME%(5,0,1), 0.0 *SET,%_FNCNAME%(6,0,1), 0.0 *SET,%_FNCNAME%(0,1,1), 1.0, 1, 0, 3.14159265358979310, 0, 0, 1 *SET,%_FNCNAME%(0,2,1), 0.0, 2, 0, 1, 1, 3, 1 *SET,%_FNCNAME%(0,3,1), 0, 1, 0, 12, 0, 0, 2 *SET,%_FNCNAME%(0,4,1), 0.0, 3, 0, 1, 2, 4, 1 *SET,%_FNCNAME%(0,5,1), 0.0, 1, 0, .75, 0, 0, 3 *SET,%_FNCNAME%(0,6,1), 0.0, 2, 0, 1, 3, 1, 1 * SET,%_FNCNAME%(0,7,1), 0.0, 1, 9, 1, 2, 0, 0 *SET,%_FNCNAME%(0,8,1), 0.0, 2, 0, 8, 0, 0, 1 *SET,%_FNCNAME%(0,9,1), 0.0, 3, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,10,1), 0.0, 1, 0, 22, 0, 0, 3 *SET,%_FNCNAME%(0,11,1), 0.0, 2, 0, 1, 1, 1, 3 *SET ,%_FNCNAME%(0,12,1), 0.0, 99, 0, 1, 2, 0, 0 ! End of equation: 22+8*sin((PI*{TIME}/12)+.75) ! -> *DEL,_FNCNAME *DEL,_FNCMTID *DEL,_FNCCSYS *SET,_FNCNAME,'HGEN' *SET,_FNCCSYS,0 ! /INPUT,D: \ My Folder \ Thesis \ Ansys Tables \ HGEN9.func,,,1 *DIM,%_FNCN AME%,TABLE,6,12,1,,,,%_FNCCSYS% ! ! Begin of equation: 7043.75*exp( 1.75*{TIME}/24) *SET,%_FNCNAME%(0,0,1), 0.0, 999 *SET,%_FNCNAME%(2,0,1), 0.0 *SET,%_FNCNAME%(3,0,1), 0.0 *SET,%_FNCNAME%(4,0,1), 0.0 *SET,%_FNCNAME%(5,0,1), 0.0 *SET,%_FNCN AME%(6,0,1), 0.0 *SET,%_FNCNAME%(0,1,1), 1.0, 1, 0, 0, 0, 0, 0 *SET,%_FNCNAME%(0,2,1), 0.0, 2, 0, 1, 0, 0, 1

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124 *SET,%_FNCNAME%(0,3,1), 0, 3, 0, 1, 1, 2, 2 *SET,%_FNCNAME%(0,4,1), 0.0, 1, 0, 1.75, 0, 0, 3 *SET,%_FNCNAME%(0,5,1), 0.0, 2, 0, 1, 3, 3, 1 *SET,%_FNCNAME%(0,6,1), 0.0, 1, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,7,1), 0.0, 2, 0, 24, 0, 0, 1 *SET,%_FNCNAME%(0,8,1), 0.0, 3, 0, 1, 1, 4, 2 *SET,%_FNCNAME%(0,9,1), 0.0, 1, 7, 1, 3, 0, 0 *SET,%_FNCNAME%(0,10,1), 0.0, 2, 0, 7043.75, 0, 0, 1 *SET,%_FNCNAME%(0,11,1), 0.0, 3, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,12,1), 0.0, 99, 0, 1, 3, 0, 0 ! End of equation: 7043.75*exp( 1.75*{TIME}/24) ! -> /AUX15 !* IOPTN,IGES,SMOOTH IOPTN,MERGE,YES IOPTN,SOLID,YES IOPTN,SMALL,YES IOPTN, GTOLER, DEFA IGESIN,'STG Model Exploded 1 column reoriented','iges','D: \ My Folder \ Thesis \ KP MODEL \ ' VPLOT !* !* /NOPR KEYW,PR_SET,1 KEYW,PR_STRUC,0 KEYW,PR_THERM,1 KEYW,PR_FLUID,0 KEYW,PR_ELMAG,0 KEYW,MAGNOD,0 KEYW,MAGEDG,0 K EYW,MAGHFE,0 KEYW,MAGELC,0 KEYW,PR_MULTI,0 /GO !* /COM, /COM,Preferences for GUI filtering have been set to display: /COM, Thermal !* FINISH /PREP7 !* ET,1,SOLID70 !* TOFFST,273 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,KXX,1,,1 0.6 MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,C,1,,.75 MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,DENS,1,,2300 FLST,2,6,5,ORDE,2 FITEM,2,7 FITEM,2, 12 AESIZE,P51X,.4064, MSHAPE,0,3D MSHKEY,1

