Citation
Comparison of refined and simplified analysis methods for prestressed concrete I-beam bridge decks

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Title:
Comparison of refined and simplified analysis methods for prestressed concrete I-beam bridge decks
Creator:
Aswad, Ghassan Guy
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
xiii, 137 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Concrete beams ( lcsh )
Bridges -- Design and construction ( lcsh )
Bridges -- Design and construction ( fast )
Concrete beams ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (M.S.)--University of Colorado at Denver, 1994.
Bibliography:
Includes bibliographical references (leaves 136-137).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Civil Engineering
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Ghassan Guy Aswad.

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University of Colorado Denver
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|Auraria Library
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All applicable rights reserved by the source institution and holding location.
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32480736 ( OCLC )
ocm32480736

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COMPARISON OF REFINED AND SIMPLIFIED ANALYSIS METHODS FOR PRESTRESSED CONCRETE I-BEAM BRIDGE DECKS by Ghassan Guy Aswad RS., University of Colorado, 1990 A thesis submitted to the Faculty of the Graduate School of the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Science Civil Engineering 1994

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This thesis for the Master of Science degree by Ghassan Guy Aswad has been approved for the Graduate School by Date

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Aswad, Ghassan Guy (M.S., Civil Engineering) Comparison of Refined and Simplified Analysis Methods for Prestressed Concrete IBeam Bridge Decks Thesis directed by Professor John R. Mays ABSTRACT One of the most important shapes used in bridge construction is the prestressed, precast !-beam. Its span capability ranges from 40 to 150 ft. and it is widely used across the United States and Canada. The section offers many advantages including economy, ready availability and simplicity of construction. Past studies have shown that the des.ign of typical bridge decks is usually controlled by the first interior beam. Therefore, this study will focus on these beams in non-skewed bridge layouts. The research examines the impact of the upcoming LRFD code on design of three-lane bridge decks using I-beanis whose depth ranges -from 45 in. to 72 in. It is found that using refined analysis methods--such as the finite element and grillage analogy--results in significant reductions in the live load distribution factors when compared to the current simplified AASHTO code formula. The 111

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reductions are due to the cumulative effects of better analytical tools and multilane reduction of vehicle weights. Detailed prestressing designs are also conducted. They show that the reduction in the required prestressing reinforcement is substantial if the legal load remains the HS-20 truck. On the other hand, if the heavier LRFD vehicle lane weights are adopted, it is possible to use the same current reinforcing provided refined analytical methods are used. It is concluded that design engineers and departments of transportation should adopt refined analytical tools in most superstructure layouts due to the available econonric advantages. This abstract accurately represents the content of the candidate's thesis. I recommend its publications. signed / John R. Mays lV

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ACKNOWLEDGEMENT I would like to express my appreciation to Dr. John R. Mays, Dr. Judith J. Stalnaker and Dr. Ernest C. Harris for their guidance, support and encouragement throughout this study. I am also deeply grateful to F. Jeny Jacques, President, iacques & Aswad, Inc., for loaning me the design softwares "BRIDGE89" and "NUBRIDGE" used in the prestressing reinforcement studies. Finally, my sincerest thanks go to Centennial Engineering, Inc., and Morrison Knudsen Co. for graciously allowing the use of their advanced computers and CADD system in the preparation of this .study. v

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CONTENTS Chapter 1. Introduction and Background . . . . . . . . . . . . . . . 1 2. Objectives . . . . . . . . . . . . . . . . . . . . . . 9 3. Literature Review . . . . . . . . . . . . . . . . . . . 10 3.1 Lehigh University Report on St. Venant Constant . . . . . . . 11 3.2 Lehigh University Report on Live Load Distribution Factors for 1-Bearn. Bridges . . . . . . . . . . . . . . . . 12 3.3 "Bridge Deck Behavior", by E.C. Hambly . . . . . . . . . . 14 3.4 "Distribution of Wheel Loads on Highway Bridges", by Imbsen & Associates . . . . . . . . . . . . . . . . 16 3.5 The Grillage Analogy in Bridge Analysis, by Jaeger and Bakht ...................... . . . . . . . . . . 18 3.6 NCHRP's 4th Draft LRFD Bridge Design Specification . . . . . 19 4. Study Scope and Material Criteria . . . . . . . . . . . . . 28 5. Section Properties . . . . . . . . . . . . . . . . . . 33 5.1 Section Inertias . . . . . . . . . . . . . . . . . . . 33 5.2 St. Venant Torsional Constant . . . . . . . . . . . . . . 34 6. Simplified and Refined Analysis Methods . . . . . . . . . . 37 6.1 Simplified Method in the LRFD Specification . . . . . . . . 37 v1

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6.2 Refined Methods of Analysis . . . . . . . . . . . . . . . 38 6.2.1 Finite Element Modeling Using the ADINA Software . . . . . . 39 6.2.2 Computation of the Composite Girder Moment . . . . . . . . 41 6.2.3 Quality Control Checks for ADINA . . . . . . . . . . . . 43 6.3 Comparison Between Finite Element and Griilage Analyses ............................................ 44 7. Parametric Study Results for Distribution Factors . . . . . . . . 52 7.1 Methodology . . . . . . . . . . . . . . . . . . . . 52 7.2 Moments and Distribution Factors Results . . . . . . . . . . 53 8. Flexural Designs of Selected Beams . . . . . . . . . . . . 60 8.1 Stress Checks on Release and Under Service Loads . . . . . . . 60 8.2 Ultimate Strength Check . . . . . . . . . . . . . . . . 62 8.3 Stress Limits and Load Factors . . . . . . . . . . . . . . 64 8.4 Flexural Designs . . . . . . . . . . . . . . . . . . . 64 9. Conclusions and Recommendations . . . . . . . . . . . . 68 Appendix A. Sample Input/Output for Computing Icomp . . . . . . . . . . 71 B. Sample Input/Output for Computing Basic neam's J (St. Venant's Torsional Constant) . . . . . . . . . . . . . 73 C. ADINA Input/Output Files for Case Study L=80 ft, S=9 ft and Corresponding STAAD-111 Files Using Grillage Analogy . . . . . . . . . . . . . . . . . . . 75 Vll

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D. Comparison of The Accuracy Between Two STAAD .. III Runs By The Grillage Method With One Containing Additional Intermediate Joints . . . . . . . . 85 E. Input/Output Files for Grillage Analyses by STAAD-111 .......................................... 90 F. Concise Input/Output Files for The Designs of Prestressed Girders Using Three Different Methods: AASHTO Simplified, Grillage and LRFD's . . . . . . . . . 123 References . . . . . . . . . . . . . . . . . . . . . . . 13 6 Vlll

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FIGURES Figure 1.1 Typical Bridge Deck Using 1-Beams .......................... 5 1.2 Current AASHTO-PCI Type Beams .......................... 6 1.3 Standard AASHTO HS-20 Truck . . . . . . . . . . . . . . 7 1.4 LRFD Lane Load and Lane Positioning for Maximum Effects in Beams . . . . . . . . . . . . . . . . . . . 8 3.1 General 1-Beam, Discretizations and Finite Difference Operator (Edy et al. 1973) . . . . . . . . . . . . . . . . 21 3.2 Comparison of the Finite Difference Method with Other Procedures (Edy et al. 1973) . . . . . . . . . . . . . . . 22 3.3 Comparison of Proposed Lehigh D.F. with Current AASHTO, NB = 5 (Zellin et al. 1976) . . . . . . . . . . . 23 3.4 Beam-and-Slab Decks and Their Discretization . . . . . . . . 24 3.5 Distribution of Wheel Load to Adjacent Nodes (Zokaie et al. 1991) . . . . . . . . . . . . . . . . . . 25 3.6 Method of Determining Composite Girder Overall Moment and Shear for 1-beam Decks (Zokaie et al. 1991) .......... 26 3.7 Effect of Additional Nodes in Transverse Members . . . . . . . 27 4.1 Typical Three-Lane, Seven-Stringer Section . . . . . . . . . . 31 4.2 Typical Three-Lane, Five-Stringer Section . . . . . . . . . . 32 IX

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5.1 Typical Composite 1-beam Section . . . . . . . . . . . . . 36 6.1 Distribution Factor for Common Beam-and-Slab Bridge Decks (NCHRP 1993) .................................. 46 6.2 (a) Quadrilateral Shell Element, and (b) Beam (stiffener) Element . . . . . . . . . . . . . . . 47 6.3 2-Plate Mesh Discretization and Orthotropy Factor (example) (Zellin et al. 1976) . . . . . . . . . . . . . . 48 6.4 Typical Bridge Deck Discretization (F.E. Analysis) . . . . . . . 49 6.5 Actual and Idealized Cross Section . . . . . . . . . . . . . 50 6.6 Cross-Sectional Dimensions of Beams and Midspan Diaphragm (example) . . . . . . . . . . . . . . . . . 51 7.1 Grillage Model for the 5-Beam Bridge Deck . . . . . . . . . 57 7.2 Grillage Model for the 7-Beam Bridge Deck . . . . . . . . . 58 7.3 Transverse Positioning of Truck Loads . . . . . . . . . . . 59 8.1 Typical Prestressing Reinforcement and Profile . . . . . . . . 67 9.1 Comparison of D.F. by Grillage, LRFD and Eq. (9.1) Methods ... . . . . . . . . . . . . . . . . . 70 X

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TABLES 3.1 Comparison of Interior Girder Moment D.P.'s by Varying Levels of Accuracy . . . . . . . . . . . . . . 18 5.1 Values of Composite Inertia and Section Modulus . . . . . . . 34 5.2 St. Venant Torsional Constants for Longitudinal and Transverse Beams ..................................... 35 6.1 Finite Element Analysis Case (L=80 ft), and Results Summary . . . . . . . . . . . . . . . . . . . . . 45 7.1 Moments and D.P.'s Results for First Interior beam by Three Methods (S=6'-8") . . . . . . . . . . . . . . . 55 7.2 Moments and D.P.'s Results for First Interior beam by Three Methods (S=l0'-0") . . . . . . . . . . . . . . . 56 8.1 Comparison of reinforcing and release strength requirements, f' ci' by 3 different procedures . . . . . . . . . . 66 xi

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LIST OF SYMBOLS A,Ac = cross-sectional area, in2 = area of prestressing steel, in2 b = compression block width d = depth to centroid of prestressing steel D.F. = distribution factor, per lane e = eccentricity, distance from e.g. of strands to e.g. of basic beam eg = distance between the centers of gravity of the basic beam and deck, in. E = Young modulus, ksi f c = concrete strength at age of 28 days, psi G =shear modulus, ksi H = basic beam depth, in. He = overall composite beam depth, in. I = inertia of basic beam, in4 Ic = inertia of transformed, composite beam, in4 IT = inertia of transverse beam, in4 J =St. Venant torsional constant for basic beam, in4 Xll

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Kg = longitudinal stiffness parameter, in4 = n (I+ A.eg2 ) L =beam span, center-to-center of supports, ft. m = multilane presence factor Mb =resultant moment in basic beam (ADINA) n = modular ratio = N = modular ratio = Es1Aeam N5 =number of 112" diameter strands p =prestressing steel ratio P =resultant axial force in basic beam (ADINA) S = typical beam spacing in a bridge deck, ft. Sb = section moduius at bottom of basic beam, in3 sbc = section modulus ()f composite beam, in3 t = slab thickness, in. 1.1. = Poisson's ratio = stress function in the torsion problem xiii

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1. Introduction and Background The prestressed concrete I-beam is one of the most widely used beam shapes for bridge superstructures in the United States and Canada. Its practical span capability today varies between 40 and 150 ft. Considering that 90% of roadway bridges in the United States have spans of less than 130 ft, the potential use forI-beams is considerable. Typical composite I-beam decks, Figure 1.1 have grown in popularity because of their relative economy, ready availability nationwide and simplicity of construction. These decks are constructed by placing a number of precast concrete sections--usually a minimum of four--at a typical spacing between 6'-0" and 10'-0", setting the formwork for the slab and then casting the 8 to 9-in. concrete slab in situ. Several weeks after concrete hardening, a bituminous wear course may be placed to provide a smooth riding surface. The basic
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carried by the basic beam; they are required to carry a. portion of a standard AASHTO truck load, Figure 1.3, which, together with the wear surface and parapet load, act on the composite section. The composite section consists of the basic beam plus the associated cast-in-place (C.I.P.) slab. For interior beams, the associated slab width is taken as the girder spacing, S, provided it does not exceed approximately 11 ft. For S > 11 ft, shear lag effect may reduce the effective slab width. The exterior slab overhang rarely exceeds 4'-0". In designing bridge_ superstructures, dead and permanent loads are routinely calculated and present no uncertainty. Thus, this :report will focus on live (vehicle) loads only. In the standard AASHTO procedure, the ratio of a truck load that is carried by a single composite beam is called the Distribution Factor (D.F.). Distribution Factor is used to multiply the total longitudinal response of the bridge due to a single truck in order to determine the maxinium response of single girder. For interior 1-beams, the simplified method stipulates that D.F. = S/11 (1.1) For exterior beams, the distribution factor is based on simple distribution by statics and would normally be less than Eq. (1) ). Based on current practice, the exterior beam must have at least the same strength as an interior beam. Therefore, I -beam design is usually controlled by the first interior beam and this research will focus on this component in right angle layouts (zero skew). For skew 25, 2

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the deck analysis for D.F. deviates very little from the non-skewed layouts. Thus, this investigation should cover a large majority of future deck cases. In 1988, the Transportation Research Board (TRB) funded a 4-year revolutionary project to completely overhaul the AASHTO Bridge Design Specifications. The new specification (NCHRP 1993) is in a Load and Resistance Factor Design (LRFD) format. In 1993, the AASHTO Committee on Bridges voted to adopt the new LRFD Specification and to consider phasing out the current code by 1995. The new LRFD codecontains a 'Simplified Method' for calculation of the D.F. as well as an option for the use of 'Refined' Procedures, such as finite element and grillage analogy methods. As an example, the D.F. for interior 1beams is given by D.F. = 0.075 + (S/9.5)0 6 (SJLt2 (K/12Lt3 ) 0 1 (Symbols are defined on pages xii-xiii) (1.2) The simplified procedure, Eq. (1.2), should yield a somewhat lower D.F. than the one based on AASHTO's Eq. (1.1 ). On the other hand, the use of refined procedures, will result in significantly lower D.F.s for the following reasons: a. The analysis is inherently more accurate; and b. Based on the Probability Theory, LRFD allows vehicle loads to be multiplied by m=0.85 if three loaded lanes are present on the carriageway, and by m=0.65 if four (or more) lanes are present. 3

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In this report, the commonly used three-lane carriageways will be concerned. Therefore, there is a need to investigate interior beams for two loading cases and related factors: I Two lanes present (m=l.O) 2 Three lanes present (m=0.85) and then choose the one that results in the largest force in the composite section. Since the size, prestressing and cost of a beam are mostly dependent on its maximum bending moment (near midspan), the subject of shear forces will not be discussed herein. Another item of interest is the new LRFD equivalent vehicle loading, Figure 1.4-a, which is significantly higher than the present AASHTO load; the transverse lane positioning, Figure 1.4-b, however, is the same as in current AASHTO. Research and systematic parametric studies are, therefore, needed in order to assess the relative merits and impacts of the LRFD methods for 1-beams and to recommend an appropriate course of action. 4

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VMIA81 E :;r .. .(.ING SECTION VI\P.I,..BLE SPf,N L ELEVATION Figure 1.1 Typical Bridge Deck Using 1-Beam 5 C Pr.EC .. .ST PAr.Af'ET

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Type I 35 to 45 It Type IV 70 to 100 ft Type I II Ill IV v VI Type If 40 to 50 ft Type V 90 to 120 ft Type Ill 55 [0 80 ft Type VI 110 to 140 ft Section Properties of AASHTO Bridge Girders h Ac fg c, c2 (in.) (in.2 ) (in.4 ) (in.) (in.) 28 276 22,750 15.41 12.59 36 369 50,979 20.17 15.83 45 560 125,390 24.73 20.27 54 789 260,741 29.27 24 .. 73 63 1,013 521,180 31.04 31.96 72 1,085 733,320 35.62 36.38 r2 wo (in.2 ) (plf) 82 288 138 384 224 583 330 822 514 1055 676 1130 Note: h =beam depth c1=distance from the neurarl axis to top of the beam Ac=cross-sectional area e:z=distance from the neurarl axis to bottom of the beam 11= moment of inertia rl=radius of gyration =IJAc w.=unit weight of beam Figure 1.2 Curren.t AASHTO-PCI Type Beams 6

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HS20-44 8.000 LBS. HS15-44 6.000 LBS. 32.000 LBS. 24.000 LBS. 32.000 LBS. 24.000 LBS. 14'-{)" 6i v 6j --jo L J--.,..i o. w+-1 --10.4 w l I ----$}W = COMBINED WEIGHT ON THE FIRST TWO AXLES WHICH IS THE SAME AS FOR THE CORRESPONDING H TRUCK. V = VARIABLE SPACING-14 FEET TO 30 FEET INCLUSIVE. SPACING TO BE USED IS THAT WHICH PRODUCES MAXIMUM STRESSES. CLEARANCE AND AD LANE WIDTH 10'-Q" Figure 1.3 Standard AASHTO HS-20 Truck7

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For short spans 25 K. 25" 0.64 KJFT For medium ............. .............................. ... and long \.__ spans 0.64 KJFT PROPOSED LIVE LOADS DESIGN LANE V.1DTH DESIGN LANE \\1DTH 4'CI' :.. LANE LOAD "!J'-G" "!J'-G" z-o. T T T : I 4'' max 1 r .. 1.ini .. (" n +--' OR PARAPET I : I Cross Section for Lane Positioning at Exterior Girder Figure 1.4 LRFD Lane Load and Lane Positioning for Maximum Effects in Beams 8

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2. Objectives The general objectives of the proposed research may be summarized as follows: 1. Using a combination of Finite Element analysis software (such as ADINA) and Grillage Analogy programs (such as STAAD-III) derive more accurate load fractions (D.F.) assigned to interior beams in 1-girder decks. This will be done through a significant and systematic parametric study encompassing various AASHTO sections. Spans L and spacing S will bracket the practical range of these prestressed shapes. 2. Show when 3-loaded lanes control the design versus 2-loaded lanes, in a standard three-lane carriageway. Quantify the results of parametric studies. 3. Conduct several full designs of prestressed beams using appropriate software in conjunction with the refined distribution factors and compare to designs by current (simplified) AASHTO methodology. 4. Propose a new empirical guideline that would apply to 3-Lane bridges but would be more accurate than previous Eqs. (1.1) and (1.2) and would account for the multiple-lane reduction. 9

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3. Literature Review Live load distribution in highway bridges has been studied for many years, both in the U.S. and abroad. Though the previous work has resulted in a better understanding of the behavior of bridges, a number of simplifying assumptions were made in each case in order to overcome certain mathematical difficulties involved in the solution procedures. The methods used to study the behavior of bridges have been the grillage analysis, orthotropic plate theories, the finite difference method, the finite strip method, and the finite element method. Of all the methods, the finite element approach requires the simplifying assumptions in accounting for the greatest number of variables which govern the structural resporise of the bridge. However, input preparation time and derivation of overall forces for a composite beam are usually quite tedious. To better understand the progression of the design philosophy, some of the important works related to live load distribution on prestressed concrete 1-beam bridges will be reviewed. These decks are also called "beam-and-slab decks" in the technical literature. 10

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3.1 Lehigh University Report on St. Venant Torsional Constant (Eby et al. 1973) This 1973 report by Eby et al. is a comprehensive study on the various theoretical and approximate methods for evaluating the St. Venant torsional constant, J, in the general 1-beam case, Figure 3.1-a. The difficulty in this case is the fact that neither the flanges nor the web can be considered thin. Therefore, the use of the familiar formula for open, thin sections: J = (113) 1: bit? is not appropriate. The authors use a refined mesh, Figure 3.1-b, and a finite difference scheme to solve the torsion problem equations: In the region: + On the boundary: = 0.0 J = dx dy Using the finite difference method as the 'exact' solution, the authors proceed to compare it to other procedures. As seen in Figure 3.2-a, the (3.1) (3.2) (3.3) (3.4) discrepancy with Eq. (3.1) ranges between -30% and +60%. This, of course, is unacceptable. The investigators then used 22 various shapes to develop an algebraic, curve-fitted solution to the problem as follows: where J = 0.333 (b1 t1 3+b2 + d3 b/) + a1 D1 4 + a2 D2 4 -0.21 (tl4 + 4 ) 11 (3.5) (3.6)

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a1 = -0.042 + 0.2204 (b/t1 ) 0.0725 (b/t1 ) 2 a2 = -0.042 + 0.2204 0.0725 (b/tJ2 (Please see Figure 3.1-a for definition of symbols) (3.7) (3.8) (3.9) As seen in Figure 3.2-b, the correlation between the 'exact' method and the algebraic solution is excellent. The average error is 3% only. Thus, this solution was adopted in our research to evaluate J, and an appropriate spreadsheet program was written and used. 3.2 Lehigh University Report 387.2B on Live Load Distribution Factors for 1-Beam Bridges ( Zellin et al. 1976) This 1976 report by Zellin et al. was the only comprehensive study of distribution factors using the finite element method. The deck was modeled as a stiffened plate, where the plate response was divided into out-of-plane (bending) and in-plane (membrane) actions. The beam elements ("stiffeners") were positioned between the plate nodes, and the in-plane and out-of-plane responses are considered simultaneously. The torsional response is treated separately. Strain compatibility between the plate (slab) and the beam was maintained because of the composite behavior. The results of the study showed conclusively that the approximate D.F. by 12

