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Inspection and rating system for tubular steel pedestrian bridges

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Title:
Inspection and rating system for tubular steel pedestrian bridges
Creator:
Gogel, Michael Eugene
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English
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306 leaves : ; 28 cm

Subjects

Subjects / Keywords:
Tubular bridges -- Inspection ( lcsh )
Tubular bridges -- Evaluation ( lcsh )
Footbridges -- Inspection ( lcsh )
Footbridges -- Evaluation ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 305-306).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Michael Eugene Gogel.

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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.
Resource Identifier:
49642259 ( OCLC )
ocm49642259
Classification:
LD1190.E53 2001m .G63 ( lcc )

Full Text
INSPECTION AND RATING SYSTEM FOR TUBULAR
STEEL PEDESTRIAN BRIDGES
by
Michael Eugene Gogel
B.S., University of Colorado at Denver, 1999
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
2001


This thesis for the Master of Science
degree by
Michael Eugene Gogel
has been approved
by
^Bruce A. E^arnes


Gogel, Michael Eugene (MS, Civil Engineering)
Inspection and Rating System for Tubular Steel Pedestrian Bridges
Thesis directed by Associate Professor Kevin L. Rens
ABSTRACT
With today's growing economy and population come increased concern about the
environment. The threat of global warming has aided in turning many people to
alternate forms of transportation, such as bicycles. This increase in pedestrian traffic
has resulted in a growing need for pedestrian paths. Many municipalities have
incorporated these paths into parks and open spaces. Tubular steel pedestrian
bridges have allowed the paths to bridge across obstacles while remaining
aesthetically pleasing.
Pedestrian bridges, like all bridges, must be inspected and maintained to limit the
threat to life and safety. While many types of bridge inspection systems are in use
today, the generally accepted method used to measure corrosion is visual inspection.
Because of the geometry of tubular members, it is difficult to measure their thickness
and determine if there has been any section loss. With the use of non-destructive
evaluation (NDE) and testing techniques, specifically the use of an ultrasonic flaw
detector, the thickness of the structural members can be accurately measured.
Therefore, the guesswork involved with determining the amount of section loss is
reduced.
However, measuring the thickness of a member eliminates only part of the problem.
Over time, this increasing section loss decreases the structural capabilities of the
bridge. Therefore, the structural capacity of the bridge as it relates to the thickness
of the members must be analyzed.
in


I
The contents of this thesis will explain the analysis procedures performed on 43
separate structures. From these procedures, a relationship between the thickness of
the bridge members and the structural capacity of the bridges were identified. From
these relationships, various formulas used to calculate the stress in each of the
members were developed.
In addition to establishing a method to calculate the stress in each member, a rating
system for tubular steel pedestrian bridges was developed. This system will give
inspectors the ability to quickly and easily measure the quality of the structure based
on its geometry and the thickness of its members. Because the rating system is a
function of the calculated stress in each member, it is unbiased and reduces the
chance for discrepancies between inspectors.
This abstract accurately represents the content of the candidate's thesis. I
recommend its publication.
Signed
IV


DEDICATION
I would like to dedicate this to my wife. Through the duration of this project, she
has been very understanding of the long hours I would sometimes commit to it.
While she did not fully understand what I was doing, she was aware of its
importance to me and others.


ACKNOWLEDGMENT
Many people and organizations have made this research project possible. Among
those, I would like to acknowledge the City and County of Denver Department of
Public Works for financing the project. While the City and county of Denver funded
the project, Terry Gruber was the one who initially saw the need for a change and
therefore, promoted the research.
I would like to thank Bill Melton, also with the City and County of Denver. As the
primary bridge inspector on these structures for many years, he assisted me with
inspections and pointed out problems he has seen escalate over the years. With his
help, the research and inspection time was greatly reduced.
1 would also like to acknowledge the faculty and staff of the University of Colorado
at Denver. They provided me with the knowledge and ability to work through
problems and overcome obstacles. The graduate and undergraduate students
working on the various projects for the City and County of Denver assisted in many
ways. Whether it was inspections or data collection, without them, my tasks would
have been lengthy and more difficult.
A special thanks goes to Kevin L. Rens, Ph.D., P.E.. He was the one who organized
and initiated the research project at the very beginning. Because of the confidence
he and Terry Gruber had had in me, I was presented with the opportunity to make a
difference and simplify the work of others. Dr. Rens provided me with the initial
concept and guided me through the entire project.