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125 !* CM,_Y,VOLU VSEL, , , , 1 CM,_Y1,VOLU CHKMSH,'VO LU' CMSEL,S,_Y !* VMESH,_Y1 !* CMDELE,_Y CMDELE,_Y1 CMDELE,_Y2 !* /UI,MESH,OFF !* ANTYPE,4 !* TRNOPT,FULL LUMPM,0 !* FLST,2,5,5,ORDE,3 FITEM,2,7 FITEM,2,9 FITEM,2, 12 /GO !* !* SFA,P51X,1,CONV,8.17, %ATEMP% FL ST,2,1,5,ORDE,1 FITEM,2,8 /GO !* !* SFA,P51X,1,CONV,7.73, %ATEMP% FLST,2,1,6,ORDE,1 FITEM,2,1 /GO !* !* BFV,P51X,HGEN, %HGEN% FLST,2,1225,1,ORDE,2 FITEM,2,1 FITEM,2, 1225 IC,P51X,TEMP,28, FINISH /SOL !* ANTYPE,4 !* T RNOPT,FULL LUMPM,0 !* DELTIM,1,.1,1 OUTRES,ERASE OUTRES,ALL,1 LNSRCH,1 NEQIT,100 TIME,1000 !* /STATUS,SOLU SOLVE FINISH

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126 Tabletop Thermal Analysis Command Data /COM,ANSYS RELEASE Release 19.0 BUILD 19.0 UP20171214 15: 26:50 /input,start,ans,'C: \ Program Files \ ANSYS Inc \ ANSYS Student \ v190 \ ANSYS \ apdl \ ' !* /FILNAME,Tabletop,0 *DEL,_FNCNAME *DEL,_FNCMTID *DEL,_FNCCSYS *SET,_FNCNAME,'ATEMP' *SET,_FNCCSYS,0 ! /INPUT,D: \ My Folder \ Thesis \ Ansys Tables \ Tabletop Amb ient Temp.func,,,1 *DIM,%_FNCNAME%,TABLE,6,10,1,,,,%_FNCCSYS% ! ! Begin of equation: 17+3.5*sin(.261799*{TIME}+4.3) *SET,%_FNCNAME%(0,0,1), 0.0, 999 *SET,%_FNCNAME%(2,0,1), 0.0 *SET,%_FNCNAME%(3,0,1), 0.0 *SET,%_FNCNAME%(4,0,1), 0.0 *SET,%_FNC NAME%(5,0,1), 0.0 *SET,%_FNCNAME%(6,0,1), 0.0 *SET,%_FNCNAME%(0,1,1), 1.0, 1, 0, .261799, 0, 0, 1 *SET,%_FNCNAME%(0,2,1), 0.0, 2, 0, 1, 1, 3, 1 *SET,%_FNCNAME%(0,3,1), 0, 1, 0, 4.3, 0, 0, 2 *SET,%_FNCNAME%(0,4,1), 0.0, 3, 0, 1, 2, 1, 1 *SET ,%_FNCNAME%(0,5,1), 0.0, 1, 9, 1, 3, 0, 0 *SET,%_FNCNAME%(0,6,1), 0.0, 2, 0, 3.5, 0, 0, 1 *SET,%_FNCNAME%(0,7,1), 0.0, 3, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,8,1), 0.0, 1, 0, 17, 0, 0, 3 *SET,%_FNCNAME%(0,9,1), 0.0, 2, 0, 1, 1, 1, 3 *SET,%_FNCN AME%(0,10,1), 0.0, 99, 0, 1, 2, 0, 0 ! End of equation: 17+3.5*sin(.261799*{TIME}+4.3) ! -> *DEL,_FNCNAME *DEL,_FNCMTID *DEL,_FNCCSYS *SET,_FNCNAME,'HGEN' *SET,_FNCCSYS,0 ! /INPUT,D: \ My Folder \ Thesis \ Ansys Tables \ HGEN9.func,,,1 *DIM,%_FNCNAME %,TABLE,6,12,1,,,,%_FNCCSYS% ! ! Begin of equation: 7043.75*exp( 1.75*{TIME}/24) *SET,%_FNCNAME%(0,0,1), 0.0, 999 *SET,%_FNCNAME%(2,0,1), 0.0 *SET,%_FNCNAME%(3,0,1), 0.0 *SET,%_FNCNAME%(4,0,1), 0.0 *SET,%_FNCNAME%(5,0,1), 0.0 *SET,%_FNCNAME %(6,0,1), 0.0 *SET,%_FNCNAME%(0,1,1), 1.0, 1, 0, 0, 0, 0, 0 *SET,%_FNCNAME%(0,2,1), 0.0, 2, 0, 1, 0, 0, 1 *SET,%_FNCNAME%(0,3,1), 0, 3, 0, 1, 1, 2, 2 *SET,%_FNCNAME%(0,4,1), 0.0, 1, 0, 1.75, 0, 0, 3 *SET,%_FNCNAME%(0,5,1), 0.0, 2, 0, 1, 3 , 3, 1 *SET,%_FNCNAME%(0,6,1), 0.0, 1, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,7,1), 0.0, 2, 0, 24, 0, 0, 1 *SET,%_FNCNAME%(0,8,1), 0.0, 3, 0, 1, 1, 4, 2 *SET,%_FNCNAME%(0,9,1), 0.0, 1, 7, 1, 3, 0, 0 *SET,%_FNCNAME%(0,10,1), 0.0, 2, 0, 7043.75, 0, 0, 1 *SET,%_FNCNAME%(0,11,1), 0.0, 3, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,12,1), 0.0, 99, 0, 1, 3, 0, 0 ! End of equation: 7043.75*exp( 1.75*{TIME}/24) ! -> /AUX15