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AASHTO, Eq. (1.1), is always conservative for interior girders, Figure 3.3. The investigators proposed a revised equation for distribution factors of interior girders as follows: where D.F. = (NdN8 ) + k1 (SIL)0 "33 k1 = 0.056 (W/N8 ) (W/12NL)I.s NL =number of design traffic lanes = W /12, reduced to nearest whole number N8 = number of beams (3 N8 17) S =beam spacing, in feet (4 S 11) L = spanlength, mfeet (30 L 135) (3.10) (3.11) W =roadway width between curbs, in feet (24 W 72) Unfortunately, this report was never adopted by AASHTO despite its rational approach. As for its application in today's practice we find its theoretical approach and assumptions to be fully valid. Its proposed Eq. (3.10), however, is not adequate today and is too conservative for the following reasons: a. The curve-fitted formula was based on precast sections that were deeper and less efficient than today's shapes. b. The formula does not consider the multilane presence factor (m = 0.85 or 0.65) for 3 and 4 lanes, respectively. c. Precast concrete strengths are much higher today (7500 to 9000 psi) than 13

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the common 5000 psi value in the early 1970's. d. Span and spacing limits are somewhat restrictive. 3.3 "Bridge Deck Behavior" by E.C. Hambly (Hambly 1976) This 1976 book is a classical reference on the subject of bridge decks in general and on grillage analysis of 1-beam decks For the purpose of design, these grillages can be thought of as two-dimensional structures, Figure 3.4. The longitudinal beams are spaced a distance S apart. Sometimes, transverse beams called 'diaphragms' are placed to connect the longitudinal beams over the supports and at several sections along the span as shown in Figure 3 .4-a. The use of transverse diaphragms has dropped considerably in the 1980's; usually, only one at midspan is used. Thus, the structural model resembles more the one in Figure 3.4-b. The behavior of i-beam decks without multiple diaphragms can be idealized as a simple combination of beams spanning longitudinally and slab segments sparining transversely, Figure 3.4-c. For longitudinal bending, the slab acts as top flange of the 1-beams with which it is associated. For transverse bending, the slab flexes with much greater curvatures than longitudinally because its bending stiffness is only a fraction of that of the composite beams. To solve the grillage problem, standard matrix analysis is used and set up to satisfy linear elastic 14

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behavior, equilibrium and compatibility of deformations at the nodes. For a suitable grillage mesh, Hambly recommends placing the longitudinal members such that they are coincident with the center lines of beams. As for transverse grillage members, the suggested spacing is .118 of span L. Tiris should produce a fine enough mesh for the grillage to deform in a smooth surface in both directions, Figure 3.4-d, as contrasted to the rather irregularly deformed surface in case of a coarse mesh, Figure 3 .4-e. In the calculation of longitudinal member properties, the inertia of typical composite sections (1-beam plus associated slab) is a routine statics problem. Since Young modulus of the slab is smaller than the beam's modulus, the effective width of associated slab is multiplied by N=E51aJ&,eam. As for the St. Venant torsion constant, it is calculated as follows: __:_ 3 JL -Jbeam + N{b.t /6) (3.12) where b = slab width, equal to S for interior beams t = slab thickness For transverse beams, the torsion constant is: (3.13) and the inertia is calculated as (3.14) where bT is transverse beam width. It is clear from Eqs. (3.12) and (3.13) that the 15

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torsion constant terms are only half as much as the usual be/3 for thin slabs. The full explanation of this is shown in the text. Equations (3.12) to (3.14) have been adopted in (Zokaie et al. 1991) and will be used later in our grillage analysis. 3.4 "Distribution of Wheel Loads on Highway Bridges" by Imbsen and Associates (Zokaie et al. 199i.) This 1991 Report to the Transportation Research Board is a major overhaul of current AASHTO simplified equations which are 25 to 4 7 years old. This report constitutes the basis for the new simplified equations in the LRFD code (NCHRP 1993). It also has up-to-date recommendations on modeling bridge superstructures for various methods. In addition, the report sets hierarchies in the accuracy of various procedures as follows: Level 1 Analysis: a new set of equations similar to Eq. (1.2). These are meant for simple and conservative hand calculations. Level 2 Analysis: for grillages using grid models and series-harmonic solutions. Level 3 Methods: for detailed bridge deck analysis by finite element methods such as SAP, STRUDL and GENDEK .. The GENDEK program, which uses plate elements for the slab and eccentric stiffeners for the beams, was found to be most versatile and quite accurate. 16

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Several pertinent recommendations were made in the report, many of them borrowed from (Hambly 1976): a) Wheel load distribution to nodal points: by the 'contributing area' method as shown in Figure 3.5-a or Figure 3.5-b. Tiris will avoid tedious double interpolations. b) Grillage Analysis: shear deformations are neglected. A total of 9 transverse beams are used within the span. Section properties for the longitudinal and transverse beams are computed following previous Eq. (3.12) to (3.14). c) Finite Element Analysis: The determination of the composite girder overall moment and shear is illustrated in Figure 3.6. Of particular interest is this final comment by the investigators on the grillage analysis as compared to other methods:. Also grillage analysis presents a good alternative to other simplified bridge deck analysis methods, and will generally produce more accurate results. Grillage analogy may be used to model most common bridge types. Guidelines for modeling these bridge types and sample problems to illustrate thefr application are given in Appendix G of this report. A major advantage of plane grid analysis is that shear and moment values for girders are directly obtained and integration of stresses is not needed. Loads normally need to be applied at nodal points, and it is recommended that simple beam distribution to be used to distribute wheel loads to individual nodes. If the model is generated according to Appendix G recommendations and the loads are placed in their correct locations, the results will be close to those of detailed finite element analysis. This statement is strongly supported by the results from a comparison 17

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between the finite element and grillage analyses as shown in Table 3.1 below. Table 3.1 Comparison of interior girder moment distribution factors by varying levels of accuracy using an "average span" for each bridge type Current LRFD AASHTO Simplified Grillage Bridge Type (Level 1) (Level 2) Beam-and-slab 0.717 0.729 0.684 Box girder 0.572 0.572 0.485 Adjacent box beam 0.323 0.299 0.270 Spread box beam 0.782 0.641 0.624 3.5 The Grillage Analogy in Bridge Analysis, by Jaeger and Bakht (Jaeger and Bakht 1982) Finite Element (Level 3) 0.689 0.503 0.276 0.621 This 1982 paper is by two noted researchers on grid analyses. They attempt to provide guidance on grillage idealization and mesh layouts of various types of deck shapes, including beam-and-slab decks. Reduction of effective width of the slab because of shear lag is shown to be negligibly small for span/width ratios > 4 which is the sort of dimensions encountered in real-life bridges. The torsional constant for longitudinal beams is reconunended equal to Eq. (3.12). One interesting conunent is related to the assignment of concentrated loads to adjacent nodal points. The authors show that adding notional joints half-way between nodal points on transverse beams may improve the accuracy, as 18

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demonstrated in the case of a 4-beam deck, Figure 3.7. These additional joints, however, show the girder moment decreasing for the exterior girder and remaining unchanged for the first interior beam. 3.6 NCHRP's "4th Draft LRFD Bridge Design Specifications" developed by Modjeski and Masters, Inc. (NCHRP 1993) This 1993 Specification was adopted by AASHTO recently as a substitute for the current code--which will probably expire in 1995. Simplified distribution factors are those developed by lmbsen (Zokaie et al. 1991 ) .. Accepted refined methods include finite element and grillage analyses due to the close correlation between the two procedures as illustrated in previous Table 3.1. The following guidelines are suggested for refined methods: A minimum of nine nodes per beam span is preferred. For grid analyses, composite properties should be used. St. Venant torsional constant, J, to be determined rationally. Only one-half of the effective width of the flexural section, before transformation, should be used in computing J same as (Hambly 1976 and (NCHRP 1993). In finite element analysis, an element should have membrane capability. Aspect ratio of finite elements and grid panels should not exceed 5.0. 19

PAGE 33

Nodal loads shall be statically equivalent to the actual point load being applied. In conclusion, the upcoming LRFD Specification expiicitly confirms the current geometric and other guidelines normally used for accurate analysis of bridge decks. 20

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I b I I cl I cl b I (A) 4 1 4 ......... [4 Typeo of Meoh Poiata I I b I l I It, b (B) I General I-Beam and Diserethatlana (C) FIAlte Difference Oj>erotor Figure 3.1 General 1-Beam, Discretizations and Finite Difference Operator (Edy et al. 1973) 21

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00 0 0 0 0 -00 e 0 assuming J .. I.! bt3 3 I I 0 0 0 0 0 results (_'exact'') 2 4 6 8 10 12 14 16 18 20 22 Beam Number Assuming Proposed Equation: J .. .! (b t3 + b t3 + b t3 3 ) + a + a D" 0.21(t,4+ti4 ) 1 3 I I 2 2 3 1 I 2 2 I I 2 4 6 8 10 12 14 16 18 20 22 Beam Number Figure 3.2 Comparison of the Finite Difference Method with Other Procedures (Edy et al. 1973) 22

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D.F. L=50' 0 Interior Girders Current Specification (1976): y We, ft. 24 28 32 5, ft. 6 7 8 Note: We: Width between curbs, (ft) s Beam spacing, (ft) 36 9 eo' 125' Exterior Girders Proposed Specification Equation 40 44 10 II Figure 3.3 Comparison of Proposed Lehigh D.F. with Current AASHTO, NB = 5 (Zellin et al. 1976) 23 48 12

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Figure 3.4 Beam-and-Slab Decks and Their Discretization 24

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19 Node 18 Load: Node 19 Lo"ad: 30 29 16k = 10.48k 16k = 5.52k Simple Beam Distribution of Wheel Loads Placed on Girders Total Area 93 58. 5394 in2 Area 20 31 620 Areaa31.38a1178 Area 62 20 1240 0 Area 62 38 2356 r-356) Node 18 Load= 16k = (1240). k Node 19 Load = 5394 16 = 3.68k (1178) k Node 29 Load = 5394 16 = ( 620). k Node 30 Load = 5394 16 = _LB!k 16.00k checks Figure 3.5 Distribution of Wheel Load to Adjacent Nodes (Zokaie et al. 1991) 25

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s typical composite girder GirderMoment Mb+ Pb e +(MP, + MP2)* Girder Shear. V 11 + (V P' + V pz) where: Mb Moment in beam P11 Axial force in beam e Distance from slab midpoint to beam centroid Mp, Momenuunit length in Plate 1 Mp2 MomenUunit length in Plate 2 V P' Shear/unit length in Plate 1 V pz Shear/unit length in Plate 2 The plate stresses are output at the plate integration points, and are force per unit length of plate. Figure 3.6 Method of betermit;ting Composite Girder Overall Moment and Shear for 1-beam Decks (Zokaie et al. 1991) 26

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E 2,500 z .. !: 2 000 z "' .... ... c i 1 500 r"l n LOAD CASE 3 ... "' n n LDADCASEZ ... ::; 1,000 CJI CASE I :I: : -... Q a: 11.71 12. 12 1 IZ.I 11.71 ,_ .. 34.9' ltO I ml :, Ill a D p _, . PLAN OF ACTUAL BAIOGE PLAN OF IDEALIZED Ci Effcc:t of all!litiunal in trllnsvcrsc members .. Norcs lor between girders: ---with notional in tr:msverse beams between 1 Figure 3.7 Effect of Additional Nodes in 1 (see dashed lines) 27

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4. Study Scope arid Material Criteria One major objective of this study is the computation of distribution factors for various beam-and-slab bridges covering a substantial portion of real-life situations. A good source of information on feasible spans is the CORESLAB brochure, (Jacques 1987), which is commonly used in the U.S. Southwest and the Rocky Mountain states. This brochure lists feasible simple spans for given spacings and follows the simplified AASHTO procedure for D.F.'s. The approximate concrete strength criteria are approximately 45.00 psi at release and 6000 psi at 28 days. AASHTO types III to VI are included in addition to other shapes and boxes. For the present study it was decided to increase the feasible simple span L (for a given spacingS) for two reasons: 1) Concrete technology is constantly improving and release strengths of 6000 psi or more are feasible today. 2) Refmed methods of analysis come into play when the design engineers have exhausted the capacity of a given 1-shape and they want to stretch the span further. After consultation with design engineers and precast producers the 28

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following pairs of spans and spacings were selected for 3-lane bridges: Beam Type AASHTOIII AASHTO N AASHTO V AASHTO VI Span L for 8=6'-8" 90ft 110 128 146 Span L for S=10'-0" 70ft 90 106 122 It is noticed that the two limiting spacings, S=6'-8" and 10'-0", respectively, represent fairly well the current industry limits (6'-0" to 10'-6") and result in a 48 ft slab width for a 3-lane carriageway. As illustrated in Figure 4.1, this section has 7 longitudinal stringers, while Figure 4.2 is representative of the 5-stringer solution. As for material properties, the following values and constants were assumed throughout: Poisson's ratio: J.L;,.0.20; shear modulus G=0.417E. The 28-day concrete strength for the basic beam is equal to 7500 psi, and the slab strength equal to 4500 psi (very common in many states). Beam's Young Modulus: using the standard AASHTO Equation: Ec = 0.033wl.5 -Jfi; results in the following: &,earn= 5,250 ksi Estab = 4,067 ksi 29

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N = = 4067/5250 = 0. 775 As for the slab thickness, the following values. were assumed as industry averages: For S = 6'-8" : t = 8 in. For S = 10'-0": t = 9 in. Since girder spacing S < 11 ft, there is no need to account for shear lag reduction of effective slab width by AASIITO standards or by analytical considerations. 30

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..-------= I 0 I :;... io I iD io I iD CD .I Ul io I iD CD .I Ul 0 .I .... Figure 4.1 Typical Tirree-Lane, Seven-Stringer Se 31

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0 I 0 I Q I 0 I Q 1.....----....J= ..------= I 0 I Q 1.....-------'....J= 0 I Figure 4.2 Typical Three-Lane, 32

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5. Section Properties Two sets of major properties are required to effect a grillage or finite element analysis: 5.1 Section Inertias: In the finite element analysis, the basic (non-composite) beam inertia is shown in Figure 1.2. As for the grillage model, the moment of inertia of the composite section, Figure 5.1, with an associated slab width, S, is required. The calculation of the centroid and transformed inertia is a simple statics matter where the effective slab width is beff = N x S. A standard software (SECTION1 1989), has been used to generate the data for the transformed composite inertia Ic based on S = 6'-8". and 10'-0", respectively, and on N = 0.775. A sample input/output is shown in Appendix A. The full set of results for the AASHTO beams is shown in Table 5.1. Also listed are the section.moduli, Sbc for the bottom fiber. The inertia IT of transverse beams follows Eq. (3.14) and is also listed in Table 5.1. 33

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Table 5.1 Values of composite inertia and section modulus AASHTO S=6'-8" S=10'-0" Section Ic sbc IT Ic sbc IT Type III 345,144 10,222 2,976 417,705 11,055 3,296 IV 600,488 15,982 3,637 729,565 17,324 4,237 v 932,643 21,451 4,233 1,105,722 23,017 4,991 VI 1,270,294 26,025 4,828 1,499,513 27,845 5,744 5.2 St. Venant Torsional Constant Calculation of this constant for the basic beam follows the refined approach recommended in the Lehigh report (Eby et al. 1973). A spreadsheet type program was written and the various section dimensions of Figure 1.2 were entered for each AASHTO III to VI shape. The obtained J values are listed here below: Basic Section Type AASHTOIII AASHTO IV AASHTO V AASHTO VI A sample input/output is listed in Appendix B. J value. ilL 16,845 32,265 33,371 34,907 As for the grillage analysis, the torsional constants JL and JT are required for the longitudinal stringers and transverse beams. These values are computed 34

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using Eqs. (3.12) and (3.13) and displayed in Table 5.2. AASHTO Section Type III IV v VI Table 5.2 St. Venant Torsional Constants for Longitudinal and Transverse Beams S=6'-8" S=I0'-0" JL JT JL JT 22,136 5,952 28,145 6,591 37,556 7,275 43,565 8,475 38,662 8,465 44,671 9,980 40,198 9,656 46,207 11,488 35

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.VI z II J (.JI 0 c.. E 0 () .cl.c :::I!: VI c -o 0-0 > w Figure 5.1 Typical Composite 1-beam Section 36

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6. Simplified and Refined Analysis Methods In the following sections, the basis and assumptions for these analyses will be explained and summarized. 6.1 Simplified Method in the LRFD Specification The simplified formula for lateral distribution of live loads (per lane) for moment in interior beams is given by Eq. (1.2) repeated herebelow D.F. = 0.075 + (S/9.5)0 6 (S/L)0 2 (K/12Lf)0.! (6.1) Applicable cross-sections are shown in Figure 6.1 and cover our cases. Multiple lane reduction factors are built into the formula in an approximate fashion. The following notation is used in Figure 6.1 and Eq. (6.1): A =area of stringer, beam or girder (in2 ) I = inertia of basic beam (in4 ) = longitudinal stiffness parameter L =span ofbeam (ft) S = spacing of beams (ft) t = depth (thickness) of concrete slab (in) The longitudinal stiffness parameter, is taken as: 37

PAGE 51

where: n = modular ratio between beam and deck materials eg = distance between the centers of gravity of the basic beam and deck (in), Figure 5.1. The transverse post-tensioning shown for some cross-sections in Figure 6.1 is intended to make the units act together. This type of construction acts as a monolithic unit if sufficiently interconnected. The equation is the so-called "lmbsen" formula and was borrowed from an earlier NCHRP study (Zokaie et al.1991) developed by lmbsen and Associates. Although it is more complicated than current AASHTO equation, it was chosen to be more accurate. Different distribution factor equations are specified for shear and exterior girders. The design for shear, though vastly changed from current AASHTO, is probably considered secondary when viewed from the perspective of span capability, production constraints and economy of prestressed girders. 6.2 Refined Methods of Analysis Section 4.6.3 of the LRFD Specification (NCHRP 1993) allows the use of refined methods for bridge analysis on an equal footing. Two of these methods are: 38

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the finite element method, and the grillage analogy method When such methods are used, consideration must be given to the number of nodes per span, aspect ratios of plate/shell-like elements and maintaining the relative vertical distances between various elements (say plates and stiffeners). The St. Venant torsional constant should be evaluated using rational methods (Eby et al. 1973). Although access to advanced software for refined methods is not widespread, this situation is slowly changing. In this report, the following software programs were used in conjunction with hari.d calculations: The ADINA program, (version 3.0), a well known and general finite element program by ADINA, Inc., Cambridge, MA. The STAAD-111 program, by Research Engineers, Inc., Orange, CA (version 19.0) (STAAD 1994). The majority of the runs for this report were conducted using STAAD-111. One was done using ADINA. The sections below highlight features of ADINA that were used in the elastic analyses of the deck. The grillage analogy has been discussed earlier in sections 3.3 and 3.4. 6.2.1 Finite Element Modeling Using the ADINA Software The bridge deck structural system was modeled using both "shell" and 39

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"beam" (stiffeners) elements, Figure 6.2. A standard quadrilateral (four-noded) shell element of constant thickness was incorporated in modeling the horizontal slab. Stiffeners were described using a standard isoparametric beam element. The composite action of the beam and slab was effected by connecting the centers of the slab and beam with rigid links. This produced the correct constraint relations for displacements of the slab and beam. Material properties required to describe the linear, isotropic material behavior were the modulus of elasticity and Poisson's ratio (!l = 0.20). Because the slab was modeled separately from the beam, it was possible to use two different Young's moduli, E1 and E2 for each structural element. This was desirable since, typically, the concrete strength for the cast-in-place slab is lower than the one in the precast concrete beams. The St. Venant torsional constant J for the basic beam was calculated using an advanced method based on the finite difference procedure (Eby et al. 1973) as shown in Sec. 5.2. To better represent the structural behavior of the deck slab, it was modelled as an orthotropic plate as recommended in (Zellin et al. 1976). To do this, an orthotropy factor, DY, based on the ratio of center-to-center spacing S to clear span was introduced (see Figure 6.3). Its value is: Dy = (Girder Spacing/clear slab span)2 (6.2) In the ADINA program, this can be done easily by multiplying the Young's 40

PAGE 54

modulus in the transverse direction by DY. Support for the structure consisted of a roller at each end of the beams. This roller provided resistance to vertical (z-direction) movements only. The beams were, therefore, free to rotate about the transverse axis at their ends but assumed to be torsionally restrained. For structural stability, no x-displacement was allowed at a and b, Figure 6.4, and hinge support was applied to c and d. The finite element mesh was proportioned so that the maximum aspect ratio of the quadrilateral elements always remained at about two to one or less. Typical discretization of the bridge deck structure is shown in Figure 6.4, 6.5 and 6.6. There were 12 (or more) subdivisions in the longitudinal direction. The slab ("shell") elements were S/2 wide in the transverse direction, where S is girder spacing. The finite _element program ADINA consists of three parts: ADINA-IN (preprocessor), ADINA (main program), and ADINA-PL (post processor). ADINA-IN was used to prepare the input data, and ADINA-PL to scan and analyze the numerical results. 6.2.2 Computation of the Composite Girder Moment The ADINA program requires the input of the basic beam ("stiffener") properties: A, I, J, E and G, Figure 6.6, in addition to the slab ("shell") properties. The output then lists the axial force, P, and moment, Mb, that pertain to the beam 41

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element. These allow the stress computation at the centerline of the bottom flange as follows: fb =(PIA)+ (MJSb) (6.3) where Sb is the noncomposite section modulus at bottom fiber. The moment, Me, carried by one composite cross section is given by: Me= M'b +fob MslabdO (6.4) in which b is the effective width of the slab, Mslab the slab moment, and M'b is the beam moment referenced to a plane within the slab. It is usually very tedious and difficult to calculate the integral term in the latter equation unless the reference plane is set at the level of the slab compression resultant. In that case the integral becomes null. The resultant location is not known a priori. However, because of the general trapezoidal shape of the stress diagram due to live load it is reasonable to assume the plane is somewhere between 0.66t and the middle plane, 0.50t, say at 0.60t from the top of the basic beam, where t is slab thick:itess. Therefore: Me = M'b = Mb + P(y1 + 0.60t) (6.5) where y1 is the distance from basic beam centroid to its top fiber. Another way of computing Me is to use the moment formula from the beam theory: (6.6) 42