Dr. Rens not only helped me with this project, through the work on this and other
projects, he nested in me the desire to learn more about structural failure and non-
destructive evaluation and testing. What the future holds for me, only God knows.
However, from the knowledge I have gained while working under Dr. Rens and with
others on this and other projects, I feel I am better equipped to make the proper
engineering decisions that will affect the safety of others.


CONTENTS
List of Figures........................................................... x
List of Tables............................................................ xii
Chapter
1. Introduction.......................................................... 1
2. Literature Review..................................................... 8
2.1 History of Inspection and Bridge Management Systems................... 8
2.2 Survey Data Analysis................................................. 14
3. Analysis............................................................. 20
3.1 Geometry Measurements................................................ 20
3.2 Load Calculations.................................................... 21
3.3 STAAD Model.......................................................... 31
3.4 Section Property Modifications....................................... 33
3.5 Stress Relationships Based on Section Properties..................... 36
4. Field Investigations................................................. 42
4.1 Bridge Alignment and Description..................................... 42
4.2 Visual Inspection.................................................... 44
4.3 Thickness Measurements............................................... 46
5. Condition Rating System.............................................. 56
5.1 Grouping of Structures............................................... 56
5.2 Stress Calculation Formulas.......................................... 61
5.3 Examples of Pseudo Stress Calculations............................... 90
5.4 Calculated vs. Pseudo Stress......................................... 96
5.5 Condition Ratings................................................... 106


6. Summary, Conclusions, and Recommendations for Future Studies. 114
6.1 Summary.......................................................... 114
6.2 Conclusions...................................................... 115
6.3 Recommendations for Future Studies............................... 117
Appendix
A. Survey Information............................................... 120
B. Photographs...................................................... 130
C. Typical STAAD Input.............................................. 151
D. Typical STAAD Output............................................. 168
E. Graphs........................................................... 189
F. Letter of Recommendation to Close Structure D-l l-GG-140 and
Structure D-l 1-GG-150......................................... 216
G. Users Manual and Guidelines for the Epoch III Flaw Detector..... 232
H. Typical Epoch III Database Used to Measure Thickness............. 281
I. Thickness Measurements Downloaded from the Epoch III to a P.C.... 291
J. CCD Memo in Response to the Letter in Appendix F................. 301
K. Example of Inspection Rating Spread Sheet........................ 303
Bibliography
305


LIST OF FIGURES
Figures
2.1.1 Condition Index Related to X/Xmax (Stecker, et al. 1997)......
3.1.1 Typical Geometry Measurements.................................
3.2.1 Plan View of Bridge with Load Pattern 1.....................
3.2.2 Plan View of Bridge with Load Pattern 2.....................
3.2.3 Plan View of Bridge with Load Pattern 3.....................
3.2.4 Plan View of Bridge with Load Pattern 4.....................
3.2.5 Plan View of Bridge with Load Pattern 5.....................
3.2.6 Plan View of Bridge with Load Pattern 6.....................
3.2.7 Plan View of Bridge with Load Pattern 7.....................
3.2.8 Plan View of Bridge with Load Pattern 8.....................
3.2.9 Plan View of Bridge with Load Pattern 9.....................
3.2.10 Plan View of Bridge with Load Pattern 10....................
3.5.1 Lower Chord Stress from Lower Chord Thickness.................
3.5.2 Lower Chord Stress from Top Chord Thickness...................
3.5.3 Lower Chord Stress from Split Lower Chord.....................
3.5.4 Top Chord Stress from Split Lower Chord.......................
3.5.5 Lower Chord Stress from Rounded Lower Chord...................
3.5.6 Top Chord Stress from Rounded Lower Chord.....................
4.3.1 Main Screen of Epoch III Interface Program....................
4.3.2 Create Database Dialog Box on the Epoch III Interface Program
4.3.3 The Template Tab of the Create Database Dialog Box..............
4.3.4 The Memo Tab of the Create Database Dialog Box................
13
21
24
25
25
26
26
27
27
28
28
29
37
38
39
40
41
41
49
49
50
51
X