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127 !* IOPTN,IGES,SMOOTH IOPTN,MERGE,YES IOPTN,SOLID,YES IOPTN,SMALL,YES IOPTN,GTO LER, DEFA IGESIN,'STG Model Tabletop Exploded m reoirented','iges','D: \ My Folder \ Thesis \ KP MODEL \ ' VPLOT !* !* /NOPR KEYW,PR_SET,1 KEYW,PR_STRUC,0 KEYW,PR_THERM,1 KEYW,PR_FLUID,0 KEYW,PR_ELMAG,0 KEYW,MAGNOD,0 KEYW,MAGEDG,0 KEYW ,MAGHFE,0 KEYW,MAGELC,0 KEYW,PR_MULTI,0 /GO !* /COM, /COM,Preferences for GUI filtering have been set to display: /COM, Thermal !* FINISH /PREP7 !* ET,1,SOLID70 !* TOFFST,273 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,KXX,1,,10.6 MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,C,1,,.75 MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,DENS,1,,2300 SMRT,6 SMRT,7 MSHAPE,1,3D MSHKEY,0 !* CM,_Y,VOLU VSEL, , , , 1 CM,_Y1,VOLU CHKMSH,'VOLU' CMSEL,S,_Y !* VMESH,_Y1 !* CMDELE,_Y CMDELE,_Y1 CMDELE,_Y2 !* FLST,5,357,2,ORDE,2 FITEM,5,1

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128 FITEM,5, 357 CM,_Y,ELEM ESEL, , , ,P51X CM,_Y1,ELEM CMSEL,S,_Y CMDELE,_Y !* !* EREF,_Y1, , ,1,0,1,1 CMDELE,_Y1 !* !* ANTYPE,4 !* TRNOPT,FULL LUMPM,0 !* FLST,2,18,5 ,ORDE,2 FITEM,2,19 FITEM,2, 36 /GO !* !* SFA,P51X,1,CONV,8.17, %ATEMP% FLST,2,1,6,ORDE,1 FITEM,2,1 /GO !* !* BFV,P51X,HGEN, %HGEN% FLST,2,886,1,ORDE,2 FITEM,2,1 FITEM,2, 886 IC,P51X,TEMP,21, /UI,MESH,OFF FINISH /SOL !* AN TYPE,4 !* TRNOPT,FULL LUMPM,0 !* DELTIM,1,.1,1 OUTRES,ERASE OUTRES,ALL,1 LNSRCH,1 NEQIT,100 TIME,1000 /STATUS,SOLU SOLVE FINISH