PAGE 56

where Sbc is the composite section modulus for bottom fiber. The composite section includes an effective flange, b, Figure 5.1. 6.2.3 Quality Control Checks. for ADINA Finite element programs are notorious for generating stacks of printout and a variety of results. It is essential that the designer conduct some checks by independent means to detect any gross error that may be introduced in the analysis through incorrect input data. To achieve the objective two types of checks or safe measures were used: 1. Predicting the average tensile stress in the bottom fiber using the beam formula: (No. of loaded lanes) (Midspan M per lane) Aver. f= (No. of beams *Sbc) (6.7) and comparing it to the computed average stress from ADINA. As can be verified from Appendix III, the statics check shows a very small relative deviation (less than I percent). 2. Computing the composite girder moment using both Eqs. (6.5) and (6.6) and selecting the largest of the two for deriving the distribution factors. The relative difference between the two equations was within 1 to 1.5 percent and Eq. (6.6) controlled. 43

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6.3 Comparison Between Finite Element and Grillage Analyses Although Table 3.1, Sec. 3.4, shows close correlation between the results obtained by Imbsen (Zokaie et al. 1991), a study using ADINA for the finite element and STAAD-III for the grillage analyses were conducted to assess the similarities. The case considered HS-25 truck loading and a 5-beam bridge deck spanning 80ft with girders spaced 9'-0" on centers. This is described in Table 6.1 and detailed in Appendix C. For the first interior beam B2, the calculated bottom stress f=(P/A) + (MJSb) = 693 psi. The overall moment carried by the girder may be estimated by Eq. (6.6): Me = 693 X 16,848/12,000 = 973 ft-k The STAAD-III run in Appendix C lists a moment value for the interior girder Me = 1038.7 ft-k. The difference is 6% and, therefore, quite small. Since the lane moment at midspan is equal to 1440 ft-k (by statics), the D.F. for the finite element case will be: D.F. = 973/1440 = 0.676. This is 18% less than AASHTO's 9111 = 0.818. The 18% reduction is substantial. 44

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Table 6.1 Finite Element Analysis Case (L=80ft): Result Summary Bridge Section Shape : 24/54, I ; Span L = __HQ__ft. Number of Design Lanes: 3 Beam Spacing, S = Loading per Lane: HS-25 Moment at midspan/Lane = 1440 ft-k Number of Beams: 5 Out-to-out bridge width: Effective Slab Thickness used: _9_ m. Eslab = 3824 ksi; Orthotropy Factor: 1.44 Properties of basic beam: A = 816 in2 ; sb = 10083 in) Eoo.m = 4769 ksi; St. Venant J = 39648 in4 Composite Beam including tributary slab: Sbc = 16,848 in3 Midspan Diaphragm (non-composite w/slab ): assumed 1011x27" ------------------------------------------------------------------------------------ADINA'S RESULTS FOR MIDSPAN SECTION (Calculated bottom stress f =PIA+ M/Sb) Load Case 1: First wheel line right over beam B 1 B1 B2 B3 B4 B5 AVG M (in-k) = 4859 4439 4049 3481 2779 p (kip) = 209.9 206.4 198.5 174.0 138.4 f (psi) = 740 693 645 558 445 616 Load Case 2: Move all trucks by 2 ft toward bridge centerline M (in-k) = 4145 4118 4074 3801 3448 p (kip) = 183.7 197.2 200.1 186.5 160.0 f. (psi) = 636" 650 649 606 538 616 Load Case 3: Move trucks further by two more feet M (in-k) = 3447 3799 4075 4119 4146 p (kip) = 159.8 186.4 200.1 197.3 183.9 f (psi) = 538 605 649 650 637 616 I 45

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Type of Beams Applicable Disiullution Factol'll Range of CroaSectlon Applicability from Table 4.6.2.2. 1-1 Concrete Deck on b, c One Design Lane Loaded: 6.0 :!0 s :!0 11.5 Concrete Spread Box 20 s L :!0 140 Beams 18 s d :!0 65 Nb .0!: 3 Two or More Design Lanes Loaded: 6.3 Concrete Deck, Fmed k. One Design Lane Loaded: 3.5 :!0 s :!0 16.0 Grid, or Partially Filled 4.5 :!0 t. s 12.0 Grid on Steel or o.oe (_5_f' 20:SL:s240 Concrete Beams; 14 L Nb 2: 4 Concrete T-Beams, T-and Double T -Sections q Two or More Design Lanes Loaded: H sulllclendy ( sr(sr( K r COMected to 0 075 _:.:1_ act as a unit &.5 L Precast Concrete Double Integral concrete Tee Sectlim with Shear Keys and with or without Transverse Post-Tensioning post (I) tension Precast Concrete Tee Integral concrete Section with Shear Keys and with or without Transverse Post-Tensioning m tension Precast Concrete I or BulbCast-In-place concrete. Tee Sections precast concrete lr 1r 1f K (k) Figure 6.1 Distribution Factor for Common Beam-and-Slab Bridge Decks (NCHRP 1993) 46 I I

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y y (x,y) = Plane of Reference / z Figure 6.2 (a) Quadrilateral Shell Element, and (b) Beam (stiffener) Element 47 X

PAGE 61

Node (Typ.) 96" 76" 2 Orthotrophy Factor: DY = (96/76) = 1.596 Slab (shell) Element Beam Element Figure 6.3 2-Plate Mesh Discretization and Orthotropy Factor (example) (Zellin et al. 1976) 48

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a ..... ...... N M 1_/ Location of 2nd Truck Ax le c -----v---1--s 1------f----r------------------Figure 6.4 Typical Bridge Deck Discretization (F.E. Analysis) 49

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. G1 G2 G3 G4 GS I I I I I I I I I I Actual Cross Section Effective Slab Thickness 4'-0" s s s s 4'-0" Idealized Cross Section Figure 6.5 Actual and Idealized Cross Section 50

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Basic Beam Pro erties A, I, J, Yt, E, G AASHTO Type Ill Beam Example u Midspan Diaphram Figure 6.6 Cross-Sectional Dimensions of Beams and Midspan Diaphragm (example) 51

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7. Parametric Study Results for Distribution Factors 7.1 Methodology The parametric study for the distribution factors was conducted using the grillage analogy option in STAAD-111 (STAAD 1994). Spans and spacings were those mentioned in Section 4.0. Typical grillage meshes for the 5 and 7-beam decks are shown in Figure 7.1 and 7.2, respectively. They both show longitudinal beams having 12 segments. A total of 11 transverse beams are used within the span, each having a slab contributing length of L/12. The slab is considered to be composite with the girder, and the composite inertia is used as the longitudinal members' inertia in the analysis. Shear deformations effects are negligible due to the beam slenderness (high Lid ratio). Before proceeding with the detailed study, the case of a 5-beam deck spanning 1 06 ft was selected to investigate the impact on accuracy if additional notional joints were added. These were placed half-way between the transverse beam nodes of Figure 7.1 as suggested in (Jaeger and Bakht 1982). A two-lane loading was used in this test. The comparison between the moment results for the first interior beam shows a difference of less than 0.2%, as shown in Appendix D. As a conclusion, there is no significant improvement in the accuracy and Figure 52

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7.1 and 7.2 will be followed. It is worthy of note that the mesh discretizations already exceed those recommended by the LRFD code (NCHRP 1993) and by (Zokaie et al. 1991). Two truck positions in the transverse section were considered, Figure 7.3: one with the first wheel line over the exterior girder centerline, the other with the wheel line at 2'-0" from the same girder. The one that results in the largest moment in beam B2 is the controlling one. As for the controlling location in the longitudinal direction, seven different reference axle positions were tried for each transverse truck position. The one that resulted in the maximum beam moment was used in calculating the dispi.bution factors. A multi-lane reduction factor, m = 0.85, was used when three lanes were placed on the bridge as allowed by LRFD. 7.2 Moments and Distribution Factors Results Results of the grillage analyses are included in Appendix E. Table 7.1 and 7.2 display the moment and D.F. results for the first interior beam B2 by three methods: the current AASHTO's value (=S/11) the LRFD's simplified procedure as based on Eq. (6.1) 53

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the grillage analogy results By inspection of these two tables, Column (8), it is clear that the reduction in live load moment ranges from 17 to 25% when current HS-20 loading is considered. This is a significant amount in bridge practice and its impact will be examined in the next chapter. The maximum moment (per lane) for an HS-20 load is listed in Column ( 4) and obtained from (AASHTO 1989). 54

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VI VI AASHTO Type (Span) III (90') IV (110') v (128') VI (146') Table 7.1 Moments and D.P.'s Results for First Interior Beam by Three Methods (S=6'-8") Midspan Beam Ctrl. Max. Grillage Current Moment, K-ft Value, Moment n.F.= Simplif. 2-Lane 3 .. Lane K-fl:. per lane Ratio D.F.= Load Load (HS-20), (3)/(4) S/11 K-ft. (1) (2) (3) (4) (5) (6) 678 632 678 1,344 0.505 0.606 845 795 845 1,704 0.496 0.606 1005 947 1005 2,025 0.496 0.606 1161 989 1161 2,360 0.492 0.606 LRFD Ratio Simplif. (5)/(6) Eq.(6.1) (7) (8) 0.546 0.83 0.549 0.82 0.548 0.82 0.545 0.81

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VI 0'1 AASHTO Type (Span) III (70) IV (90') v (106') VI (122') Table 7.2 Moments and D.F.'s Results for First Interior Beam by Three Methods (S = 10'-0") Midspan Beam Ctrl. Max. Grillage Current Moment, K-ft Value, Moment D.F. = Simplif. 2-Lane 3-Lane K-ft . per lane Ratio D.F.= Load Load (HS-20), (3)/(4} : S/11 K-ft. (1) (2) (3) (4) (5) (6) 728 709 728 986 0.738 0.909 952 944 952 1344 0.708 0.909 1143 1140 1143 163.0 0.701 0.909 1302 1312 1312 1919 0.684 0.909 LRFD Ratio Simplif. (5)/(6) Eq.(6.1) (7) (8) 0.755 0.81 0.748 0.78 0.745 0.77 0.738 0.75

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END SUPPORTS @ 5 G I R D E R L A y 0 u T L4 X 120' = PLAN VIEW SECTION AASHTO girders (typlcall Figure 7.1 Grillage. Model for the 5-Beam Bridge Deck 57

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z ""' A. II) c 5! END SUPPORTS __J._ __ Il 0[!] 011 (!)Il f"il 0]] EJ lffi [iQ]_ fWl _ml @ riil El @ ..JEl-, ----r-!!.ZL t;j'l 6 )( 80' = 480' ---...... PLAN VIEW "1 G I R D E R L A y 0 u T AASHTO olrders ltyplcall SECTION Figure 7.2 Grillage Model for the 7-Beam Bridge Deck 58

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12' LANE 2' 6' 4' 2' r1 I 1 r rn : '-.; l LU ? dr d I I 4'-D" 6''"'"8 OR 1o-o EXTERIOR TRUCK POSITION (A) .12' LANE 4' 2' 2' 2' OR 1 o-o EXTERIOR TRUCK POSITION (B) n1 Ul Figure 7.3 Transverse Positioning of Truck Loads 59

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8. Flexural Designs of Selected Beams Before undertaking the full prestress design of selected bridge girders, we will briefly review current AASHTO (AASHTO 1989) and LRFD (NCHRP 1993) flexural requirements which differ mainly by the live load magnitudes and safety factors. Under these codes, both stresses under service load and strength under factored loads must be checked at appropriate sections. 8.1 Stress Checks on Release and Under Service Loads The compression stress in the bottom fiber of the beam at the time of release from the form is calculated as follows: (8.1) The required compression strength in the beam at release of the strands is set by AASHTO and is equal to: Req'd f ci = 1.667 (max fbi) (8.2) The design of prestressed concrete girders also requires checking the bottom stress fb at several sections under service loads using the following equation: 60

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where N5 =number of 112 in. diameter, low relaxation strands F pi = force in 112 in. diameter prestressing strands at release Fpe =effective force in 112 in. diameter strands (long-term) Ac = cross section area of precast basic beam e = eccentricity, distance from center of gravity of precast concrete beam to center of gravity of strands. Sb = section modulus with respect to bottom of basic beam Sbc =. section modulus with respect to bottom of composite section Md = self weight moment at specific section Mnc = noncomposite dead load moment ML+s = moment due to live load and superimposed dead load f c = compressive strength of concrete at 28 days The stress fb will vary along the beam length since both the eccentricity and moments vary and generally increase as sections approach the midspan in beams with draped strands. The long-term effective force in the prestressing strands is given by: Fpe = [Jacking ratio X f5 0.153 (8.4) where 0.153 in. 2 is the cross-sectional area of one 1/2 in. diameter strand, the jacking ratio varies from 0.70 to 0.75, and f5 is the ultimate strength of the 61

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prestressing steel, which is usually 270,000 psi. The AASHTO Specifications stipulate the value of total stress loss to be: = SH + ES + + CRs (8.5) The above prestress loss components--SH, ES, and CRs--are determined by detailed equations given in (AASHTO 1989). In a typical prestress bridge design, from Eq. (8.5) is substituted into Eq. (8.4), Eq. (8.4) into Eq. (8.3), and the bottom tension is checked at critical sections. If fb exceeds the code limit, another refined estimate of the number of strands, N, is made and the check is repeated until the difference between the allowable and calculated value is very close, typically 25 to 30 psi. After defining N, Eqs. (8.1) and (8.2) are used to calculate rei 8.2 IDtimate Strength Check After code stress limits are checked and satisfied, an ultimate strength check is performed. by comparing the required factored moment to the available moment capacity by AASHTO. where Required Mu= 1.3Md+s + 2.17 ML Md+s = sum of all dead load moments ML = live load moment 62 (8.6)

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The available resisting moment for a rectangular section having a width b and a depth d is determined from: Available Mu = cp (d-0.5a) where the reinforcement stress at failure is given by and fps = f's (1-0.5 p r jf'J cp = 1.0, capacity reduction factor = N (0.153 in?) p = a = reb) (8.7) (8.8) (8.9) If after substituting Eq. (8.8) into Eq. (8. 7), the available Mu is found to be less than the required Mu, then the design is unsafe and N is, therefore, incremented by one or two strands and iterations repeated until convergence is achieved. Strain compatibility may also be used as an a}tet;native to Eq. (8.8), specially in computer software. Usually, the above equations represent the essential checks in the iterative design of the beam. Other checks such as shear strength, development length and cracking moment calculations are made, but do not control the design. 63

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r 8.3 Stress Limits and Load Factors In conduCting the bottom tension stress check, the allowable limit will be assumed equal to which is normally associated with "corrosive environment". When checking bottom tension stress by LRFD, the design truck loads are multiplied by 0.80. The required concrete strength at release is determined .from Eq. (8.2). In addition to self weights, other dead loads consist of 25 psf for the asphaltic wear surface and two 350 plf concrete barriers (per bridge). The current AASHTO load factors for strength check are 1.3 for dead loads and 2.17 for live loads. On the hand, LRFD specifies a load. factor of 1.25 for beam/slab loads, 1.50 for asphaltic wear surface and 1. 75 for the new heavier live loads, Figure 1.4. 8.4 Flexural Designs Two design softWares, called BRIDGE89 (BRIDGE89 1989) and NULRFD (NULRFD 1993) were used to generate the final designs by trial-and-error since . automatic design programs are not available. The first program is in compliance with current AASHTO (AASHTO 1989) while the second one follows the new LRFD code (NCHRP 1993). Because of the time consuming nature of such designs, beam shapes were limited to types VI and Nand two spacings, S = 6'-8" 64

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and S = 1 0' -0", were considered. This required 12 different designs because of the changed D.P.'s and different LRFD load.Prestressing reinforcement was assumed to consist of 112" low-relaxation strands, initially jacked to 0.73 f's, an average industry value. The strand profile was the usual "double drape" layout, Figure 8.1. Concise printouts are included in Appendix F and the results' summary is shown in Table 8.1. Although the average moment reduction in Tables 7.1 and 7.2 was 20%, the designs by refined procedures assumed a conserVative 18% live load reduction. Columns (3) and (4) show the design results, N5 and f' ci' by current AASHTO simplified procedure. Columns ( 5) and ( 6) list the lower design values if grillage analogy is used. On the other hand, columns (9) and (1 0) display the required number of strands and concrete strength if the LRFD code, (NCHRP 1993), were adopted with the corresponding heavier truck N5 and f'ci are the two dominant parameters: that affect the prestressed beam cost and its relative economy once a beam shape is selected. 65

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0\ 0\ AASHTO Type (1) Type IV Type IV Type VI Type VI Table 8.1 Comparison of Reinforcing and Release Strength Requirement ( f' ei) by Three Different Procedures By Current By Grillage Method SPAN/SPACING Simplified (18% Load Reduction) (ft) AASHTO/HS-20 HS-20 Trucks Ns rei (psi) Ns r ci (psi) ratio. Difference (5)/(3) (4)-(6) ; (2) (3) (4) (5) (6) (7) (8) 110'/6'-8" 52. 4,874 47 4,298 0.90 576 90'/10' 49 5,208 44 4,658 0.90 550 146'/6'-8" 69 4,542 63 -3,996 0.91 546 122'/10' 66 5,115 60 4,577 0.91 538 By Grillage Method (18% Load Reduction) and LRFD Truck Ns rei (psi) (9) (10) 52 4,833 49 5,169 70 4,618 67 5,173

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1: C.G.Steel C. G. Concrete --::_------]------. ...._ c -----0.4L( +) L j,. 0 4 L ( .!. ) TYPICAL STRAND PROFILE Max. Stressing = 744 kips(top) SECTION = 1550 kips(bottom) 1'-7"""\ 2 .. 2 1'-7" Max. Hold-Up Force = 96 kips f iH (' t Max. Holddown Force = 24 kips/device ::: 6 sp. @ 2" ::: = 1'-0" ... DATE 1987 AEV'D NOTE: Maximum 18 harped strand. Verify holdup and holddown forces are not exceeded. AASHTO TYPE VI GIRDER NOTE: 64 strands total maximum. STRAND AT MIDPOINT SECTION PROPERTIES & STRAND. PATTERN STANDARD. Figure 8.1 Typical Prestressing Reinforcement and Profile 67

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9. Conclusions and Recommendations A review of Tables 7.1, 7.2 and 8.1 lead us to the following conclusions applicable to 1-beams with span-to-depth ratios larger than 18: 1. The moment reduction for live load at midspan varies between 17 and 25% when grillage analogy is used to compute bridge beam moments. 2. The percentage reduction grows larger as the girder spacing and/or span mcrease. 3. The impact of moment reduction on the prestressed beam is substantial. Assuming a conservative 18% reduction, the number of strands is reduced by 9 to 10% and the required concrete strength at release averages 550 psi less. 4. If and when the LRFD code is adopted with its heavier truck load, the required strands and concrete strength barely change from current practiceprovided refmed methods, such as grillage analogy, are used. 5. For the given spacings, the two-lane presence appears to control the design of the first interior beam, except for one case. In the latter case, the difference in moment values between the two-lane and three-lane cases was less than 0. 7%. 68

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6. Distribution factors by the new LRFD's simplified method are always larger than those obtained from the grillage analysis. The following recommendations are offered: 1. Refined analysis procedures such as the grillage method should be used by design engineers and D.O.T.'s in a systematic fashion due to the economic advantages for the majority of spans and spacings. 2. The following equation may be used for a conservative estimate of the distribution factor when span/depth > 18. : D.F. = 0.07 + 0.16 S0 8 L-0 1 (9.1) The relative error is between .1 and 6%. See figure 9.1 for comparison of results. 3. Further studies of exterior beam moment should be conducted as the grillage analyses often show their D.F. is larger than the interior beam value. 69

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0.800 -.--------"'"---------------------, 0.750 0.700 ... 0.650 = 0 I 0.600 .., iS 0.550 0.500 0.450 +--....:.__+---+---+---+----+----+---+-----1 70 80 90 100 110 Span L (ft) 120 130 -:(-Grillage Eq. 9.1 :( LRFD 140 150 Figure 9.1 Comparison ofD.F. By Grillage, LRFD, and Eq (9.1) Methods 70

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Appendix A Sample Input/Output for Computing Icomp 71

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#P030200011 COMPOSITE PROPERTIES,AASHTO III, SpacingS= 6'8; t=8 in. SECTION1, V2.00 DESIGN DATA SHEET OF DATE: 02/22/94 PAGE: 1 BY: GA H = 45.000 in. He 53.000 in. Nc = Etopping/Eprecast 0.7750 Rectangles Dist. V1 to Bottom (in) 45.000 Special Elements A (in-2) 560.000 Dist. V2 to Top (in) 53.000 I (in-4) 125390.000 Bottom Width (in) Top Width (in) 80.000 Dist From Bot to e.G. (in) 20.270 80.000 No. of units* 1 No. of units* 1 Type precast Type topping *NOTE: A minus sign in this column indicates entry of a void. * ** * ** * ***** * * ** * '!C * * * OUTPUT * * *** *** w *.*.* * ** * * * ** *** w section Properties (non-composite, without bonded steel transformed) A (in-2) 560.000 I (in-4) 125390.000 Yb (in) 20.270 Yt (in) 24.730 Sb (in-3) 6185.989 St (in-3) 5070.360 section Properties (composite, without bonded steel transformed) Ac (in-2) 1056.000 Ic (in-4) 345143.939 Ybc (in) 33.764 Ytc (in) 11. 236 NOTE: Ytc and Stc are to the top of precast. 72 sbc (in-3) 10222.127 Stc (in-3) 30718.765

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Appendix B Sample Input/Output for Computing Basic Beam's J (St. Venant's Torsional Constant) 73

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TORSIONAL CONSTANTS FOR PRESTRESSED CONCRETE I-BEAM AASIITO TYPE III: d1 :=7 d2 :=4.5 d3 := 19 b1 := 16 b2 :=22 b3 :=7 t1 :=d1 + d2{b1 + b3) 2bl t2 := d5 + d4{b3 + b2) 2b2 t3 :=b3 b32 Dl :=tl +4tl b32 D2:=t2+4t2 al :=0.042 + 0.2204--0.0725 -b3 (b3)2 t1 t1 b3 (b3)2 a2 :=0.042 + 0.22040.0725 .,__ t2 t2 d4 :=7.5 1 ( 3 3 3) 4 4 ( 4 4) J:=bl-tl +b2t2 +d3t3 +alD1 +a2D2 -0.21 t1 +t2 3 J = 16845 0 4 m 74 d5 :=7