4.3.5 The Sequential Tab of the Create Database Dialog Box.................. 52
4.3.6 The 2D Tab of the Create Database Dialog Box.......................... 53
4.3.7 The 3D Tab of the Create Database Dialog Box.......................... 53
4.3.8 The Boiler Tab of the Create Database Dialog Box...................... 54
5.1.1 Section Cut of U Shaped Pony Truss.................................... 57
5.1.2 Section Cut of H Shaped Pony Truss.................................... 58
5.2.1 Equations to find a and b for Length < 50' and Width < 7.5'........... 65
5.2.2 Equations to find a and b for Length < 100'and Width > 7.5'........... 66
5.2.3 Equations for Floor Stringer Stress, Length < 50' and Width < 7.5'.... 69
5.5.1 Cl Related to Stress/Stressmax for Tubular Steel Pedestrian Bridges. 108


LIST OF TABLES
Tables
1.1 Condition State Description Based on Pontis Inspection System.. 3
1.2 Code Descriptions for NBIS Rating System............................ 4
1.3 Levels of Corrosion from U. S. Army Corps of Engineers Rating
System......................................................... 5
2.1.1 Condition Index Scales and Zones (Stecker, et al. 1997)............ 11
5.2.1 Stress Equations for Wooden Deck with Length < 50'................. 63
5.2.2 Stress Equations for Wooden Deck with 50'< Length < 75'............ 64
5.3.1 Lower Chord Stress Calculations for Structure D-01-CC-338.......... 92
5.3.2 Top Chord Stress Calculations for Structure D-Ol-CC-338............ 92
5.3.3 Rail Post Stress Calculations for Structure D-Ol-CC-338............ 93
5.3.4 Diagonal Truss Stress Calculations for Structure D-Ol-CC-338....... 93
5.3.5 Floor Beam Stress Calculations for Structure D-Ol-CC-338........... 94
5.3.6 Floor Truss Stress Calculations for Structure D-Ol-CC-338.......... 94
5.3.7 Floor Stringer Stress Calculations for Structure D-Ol-CC-338....... 95
5.3.8 Hypothetical Member Stresses for Structure D-Ol-CC-338............. 96
5.4.1 Stress Comparison for Structure D-01-CC-336........................ 97
5.4.2 Stress Comparison for Structure D-01-CC-337........................ 97
5.4.3 Stress Comparison for Structure D-Ol-CC-338........................ 98
5.4.4 Stress Comparison for Structure D-l 1-GG-183....................... 98
5.4.5 Stress Comparison for Structure D-l 1-GG-185....................... 99
5.4.6 Stress Comparison for Structure D-l0-HC-070........................ 99
5.4.7 Stress Comparison for Structure D-l6-LG-140....................... 100


5.4.8 Stress Comparison for Structure D-27-MP-065.................. 100
5.4.9 Stress Comparison for Structure D-12-SG-050.................. 101
5.4.10 Stress Comparison for Structure D-l2-SG-060.................. 101
5.4.11 Stress Comparison for Structure D-16-LG-110.................. 102
5.4.12 Stress Comparison for Structure D-l0-HC-020.................. 102
5.4.13 Stress Comparison for Structure D-l0-HC-090.................. 103
5.4.14 Stress Comparison for Structure D-l0-HC-105.................. 103
5.4.15 Stress Comparison for Structure D-l0-HC-200.................. 104
5.4.16 Stress Comparison for Structure D-l6-LG-025.................. 104
5.4.17 Stress Comparison for Structure D-l 7-WG-068................. 105
5.5.1 Condition Index Scales for Tubular Steel Pedestrian Bridges.. 107
5.5.2 Weighted Ranking for Member Groups........................... Ill
5.5.3 Cl for Structure D-Ol-CC-338 w/out Rounded and Split Members. 112
5.5.4 Cl for Structure D-01-CC-338 with Rounded and Split Members.. 113