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129 APPENDIX B Structural Analysis Ansys Command Data Basemat Structural Analysis Command Data /COM,ANSYS RELEASE Release 19.0 BUILD 19.0 UP20171214 18:54:43 /input,menust,tmp,'' /GRA,POWER /GST,ON /PLO,INFO,3 /GRO,CURL,ON /CPLANE,1 /REPLOT,RESIZE WPSTYLE,,,,,,,,0 /REPLOT,RESIZE /CWD,'C: \ Users \ Kelsey.Petersen \ Desktop \ Ansys Stress' /FILN AME,BASEMAT1,0 *DEL,_FNCNAME *DEL,_FNCMTID *DEL,_FNCCSYS *SET,_FNCNAME,'HGEN' *SET,_FNCCSYS,0 ! /INPUT,D: \ My Folder \ Thesis \ Ansys Tables \ HGEN9.func,,,1 *DIM,%_FNCNAME%,TABLE,6,12,1,,,,%_FNCCSYS% ! ! Begin of equation: 7043.75*exp( 1.75*{TIME }/24) *SET,%_FNCNAME%(0,0,1), 0.0, 999 *SET,%_FNCNAME%(2,0,1), 0.0 *SET,%_FNCNAME%(3,0,1), 0.0 *SET,%_FNCNAME%(4,0,1), 0.0 *SET,%_FNCNAME%(5,0,1), 0.0 *SET,%_FNCNAME%(6,0,1), 0.0 *SET,%_FNCNAME%(0,1,1), 1.0, 1, 0, 0, 0, 0, 0 *SET,%_FNCNAME%( 0,2,1), 0.0, 2, 0, 1, 0, 0, 1 *SET,%_FNCNAME%(0,3,1), 0, 3, 0, 1, 1, 2, 2 *SET,%_FNCNAME%(0,4,1), 0.0, 1, 0, 1.75, 0, 0, 3 *SET,%_FNCNAME%(0,5,1), 0.0, 2, 0, 1, 3, 3, 1 *SET,%_FNCNAME%(0,6,1), 0.0, 1, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,7,1), 0.0, 2, 0, 24, 0, 0, 1 *SET,%_FNCNAME%(0,8,1), 0.0, 3, 0, 1, 1, 4, 2 *SET,%_FNCNAME%(0,9,1), 0.0, 1, 7, 1, 3, 0, 0 *SET,%_FNCNAME%(0,10,1), 0.0, 2, 0, 7043.75, 0, 0, 1 *SET,%_FNCNAME%(0,11,1), 0.0, 3, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,12,1 ), 0.0, 99, 0, 1, 3, 0, 0 ! End of equation: 7043.75*exp( 1.75*{TIME}/24) ! -> *DEL,_FNCNAME *DEL,_FNCMTID *DEL,_FNCCSYS *SET,_FNCNAME,'ATEMP' *SET,_FNCCSYS,0 ! /INPUT,D: \ My Folder \ Thesis \ Ansys Tables \ Basemat Ambient Temp.func,,,1 *DIM,%_FN CNAME%,TABLE,6,10,1,,,,%_FNCCSYS% ! ! Begin of equation: 31+11*sin(.261799*{TIME}+3.5) *SET,%_FNCNAME%(0,0,1), 0.0, 999 *SET,%_FNCNAME%(2,0,1), 0.0 *SET,%_FNCNAME%(3,0,1), 0.0 *SET,%_FNCNAME%(4,0,1), 0.0