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Appendix C ADINA Input/Output Files for Case Study L=80 ft, 8=9 ft and Corresponding STAAD-111 Files Using Grillage Analogy 75

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A 0 I N A INPUT FILE: I24S4A IN Al (YXC2/U01269 Monday, 28, 1994 2:37 pm) ADINA-IN 3.0 INPUT FILE "12454A IN A" .. PC I-GIRDER BRIDGE (L= 80 FT) SU8J. TO LOAD CASE 1 FILEUNITS LIST=8 LOG=7 ECH0=7 FCONTROL HEADING=UPPER ORIGIN=UPPERLEFT CONTROL PLOTUNIT=PERCENT HEIGHT=1.25 .. WORK 7 7475 1 0 SIZE=AUTO COL=PEN BACK=WHITE 1 BLACK 2 BLUE 3 RED 4 GREEN 5 MAGENTA 6 YELLOW 7 CYAN I CREATE HEADING '44 ft K BO ft CONC !-Girder BR under Load Case 1' .. KASTER REACTION=YES KODEX=EXECUTE SAVE NODES lOB to 112 BELOW ,INCRI'l'!ENTS OF 1 SAVENODES 108 112 1 r.._IVC=VFJ../:1:ITY IAC=ACCEL'ERATION PRINTOUT IOUT=1 IVC=O lAC=O PRINTDEF=YES PRINTNODES 108 112 1 .. PORTHOLE VOL=KAX NPUTSV=1 FORKATTED=YES FILE=60 JVC=O JTC=O SAVEDEF=YES * UNITS a KIP, INCH, SECOND Z=DISTANCE MEASURED FROM BEAM BOTI'OM; BEAM C.G. @ 25.31";5LAB C.LINE 58.5" ABOVE BOTI'OM COORDINATES ENTRIES NODE X y z 1 0 0 58.5 2 48 0 58.5 TO 10 480 0 58.5 11 52B 0 58.5 12 48 0 25.31 TO 16 4BO 0 25.31 209 600 0 25.31 TO 220 600 880 25.31 NGEN TIKES=12 NSTEP=16 YSTEP=80 1 2 TO 10 11 12 TO 16 .. 4-NODE SHELLELEMENTS: SHELLNODESDOF DOF-DEFAULT=FIVE DOF-IN=SIX 2 0 STEP 16 TO 194 0 4 0 STEP 16 TO 196 0 76

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FILE: I245'1A IN Al (YXC2/U01269 Honday, February 28, 1994 2o37 pm) 6 0 STEP 16 TO 198 I) 8 0 STEP 16 TO 200 0 10 0 STEP 16 TO r 3824*0y a/ Slab's E Poisson's Shear Modulus 202 0 # --HAT 1 O.RTHO EA=SS06 EB=3824 NUAB=0.2 GAB=1593 GAC=1593 GBC=1593 Prop.) HATERIAL 2 ELASTIC E=4769 NU=0.2 Beam Properties: E p ) MATERIAL 3 ELASTIC E=3824 NU=0.2 -----(Diaphragm Properties: E Jl ) EGROUP 1 SHELL H=l RESULTS=STRESS THICKNESS 1 9 ---(Shell 'lbickness) STRESSTABLE 1 9 11 13 15 ENODES ENTRIES EL N1 N2 N3 N4 1 18 17 1 2 TO 10 27 26 10 11 EGEN TIHES=1l ESTEP=10 NSTEP1=16 1 TO 10 EDATA ENTRIES EL SAVE 1 NO TO 120 NO BAS BEAMS PROPERTIES: RI is J; SI is Ixx inertia; A is Area; TA is shear Area EGROUP 2 BEAH H=2 SECTION 1 PROP RI=39648 SI=255194 TI=l8495 A=816 TA=432 ENODES 1 13 12 28 TO 12 189 188 204 13 14 i3 29 TO 24 190 189 205 25 15 14 30 TO 36 191 190 206 37 16 15 31 TO 48 192. 191 207 49 209 16 32 TO 60 220 i92 .208 EDATA ENTRIES EL SAVE 1 tiO TO 60 NO EGROUP 3 BEAH 11=3 ---(FOR END DIAPHRAGMS) SECTION 1 SHAtE=RECT Hl=18 H2=54 SC=O TC=-1.69 TSHE=1.0 ENODES 1 28 12 13 2 29 13 14 77

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FILE: I2454A IN A1 {YXC2/U01269 Monday February 28 1994 -2:37 pm) 68 3 -2.000 69 3 -2.000 70 3 -3. 000 71 3 -2.000 72 3 -2.000 73 3 -2-.000 82 3 -6.000 83 3 -4.000 84 3 -4.000 85 3 -4.000 86 3 -6.000 87 3 -4.000 88 3 -4.000 89 3 -4.000 98 3 -14.000 99 3 -9.334 100 3 -9.334 101 3 -9.334 102 3 -14.000 103 3 -9.334 104 3 -9.334 105 3 -9.334 114 3 -4.000 115 3 -7.. 668 116 3 -2.668 117 3 -2. 668 118 3 -4.000 119 3 -2.668 120 3 -2.668 121 3 -2.668 uo 3 -16.000 131 3 -10. 665 132 3 -10.665 133 3 -10.665 134 3 -16.000 135 3 -10.665 136 3 "10.665 137 3 -10.665 ADINA END 78

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FILE: I2454A IN 3 30 14 15 4 31 15 16 5 192 ?.04 205 6 19J 205 206 7 194 206 207 8 195 207 208 EDATA ENTRIES EL SAVE 1 NO TO 8 NO EGROUP 4 BEAK H=3 Al (YXC2/U01269 Honday, February 28, 1994 2,37 pm) SECTION 1 SHArE=RECT Hl=lO H2=27 SC=O TC=-9.19 TSHE=l.O ENODES 1 92 108 109 2 93 109 110 3 94 110 111 4 95 111 112 BOUNDARIES 001000 13 TO 15 205 TO 207 BOUNDARIES 111000 12 16 BOUNDARIES 101000 204 208 BOUNDARIES 111111 209 TO 220 RIGIDLINK TIE BEAM NODES TO SHELL1SLAB NODES) 2 12 STEP 16 TO 194 204 4 13 STEP 16 TO 196 205 6 14 STEP 16 TO 198 206 8 15 STEP 16 TO 200 207 10 16 STEP 16 TO 202 208 NOI'E: CONCEffl'R. WHEEL LOADS ARE I:ISTRIBUTED BY SIMPLE STATICS TO ADJAcmi' NODES LOADS CONCEN TYPE=NODES 50 3 -2.000 51 3 -1.333 52 3 -1.333 53 3 -1.333 54 3 -2.000 55 3 .333 56 3 -1.333 57 3 -1.333 66 3 -3.000 67 3 -2.000 79

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A D I N A OUTPUT FILE ( KIPS1 INCHES) S T R E S S C A L C U L A T I 0 N S F 0 R ELEMENT G R 0 U P 2 (BEAM) ELEMENT FORCES ARE CALCULATED IN THE LOCAL COORDINATE SYSTEM ELEMENT OUTPUT NUMBER LOCATION FORCE-R FORCE-S FORCE-T HOHENT-R HOHENT-S 1 I 0.1484E+02 -o. 2711E-01 -0.2066+02 0.2154E+02 0.6157E+03 J -0.1484E+02 0.2711E-01 0.2066+02 -0.2154E+02 0.1037E+04 2 I -0.3678+02 -0.5398E-01 -0.2034+02 0.2243+02 -0.3165E+03 J 0.3678E+02 0.5398E-01 0.2034+02 -0.2243+02 0.1944+04 3 -0.8729+02 0.5312-01 -0.2037+02 0.2290+02 -0.1254+04 J 0.8729+02 -0.5312-01 0.2037+02 -0.2290E+02 0.2884+04 4 -o .1351+03 -0.4099-01 -o .1848+02 0.2767+02 -0.2237+04 J 0.1351E+03 0.4099-01 0.1848+02 -0.2767+02 0.3716+04 5 I -0.1777E+03 0.3773+00 .-0. 1623E+02 0.3786+02 -O.ll48E+04 J 0.1777+03 -0.3773+00 0.1623+02 -0.3786+02 0.4446+04 ta\ (9 -0.2099+03 -0.1598+01 -0.1034+02 0.4528+02 -0.4032+04 J 0.2099E+03 0 .1598+01 0.1034E+02 -0.4528+02 0.4859E+04 7 -0.2185+03 0 .1511E+01 0.3781E+01 -0;5299+02 -0.4727E+04 J 0.2185+03 -o .1511+01 -0.3781E+01 0.5299+02 0.4424+04 B I -0.2046E+03 0.6763E-01 0.8289+01 -0.5076+02 -0.4581+04 J 0.2046+03 -0.6763-01 -0.8289E+01 0.5076+02 0.3918+04 9 I -0.1708E+03 -0.4074+00 0.2044E+02 -0.9101+01 -0.4344E+04 J O.'l708E+03 0.4074+00 -0.2044+02 0.9101+01 0.2709E+04 10 I -0.1221+03 -0.5219E-01 0.2105E+02 -o .t299E+02 -0.3330E+04 J 0.1221+03 0.5219-01 -0.2105E+02 0.1299+02 0.1646+04 11 I -0.7247+02 0,5465-01 0.2048+02 -0.3232+02 -0.2297+04 J 0.7247+02 -O.S465E-01 -0.2048+02 0.3232+02 0.6589+03 12 I -0.2331+02 0.6626+00 0.2072+02 -0.2878+02 -0.1303+04 J 0.2331+02 -0.6626+00 -0.2072+02 0.2878U02 -0.3541+03 13 I -o .1893E+02 -0.6620+00 -0.1714+02 0.2624+02 0.3004+03 J 0.1893+02 0.6620+00 0.1714E+02 -0.2624+02 0.1070+04 14 1 -0.6065+02 -0.1607-01 -o .1724+02 0.3872+02 -0.51&07+03 J 0.6065+02 0,1607-01 0.1724+02 -0.3872+02 0.1920+04 15 I -0 .1030+03 -0.1605-01 -0.1760E+02 0.3440+02 -0.1385+04 J 0.1030+03 0.1605-01 0.1760E+02 -0.3440E+02 0.2793+04 16 I -0 .1437+03 0.3896E-01 -0.1567E+02 0.2954+02 -0.2273+04 J 0.1437+03 -0.3896-01 0.1567+02 -0.2954+02 0.3526E+04 17 1 -o .1798E+03 0.2370+00 -0.1368+02 0.3607+02 -0.3059+04 J 0.1798+03 -0.2370+00 0.1368+02 -0.3607E+02 0.4153+04 G;'Z. 0 I -0.2064+03 -o .1147+01 -0.7853E+01 0.3645E+02 -0. 3811+04 J 0.2064E+03 0.1147+01 0.7853+01 -0.3645+02 0.4439+04 19 -0.2138+03 0.1176E+01 0.1972E+01 -o. 3190E -0. 4l39F.+Ol 80

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J 0 .1243+03 0.1222+00 0 1249+02 -0.7689+02 0.2827+04 41 I -0.1534+03 -o. 2B71E+oo -o .1067+02 0.3956+02 -0.2449+04 J 0.1534+03 0 2871+00 0.1067+02 -0.3956+02 0.3302+04 I -0. 1140+03 0.1025+01 -0.5619+01 0.1024+01 -0.3031+04 J 0 .1740+03 -0.1025+01 0 5619+01 -0.1024+01 0.3481+04 43 I -0.1795+03 -o .1136+01 0.1145+01 0 1892+02 -0.3409+04 J 0 1795+03 0.1136+01 .1145+01 -o .1892-t02 0.3318U04 44 I -o .no8E+03 0 2811+00 0 5215+01 -0. 2464+02 -0. 3461+04 J 0.1708-t03 -o. 2811E+oo 5215+01 0.2464+02 0.3044E-t04 45 I o .1435+03 0.1062-tOO O.l631E-t02 .7056-t02 -0.3405+04 J 0.1435+03 .1062-tOO -0.1631+02 0.7056E-t02 0.2101+04 46 I -o .1018+03 .2993 0.1729+02 .1019E-t03 -0.2624+04 J 0 .1018+03 0.2993-01 -0.1729+02 0.1019+03 0.1241E-t04 47 I .5954E-t02 -0.7653-01 0 .1635-t02 -0.1405+03 -0.1790+04 J 0.5954+02 0.7653-01 -0.1635+02 0.1405+03 0.4823-t03 48 I -0.1835+02 0.3882+01 0.1654-t02 -0.!1855+02 -0.1015-t04 J o .1835-t02 -0.3882+01 -0.1654+02 0.8855+02 -0.3086+03 49 5413E-t02 -0. 1629+01 -0.8902+01 0.8435+02 -0. 2044+03 J 0.5413+02 0.1&29+01 0.8902+01 -0.8435+02 0.9166E-t03 50 I -0.7311+02 0.1091-01 .8906-tOl 0 .1155-t03 .6848E-t03 J o. 73ll-t02 -0.1091-01 0.8906+01 -0.1155+03 0.1397-t04 51 I .9238-t02 -0.1219+00 -0.8689+01 0.1080+03 -o .1145+04 J 0.9238+02 0.1219+00 0.8689E-t01 .1080-t03 0 1840-t04 52 I -o .1107+03 -0.8136-01 -0.7865+01 0.8813+02 .1599U04 J 0.1107+03 0.8136-01 0.7865+01 ..;0,8813+02 0.2228E-t04 53 -0.1268+03 -0.42591i-t00 .6904E-t01 0.4956+02 -0.2026+04 J 0.1268S:-t03 0.4259+00 0.6904+01 .4956U02 0.2579-t04 @ I -o 1384+03 0.1398+01 -0. 4114+01 o. 303ZE+01 -0.2450+04 J 0.138!+03 -o .1398-t01 0.4114E+Ol -0.3032+01 0.2779+04 55 I -o .1376-tOJ -0.1421+01 0.4053+01 0.4024+02 -0.2801-t04 J 0.1376-t03 0.1421+01 -0.4053+01 .4024-t02 0.2477+04 56 I .1241-t03 -0.7100 0.6792+01 .1054U02 -0.2651!+04 J 0.1241+03 0 7100-01 .6792+01 0 1054+02 0.2107+04 57 I .1035-t03 0.5233+00 0.1033+02 -0.9953+02 .2393E-t04 J 0.1035+03 -0.5233+00 -0.1033+02 0.9953+02 0.1567+04 58 I -0.7778+02 0.7040-01 0 1139+02 .1337-t03 -0.1934+04 J 0.7778-t02 -0.7040-01 .1139-t02 0.1337+03 0.1023-t04 59 I -0. 5053+02 -O.l675E+OO 0.1162-t02 -0.1557+03 -0.1416+04 J 0.5053+02 0.1675+00 -o .1162+02 0.1557+03 0.486SE-t03 60 I -0.2206E-t02 0.3922E-t01 0.1213-tOZ -0.9186+02 -0.8880+03 J 0.2206+02 .3922-t01 -0 .1213-t02 0.9186+02 -0.8249+02 81

PAGE 95

J 0.2138+03 -0.1176+01 -0.1972+01 0.3190+02 0.4182+04 20 1 -0.2023+03 -0.2416+00 0.7084+01 -0.3306E+02 -0.4339E+04 J 0.2023E+03 0.2416E+OO -0.7084E+01 0.3306E+02 0.3772+04 21 1 -0 .1705E+03 -0.3977E-01 0.1893+02 -0.281SE+02 -0 .4178E+04 J 0 .1705+03 0.3977-01 -0. 1893+.02 0.2815+02 0.2664+04 22 I -0. 1228E+Ii3 -0.6294-02 0.2054+02 -0.3552+02 -0.3252+04 J 0 .1228+03 0.6294-02 -0.2054+02 0.3552+02 0.1609+04 23 -o. 7342E+02 -0.4860-01 0.1977+02 -0.4739+02 -0.2233+04 J 0.7342+02 0.4860-01 -0.1977+02 0.4739+02 0.6512+03 24 I -0.2430+02 0.1472+01 0.2011+02 -0.2871+02 -0.1275+04 J 0.2430+02 -0 .1472+01 -o. 2011+02 0.2871+02 -0,3336+03 25 1 -0.1872+02 -0.1852+01 -o .1629E+02 0.5570+02 0.2959+03 J 0.1872+02 0.1852+01 0.1629+02 -0.5570+02. 0.1007+04 26 1 -0.5933+02 0.2233 -0.1636+02 0.7896+02 -0.4838+03 J 0.5933+02 -0.2233-01 0.1636+02 ,..o.7896E+02 0.1793+04 27 1 -0.1004+03 0.2443-01 -0.1673+02 0.5988+02 -0, 126SE+04 J 0.1004+03 -0.2443-01 0.1673+02 -0.5988+02 0.2603+04 28 I -o .1397+03 -0.8479-03 -0.1474+02 0.4597+02 -0.2099+04 J 0.1397+03 0.8479-03 0.1474+02 -0.4597+02 0.3278+04 29 -0.1740+03 0.2986-01 -0.1263+02 0.3569+02 -0.2829+04 J 0 1740+03 -0.2986-01 0.1263+02 -0.3569+02 0.3839+04 Gi3 @) -0.1985+03 -0.3278+00 -0.6734+01 0.2036+02 -0.3510+04 J 0.3278+00 0.6734+01 -0.2036+02 0.4049+04 -31 I -0.2059+03 0.3436+00 0.8898+00 -0.1925+02 -0.3950+04 J 0.2059+03 -0.3436+00 -0.8898+00 0.1925+02 0.3879+04 32 I -0,1970+03 -0.3278 0.5383+01 -o. 3513E+o 2 -0.4026+04 J 0.1970+03 0.3278-01 -0.5383+01 0.3513+02 0.3595+04 33 I -0.1661+03 0,7123-02 0.1925+02 -0.4556+02 -0.4001+04 J 0 .1661+03 -0.7123-02 o .1925+02 0.4556+02 0.2461+04 34 I -0.1177+03 -0.4403-01 0.2012+02 -0.5993+02 -0.3064+04 J O.ll77E+03 0.4403-01 -0.2012+02 0.5993+02 0 1454+04 35 I -0.6889+02 -0.5085-01 0.1904+02 -0.8388+02 -0.2086+04 J 0.6889+02 0.5085 -o .1904+02 0.8388+02 0.5630+03 36 1 -o. 2111+02 0.2498+01 0.1925+02 -0.5303+02 -o; 1178+04 J 0. 2111+02 -0.2498+01 -0.1925+02 0,5303+02 -0.3614+03 37 I -0.1812+02 -0.2407+01 -0.1444+02 0.7949+02 0.2431+03 J 0.1812+02 0.2407+01 0.1444+02 -0.7949+02 0.9118+03 38 1 -0.5459+02. 0.1889-01 -0.1429+02 0.1164+03 -0.4385+03 J 0.5459+02 -0;1889-01 0.1429+02 -o .1164+03 0.1582+04 39 I -0.9067+02 0.8905-02 -o .1430+02 0.9626+02 -o .1u 5+04 J 0.9067+02 -0.8905-02 0.1430+02 -0.9626+02 0.2259+04 40 -0.1243+03 -0.1222+00 -0.1249+02 0.7689+02 -o. 1828+04 82

PAGE 96

S T A A D -III Revision 19.0a Proprietary Program of RESEARCH ENGINEERS, Inc. Date= JUN 26, 1994 Time= 15: 3:15 * * ,. PAGE NO. 1 * * * GRILLAGE ANALYSIS FOR COMPARISON WITH F.E.A. * 1. STAAD FLOOR 54-IN I-BEAM,L=BO FT,S=9FT/T=9"/5-GIRDER/3-LANE 2. ORTHOTROPY(DY=1.44) CONSIDERED FOR TRANSV.BEAMS 3. UNITS INCHES KIPS 5. JOINT COORDINATES 6. 1 0 0 0 5 432 0 0 1. R 12 o o eo 9. MEMBER INCIDENCES 10. 1 1 6 5 11. R 11 .5 5 13. 61 1 2 64 14. R 12 4 5 16. MEMBER PROPERTIES 17. 1 TO 60 PRISMATIC 19. 61 TO 64 PRISMATIC 21. 65 TO 84 PRISMATIC 22. 85 TO 88 PRISMATIC 23. 89 TO 108 PRISMATIC 25. 109 TO 112 PRISMATIC 27. SUPPORTS 28. 1 TO 5 61 TO 30. CONSTANTS 31. E 4769 .ALL 32. POISS 0.20 ALL 34. UNITS FEET KIPS 36. DEFINE HOVING LOAD 37. TYPE 1 HS20 1.25 38. TYPE 2 HS20 1.25 39. TYPE 3 HS20 1.25 41 LOAD GENERATION 42. TYPE 1 0 0 43. TYPE 2 12 0 44. TYPE .3 24 0 46. PERFORM ANALYSIS 28 28 28 65 1 IX IX IX IX IX IX 49.817E+3 35E+3 7.795E+3 15.013E+3 7.795E+3 35E+3 PINNED ZI ZI ZI 2 2 2 83 IZ 0.699620E+6 IZ 238E+3 IZ 5.613E+3 IZ 18.76BE+3 IZ 5.613E+3 IZ 238E+3