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130 *SET,%_FNCNAME%(5,0,1), 0.0 *SET,%_FN CNAME%(6,0,1), 0.0 *SET,%_FNCNAME%(0,1,1), 1.0, 1, 0, .261799, 0, 0, 1 *SET,%_FNCNAME%(0,2,1), 0.0, 2, 0, 1, 1, 3, 1 *SET,%_FNCNAME%(0,3,1), 0, 1, 0, 3.5, 0, 0, 2 *SET,%_FNCNAME%(0,4,1), 0.0, 3, 0, 1, 2, 1, 1 *SET,%_FNCNAME%(0,5,1), 0.0, 1, 9, 1, 3, 0, 0 *SET,%_FNCNAME%(0,6,1), 0.0, 2, 0, 11, 0, 0, 1 *SET,%_FNCNAME%(0,7,1), 0.0, 3, 0, 1, 2, 3, 1 *SET,%_FNCNAME%(0,8,1), 0.0, 1, 0, 31, 0, 0, 3 *SET,%_FNCNAME%(0,9,1), 0.0, 2, 0, 1, 1, 1, 3 *SET,%_FNCN AME%(0,10,1), 0.0, 99, 0, 1, 2, 0, 0 ! End of equation: 31+11*sin(.261799*{TIME}+3.5) ! -> /AUX15 !* !* IOPTN,IGES,SMOOTH IOPTN,MERGE,YES IOPTN,SOLID,YES IOPTN,SMALL,YES IOPTN,GTOLER, DEFA IGESIN,'STG Model Basemat Exploded m reoirented' ,'iges','D: \ My Folder \ Thesis \ KP MODEL \ ' VPLOT !* !* /NOPR KEYW,PR_SET,1 KEYW,PR_STRUC,1 KEYW,PR_THERM,0 KEYW,PR_FLUID,0 KEYW,PR_ELMAG,0 KEYW,MAGNOD,0 KEYW,MAGEDG,0 KEYW,MAGHFE,0 KEYW,MAGELC,0 KEYW,PR_MULTI,0 /GO !* /COM, /COM,Preferences for GUI filtering have been set to display: /COM, Structural !* FINISH /PREP7 !* et,1,45 TOFFST,273 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,EX,1,,8727 MPDATA,PRXY,1,,.2 MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,DENS,1,, 2300 MPTEMP,,,,,,,, MPTEMP,1,0 UIMP,1,REFT,,, MPDATA,ALPX,1,,.0000106 SMRT,6 SMRT,7

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131 MSHAPE,1,3D MSHKEY,0 !* CM,_Y,VOLU VSEL, , , , 1 CM,_Y1,VOLU CHKMSH,'VOLU' CMSEL,S,_Y !* VMESH,_Y1 !* CMDELE,_Y CMDELE,_Y1 CMDELE, _Y2 !* FLST,5,829,2,ORDE,2 FITEM,5,1 FITEM,5, 829 CM,_Y,ELEM ESEL, , , ,P51X CM,_Y1,ELEM CMSEL,S,_Y CMDELE,_Y !* !* EREF,_Y1, , ,1,0,1,1 CMDELE,_Y1 !* !* ANTYPE,0 FLST,2,1,5,ORDE,1 FITEM,2,16 !* /GO DA,P51X,ALL, /UI,MESH, OFF LDREAD,TEMP,,,1, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL NSUBST,12,0,0 OUTRES,ERASE OUTRES,ALL,1 LNSRCH,1 NEQIT,100 TIME,1 LSWRITE,1, FINISH /PREP7 LDREAD,TEMP,,,6, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,6 LSWRITE,2, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,11431 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,12, ,'BM','rth','.. \ ANSYS REV \ '

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132 FINISH /SOL TIME,12 LSWRITE,3, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE ,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,18446 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,24, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,24 LSWRITE,4, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,22493 MPDATA, PRXY,1,,0.2 LDREAD,TEMP,,,36, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,36 LSWRITE,5, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,24624 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,48, ,'BM','rth','.. \ AN SYS REV \ ' FINISH /SOL TIME,48 LSWRITE,6, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,25579 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,60, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,60 LSWRITE,7, F INISH /PREP7 !*

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133 LDREAD,TEMP,,,72, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,72 LSWRITE,8, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,26092 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,84, ,'BM','rth ','.. \ ANSYS REV \ ' FINISH /SOL TIME,84 LSWRITE,9, FINISH /PREP7 !* LDREAD,TEMP,,,96, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,96 LSWRITE,10, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1, ,26423 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,108, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,108 LSWRITE,11, FINISH /PREP7 LDREAD,TEMP,,,120, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,120 LSWRITE,12, FINISH /PREP7 !* LDREAD,TEMP,,,1 68, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,168 LSWRITE,13, FINISH /PREP7 LDREAD,TEMP,,,192, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,192 LSWRITE,14,

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134 FINISH /PREP7 LDREAD,TEMP,,,240, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TI ME,240 LSWRITE,15, FINISH /PREP7 LDREAD,TEMP,,,288, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,288 LSWRITE,16, FINISH /PREP7 LDREAD,TEMP,,,336, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,336 LSWRITE,17, FINISH /PREP7 LDREAD,TEMP, ,,384, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,384 LSWRITE,18, FINISH /PREP7 LDREAD,TEMP,,,432, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,432 LSWRITE,19, FINISH /PREP7 LDREAD,TEMP,,,480, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,480 LSWRITE,20, FINISH /PREP7 LDREAD,TEMP,,,528, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,528 LSWRITE,21, FINISH /PREP7 LDREAD,TEMP,,,576, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,576 LSWRITE,22, FINISH /PREP7 LDREAD,TE MP,,,624, ,'BM','rth','.. \ ANSYS REV \ ' /REPLOT,RESIZE FINISH /SOL TIME,624

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135 LSWRITE,23, FINISH /PREP7 LDREAD,TEMP,,,672, ,'BM','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,672 LSWRITE,24, LSSOLVE,1,24,1, FINISH /POST1 !* /EFACET,1 PLNSOL, S,1, 0,1.0 FINISH Column Structural Analysis Command Data /COM,ANSYS RELEASE Release 19.0 BUILD 19.0 UP20171214 14:03:37 /input,start,ans,'C: \ Program Files \ ANSYS Inc \ ANSYS Student \ v190 \ ANSYS \ apdl \ ' /FILNAME,ColNoFORMS,0 !* /NO PR KEYW,PR_SET,1 KEYW,PR_STRUC,1 KEYW,PR_THERM,0 KEYW,PR_FLUID,0 KEYW,PR_ELMAG,0 KEYW,MAGNOD,0 KEYW,MAGEDG,0 KEYW,MAGHFE,0 KEYW,MAGELC,0 KEYW,PR_MULTI,0 /GO !* /COM, /COM,Preferences for GUI filtering have been set to display: /COM, Structural !* /CWD,'C: \ Users \ Kelsey.Petersen \ Desktop \ Ansys Stress' /PREP7 !* !* FINISH /AUX15 !* IOPTN,IGES,SMOOTH IOPTN,MERGE,YES IOPTN,SOLID,YES IOPTN,SMALL,YES IOPTN,GTOLER, DEFA IGESIN,'STG Model Exploded 1 column reoriented','iges','D: \ My Folder \ Thesis \ KP MODEL \ ' VPLOT !* FINISH /PREP7 et,1,45 TOFFST,273

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136 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,EX,1,,8727 MPDATA,PRXY,1,,.2 MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,DENS,1,,2300 MPTEMP,,,,,,,, MPTEMP ,1,0 UIMP,1,REFT,,, MPDATA,ALPX,1,,.0000106 FLST,2,6,5,ORDE,2 FITEM,2,7 FITEM,2, 12 AESIZE,P51X,.4064, MSHAPE,0,3D MSHKEY,1 !* CM,_Y,VOLU VSEL, , , , 1 CM,_Y1,VOLU CHKMSH,'VOLU' CMSEL,S,_Y !* VMESH,_Y1 !* CMDELE,_Y CMDELE,_Y1 CMDELE,_Y2 !* FLST,2,1,5,ORDE,1 FITEM,2,8 !* /GO DA,P51X,ALL, LDREAD,TEMP,,, , ,'LargeCol','rth','.. \ ANSYS REV \ ' LDREAD,TEMP,,,1, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL NSUBST,12,0,0 OUTRES,ERASE OUTRES,ALL,1 LNSR CH,1 NEQIT,100 TIME,1 LSWRITE,1, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,10843 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,6, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,6 LSWRITE,2, FINISH /PREP7