PAGE 97

54-IN I-BEAM,L=80 FT,S=9FT/T=9"/5-GIRDER/3-LANE -PAGE NO. 3 ORTHOTROPY(DY=1.44) CONSIDERED MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS HEHB FY/ DIST LD HZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 5.92 0.00 1 -947.98 0.00 1 (Ext. o.oo 0.00 1 0.00 0.00 1 0.00 0.00 1 Beam) MIN 5.92 6.67 1 -987.47 6.67 1 o.oo 6.67 1 0.00 6.67 1 0.00 6.67 1 27 MAX 5.64 0.00 1 -1001.16 0.00 1 (1st 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 Int. MIN 5.64 6.67 1 6.67 1 Beam) 0.00 6.67 1 0.00 6.67 1 0.00 6.67 1 28 MAX 5.22 0.00 1 -957.66 0.00 1 o.oo o.oo 1 0.00 0.00 1 0.00 0.00 1 MIN 5.22 6.67 1 -992.47 6.67 1 o.oo 6.67 1 0.00 6.67 1 0.00 6.67 1 29 MAX 3.94 0.00 1 -786.37 0.00 1 0.00 0.00 1 0.00 o.oo 1 0.00 0.00 1 MIN 3.94 6.67 1 -812.65 6.67 1 0.00 6.67 1 0.00 6.67 1 0.00 6.67 1 30 MAX 3.27 o.oo 1 -466.83 0.00 1 0.00 0.00. 1 0.00 0.00 1 0.00 0.00 1 MIN 3.27 6.67 1 -488.66 6.67 1 0.00 6.67 1 0.00 6.67 1 0.00 6.67 1 31 MAX 0.70 0.00 1 -898.59 6.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -19.30 .67 1 -988.42 1.67 1 0.00 6.67 .1 0.00 6.67 1 0.00 6.67 1 32 MAX -14.89 0.00 1 -939.78 6.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -14.89 6.67 1 -1039.04 0.00 1 0.00 6.67 1 0.00 6.67 1 0.00 6.67 1 33 MAX -0.21 o.oo 1 -897.65 6.67 1 0.00 o.cio 1 0.00 0.00 1 o.oo 0.00 1 MIN -20.21 6.67 1 -992.40 0.00 1 0.00 .67 1 0.00 6.67 1 0.00 6.67 1 34 MAX -11.94 0.00 1 -733.50 6.67 1 0.00 o.oo 1 0.00 0.00 1 0.00 0.00 1 84

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Appendix D Comparison of The Accuracy Between Two STAAD-111 Runs By The Grillage Method With One Containing Additional Intermediate Joints 85

PAGE 99

PAGE NO. 1 ************************************************** * s T A AD -III * Revision 19.0a * Proprietary Program of * RESEA 10:42: 41ERS, Inc. * Date= JUL 4, 1994 * Time= 10:41:37 * * ************************************************** 1. STAAD FLOOR AASHTO V, SPAN= 106 FT, SPACING S=10 FT (2LANES) NODE MID. 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. 1 0 0 0 9 480 0 0 6. R 12 0 0 106 8. MEMBER INCIDENCES 9. 1 1 10 5 1 2 10. R 11 5 9 12. 61 1 2 68 13. R 12 8 9 15. MEMBER PROPERTIES 16. 1 TO 60 PRISMATIC 18. 61 TO 68 PRISMATIC 20. 69 TO 108 PRISMATIC 21. 109 TO 116 pRISMATIC 22. 117 TO 156 PRISMATIC 24. 157 TO 164 PRISMATIC 26. SUPPORTS IX 44671 IX 37131 IX 9981 IX 9981 IX 9981 IX 37131 27. 1 3 5 7 9 109 111 113 115 117 PINNED 29. CONSTANTS 30. E 5250 ALL 31. POISS 0.20 ALL 33. UNITS FEET KIPS 35. DEFINE MOVING LOAD 36. TYPE 1 HS20 1.00 37. TYPE 2 HS20 1.00 38. TYPE 3 HS20 0.00 40. LOAD GENERATION 7 41. TYPE 1 2 0 36 ZI 1 42. TYPE 2 12 0 36 ZI 1 43. TYPE 3 24 0 36 ZI 1 45. PERFORM ANALYSIS 86 IZ 1105722 IZ 528096 IZ 4991 IZ 4991 IZ 4991 IZ 528096

PAGE 100

AASHTO V, SPAN= 106 FT, SPACING S=10 FT (2LANES) NODE MI -PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 4.20 o.oo 4 -995.88 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.33 8.83 1 -1041.47 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 27 MAX 5.96 0.00 4 -1067.42 8.83 1 0.00 o.oo 1 0.00 0.00 1 0.00 0.00 1 MIN -2.59 83 1 -1143.42 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 28 MAX 3.42 0.00 4 -738.70 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -1.07 8.83 1 -780.39 8.83 4 0.00 .83 7 0.00 8.83 7 o.oo 8.83 7 29 MAX 1. 04 0.00 7 -286.78 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.57 8.83 1 -299.07 8.83 7 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 30 MAX .09 0.00 1 6.63 0.00 1 0.00 o.oo 1 0.00 0.00 1 0.00 0.00 1 MIN -0.10 8.83 7 5.48 0.00 7 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 31 MAX -8.93 0.00 7 -884.30 8.83 1 0.00 0 .. 00 1 0.00 0.00 1 0.00 0.00 1 MIN -13.43 8.83 4 -1041.22 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 32 MAX -14. 02 0.00 7 -889.59 8.83 1 .. ri. 00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -22.64 8.83 4 -1143.94 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 33 MAX -7.99 0.00 7 -637.09 8.83 1 0.00 0.00 1 0.00 0.00 1 o.oo 0.00 1 MIN -12.47 8.83 4 -780.44 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 34 MAX -1.27 0.00 7 -276 .. 93 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 87

PAGE 101

PAGE NO. 1 ************************************************** * S T A AD -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUL 4, 1994 * Time= 10:43: 5 * * ************************************************** 1. STAAD FLOOR AASHTO V, SPAN= 106 FT, SPACING S=10 FT (3LANES} NODE MID. 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. 1 0 0 0 9 480 0 0 6. R 12 0 0 106 8. MEMBER INCIDENCES 9. 1 1 10 5 1 2 10. R 11 5 9_ 12. 61 1 2 68 13. R 12 8 9. 15. MEMBER PROPERTIES 16. 1 TO 60 PRISMATIC 18. 61 "TO 68 PRISMATIC 20. 69 TO 108 PRISMATIC 21. 109 TO 116 PRISMATIC 22. 117 TO 156 PRISMATIC 24. 157 TO 164 PRISMATIC 26. SUPPORTS IX 44671 IX 37131 IX 9981 IX 9981 IX 9981 IX 37131 27. 1 3 5 7 9 109 111 113 115 117 PINNED 29. CONSTANTS 30. E 5250 ALL 31. POISS 0.20 ALL 33. UNITS FEET KIPS 35. DEFINE MOVING LOAD 36. TYPE 1 HS20 0,85 37. TYPE 2 HS20 0.85 38. TYPE 3 HS20 0.85 40. LOAD GENERATION 7 41. TYPE 1 2 0 ZI 1 42. TYPE 2 12 0 36 ZI 1 43. TYPE 3 24 0 36 ZI 1 45. PERFORM ANALYSIS 88 IZ 1105722 IZ 528096 IZ 4991 IZ 4991 IZ 4991 IZ 528096

PAGE 102

AASHTO V, SPAN= 106 FT, SPACING S=10 FT (3LANES) NODE MI --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 3.62 0.00 4 -855.34 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.17 8.83 1 -894.11 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 27 MAX 5.49 0.00 4 -1073.31 8.83 1 0.00 0. 00. 1 o.oo 0.00 1 0.00 0.00 1 MIN -1.85 8.83 1 -1140 .. 47 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 28 MAX 4.68 0.00 4 -1016.48 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -1.70 8.83 1 -1075.03 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 29 MAX 3.80 0.00 4 -720.53 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -9.97 8.83 1 -765.21 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 30 MAX 0.90 0.00 7 -267.29 o.oo 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.48 8.83 1 -279.41 8.83 7 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 31 MAX -7.52 0.00 7 -761.94 8.83 1 0.00 0.00 1 0.00 o.oo 1 0.00 0.00 1 MIN -11.29 8.83 4 -893.86 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 32 MAX -12.59 0.00 7 -914.18 8.83 1 0.00 0.00 1 0.00 o:oo 1 0.00 0.00 1 MIN -19.97 8.83 4 -1140.'75 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 33 MAX -11.39 0.00 7 -871.80 8.83 1 0.00 0.00 1 0.00 0.00 "1 0.00 0.00 1 MIN -17.74 8.83 4 -1075.14 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 34 MAX 0.93 0.00 7 -618.40 8.83 1 o.oo 0.00 1 0.00 0.00 1 0.00 o.oo 1 89

PAGE 103

Appendix E Input/Output Files for Grillage Analyses by STAAD-III 90

PAGE 104

PAGE NO. 1 ************************************************** * s TAAD -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUL 4, 1994 * Time= 9:21: 0 * * ************************************************** 1. STAAD FLOOR AASHTO III, SPAN= 70 FT, SPACING S=lO FT (2LANES) 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. 1 0 0 0 5 4BO 0 0 6. R 12 0 0 70 B. MEMBER INCIDENCES 9. 1 1 6 5 10. R 11 5 5 12. 61 1 2 64 13. R 12 4 5 15. MEMBER PROPERTIES 16. 1 TO 60 PRISMATIC IX 2Bl45 IZ 417705 lB. 61 TO 64 PRISMATIC IX 27401 IZ 206B45 20. 65 TO B4 PRISMATIC IX 6591 IZ 3296 21. B5 TO BB PRISMATIC IX 6591 IZ 3296 22. B9 TO lOB PRISMATIC IX 6591 IZ 3296 24. 109 TO 112 PRISMATIC IX 27401 IZ 206B45 26. SUPPORTS 27. 1 TO 5 61 TO 65 PINNED 29. CONSTANTS 30. E 5250 ALL 31. PO ISS 0.20 ALL 33. UNITS FEET KIPS 35. DEFINE MOVING LOAD 36. TYPE 1 HS20 1.00 37. TYPE 2 HS20 1.00 3B. TYPE 3 HS20 0.00 40. LOAD GENERATION 7 41. TYPE 1 2 0 lB ZI 1 42. TYPE 2 12 0 lB ZI 1 43. TYPE 3 24 0 lB ZI 1 45. PERFORM ANALYSIS 91

PAGE 105

AASHTO III, SPAN= 70 FT, SPACING S=10 FT (2LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 4.85 0.00 4 -554.22 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -1.69 5.83 1 -606.04 5.83 6 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 27 MAX 7.94 0.00 4 -646.92 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -5.21 5.83 1 -728.27 5.83 4 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 28 MAX 4.33 o."oo 4 -438.65 5.83 i 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -2.30 5.83 1 -484.51 5.83 4 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 29 MAX 0.76 0.00 7 -146.56 0.00 1 0.00 0.00 1 o .-oo 0.00 1 0.00 0.00 1 MIN 0.53 5.83 1 -159.78 5.83 6 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 30 MAX -0.03 0.00 1 14.61 5.83 6 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.15 5.83 7 13.33 0.00 1 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 31 MAX -5.59 0.00 7 -492.02 .83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -12.15 5.83 4 -6Q5.86 0.00 6 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 32 MAX -8.49 0.00 7 -540.48 5. 83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -21.92 5.83 4 -728.80 0.00 4 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 33 MAX -5.02 0.00 7 -379.71 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -11.72 5.83 4 -484.54 0.00 4 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 34 MAX -0.90 0.00 4 -143.36 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 92

PAGE 106

************************************************** * s T A AD -III * Revision l9.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUL 4, 1994 * Time= 9:3B:53 * * ************************************************** PAGE NO. l l. STAAD FLOOR AASHTO III, SPAN= 70 FT, SPACING S=lO FT (3LANES) 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. l. 0 0. 0 5 4BO 0 0 6. R 12 0 0 70 B. MEMBER INCIDENCES 9. l l 6 5 lO. R ll 5 5 12. 61 l 2 64 13. R 12 4 5 15. MEMBER PROPERTIES 16. l TO 60 PRISMATIC lB. 61 TO 64 PRISMATIC 20. 65 TO B4 PRISMATIC 21. B5 TO BB PRISMATIC 22. B9 TO lOB PRISMATIC 24. 109 TO ll2 PRISMATIC 26. SUPPORTS IX 2Bl45 IX 27401 IX 6591 IX 6591 IX 6591 IX 27401 27. l TO 5 61 TO 65 PINNED 29. CONSTANTS 30. E 5250 ALL 31. POISS 0.20 ALL 33. UNITS FEET KIPS 35. DEFINE.MOVING LOAD 36. TYPE l HS20 O.B5 37. TYPE 2 HS20 O.B5 JB. TYPE 3 HS20 O.B5 40. LOAD GENERATION 7 41. TYPE l 2 0 lB ZI l 42. TYPE 2 12 0 lB ZI l 43. TYPE 3 24 0 lB ZI l 45. PERFORM ANALYSIS 93 IZ 417705 IZ 206B45 IZ 3296 IZ 3296 IZ 3296 IZ 206B45

PAGE 107

AASHTO III, SPAN= 70 FT, SPACING S=10 FT (3LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 4.09 0.00 4 -466.58 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -1.43 5. 83 1 -510.27 5.83 6 0.00 5.83 7 0.00 5.83 7 o.oo 5.83 7 27 MAX 7.10 0.00 4 -636.70 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -4.05 5.83 1 -709.36 5. 83 4 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 28 MAX 5.99 0.00 4 -612.29 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -3.47 5.83 1 -676.54 5.83 4 ci. oo 5.83 7 0.00 5.83 7 0.00 5.83 7 29 MAX 4.89 0.00 4 -422.56 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -9.06 5.83 1 -468.25 5.83 4 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 30 MAX 0.53 0.00 7 -128.36 0.00 1 0.00 0.00 1 0.00 0. 00 1 0.00 0.00 1 MIN 0.23 5.83 1 -137.86 5.83 7 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 31 MAX -4.63 0.00 7 -414.70 5.83 1 o.oo 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -10.19 5.83 4 -510.11 0.00 6 'o.oo 5.83 7 a. oo 5.83 7 0.00 5.83 7 32 MAX -7.72 0.00 7 -543.00 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -19.06 5.83 4 -709.65 0.00 4 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 33 MAX -7.18 0.00 7 -527.75 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -16.76 5.83 4 -676.62 0.00 4 0.00 5.83 7 0.00 5.83 7 0.00 5.83 7 34 MAX 1. 72 0.00 7 -362.37 5.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 94

PAGE 108

PAGE NO. 1 ************************************************** * S T A A D -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUN 30, 1994 * Time= 20:41:45 * * ************************************************** 1. STAAD FLOOR AASHTO III, SPAN= 90 FT, SPACING S=6'-8" (2LANES) 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. 1 0 0 0 7 480 0 0 6. R 12 0 0 90 8. MEMBER INCIDENCES 9. 1 1 8 7 10. R 11 7 7 12. 85 1 2 13. R 12 6 7 15. MEMBER PROPERTIES 16. 1 TO 84 PRISMATIC IX 22136 IZ 345144 18. 85 TO 90 PRISMATIC IX 26635 IZ 207059 20. 91 TO 120 PRISMATIC IX 5952 IZ 2976 21. 121 TO 126 PRISMATIC IX 5952 IZ 2976 22. 127 TO 156 PRISMATIC IX 5952 IZ 2976 24. 157 TO 162 PRISMATIC IX 26635 IZ 207059 26. SUPPORTS 27. 1 TO 7 85 TO 91 PINNED 29. CONSTANTS 30. E 5250 ALL 31. POISS 0.20 ALL 33. UNITS FEET KIPS 35. DEFINE MOVING LOAD 36. TYPE. 1 HS20 1.00 37. TYPE 2 HS20 1.00 38. TYPE 3 HS20 0.00 40. LOAD GENERATION 7 41. TYPE 1 2 0 28 ZI 1 42. TYPE 2 12 0 28 ZI 1 43. TYPE 3 24 0 28 ZI 1 45. PERFORM ANALYSIS 95

PAGE 109

AASHTO III, SPAN= 90 FT, SPACING S=6'-8" (2LANES} --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 36 MAX 3.78 0.00 3 -623.71 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -7.66 7.50 2 -657.42 7.50 6 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 37 MAX 6.43 0.00 1 -622.68 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -16.02 6.88 3 -677.91 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 38 MAX 6.28 0.00 1 -553.48 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -16.16 7.50 3 -608.85 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 39 MAX 3.47 0.00 1 -401.70 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -8.34 7.50 3 -434.05 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 40 MAX 0.90 0.00 7 -225.77 0.00 3 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.07 7.50 1 -236.07 7 .so 7 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 41 MAX 0.39 0.00 3 -87.63 0.00 3 0 .. 00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.33 7.50 5 -94.01 7.50 7 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 42 MAX -0.01 0.00 1 9,54 7.50 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.11 7.50 7 6. 72 0.00 7 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 43 MAX 0.79 0.00 5 -552.55 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -10.62 7.50 7 -658.66 1.88 6 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 44 MAX 6.06 0.00 5 -529.15 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 96

PAGE 110

************************************************** * S T A AD -III * Revision 19.0a * Program of * RESEARCH ENGINEERS, Inc. * Date= JUL 4, 1994 .. Time= 9:39:59 * * ************************************************** PAGE NO. 1 1. STAAD FLOOR AASHTO III, SPAN= 90 FT, SPACING S=6'-8" (3LANES) 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. 1 0 0 0 7 480 0 0 6. R 12 0 0 90 8. MEMBER INCIDENCES 9. 1 1 8 7 10. R 11 7 7 12. 85 1 2 90 13. R 12 6 7 15. MEMBER PROPERTIES 16. 1 TO 84 PRISMATIC 18. 85 TO 90 PRISMATIC 20. 91 TO 120 PRISMATIC 21. 121 TO 126 PRISMATIC 22 .. 127 TO 156 PRISMATIC 24. 157 TO 162 PRISMATIC 26. SUPPORTS IX 22136 IX 26635 IX 5952 IX 5952 IX 5952 IX 26635 27. 1 TO 7 85 TO 91 PINNED 29. CONSTANTS 30. E "5250 ALL 31. POISS 0.20 ALL 33. UNITS FEET KIPS 35. DEFINE MOVING LOAD 36. TYPE 1 HS20 0.85 37. TYPE 2 HS20 0.85 38. TYPE 3 HS20 0.85 40. LOAD GENERATION 7 41. TYPE 1 2 0 28 ZI 1 42. TYPE 2 12 0 28 ZI 1 43. TYPE 3 24 0 28 ZI 1 45. PERFORM ANALYSIS 97 IZ 345144 IZ 207059 IZ 2976 IZ 2976 IZ 2976 IZ 207059

PAGE 111

AASHTO III, SPAN= 90 FT, SPACING S=6'-8" (3LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 36 MAX 3.22 0.00 3 -532.86 0.00 3 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -6.49 7.50 2 -561.74 7.50 6 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 37 MAX 5.69 0.00 1 -585.29 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -13.36 7.50 3 -631.67 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 38 MAX 5.38 0.00 1 -596.86 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 o.oo 1 MIN -13.30 7.50 3 -644.33 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 39 MAX 4.40 0.00 1 -552.58 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -11.21 6.88 3 -596.07 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 40 MAX 4.77 0.00 1 -456.93 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -11.43 7.50 3 -499.89 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 41 MAX 2.22 0.00 1 -314.88 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -4.86 7.50 3 -333.34 7.50 5 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 42 MAX 0.63 0.00 3 -156.70 0.00 3 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.16 7.50 4 -169.46 7.50 7 0.00 7.50 7 0.00 7 .so 7 0.00 7.50 7 43 MAX 0.76 0.00 5 -473.41 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -8.96 7.50 7 -562.92 l. 88 6 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 44 MAX 4.92 0.00 5 -504.00 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 98

PAGE 112

PAGE NO. 1 ************************************************** * S T A AD -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUN 30, 1994 * Time= 20:41:23 * * ************************************************** 1. STAAD FLOOR AASHTO IV, SPAN= 90 FT, SPACING S=10 FT (2LANES) 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. 1 0 0 0 5 480 0 0 6. R 12 0 0 90 a. MEMBER INCIDENCES 9. 1 1 6 5 10. R 11 5 5 12. 61 1 2 64 13. R 12 4 5 15. MEMBER PROPERTIES 16. 1 TO 60 PRISMATIC IX 43565 IZ 729565 18. 61 TO 64 PRISMATIC IX 32361 IZ 344901 20. 65 TO 84 PRISMATIC IX 8475 IZ 4237 21. 85 TO 88 PRISMATIC IX 8475 IZ 4237 22. 89 TO 108 PRISMATIC IX 8475 IZ 4237 24. 109 TO 112 PRISMATIC IX 32361 IZ 344901 26. SUPPORTS 27. 1 TO 5 61 TO 65 PINNED 29. CONSTANTS 30. E 5250 ALL 31. PO ISS 0.20 ALL 33. UNITS FEET KIPS 35. DEFINE MOVING LOAD 36. TYPE 1 HS20 1. 00 37. TYPE 2 HS20 1. 00 38. TYPE 3 HS20 0.00 40. LOAD GENERATION 7 41. TYPE 1 2 0 28 ZI 1 42. TYPE 2 i2 0 28 ZI 1 43. TYPE 3 24 0 28 ZI 1 45. PERFORM ANALYSIS 99

PAGE 113

AASHTO IV, SPAN= 90-FT, SPACING S=10 FT (2LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 4.40 0.00 4 -800.52 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.88 7.50 1 -847.27 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 27 MAX 6.65 0.00 4 -878.16 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -3.52 7.50 1 -951.54 7.50 4 0. 00 7.50 7 0.00 7.50 7 0.00 7.50 7 28 MAX 3.72 0.00 4 -604.80 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -1.54 7.50 1 -646.31 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 29 MAX 0.94 0.00 7 -227.24 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.54 7.50 1 -239.48 7.50 7 0.00 7:50 7 0.00 7.50 7 0.00 7.50 7 30 MAX 0.07 0.00 1 3.32 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.08 7.50 7 2.53 0.00 7 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 31 MAX -7.79 0.00 7 -710.20 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -13.06 7.50 4 -847.01 0.00 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 32 MAX -12.03 0.00 7 -732.29 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -22.24 7.50 4 -952.09 0.00 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 33 MAX -6.93 0.00 7 -522.05 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -12.19 7.50 4 -646.35 0.00 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 34 MAX -1.17 0.00 7 -219.92 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 100