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137 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,16363 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,12, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,12 LSWRITE,3, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,21089 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,24, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,24 LSWRITE,4, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,24019 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,36, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,36 LSWRITE,5, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,25068 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,48, ,'Lar geCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,48 LSWRITE,6, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,25579 MPDATA,PRXY,1,,0.2

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138 LDREAD,TEMP,,,60, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TI ME,60 LSWRITE,7, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,26092 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,72, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,72 LSWRITE,8, FINISH /PREP7 LDREAD,T EMP,,,84, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,84 LSWRITE,9, FINISH /PREP7 LDREAD,TEMP,,,96, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,96 LSWRITE,10, FINISH /PREP7 LDREAD,TEMP,,,108, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,108 LSWRITE,11, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,25423 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,120, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,120 LSWRITE,12, FINISH /PREP7 LDREAD,TEMP,,,168, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,168 LSWRITE,13, FINISH /PREP7

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139 LDREAD,TEMP,,,192, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,192 LSWRITE,14, FINISH /PREP7 LDREAD,TEMP,,,240, ,'LargeCol', 'rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,240 LSWRITE,15, FINISH /PREP7 LDREAD,TEMP,,,288, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,288 LSWRITE,16, FINISH /PREP7 !* LDREAD,TEMP,,,336, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL T IME,336 LSWRITE,17, FINISH /PREP7 LDREAD,TEMP,,,384, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,384 LSWRITE,18, FINISH /PREP7 LDREAD,TEMP,,,432, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,432 LSWRITE,19, FINISH /PREP7 LDR EAD,TEMP,,,480, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,480 LSWRITE,20, FINISH /PREP7 LDREAD,TEMP,,,528, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,528 LSWRITE,21, FINISH /PREP7 LDREAD,TEMP,,,576, ,'LargeCol','rth','.. \ ANSY S REV \ ' FINISH /SOL TIME,576 LSWRITE,22, FINISH

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140 /PREP7 LDREAD,TEMP,,,624, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,624 LSWRITE,23, FINISH /PREP7 LDREAD,TEMP,,,672, ,'LargeCol','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,672 LSWRITE,24, LSSOLVE,1,24,1, FINISH /POST1 !* /EFACET,1 PLNSOL, S,1, 0,1.0 FINISH Tabletop Structural Analysis Command Data /COM,ANSYS RELEASE Release 19.0 BUILD 19.0 UP20171214 13:15:28 /input,start,ans,'C: \ Program Files \ ANSYS Inc \ AN SYS Student \ v190 \ ANSYS \ apdl \ ' !* /FILNAME,TTTEST,0 /CWD,'C: \ Users \ Kelsey.Petersen \ Desktop \ Ansys Stress' /AUX15 !* !* /NOPR KEYW,PR_SET,1 KEYW,PR_STRUC,1 KEYW,PR_THERM,0 KEYW,PR_FLUID,0 KEYW,PR_ELMAG,0 KEYW,MAGNOD,0 KEYW,MAGEDG,0 KEYW,MAGHFE,0 KEYW,MAGELC,0 KEYW,PR_MULTI,0 /GO !* /COM, /COM,Preferences for GUI filtering have been set to display: /COM, Structural !* FINISH /PREP7 et,1,45 !* TOFFST,273 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,EX,1,,8727 MPDATA,PRXY,1,,.2 MPTEMP,,,,,,,, MPTEMP,1,0 MPDATA,DENS,1,,2300 MPTEMP,,,,,,,,

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141 MPTEMP,1,0 UIMP,1,REFT,,, MPDATA,ALPX,1,,.0000106 /DIST, 1 ,1.082226,1 /REP,FAST /DIST, 1 ,1.082226,1 /REP,FAST /DIST, 1 ,1.082226,1 /REP,FAST /DIST, 1 ,1.082226,1 /REP,FAST /DIST, 1 ,1.082226,1 /REP,FAST /DIST, 1 ,1.082226,1 /REP,FAST /DIST, 1 ,1.082226,1 /REP,FAST SMRT,6 SMRT,7 MSHAPE,1,3D MSHKEY,0 !* !* !* FINISH /AUX15 !* IOPTN,IGES,SMOOTH IOPTN,MERGE,YES IOPTN,SOLID, YES IOPTN,SMALL,YES IOPTN,GTOLER, DEFA IGESIN,'STG Model Tabletop Exploded m reoirented','iges','D: \ My Folder \ Thesis \ KP MODEL \ ' VPLOT !* FINISH /PREP7 CM,_Y,VOLU VSEL, , , , 1 CM,_Y1,VOLU CHKMSH,'VOLU' CMSEL,S,_Y !* VMESH, _Y1 !* CMDELE,_Y CMDELE,_Y1 CMDELE,_Y2 !* FLST,5,357,2,ORDE,2 FITEM,5,1 FITEM,5, 357 CM,_Y,ELEM ESEL, , , ,P51X CM,_Y1,ELEM CMSEL,S,_Y CMDELE,_Y !* !* EREF,_Y1, , ,1,0,1,1 CMDELE,_Y1 !*

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142 !* /UI,MESH,OFF ANTYPE,0 FLST,2,1 ,5,ORDE,1 FITEM,2,31 !* /GO DA,P51X,ALL, LDREAD,TEMP,,,1, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL NSUBST,12,0,0 OUTRES,ERASE OUTRES,ALL,1 LNSRCH,1 NEQIT,100 TIME,1 LSWRITE,1, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,9495 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,6, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,6 LSWRITE,2, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,14281 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,12, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,12 LSWRITE,3, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,21089 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,24, ,'Tabl etop','rth','.. \ ANSYS REV \ ' FINISH /SOL FINISH /AUX12 FINISH /SOL TIME,24

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143 LSWRITE,4, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,23203 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,36, ,'Tabletop','rth','. . \ ANSYS REV \ ' FINISH /SOL TIME,36 LSWRITE,5, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,25068 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,48, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,48 LSWRITE, 6, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,25579 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,60, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,60 LSWRITE,7, FINISH /PREP7 !* MPTEMP,,,,,,,, M PTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,25579 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,72, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,72 LSWRITE,8, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1

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144 MPDE,PRXY,1 MPDATA,E X,1,,26092 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,84, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,84 LSWRITE,9, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 MPDE,PRXY,1 MPDATA,EX,1,,26092 MPDATA,PRXY,1,,0.2 LDREAD,TEMP, ,,96, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,96 LSWRITE,10, FINISH /PREP7 !* LDREAD,TEMP,,,108, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,108 LSWRITE,11, FINISH /PREP7 !* MPTEMP,,,,,,,, MPTEMP,1,0 MPDE,EX,1 M PDE,PRXY,1 MPDATA,EX,1,,26423 MPDATA,PRXY,1,,0.2 LDREAD,TEMP,,,120, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,120 LSWRITE,12, FINISH /PREP7 LDREAD,TEMP,,,168, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,168 LSWRITE,13, FINISH /PREP7 LDREAD,TEMP,,,192, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,192 LSWRITE,14, FINISH /PREP7 LDREAD,TEMP,,,240, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL

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145 FINISH /PREP7 LDREAD,TEMP,,,240, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,240 LSWRITE,15, FINISH /PREP7 LDREAD,TEMP,,,288, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,288 LSWRITE,16, FINISH /PREP7 LDREAD,TEMP,,,336, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,336 LSWRITE,17, FINIS H /PREP7 LDREAD,TEMP,,,384, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,384 LSWRITE,18, FINISH /PREP7 LDREAD,TEMP,,,432, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,432 LSWRITE,19, FINISH /PREP7 LDREAD,TEMP,,,480, ,'Tabletop ','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,480 LSWRITE,20, FINISH /PREP7 LDREAD,TEMP,,,528, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,528 LSWRITE,21, FINISH /PREP7 LDREAD,TEMP,,,576, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME ,576 LSWRITE,22, FINISH /PREP7 LDREAD,TEMP,,,624, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,624 LSWRITE,23,

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146 FINISH /PREP7 LDREAD,TEMP,,,672, ,'Tabletop','rth','.. \ ANSYS REV \ ' FINISH /SOL TIME,672 LSWRITE,24, LSSOLVE,1,24,1, FINISH /POST1 !* /EFACET,1 PLNSOL, S,1, 0,1.0 FINISH