PAGE 114

1. 2. 4. 5. 6. 8. 9. 10. 12. 13. 15. 16. 18. 20. 21. 22. 24. 26. 27. 29. 30. 31. 33. .35. 36. 37. 38. 40. 41. 42. 43. 45. ************************************************** * s T A AD -III * Revision 19.0a * Proprietary Program of '* RESEARCH ENGINEERS, Inc. * Date= JUL 4, 1994 '* Time= 9:40:26 '* '* * '* ************************************************** PAGE NO. 1 STAAD FLOOR AASHTO IV, UNITS INCHES KIPS JOINT COORDINATES SPAN= 90 FT, SPACING S=10 FT (3LANES) 1 0 0 5 480 0 0 R 12 0 0 90 MEMBER INCIDENCES 1 1 6 5 R 11 5 5 61 1 2 64 R 12 4 5 MEMBER PROPERTIES 1 TO 60 PRISMATIC 61 TO 64 PRISMATIC 65 TO 84 PRISMATIC 85 TO 88 PRISMATIC 89 TO 108 PRISMATIC 109 TO 112 PRISMATIC SUPPORTS 1 TO 5 61 TO 65 CONSTANTS E .5250 ALL POISS 0.20 ALL UNITS FEET KIPS DEFINE MOVING LOAD TYPE 1 HS20 0.85 TYPE 2 HS20 0.85 TYPE 3 HS20 0.85 LOAD GENERATION 7 TYPE 1 2 0 28 TYPE 2 12 0 28 TYPE 3 24 0 28 PERFORM ANALYSIS IX 43565 IX 32361 IX 8475 IX 8475 IX 8475 IX 32361 PINNED ZI 1 ZI 1 ZI 1 101 IZ 729565 IZ 344901 IZ 4237 IZ 4237 IZ 4237 IZ 344901

PAGE 115

AASHTO IV, SPAN= 90 FT, SPACING S=10 FT (3LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 3.78 0.00 4 -686.11 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.67 7.50 1 -725.95 7.50 4 0.00 7.50 7 0.00 7.50 7 o.oo 7.50 7 27 MAX 6.05 0.00 4 -878.08 7.50 1 0.00 .0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -2.65 7.50 1 -943.74 7.50 4 0.00 7 .so. 7 0.00 7.50 7 0.00 7.50 7 28 MAX 5.10 0.00 4 -835.57 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -2.39 7.50 1 -892.87 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 29 MAX 4.21 0.00 4 -586.55 7.50 1 0.00 0 1 0.00 0.00 1 0.00 0.00 1 MIN -9.63 7.50 1 -632.53 7.50 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 30 MAX 0.79 0.00 7 -213.69 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.37 7.50 1 -224.56 7.50 7 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 '31 MAX -6.55 0.00 7 -610.42 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -:10.99 7.50 4 -725.70 0.00 4 o:oo 7.50 7 0.00 7.50 7 o.oo 7.50 7 32 MAX -10.85 0.00 7 -748.10 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -19.57 7.50 4 0.00 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 33 MAX -9.89 0.00 7 -717.38 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -17.37 7.50 4 -892.99 0.00 4 0.00 7.50 7 0.00 7.50 7 0.00 7.50 7 34 MAX 1.21 0.00 7 -503.44 7.50 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 102

PAGE 116

1. 2. 4. 5. 6. 8. 9. 10. 12. 13. 15. 16. 18. 20. 21. 22. 24. 26. 27. 29. 30. 31. 33. 35. 36. 37. 38. 40. 41. 42. 43. 45. ************************************************** * s T A AD -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUN 30, 1994 * Time= 20:40: 3 * * ************************************************** STAAD FLOOR AASHTO IV, SPAN= 110 FT, SPACING S=6'-8" UNITS INCHES KIPS JOINT COORDINATES 1 0 0 0 7 480 0 0 R 12 0 0 110 MEMBER INCIDENCES 1 1 8 7 R 11 7 7 85 1 2 90 R 12 6 7 MEMBER PROPERTIES 1 TO 84 PRISMATIC IX 35556 IZ 600488 85 TO 90 PRISMATIC IX 31314 IZ 342731 91 TO 120 PRISMATIC IX 7275 IZ 3637 121 TO 126 PRISMATIC IX 7275 IZ 3637 127 TO 156 PRISMATIC IX 7275 IZ 3637 157 TO 162 PRISMATIC IX 31314 IZ 342731 SUPPORTS 1 TO 7 85 TO 91 PINNED CONSTANTS E 5250 ALL PO ISS 0.20 ALL UNITS FEET KIPS DEFINE MOVING LOAD TYPE 1 HS20 1. 00 TYPE 2 HS20 1. 00 TYPE 3 HS20 0.00 LOAD GENERATION 7 TYPE 1 2 0 38 ZI 1 TYPE 2 12 0 38 ZI 1 TYPE 3 24 0 38 ZI 1 PERFORM ANALYSIS 103 PAGE NO. 1 (2LANES)

PAGE 117

AASHTO IV, SPAN= 110 FT, SPACING S=6'-8" (2LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 36 MAX 3.33 0.00 1 -799.45 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -8.03 9.17 3 -834.65 9.17 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 37 MAX 5.60 0.00 1 -789.93 9.17 1 0.00 0.00 1 0.00 0.00 1 0.00 o.oo 1 MIN -16.33 9.17 3 -844.60 9.17 4 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 38 MAX 5.45 0.00 1 -699.11 9.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -16.53 9.17 3 -754.34 9.17 4 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 39 MAX 3.04 0.00 1 -510.94 9.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -8.65 9.17 3 -543.73 9.17 4 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 40 MAX 1. OS 0.00 7 -293.93 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.19 9.17 1 -305.43 9.17 7 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 41 MAX 0.43 .00 7 -125.29 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.36 9.17 1 -132.29 9.17 7 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 42 MAX 0.06 0.00 1 -4.10 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.04 9.17 7 -7.04 0.00 7 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 43 MAX 0.51 0.00 5 -707.87 9.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -10.90 9.17 7 -834.88 0.76 5 0.00 9".17 7 0.00 9.17 7 0.00 9.17 7 44 MAX 5.88 0.00 5 -671.27 9.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 104

PAGE 118

PAGE NO. 1 ************************************************** * S T A AD -III * Revision l9.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUL 4, 1994 * Time= 9:40:53 * * ************************************************** l. STAAD FLOOR AASHTO IV, SPAN= 110 FT, SPACING S=6'-8 {3LANES) 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. 1 0 0 0 7 480 0 0 6. R 12 0 0 110 8. MEMBER INCIDENCES 9. l 1 8 7 10. R 11 7 7 12. 85 l 2 90 13. R 12 6 7 15. MEMBER PROPERTIES 16. 1 TO 84 PRISMATIC IX 35556 IZ 600488 lB. 85 TO 90 PRISMATIC IX 31314 IZ 342731 20. 91 TO 120 PRISMATIC IX 7275 IZ 3637 21. 121 TO 126 PRISMATIC IX 7275 IZ 3637 22. 127 TO 156 PRISMATIC IX 7275 IZ 3637 24. 157 TO 162 PRISMATIC IX 31314 IZ 342731 26. SUPPORTS 27. 1 TO 7 85 TO 91 PINNED 29. CONSTANTS 30. E 5250 ALL 31. PO ISS 0.20 ALL 33. UNITS FEET KIPS 35. DEFINE MOVING LOAD 36. TYPE 1 HS20 0.85 37. TYPE 2 HS20 o.a5 38. TYPE 3 HS20 0.85 40. LOAD GENERATION 7 41. TYPE 1 2 0 38 ZI l 42. TYPE 2 12 0 38 ZI 1 43. TYPE 3 24 0 38 ZI l 45. PERFORM ANALYSIS 105

PAGE 119

AASHTO IV, SPAN= 110 FT, SPACING S=6'-8" (3LANES) -PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 36 MAX 2.91 0.00 1 -691.06 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -6.77 8.40 3 -723.35 9.17 5 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 37 MAX 4.98 0.00 1 -749.25 9.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -13.65 9.17 3 -794.89 9.17 4 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 38 MAX 4.72 0.00 1 -755.86 9.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -13.77 9.17 3 -803.25 9.17 4 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 39 MAX 3.88 0.00 1 -697.69 9.17 1 0.00 0.00 1 o.oo 0.00 1 0.00 0.00 1 MIN -11.61 8.40 3 -741.92 9.17 4 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 40 MAX 4.14 0.00 1 -581.65 9.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -11.67 9.17 3 -624.77 9.17 4 0.00 9.17 7 0.00 9.17. 7 0.00 9.17 7 41 MAX 2.03 0.00 1 -410.85 9.17 1 0.00 0. 00 1 0.00 0.00 1 0.00 0.00 1 MIN -4.99 9.17 3 -429.54 9.17 5 0.00 9.17 7 0.00 9.17 7 0.00 9.17 7 42 MAX 0.74 0.00 7 -223.52 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.33 9.17 4 -238.27 9.17 7 0.00 . 9.17 7 0.00 9.17 7 0.00 9.17 7 43 MAX 0.47 0.00 5 -616.03 9.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -9.25 9.17 7 -723.56 0.76 5 0.00 9.17 7. 0.00 9.17 7 0.00 9.17 7 44 MAX 4.72 0.00 5 -645.51 9.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 106

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1. 2. 4. 5. 6. B. 9. 10. 12. 13. 15. 16. 18. 20. 21. 22. 24. 26. 27. 29. 30. 31. 33. 35. 36. 37. 38. 40. 41. 42. 43. 45. ************************************************** s TAAD -III Revision 19.0a Proprietary Program of RESEARCH ENGINEERS, Inc Date= JUN 30, 1994 Time= 20:42:40 ************************************************** PAGE NO. 1 STAAD FLOOR AASHTO v, SPAN= 106 FT, SPACING S=10 FT (2LANES) UNITS INCHES KIPS JOINT COORDINATES 1 0 0 0 5 480 0 0 R 12 0 0 106 MEMBER INCIDENCES 1 1 6 5 R 11 5 61 1 2 64 R 12 4 5 MEMBER PROPERTIES 1 TO 60 PRISMATIC IX 44671 IZ 1105722 61 TO 64 PRISMATIC IX 37131 IZ 528096 65 TO 84 PRISMATIC IX 9981 IZ 4991 85 .. TO 88 PRISMATIC IX 9981 IZ 4991 89 TO 108 PRISMATIC IX 9981 IZ 4991 109 TO 112 PRISMATIC IX 37131 IZ 528096 SUPPORTS 1 TO 5 61 TO 65 PINNED CONSTANTS E 5250 ALL PO ISS 0.20 ALL UNITS FEET KIPS DEFINE MOVING LOAD TYPE 1 HS20 1. 00 TYPE 2 HS20 1. 00 TYPE 3 HS20 0.00 LOAD GENERATION 7 TYPE 1 2 0 36 ZI 1 TYPE 2 12 0 36 ZI 1 TYPE 3 24 0 36 ZI 1 PERFORM ANALYSIS 107

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AASHTO V, SPAN= 106 FT, SPACING S=10 FT (2LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL-SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 4.20 0.00 4 -995.88 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.33 8.83 1 -1041.47 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 27 MAX 5.96 0.00 4 -1067.42 8.83 1 0.00 .0 .00 1 0.00 0.00 1 0.00 0.00 1 MIN -2.59 8.83 1 -1143.42 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 28 MAX 3.42 0.00 4 -738.70 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -1.07 8.83 1 -780.39 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 29 MAX 1. 04 0.00 7 -286.78 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.57 8.83 1 -299.07 8.83 7 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 30 MAX 0.09 0.00 1 6.63 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.10 8.83 7 5.48 0.00 7 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 31 MAX -8.93 0.00 7 -884.30 8.83 1 0.00 0.00 1 0.00 0.00 1 o:oo 0.00 1 MIN -13.43 8.83 4 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 32 MAX -14.02 0.00 7 -889.59 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -22.64 8.83 4 -1143.94 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 33 MAX -7.99 0.00 7 -637.09 8.83 1 0.00 0. 00. 1 0.00 0.00 1 0.00 0.00 1 MIN -12.47 8.83 4 -780.44 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 34 MAX -1.27 0.00 7 -276.93 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 108

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PAGE NO. 1 ************************************************** * s T A AD -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUL 4, 1994 * Time= 9:41:24 * * ************************************************** 1. STAAD FLOOR AASHTO V, SPAN= 106 FT, SPACING S=lO FT (3LANES) 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. 1 0 0 0 5 480 0 0 6. R 12 0 0 106 8. MEMBER INCIDENCES 9. 1 1 6 5 10. R 11 5 5 12. 61 1 2 64 13. R 12 4 5 15. MEMBER PROPERTIES 16. 1 TO 60 PRISMATIC IX 44671 IZ 1105722 18. 61 TO 64 PRISMATIC IX 37131 IZ 528096 20. 65 TO 84 PRISMATIC IX 9981 IZ 4991 21. 85 TO 88 PRISMATIC IX 9981 IZ 4991 22. 89 TO lOB PRISMATIC IX 9981 IZ 4991 24. 109 TO 112 PRISMATIC IX 37131 IZ 528096 26. SUPPORTS 27. 1 TO 5 61 TO 65 PINNED 29. CONSTANTS 30. E 5250 ALL 31. POISS 0.20 1i.LL 33. UNITS FEET KIPS 35. DEFINE MOVING LOAD 36. TYPE 1 HS20 0.85 37. TYPE 2 HS20 0.85 38. TYPE 3 HS20 0.85 40. LOAD GENERATION 7. 41. TYPE 1 2 0 36 ZI 1 42. TYPE 2 12 0 36 ZI 1 43. TYPE 3 24. 0 36 ZI 1 45. PERFORM ANALYSIS 109

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AASHTO V, SPAN= 106 FT, SPACING S=10 FT (3LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 3.62 0.00 4 -855.30 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.17 8.83 1 -894.06 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 27 MAX 5.49 0.00 4 -1073.34 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -1.85 8.83 1 -1140.47 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 28 MAX 4.70 0.00 4 -1016.91 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -1.71 8.83 1 -1075.63 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 29 MAX 3.78 0.00 4 -720.09 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -9.97 8.83 1 -764.61 8.83 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 30 MAX 0.90 0.00 7 -267.33 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.48 8.83 1 -279.45 8.83 7 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 31 MAX -7.52 0.00 7 -761.90 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -11.29 .. 8.83 4 -893.82 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 32 MAX -12.59 0.00 7 -914.23 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -19.97 8.83 4 -1140.75 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 33 MAX -11.42 0.00 7 -871.95 8.83 1 0.00 0.00 1 o;oo 0.00 1 0.00 0.00 1 MIN -17.79 8.83 4 -1075.75 0.00 4 0.00 8.83 7 0.00 8.83 7 0.00 8.83 7 34 MAX 0.95 0.00 7 -618.25 8.83 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 110

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1. 2. 4. 5. 6. 8. 9. 10. 12. 13. 15. 16. 18. 20. 21. 22. 24. 26. 27. 29. 30. 31. 33. 35. 36. 37. 38. 40. 41. 42. 43. 45. ************************************************** * S T A AD -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUN 30, 1994 * Time= 20:47:35 * * ************************************************** STAAD FLOOR AASHTO V, SPAN= 128 FT, SPACING S=6'-8" UNITS INCHES KIPS JOINT COORDINATES 1 0 0 0 7 480 0 0 R 12 0 0 128 MEMBER INCIDENCES 1 1 8 7 R 11 7 7 85 1 2 90 R 12 6 7 MEMBER PROPERTIES 1 TO 84 PRISMATIC IX 38662 IZ 932643 85 TO. 90 PRISMATIC IX 35927 IZ 525431 91 TO 120 PRISMATIC IX 8465 IZ 4233 121 TO 126 PRISMATIC IX 8465 IZ 4233 127 TO i56 PRISMATIC IX 8465 IZ 4233 157 To 162 PRISMATIC IX 35927 IZ 525431 SUPPORTS 1 TO 7 85 TO 91 PINNED CONSTANTS E 5250 ALL POISS. 0.20 ALL UNITS FEET KIPS DEFINE MOVING LOAD TYPE 1 HS20 .00 TYPE 2 HS20 1. 00 TYPE 3 HS20 0.00 LOAD GENERATION 7 TYPE 1 2 0 47 ZI 1 TYPE 2 12 047 ZI 1 TYPE 3 24 0 47 ZI 1 PERFORM ANALYSIS Ill PAGE NO. 1 (2LANES)

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AASHTO V, SPAN= 128 FT, SPACING S=6'-8" (2LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 36 MAX 3. 2.3 0.00 1 -962.75 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -8.09 10.67 3 -1002.92 10.67 5 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 37 MAX 5.02 0.00 1 -949.23 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -16.77 10.67 3 -1004.72 10.67 4 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 38 MAX 4.84 0.00 1 -837.11 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -17.01 10.67 3 -893.49 10.67 4 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 39 MAX 2.77 0.00 1 -612.05 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -8.65 10.67 3 -645.33 10.67 4 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 40 MAX 1.13 0.00 7 -351.87 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.35 10.67 1 -364.48 10.67 7 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 41 MAX 0.44 0.00 7 -149.65 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.37 10.67 1 -157.43 10.67 7 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 42 MAX 0.05 0.00 1 0.37 10.67 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.05 10.67 7 -3.15 0.00 7 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 43 MAX 0.25 0.00 5 -857.16 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -11.10 10.67 7 -1003.00 0.89 5 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 44 MAX 5.77 0.00 5 -8Q7.11 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 112

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1. 2. 4. 5. 6. 8. 9. 10. 12. 13. 15. 16. 18. 20. 21. 22. 24. 26. 27. 29. 30. 31. 33. 35. 36. 37. 38. 40. 41. 42. 43. 45. * s T A AD -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUL 4, 1994 * Time= 9:41:46 * * ************************************************* STAAD FLOOR AASHTO V, SPAN= 128 FT, SPACING S=6'-8" UNITS INCHES KIPS JOINT COORDINATES 1 0 0 0 7 480 0 0 R 12 0 0 128 MEMBER INCIDENCES 1 1 8 7 R 11 7 7 85 1 -2 90 R 12 6 7 MEMBER PROPERTIES 1 TO 84 PRISMATIC IX 38662 IZ 932643 85 TO 90 PRISMATIC IX. 35927 IZ 525431 91 TO 120 PRISMATIC. IX 8465 IZ 4233 121 TO 126 PRISMATIC IX 8465 IZ 4233 127 TO 156 .PRISMATIC IX 8465 IZ 4233 157 "TO 162 PRISMATIC. IX 35927 IZ 525431 SUPPORTS 1 TO 7 85 TO 91 PINNED E 5250 ALL PO ISS 0.20 ALL UNITS FEET KIPS DEFINE MOVING LOAD TYPE 1 HS20 0. 85. TYPE 2 HS20 0.05 TYPE 3 HS20 0.85 LOAD GENERATION 7 TYPE 1 2 0 47 ZI 1 TYPE 2 12 0 47 ZI 1 TYPE. 3. 24 0 47 ZI 1 PERFORM ANALYSIS 113 PAGE NO. 1 (3LANES)

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AASHTO V, SPAN= 128 FT, SPACING S=6'-8" (3LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 36 MAX 2.83 0.00 1 -831.85 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -6.81 10.67 3 -868.75 10.67 5 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 37 MAX 4.50 0.00 1 -901.22 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -14.02 9.78 3 -947.26 10.67 4 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 38 MAX 4.28 0.00 1 -905.67 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -14.10 10.67 3 -953.86 10.67 4 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 39 MAX 3.57 0.00 1 -834.69 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -11.84 9.78 3 -879.88 10.67 4 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 40 MAX 3.69 0.00 1 -696.24 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -12.01 10.67 3 -740.22 10.67 4 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 41 MAX 1. 90 0.00 1 -492.66 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -5.08 10.67 3 -511.29 10.67 5 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 42 MAX 0.80 0.00 7 -266.47 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.40 10.67 4 -283.21 10.67 7 0;00 10.67 7 0.00 10.67 7 0.00 10.67 7 43 MAX 0.26 0.00 5 -745.54 10.67 1 o. oo 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -9.41 10.67 7 -868.84 0.89 5 0.00 10.67 7 0.00 10.67 7 0.00 10.67 7 44 MAX 4.62 0.00 5 -776.92 10.67 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 114

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************************************************** * S T A AD -III * Revision 19.0a * Proprietary. Program of * RESEARCH ENGINEERS, Inc. * Date= JUN 30, 1994 * Time= 20:38:59 * * ************************************************** PAGE NO. 1 1. STAAD FLOOR AASHTO VI, SPAN= 122 FT, SPACING S=10 FT (2LANES) 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. 1 0 0 0 5 480 0 0 6. R 12 0 0 122 8. MEMBER INCIDENCES 9. 1 1 6 5 10. R 11 5 5 12. 61 1 2 64 13. R 12 4 5 15. MEMBER PROPERTIES 16. 1 TO 60 PRISMATIC 18. 61 TO PRISMATIC 20. 65 TO .84 PRISMATIC 21. 85 TO 88 PRISMATIC 22. 89 TO 108 PRISMATIC 24. 109 TO 112 PRISMATIC 26. SUPPORTS IX 46207 IX 41902 IX 11488 IX 11488 IX 11488 IX 41902 27. 1 TO 5 61 TO 65 PINNED 29. CONSTANTS 30. E 5250 ALL 31. POISS 0.20 ALL 33. UNITS FEET KIPS 35. DEFINE MOVING LOAD 36. TYPE 1 HS20 .1. 00. 37. TYPE 2 HS20 1.00 38. TYPE 3 HS20 0.00 40. LOAD GENERATION 7 41. TYPE 1 2 0 44 ZI 1 42. TYPE 2 12 0 44 ZI 1 43. TYPE 3 24 0 44 ZI 1 45. PERFORMANALYSIS 115 IZ 1499513 IZ 767123 IZ 5744 IZ 5744 IZ 5744 IZ 767123

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AASHTO VI, SPAN= 122 FT, SPACING S=10 FT (2LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 4.65 0.00 1 -1222.11 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -11.63 10.17 3 -1279.84 10.17 5 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 27 MAX 7.79 0.00 1 -1201.96 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -25.97 10.17 3 -1301.74 10.17 4 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 28 MAX 4.00 0 0 00 1 -845.89 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -12.56 10.17 3 -897.15 10.17 4 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 29 MAX 1.19 0.00 7 -361.73 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.47 10.17 1 -379.00 10.17 7 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 30 MAX 0.13 0.00 1 -6.38 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.04 10.17 7 -14.59 0.00 7 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 31 MAX 1.08 0.00 5 -1089.62 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -15.27 10.17 7 -12,80 0 61 0.85 5 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 32 MAX 9.97 0.00 5 -1007.41 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -23.68 10.17 7 -1302.18 0.00 4 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 33 MAX 3.17 0.00 5 -727.34 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -13.40 10.17 7 -897.22 0.00 4 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 34 MAX -1.84 0.00 4 -344.64 10.17 1 0.00 o.oo 1 0.00 0.00 1 0.00 0.00 1 116

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1. 2. 4. 5. 6. B. 9. 10. 12. 13. 15. 16. lB. 20. 21. 22. 24. 26. 27. 29. 30. 31. 33. 35. 36. 37. 3B. 40. 41. 42. 43. 45. ************************************************** * S T A AD -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUL 4, 1994 * Time= 9:42:21 * * ************************************************** STAAD FLOOR AASHTO VI, SPAN= 122 FT, SPACING S=lO FT UNITS INCHES KIPS JOINT COORDINATES 1 0 0 0 5 4BO 0 0 R 12 0 0 122 MEMBER INCIDENCES 1 1 6 5 R 11 5 5 61 1 2 64 R 12 4 5 MEMBER PROPERTIES 1 TO 60 PRISMATIC IX 46207 IZ 1499513 6:!. TO 64 PRISMATIC IX 41902 IZ 767123 65 TO B4 PRISMATIC IX 114BB IZ 5744 85 TO 88 PRISMATIC IX 11488 IZ 5744. 89 TO lOB PRISMATIC 11488 IZ 5744 109 TO 112 PRISMATIC IX 41902 IZ 767123 SUPPORTS 1 TO 5 61 TO 65 PINNED CONSTANTS E 5250 ALL PO ISS 0.20 ALL UNITS FEET KIPS DEFINE MOVING LOAD TYPE 1 HS20 O.B5 TYPE 2 HS20 0.35 TYPE 3 HS20 O.B5 LOAD GENERATION 7 TYPE 1 2 0 44 ZI 1 TYPE 2 12 0 44 ZI 1 TYPE 3 24 0 44 ZI 1 PERFORM ANALYSIS 117 PAGE NO. 1 (3LANES)

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AASHTO VI, SPAN= 122 FT, SPACING S=10 FT (3LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 26 MAX 4.09 0.00 1 -1059.63 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -9.79 9.32 3 -1113.37 10.17 5 0.00 10.17 7 0.00 10.17 7 o.oo 10.17 7 27 MAX 6.90 0.00 1 -1228.58 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -21.63 10.17 3 -1312.31 10.17 4 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 28 MAX 5.31 0.00 1 -1151.45 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -17.14 9.32 3 -1228.85 10.17 4 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 29 MAX 4.89 0.00 1 -850.37 10.17 1 0.00 0.00 1 0.00 o.oo 1 0.00 0.00 1 MIN -15.13 10 .. 17 3 -892.84 10.17 4 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 30 MAX 1.12 0.00 7 -352.81 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.56 10.17 1 -377.75 10.17 7 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 31 MAX 0.99 0.00 5 -952.66 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -12.94 10.17 7 -1114. OS 0.85 5 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 32 MAX 7.31 0.00 5 -1049.56 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -21.16 10.17 7 -1312.55 0.00 4 0.00 .17 7 0.00 10.17 .7 0.00 10.17 7 33 MAX 4.04 0.00 5 -987.01 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -18.42 10.17 7 -1228.96 0.00 4 0.00 10.17 7 0.00 10.17 7 0.00 10.17 7 34 MAX 5.32 0.00 5 -727.46 10.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 118

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PAGE NO. 1 ************************************************** * s T A AD -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS, Inc. * Date= JUN 30, 1994 * Time= 20:45:39 * * ************************************************** 1. STAAD FLOOR AASHTO VI, SPAN= 146 FT, SPACING S=6'-8" (2LANES) 2. UNITS INCHES KIPS 4. JOINT COORDINATES 5. 1 0 0 0 7 480 0 0 6. R 12 0 0 146 8. MEMBER INCIDENCES 9. 1 1 8 7 10. R 11 7 7 12. 85 1 2 90 13. R 12 6 7 15. MEMBER PROPERTIES 16. 1 TO 84 PRISMATIC IX 40198 IZ 1270294 18. 85 TO 90 PRISMATIC IX 40540 IZ 763920 20. 91 TO 120 PRISMATIC IX 9656 IZ 4828 21. 121 TO 126 PRISMATIC IX 9656 IZ 4828 22. 127 TO 156 PRISMATIC IX 9656 IZ 4828 24. 157 TO 162 PRISMATIC IX 40540 IZ 763920 26. SUPPORTS 27. 1 TO 7 85 TO 91 PINNED 29. CONSTANTS 30. E 5250 ALL 31. PO ISS 0.20 ALL 33. UNITS FEET KIPS 35. DEFINE MOVING LOAD 36. TYPE 1 HS20 1.00 37. TYPE 2 HS20 1. 00 38. TYPE 3 HS20 0.00 40. LOAD GENERATION 7 41. TYPE 1 2 0 56 ZI 1 42. TYPE 2 12 0 56 ZI 1 43. TYPE 3 24 0 56 ZI 1 45. PERFORM ANALYSIS 119

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AASHTO VI, SPAN= 146FT, SPACING S=6'-8" (2LANES) -PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 36 MAX 14.00 0.00 6 -1123.73 0.00 7 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -8.12 12.17 3 -1172.55 12.17 5 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 37 MAX 23.30 0.00 6 -1094.90 0.00 7 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -17.11 12.17 3 -1160.83. 12.17 4 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 38 MAX 22.96 0.00 6 -962.16 0.00 7 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -17.38 12.17 3 -1026.75 12.17 4 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 39 MAX 12.85 0.00 6 -703.67. 0.00 7 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -9.01 12.17 3 -744.27 12.17 4 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 40 MAX 1.22 0.00 7 -410.73 0.00 7 0.00 0.00 1 0.00 0.00 1 0. 0,0 0.00 1 MIN 0.48 12.17 1 -425.63 12.17 6 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 41 MAX 0.46 0.00 7 -178.33 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.38 12.17 1 -186.90 12.17 7 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 42 MAX 0.05 0.00 1 0.49 12.17 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -0.06 12.17 7 -3.50 0.00 7 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 43 MAX 0.04 0.00 5 -1004.66 12.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -13.63 12.17 2 -1172.42 0.00 5 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 44 MAX 5.71 0.00 5 -933.10 12.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 120

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1. 2. 4. 5. 6. 8. 9. 10. 12. 13. 15. 16. 18. 20. 21. 22. 24. 26. 27. 29. 30. 31. 33. 35. 36. 37. 38. 40. 41. 42. 43. 45. ************************************************** * s T A AD -III * Revision 19.0a * Proprietary Program of * RESEARCH ENGINEERS I Inc. * Date= JUL 4, 1994 * Time= 9:42:52 * * ************************************************** STAAD FLOOR AASHTO VI, UNITS INCHES KIPS JOINT COORDINATES 1 0 0 0 7 480 0 0 R 12 0 0 146 MEMBER INCIDENCES 1 1 8 7 R 11 7 7 85 1 2 90 R 12 6 7 MEMBER PROPERTIES 1 TO 84 PRISMATIC 85 TO 90 PRISMATIC 91 TO 120 PRISMATIC 121 TO 126 PRISMATIC 127 TO 156 PRISMATIC 157 TO 162 PRISMATIC SUPPORTS 1 TO 7 85 TO 91 CONSTANTS E 5250 ALL POISS 0.20 ALL UNITS FEET KIPS DEFINE MOVING LOAD TYPE 1 HS20 0.85 TYPE 2 HS20 o.ss TYPE 3 HS20 0.85 LOAD GENERATION 7 TYPE 1 2 0 56 TYPE 12 0 56 TYPE 3 24 0 56 PERFORM ANALYSIS SPAN= 146 FT, SPACING S=6'-8" IX 40198 IX 40540 IX 9656 IX 9656 IX 9656 IX 40540 PINNED ZI 1 ZI 1 ZI 1 121 IZ 1270294 IZ 763920 IZ 4828 IZ 4828 IZ 4828 IZ 763920 PAGE NO. 1 (3LANES)

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AASHTO VI, SPAN= 146 FT, SPACING S=6'-8" (3LANES) --PAGE NO. 3 MEMBER FORCE ENVELOPE ---------------------ALL UNITS ARE KIPS FEET MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS MEMB FY/ DIST LD MZ/ DIST LD FZ DIST LD MY DIST LD FX DIST LD 36 MAX 11.94 0.00 6 -977.09 0.00 7 0.00 0.00 1 0.00 0.00 1 o.oo 0.00 1 MIN -6.84 12.17 3 -1018.91 12.17 5 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 37 MAX 20.08 0.00 6 -1041.78 0.00 7 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -14.29 12.17 3 -1098.56 12.17 4 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 38 MAX 20.11 0.00 6 -1040.69 0.00 7 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -14.36 12.17 3 -1099.36 12.17 4 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 39 MAX 17.24 0.00 6 -956.78 0.00 7 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -12.03 12.17 3 -1011.97 12.17 4 0.00 12.17 7. 0.00 12.17 7 0.00 12.17 7 40 MAX 16.77 0.00 6 -800.46 0.00 7 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -12.28 12.17 3 -852.40 12.17 4 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 41 MAX 8.19 0.00 6 -569.72 0.00 7 0. 00. 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -5.14 12.17 3 -595.08 12.17 5 0.00 12.17 7 0.00 12.17 7 0 .'00 12.17 7 42 MAX 0.86 0.00 7 -317.34 0.00 4 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN 0.46 12.17 4 -335.99 12.17 7 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 43 MAX 0.08 0.00 5 -877.01 12.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 MIN -11.51 12.17 2 -1018.78 0.00 5 0.00 12.17 7 0.00 12.17 7 0.00 12.17 7 44 MAX 4.55 0.00 5 -902.10 12.17 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 122

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Appendix F Concise Input/Output Files for The Designs of Prestressed Girders Using Three Different Methods: AASHTO Simplified, Grillage and LRFD's 123

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>>>REFINED METHOD(18% RED.);LRFD's HEAVIER LOADING gus6Z122: TYPE VI, L = 122 ft; S = 10 ft SHEET OF NUBRIDGE, V1.00, (C) 1992 JACQUES & ASWAD, INC. DATE: 06/29/94 PAGE: 1 BY: G.A DESIGN DATA: AASHTO VI,SPAN L = 122 ft, SPACING s = 10 ft SPAN 122.00 FT. YB 36.38 IN. YT 35.62 IN. A c 1085.00 IN-2 I 733320 IN-4 CIP B 120.00 IN. H 72.00 IN. 58 = 20157.0 IN-3 CIP T = 9.00 IN. AC 1921.56 IN-2 IC 1499271 IN-4 HC 81.00 IN. STC c 82589.5 IN-3 SBC= 27843.3 IN-3 YBC 53.85 IN. STRAND: TYPE = LOW RELAXATION PULL = 0.730 NUMBER= 67.00 AREA/STR. = 0.1530 IN-2 TOTAL AREA >=10.251 IN-2 PROFILE: X STRAND C.G. DESCRIPTION 0.00 26.000 HOLDOOWN 0.00 IN. TO e.G. OF STRAND 51.00 6.700 HOLD DOWN 6.70 IN. TO e.G. OF STRAND 71.00 6.700 HOLD DOWN 6.70 IN. TO e.G. OF STRAND 122.00 26.000 HOLDDOWN 0.00 IN. TO e.G. OF STRAND LOADS: BEAM WT = 1.130 KLF BARRIER WT = 0.200 KLF PEDESTRIAN 0.000 KLF CIP DECK= 1.125 KLF WEAR-SURFACE= 0.250 KLF DIAPH.WT = 0.000 KIPS AT 1/0 POINTS ALONG GIRDER LIVE LOAD = TANDEM AXLES = 25.00 KIPS + LANE LOAD 0.640 KLF -OR --NCHRP 12-33 DESIGN TRUCK + LANE LOAD = 0.640 KLF AND OTHER FACTORS: LOAD, RESISTANCE PHI: FLEXURE LOAD: DEAD OTHER: DYNAMIC = 1.000 SHEAR = 0.900 = 1.250 WEAR SURFACE= 1.500 LIVE 1.750 ALL. (TRUCK ONLY) = 33.00% MULTI-LANE (OR OTHER) DISTRIBUTION FACTORS: INPUTTED FLEXURAL D.F.= 0.745 SHEAR D.F.= 1.000 INITIAL STRESSES: REQD F'CI 5.173 KSI AT X= 51.00 FT. PRESTRESS LOSSES: TOTAL LOSSES = 53.403 KSI BY NCHRP 12-33 SPECS FINAL STRESSES: (NEGATIVE NUMBERS INDICATE TENSION) FP + ALL DL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION FP + ALL DL + LL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION 2.082 KSI 1. 796 KSI 0.000 KSI 2.015 KSI 2.120 KSI = -0.268 KSI 4.711 KSI 3.090 KSI REQD. F'C= 2.120/0.45 MAXIMUM LL STRAND STRESS = <<< <<< AT X = 61.00 FT. AT X = 61.00 FT. 1.000 ULTIMATE MOMENT AT -SECTION W/ LEAST RESERVE CAPACITY: AT X = 61.00 FT. PROV. MOMENT = 197300 K-IN REQD. MOMENT = 135454 K-IN DEFLECTIONS: (NEGATIVE VALUES INDICATE CAMBER) APPROX. CAMBER AT ERECTION -3.761 IN. BASED ON -2.140 IN. RELEASE CAMBER SPAN/MOVING LL DEFLECTION = 2448 (BASED ON MOMENT DISTRIBUTION FACTOR) 124

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>>>REFINED METHOD(18t RED.); LRFD's HEAVIER LOADING gus6Z146: TYPE VI, L = 146 ft; S = 6ft-Bin. NUBRIDGE, V1.00, (C) 1992 JACQUES ASWAD, INC. SHEET OF DATE: 06/29/94 PAGE: 1 BY: G.A DESIGN SPAN A H AC STC DATA: AASHTO VI,SPAN L 146.00 FT. YB = 1085.00 IN-2 I 72.00 IN. SB = = 1580.74 IN-2 IC 54758.6 IN-3 SBC= = 146 ft, SPACING 36.38 IN. 733320 IN-4 20157.0 IN-3 1270091 IN-4 26023.4 IN-3 s = 6ft-sin. YT 35.62 CIP B = 80.00 CIP T = 8.00 HC 80.00 YBC 48.81 IN. IN. IN. IN. IN. STRAND: TYPE AREA/STR. PULL TOTAL AREA DESCRIPTION HOLDDOWN = LOW RELAXATION = 0.1530 IN-2 STRAND C.G. 26.000 = 0.730 NUMBER= 70.00 =10.710 IN-2 PROFILE: X o.oo 63.00 83.00 146.00 LOADS: 6.750 HOLD DOWN 6.750 HOLD DOWN 26.000 HOLD DOWN 0.00 6.75 6.75 o.oo IN. IN. IN. IN. TO C.G. OF TO C.G. OF TO C.G. OF TO C.G. OF STRAND STRAND STRAND STRAND BEAM WT 1.130 RLF CIP DECR = 0.667 RLF WEAR SURFACE = 0.167 XLF BARRIER WT = 0.100 RLF DIAPH.WT = 0.000 KIPS AT 1/0 POINTS ALONG GIRDER PEDESTRIAN = 0.000 KLF LIVE LOAD =TANDEM AXLES = 25.00 KIPS + LANE LOAD 0.640 KLF -OR -NCHRP 12-33 DESIGN TRUCR + LANE LOAD 0.640 KLF LOAD, RESISTANCE AND OTHER FACTORS: PHI: FLEXURE= 1.000 SHEAR = 0.900 LOAD: DEAD = 1.250 WEAR SURFACE= 1.500 LIVE = 1.750 OTHER: DYNAMIC ALL . (TRUCK ONLY) = 33.00% MULTI-LANE (OR OTHER) DISTRIBUTION FACTORS: INPUTTED FLEXURAL D.F.= 0.497 SHEAR D.F.= 1.000 INITIAL STRESSES: REQD F'CI 4.618 KSI AT X = 63.00 FT. PRESTRESS LOSSES: TOTAL LOSSES = 51.079 XSI BY NCHRP 12-33 SPECS FINAL STRESSES: (NEGATIVE NUMBERS INDICATE TENSION) FP + ALL DL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION = MAX. BOT. TENSION FP + ALL DL + LL: MAX . BOT. COMPRESSION MAX. TOP = MAX. BOT. TENSION REQD. F'C= 2.553/0.45 MAXIMUM LL STRAND STRESS = 2.154 KSI 2.137 KSI 0.000 KSI 2.103 2.553 -0.297 5.673 3.136 RSI KSI KSI KSI KSI <<< .<<< AT X = 73.00 FT. AT X = 73.00 FT. 1.000 ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT X = 73.00 FT. PROV. MOMENT = 197863 K-IN REQD. MOMENT = 134265 K-IN DEFLECTIONS: (NEGATIVE VALUES INDICATE CAMBER) APPROX. CAMBER AT ERECTION -3.856 IN. BASED ON -2.253 IN. RELEASE CAMBER SPAN/HOVING LL DEFLECTION 2149 (BASED ON MOMENT DISTRIBUTION FACTOR) 125

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>>>REFINED METHOD(18% RED.);LRFD's HEAVIER LOADING gus4Z90 :TYPE IV, L = 90 ft; S = 10 ft SHEET OF NUBRIDGE, V1.00, (C) 1992 JACQUES & ASWAD, INC. DATE: 06/29/94 PAGE: 1 BY: G.A DESIGN SPAN A H AC STC DATA: AASHTO IV,SPAN 90.00 FT. YB 789.00 IN-2 I 54.00 IN. SB L = 90 ft, SPACING 24.73 IN. 260730 IN-4 10543.0 IN-3 688430 IN-4 16843.4 IN-3 = 1532.61 IN-2 IC = 52441.6 IN-3 SBC= s = 10 ft YT 29.27 IN. CIP B 120.00 IN. CIP T 8.oo IN. HC 62.00 IN. YBC 40.87 IN. STRAND: TYPE AREA/STR. = LOW RELAXATION = 0.1530 IN-2 STRAND C.G. 17.000 PULL TOTAL AREA DESCRIPTION HOLODOWN = HOLD DOWN = 0.730 NUMBER= 49.00 7.497 IN-2 PROFILE: X LOADS: o.oo 39.00 51.00 90.00 6.000 6.000 17.000 HOLD DOWN HOLDDOWN = 0.00 6.00 6.00 0.00 IN. TO IN. TO IN. TO IN. TO C.G. OF C.G. OF C.G. OF C.G. OF STRAND STRAND STRAND STRAND BEAM WT BARRIER WT PEDESTRIAN LIVE LOAD 0.822 KLF CIP DECK = 1.125 KLF WEAR SURFACE= 0.250 KLF 0.200 KLF DIAPH.WT = 0.000 KIPS AT 1/0 POINTS ALONG GIRDER 0.000 KLF -OR --TANDEM AXLES = 25.00 KIPS + LANE LOAD 0.640 KLF NCHRP 12-33 DESIGN TRUCK + LANE LOAD = 0.640 KLF LOAD, RESISTANCE AND OTHER FACTORS: PHI: FLEXURE = 1.000 SHEAR = 0.900 LOAD: DEAD = 1.250 WEAR SURFACE = 1.500 LIVE = 1.750 OTHER: DYNAMIC ALL. (TRUCK ONLY) = 33.00% MULTI-LANE (OR OTHER) DISTRIBUTION FACTORS: INPUTTED FLEXURAL D.F.= 0.745 SHEAR D.F.= 1.000 INITIAL STRESSES: REQD F'CI 5.169 KSI AT X = 39.00 FT. PRESTRESS LOSSES: TOTAL LOSSES = 52.685 KSI BY NCHRP 12-33 SPECS FINAL STRESSES: (NEGATIVE NUMBERS INDICATE TENSION) .FP +ALL DL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION FP + ALL DL + LL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION 2.073 KSI 1.849 KSI 0.000 KSI 1.975 2.181 = -0.283 4.847 2.764 REQD. F'C= 2.181/0.45 MAXIMUM LL STRAND STRESS = KSI KSI KSI KSI KSI <<< <<< AT X = 45.00 FT. AT X = 45.00 FT. 1.000 ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT X PROV. MOMENT = 108891 K-IN 45.00 FT. REQD. MOMENT = 75273 K-IN DEFLECTIONS: (NEGATIVE VALUES INDICATE CAMBER) APPROX. CAMBER AT ERECTION -3.041 IN. BASED ON -1.720 IN. RELEASE CAMBER SPAN/MOVING LL DEFLECTION 2122 (BASED ON MOMENT DISTRIBUTION FACTOR) 126

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SHEET OF >>>REFINED METHOD(18% RED.); LRFD's HEAVIER LOADING gus4Z110: TYPE IV, L = 110 ft; S = 6ft-Bin. NUBRIDGE, V1.00, (C) 1992 JACQUES & ASWAD, INC. DATE: 06/29/94 PAGE: 1 BY: G.A DESIGN DATA: AASHTO IV,SPAN L = 110 ft, SPACING 24.73 IN. 260730 IN-4 10543.0 IN-3 600365 IN-4 15980.8 IN-3 s = 6ft-Bin. SPAN = 110.00 FT. YB A 789.00 IN-2 I H 54.00 IN. SB AC 1284.74 IN-2 IC STC 36536.2 IN-3 SBC= STRAND: TYPE AREA/STR. PROFILE: X o.oo 47.00 63.00 110.00 PULL = LOW RELAXATION = 0.1530 IN-2 STRAND C.G. 17.000 0.00 6.00 6.00 o.oo TOTAL AREA DESCRIPTION HOLDDOWN HOLDDOWN = HOLDDOWN 6.000 6.000 17 .ooo HOLD DOWN LOADS: YT 29.27 CIP B 80.00 CIP T 8.00 HC 62.00 YBC 37.57 IN. IN. IN. IN. IN. 0.730 NUMBER "' 52.00 7.956 IN-2 IN. TO e.G. OF STRAND IN. TO e.G. OF STRAND IN. TO e.G. OF STRAND IN. TO e.G. OF STRAND .. BEAM WT BARRIER WT PEDESTRIAN LIVE LOAD 0.822 KLF CIP DECK = 0.667 KLF WEAR SURFACE = 0.167 KLF 0.100 KLF DIAPH.WT = 0.000 KIPS AT 1/0 POINTS ALONG GIRDER 0.000 KLF -OR --TANDEM AXLES = 25.00 KIPS + LANE LOAD 0.640 KLF NCHRP 12-33 DESIGN TRUCK + LANE LOAD .640 KLF LOAD, RESISTANCE AND OTHER FACTORS: PHI: FLEXURE =.000 SHEAR = 0.900 LOAD: DEAD = 1.250 WEAR SURFACE= 1.500 LIVE 1.750 OTHER: DYNAMIC ALL. (TRUCK ONLY) = 33.00% (OR OTHER) DISTRIBUTION FACTORS: INPUTTED FLEXURAL D.F.= 0.497 SHEAR D.F.= 1.000 INITIAL STRESSES: REQD F'CI 4.833 KSI AT X = 47.00 FT. PRESTRESSLOSSES: TOTAL LOSSES= 51.760 KSI BY NCHRP 12-33 SPECS FINAL STRESSES: (NEGATIVE NUMBERS INDICATE TENSION) FP + ALL DL: MAX. BOT .. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION FP + ALL DL + LL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION REQD. F'C= 2.616/0.45 MAXIMUM LL STRAND STRESS 2 .185. J(SI 2.193 J(SI o.ooo }(51 2.111 2.616 -0.286 5.813 2.807 XSI XSI KSI KSI XSI <<< <<< AT X = 55.00 FT. AT X = 55.00 FT. 1.000 ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT X = 55.00 FT. PROV. MOMENT = 112755 K-IN REQD. MOMENT = 74345 K-IN DEFLECTIONS: (NEGATIVE VALUES INDICATE CAMBER) APPROX. CAMBER AT ERECTION -3.663 IN. BASED ON -2.106 IN. RELEASE CAMBER SPAN/MOVING LL DEFLECTION 1821 (BASED ON MOMENT DISTRIBUTION FACTOR) 127

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GRILLAGE RESULTS: BY AASHTO: REFINED METHOD(18 % RED.)HS-20 Loading GUSY122 :Type VI, L=122 ft, Spacing S = 10 ft BRIDGE89, V1.01, (C) 1988-1993 JACQUES & ASWAD, INC. DESIGN DATA: SPAN c 122.00 FT. A =1085.00 IN-2 H 72.00 IN. NS = 60.00 AREA APS= 9.180 IN-2 HOLDDOWN 1 c 6.10 HOLDDOWN 2 = 6.10 LOADS: AASHTO TYPE VI I 733320 IN-4 CIP B SB = 20157.0 IN-3 CIP T EA.STR.= 0.153 IN-2 EFF. PULL STRAND TYPE = LOW RELAXATION (IN) AT X = 51.00 (FT) (IN) AT X = 71.00 (FT) SHEET OF DATE: 06/29/94 PAGE: 1 BY: G.A 120.00 IN. 9.00 IN. 0.730 BEAM WT = 1.130 KLF CIP DECK= 1.125 KLF ASPHALT WT DIAPH.WT= 0.000 KIPS HS LOAD 20.00 -44 PEDESTRIAN D.F.=S/D= 1.491* WHEEL LOAD 0.450 KLF 0.000 KLF INITIAL STRESSES: REQD F'CI = 4.577 KSI AT X 51.00 FT. PRESTRESS LOSSES: TOTAL LOSSES = 47.843 KSI BY AASHT0-89 FINAL STRESSES: FP + ALL DL: MAX. BOT. COMPRESSION 2.105 KSI MAX. TOP COMPRESSION 1.811 KSI MAX. BOT. TENSION 0.000 KSI FP + ALL DL + LL: MAX. BOT. COMPRESSION 2.052 KSI MAX. TOP COMPRESSION = 2.061 KSI MAX. BOT. TENSION =-0.263 KSI REQD . F'C= 2.105/0.4 = 5.262 KSI AT X= 2.08 FT. ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT X c 61.00 FT. PROV. MOMENT 178919 K-IN REQD. MOMENT = 123315 K-IN DEFLECTIONS: APPROX. CAMBER AT ERECTION = -3.003 IN. BASED ON -2.002 IN. RELEASE CAMBER SPAN/HOVING LL DEFLECTION c 2824 128

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GRILLAGE RESULTS: BY REFINED ASSHTO METHOD(18% RED.);HS-20 Loading GUSY146: Type VI, L=146 ft, Spacing S 6ft-Bin BRIDGE89, V1.01, (C) 1988-1993 JACQUES & ASWAD, INC. DESIGN DATA: SPAN 146.00 FT. A =1085.00 IN-2 H 72.00 IN. NS = 63.00 AREA APS= 9.639 IN-2 HOLDDOWN 1 6.40 HOLDDOWN 2 = 6.40 LOADS: AASHTO TYPE VI I 733320 IN-4 CIP B SB = 20157.0 IN-3 CIP T EA.STR.= 0.153 IN-2 EFF. PULL STRAND TYPE = LOW RELAXATION (IN) AT X 63.00 (FT) (IN) AT X = 83.00 (FT) SHEET OF DATE: 06/29/94 PAGE: 1 BY: G.A 80.00 IN. 8.00 IN. 0.730 BEAM WT = 1.130 RLF CIP DECK o 0.666 RLF ASPHALT WT = 0.267 KLF DIAPH.WT= 0.000 RIPS HS LOAD =HS-20.00 -44 PEDESTRIAN = 0.000 RLF D.F.=S/0= 0,994 WHEEL LOAD INITIAL STRESSES: REQD F'CI = 3.996 KSI AT X = 63.00 FT. PRESTRESS LOSSES: TOTAL LOSSES = 45.182 KSI BY AASHT0-89 FINAL STRESSES: FP + ALL DL: MAX. BOT. COMPRESSION 1.846 RSI MAX. TPP-COMPRESSION = 2.179 RSI MAX. BOT. TENSION = 0.000 KSI FP + ALL DL + LL: MAX. BOT. COMPRESSION = 1.809 KSI MAX. TOP COMPRESSION 2.464 KSI MAX. BOT. TENSION =-0.274 KSI REQD. F'C= 2.464/0.4 = 6.159 KSI AT X= 73.00 FT. ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT X = 58.40 FT. PROV. MOMENT -175384 K-IN REQD. MOMENT = 117227 K-IN DEFLECTIONS: APPROX. CAMBER AT -2.540 IN. BASED ON -1.693 IN. RELEASE CAMBER SPAN/MOVING LL DEFL_ECTION = --2318 129

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,. GRILLAGE RESULTS: BY REFINED AASHTO METHOD(18% RED.);HS20 LOADING GUS4Y90: TYPE IV; L = 90 ft; Spacing S =10 ft BRIDGE89, V1.01, (C) 1988-1993 JACQUES & ASWAD, INC. DESIGN DATA: SPAN 90.00 FT. A = 789.00 IN-2 H 54.00 IN. NS = 44.00 AREA APS= 6.732 IN-2 HOLDDOWN 1 5.40 HOLDDOWN 2 = 5.40 LOADS: AASHTO TYPE IV I 260730 IN-4 CIP B SB = 10543.0 IN-3 CIP T = EA.STR.= 0.153 IN-2 EFF. PULL = STRAND TYPE = LOW RELAXATION (IN) AT X = 39.00 (FT) (IN) AT X = 51.00 (FT) SHEET OF DATE: 06/29/94 PAGE: 1 BY: G.A 120.00 IN. 9.00 IN. 0.730 BEAM WT = 0.822 KLF CIP DECK= 1.125 KLF ASPHALT WT DIAPH.WT= 0.000 KIPS HS LOAD =HS-20.00 -44 PEDESTRIAN D.F.=S/D= 1.491 *WHEEL LOAD 0.450 KLF 0.000 KLF INITIAL STRESSES: REQD F'CI = 4.658 KSI AT X = 39.00 FT. PRESTRESS LOSSES: TOTAL.LOSSES = 48.016 KSI BY AASHT0-89 FINAL STRESSES: FP + ALL DL: MAX. BOT. COMPRESSION = MAX. TOP COMPRESSION = MAX. BOT. TENSION 1.889 KSI 1.834 KSI 0.000 KSI FP + ALL DL + LL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION 1.806KSI 2.076 KSI =-0.287 KSI REQD. F'C= 2.076/0.4 = 5.190 KSI AT X= 45.00 FT. ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT X = 45.00 FT. PROV. MOMENT 101136 K-IN REQD. MOMENT = 70026 K-IN DEFLECTIONS: APPROX. CAMBER AT ERECTION =.-2.315 IN. BASED ON -1.544 IN. RELEASE CAMBER SPAN/MOVING LL DEFLECTION = 2530 130

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GRILLAGE RESULTS: BY REFINED AASHTO METHOD(18 t RED.);HS20 LOADING GUS4Y110:TYPE IV; L =110 ft; Spacing S =6ft-Bin. BRIDGE89, V1.01, (C) 1988-1993 JACQUES & ASWAD, INC. DESIGN DATA: SPAN = 110.00 FT. A = 789.00 IN-2 H 54.00 IN. NS 47.00 AREA APS= 7.191 IN-2 HOLDDOWN 1 5.60 HOLDDOWN 2 = 5.60 LOADS: AASHTO TYPE IV I 260730 IN-4 CIP B SB = 10543.0 IN-3 CIP T EA.STR.= 0.153 IN-2 EFF. PULL STRAND TYPE = LOW RELAXATION (IN) AT X 47.00 (FT) (IN) AT X = 63.00 (FT) SHEET OF DATE: 06/29/94 PAGE: 1 BY: G.A 80.00 IN. 8.oo IN. 0.730 BEAM WT = 0.822 KLF CIP DECK = 0.667 KLF ASPHALT WT DIAPH.WT= 0.000 KIPS HS LOAD =HS-20.00 -44 PEDESTRIAN D.F.=S/D= 0.994 WHEEL LOAD 0.267 KLF 0.000 KLF INITIAL STRESSES: REQD F'CI = 4.298 KSI AT .x = 47.00 FT. PRESTRESS LOSSES:. TOTAL LOSSES= 46.710 KSI BY AASHT0-89 FINAL STRESSES: FP + ALL DL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION FP + ALL DL + LL: 2.006 KSI 2.210 KSI 0.000 KSI 1.945 KSI 2.547 KSI =-0.288 KSI MAX. BOT. COMPRESSION = MAX. TOP COMPRESSION MAX. BOT. TENSION REQD. F'C= 2.547/0.4 = 6.368 KSI AT X = 55.00 FT. ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT X = 55.00 FT. PROV. MOMENT 103387 K-IN REQD. MOMENT = 68168 K-IN DEFLECTIONS: APPROX. CAMBER AT ERECTION= -2.718 IN. BASED ON -1.812 IN. RELEASE CAMBER SPAN/MOVING LL DEFLECTION = 2084 131

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BY SIMPLIFIED AASHTO METHOD (S/11); HS-20 Loading GUS6X122:Type VI, L=122 ft, Spacing S = 10 ft BRIDGE89, Vl.01, (C) 1988-1993 JACQUES & ASWAD, INC. DESIGN DATA: AASHTO TYPE VI SHEET OF DATE: 06/29/94 PAGE: 1 BY: G.A SPAN = 122.00 FT. A =1085. 00 IN-.2 I 733320 IN-4 CIP B = 120.00 IN. H 72.00 IN. SB = 20157.0 IN-3 CIP T 9.00 IN. NS = 66.00 AREA APS= 10.098 IN-2 HOLDDOWN 1 6.70 HOLDDOWN 2 = 6.70 LOADS: EA.STR.= 0.153 IN-2 EFF. PULL 0.730 STRAND TYPE = LOW RELAXATION (IN) AT X = 51.00 (FT) (IN) AT X = 71.00 (FT) BEAM WT = 1.130 KLF CIP DECK = 1.125 KLF ASPHALT WT DIAPH.WT= 0.000 KIPS HS LOAD =HS20.00 -44 PEDESTRIAN D.F.=S/D= 1.818 WHEEL LOAD INITIAL STRESSES: REQD F'CI = 5.115 KSI AT X = 51.00 FT. PRESTRESS LOSSES: TOTAL LOSSES = 51.829 KSI BY AASHT0-89 FINAL STRESSES: FP + ALL DL: MAX. BOT. COMPRESSION 2.120 KSI MAX. TOP COMPRESSION 1.801 KSI MAX. BOT. TENSION == 0.000 KSI FP + ALL DL + LL: MAX. BOT. = 2.056 KSI MAX. TOP COMPRESSION 2.105 KSI MAX. BOT. TENSION =-0.233 KSI REQD. F'C= 2.120/0.4 = 5.301 KSI AT X = 2.08 FT. ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT X = 61.00 FT. PROV. MOMENT 194565 K-IN REQD. MOMENT = 133145 K-IN DEFLECTIONS: 0.450 KLF 0.000 KLF APPROX. CAMBER AT -3.100 IN. BASED ON -2.067 IN. RELEASE CAMBER SPAN/MOVING LL DEFLECTION = 2315 132

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BY SIMPLIFIED AASHTO METHOD (S/11); HS-20 Loading GUS6X146:Type VI, L=146 ft, Spacing S = 6ft-Bin BRIDGE89, V1.01, (C) 1988-1993 JACQUES & ASWAD, INC. DESIGN DATA: SPAN = 146.00 FT. AASHTO TYPE VI A =1085.00 IN-2 I 733320 IN-4 CIP B = H 72.00 IN. SB = 20157.0 IN-3 CIP T = NS = 69.00 AREA EA.STR.= 0.153 IN-2 EFF. PULL = APS= 10.557 IN-2 STRAND TYPE = LOW RELAXATION HOLDDOWN 1 = 6.85 (IN) AT X 63.00 (FT) HOLDDOWN 2 = 6.85 (IN) AT X = 83.00 (FT) LOADS: SHEET OF DATE: 06/29/94 PAGE: 1 BY: G.A eo.oo IN. e.oo IN. 0.730 BEAM WT = 1.132 KLF CIP DECK= 0.667 KLF ASPHALT WT 0.267 KLF DIAPH.WT= 0.000 KIPS HS LOAD =HS-20.00 -44 PEDESTRIAN = 0.000 KLF D.F.=S/D= 1.213 WHEEL LOAD INITIAL STRESSES: REQD F'CI = 4.542 KSI AT X= 63.00 FT. PRESTRESS LOSSES: TOTAL LOSSES = 49.358 KSI FINAL STRESSES: FP + ALL DL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION FP + ALL DL + LL: MAX.BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION BY AASHT0-89 2.071 KSI 2.163 KSI 0.000 KSI 2.025.KSI 2.518 KSI =-0.223 KSI REQD. F'C= 2.518/0.4 = 6.295 KSI AT X = 73.00 FT. ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT X= 58.40FT. PROV. MOMENT = 188067 K-IN REQD. MOMENT = 125018 K-IN DEFLECTIONS: APPROX. CAMBER AT ERECTION = IN. BASED ON -2.048 IN. RELEASE CAMBER SPAN/HOVING LL DEFLECTION = 1900 133

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BY SIMPLIFIED ASSHTO (S/11); HS20 Loading GUS4X90: TYPE IV; L = 90 ft; Spacing S =10 ft V1.01, (C) 1988-1993 JACQUES & ASWAD, INC. DESIGN DATA: SPAN 90.00 FT. A = 789.00 IN-2 H = 54.00. IN. NS = 49.00 AREA APS= 7.497 IN-2 HOLDDOWN 1 = 6.00 HOLDDOWN 2 = 6.00 LOADS: AASHTO TYPE IV I 260730 IN-4 CIP B SB = 10543.0 IN-3 CIP T EA.STR.= 0.153 IN-2 EFF. PULL STRAND TYPE LOW RELAXATION (IN) AT X = 39.00 (FT) (IN) AT X = 51.00 (FT) SHEET OF DATE: 06/28/94 PAGE: 1 BY: G.A 120.00 IN. 9.00 IN. 0.730 BEAM WT = 0.822 KLF CIP DECK = 1.125 KLF ASPHALT WT DIAPH.WT= 0.000 KIPS HS LOAD =HS-20.00 -44 PEDESTRIAN D.F.=S/D= 1.818 *WHEEL LOAD 0.450 KLF 0.000 KLF INITIAL STRESSES: REQD F'CI = 5.208 KSI AT X = 39.00 FT. PRESTRESS LOSSES: TOTAL LOSSES = 51.893 KSI BY AASHT0-89 FINAL STRESSES: FP + ALL DL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION FP + ALL DL + LL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION 2.082 KSI 1.833 KSI 0.000 KSI 1.980 KSI 2.125 KSI =-0. 272 KSI REQD. F'C= 2.125/0.4 = 5.313 KSI AT X = 45.00 FT. ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT.X = 45.00 FT. PROV. MOMENT 110950 K-IN REQD. MOMENT = 77084 K-IN DEFLECTIONS: APPROX. CAMBER AT ERECTION = -2.487 IN. BASED ON -1.658 IN. RELEASE CAMBER SPAN/MOVING LL DEFLECTION= 2075 134

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.BY SIMPLIFIED ASSHTO (S/11); HS20 Loading GUS4X110:TYPE IV; L =110 ft; Spacing S =6ft-Bin. BRIDGE89, V1.01, (C) 1988-1993 JACQUES & ASWAD, INC. DESIGN DATA: SPAN = 110.00 FT. A = 789.00 IN-2 H 54.00 IN. II>NS = 52.00 AREA APS= 7.956 IN-2 HOLDDOWN 1 6,00 HOLDDOWN 2 = 6.00 LOADS: AASHTO TYPE IV I 260730 IN-4 CIP B SB = 10543.0 IN-3 CIP T = EA.STR.= 0.153 IN-2 EFF. PULL STRAND TYPE = LOW RELAXATION (IN) AT X 47.00 (FT) (IN) AT X = 63.00 (FT) SH"EET OF DATE: 06/28/94 PAGE: 1 BY: G.A 80.00 IN. 8.00 IN. 0.730 BEAM WT = 0.822 KLF CIP DECK= 0.667 KLF ASPHALT WT DIAPH.WT= 0.000 KIPS HS LOAD =HS-20.00 -44 PEDESTRIAN D.F.=S/D= 1.213* WHEEL LOAD 0.267 KLF 0.000 KLF INITIAL STRESSES: REQD F'CI = 4.874 KSI AT X = 47.00 FT. PRESTRESS LOSSES: TOTAL LOSSES = 50.940 KSI BY AASHT0-89 FINAL STRESSES: FP + ALL DL: MAX. BOT. COMPRESSION MAX. TOP COMPRESSION MAX. BOT. TENSION FP + ALL DL + LL: MAX. BQT. COMPRESSION MAX TOP COMPRESSION MAX. BOT. TENSION REQD. F'C= 2.602/0.4 2.151 KSI 2.190 KSI 0.000 KSI 2.077 KSI 2.602 KSI =-0.249 KSI = 6.504 KSI AT X = 55.00 FT. 1 ULTIMATE MOMENT AT SECTION W/ LEAST RESERVE CAPACITY: AT X = 55.00 FT. PROV. MOMENT 112006 K-IN REQD. MOMENT = 74052 K-IN DEFLECTIONS: APPROX. CAMBER AT ERECTION = -3.002 IN. BASED ON -2.001 IN. RELEASE CAMBER SPAN/HOVING LL DEFLECTION= 1708 135

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REFRENCES AASHTO 1989. "Standard Specifications for Highway Bridges," American Association of State Highway and Transportation Officials, 14th Edition, Washington, DC. "BRIDGE89" 1989. A program and user's manual published by Jacques & Aswad, Inc., Denver, CO. Eby, C. C., Kulicki, J.M.,. and Kostem, C.N. 1973. "The Evaluation of St. Venant Torsional Constants for Prestressed Concrete I-Beams," Fritz Engineering Laboratory Report No. 400.12, Lehigh University. Hambly, E.C. 1976. "Bridge Deck Behavior" New York: J. Wiley & Sons. Jacques, F.J., and Aswad, A. 1987. "Simple Span Design Tables and Details," CORESLAB Structures, Inc., Phoenix, AZ. Jaeger, L.G.; and. Bakht, B. 1982. "The Grillage Analogy in Bridge Analysis," Canadian Journal of Civil Engineering, Vol.9, pp. 224-235. National Cooperative Highway Research Program 1993. "4th Draft LRFD Bridge Design Specifications and Commentary," prepared by Modjeski and Masters, Inc., Harrisburg, P A. "NULRFD" 1993. A program by Jacques & Aswad, Inc., Denver, CO. "SECTION1" 1989. A program and user's manual, published by Jacques & Aswad, Inc., Denver, CO. "ST AAD-111" 1994. A program and user's manual, published by Research Engineers, Inc., Yorba Linda, CA. 136

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Zellin, M.A., Kostem, C.N., VanHorn, D.A., and Kulicki, J.M. 1976. "Live Load Distribution Factors for Prestressed Concrete !-Beam Bridges" Fritz Engineering Laboratory Report No. 387.2B, Lehigh University. Zokaie, T., Osterkamp, T.A., and Imbsen, R.A. 1991.. "Distribution of Wheel Loads on Highway Bridges," A report prepared for N.C.H.R.P., Transportation Research Board. 137