1. Introduction
Many people within our growing society have become more active in outdoor
recreation and fitness. Along with this growing interest comes the need for open
space as well as other forms of transportation. Additional pedestrian walkways and
bikeways help to satisfy both of these needs. However, with the addition of these
pathways comes the need for pedestrian bridges. While these pedestrian bridges
may be smaller in size then the traditional vehicular bridge, the functions of each are
the same. Both provide a crossing over waterways, roadways, railroad tracks, etc.
In other words, the bridge provides access from one side of a barrier to the other.
Although these pedestrian bridges may be subjected to smaller loads and lighter
traffic then those found on a highway, they still pose a threat to life safety if they
begin to function improperly. Therefore, just like the larger highway bridges,
pedestrian bridges must be inspected and maintained. In fact, based on a survey
developed by the author of this thesis and submitted to various agencies in the
United States and Canada, most feel that inspections of pedestrian bridges are
warranted (see Appendix A).
During a routine inspection performed by the City and County of Denver (CCD) on
various pedestrian bridges distresses were found with several of the tubular steel
type pedestrian bridges. While this type of structure may be aesthetically pleasing,
there are various problems associated with this type of structure that can not always
be seen by the naked eye. As a result, simple visual inspections may prove to be
inadequate.


There are many widely known bridge inspection systems such as Pontis, which is a
rating system developed under the guidance of the Federal Highway Association and
used by many state Department of Transportation's. In addition, other rating systems
include the National Bridge Inspection Standards (NBIS) and even several Bridge
Management Systems (BMS) developed by various government and private agencies
that deal with visual inspections of a structure. Many of these systems simply ask
the inspector to look for specific problems and quantify the problem based on the
entire structure. From that, the condition of the bridge can be determined as well as
what maintenance work needs to be performed. In many of these types of inspection
systems, corrosion is one of the specific problems the inspector is prompted to look
for. If an area of corrosion is found on a structural member, these inspection systems
require it to be visually inspected, measured, and quantified based on the amount of
section loss the member has been subjected to.
For example, Pontis has 4 different condition states (Hartle, et al. 1991) for
unpainted steel elements based on the amount of corrosion found (see Table 1.1).
Depending on the condition state, various modifications and/or measures are
recommended.
2


Condition Description
1 There is little or no corrosion of the unpainted steel. The weathering steel is coating uniformly and remains in excellent condition.
2 Surface rust, surface pitting, has formed or is forming on the unpainted steel. The weathering steel has not corroded beyond design limits, and the color is yellow orange to light brown.
3 Steel has measurable section loss due to corrosion but does not warrant structural analysis. Weathering steel is dark brown to black.
4 Corrosion is advanced. Section loss is sufficient to warrant structural analysis to ascertain the impact on the ultimate strength and/or serviceability of either the element or the bridge.
Table 1.1. Condition descriptions based on the Pontis system (Hartle, et al. 1991).
As Table 1.2 shows, NBIS rating systems classify corrosion in a similar manner
(Hartle, et al. 1991). This program requires a code be given to a structural element
based on the condition of the element.
3


Code Description
N Not Applicable
9 Excellent Condition
8 Very Good Condition: no problems noted.
7 Good Condition: some minor problems.
6 Satisfactory Condition: structural elements show some minor deterioration.
5 Fair Condition: all primary structural elements are sound but may have minor section loss, cracking, spalling or scour.
4 Poor Condition: advanced section loss, deterioration spalling or failures possible. Fatigue cracks in steel or shear cracks in concrete may be present.
3 Serious Condition: loss of section, deterioration, spalling or scour have seriously affected primary structural components.
2 Critical Condition: advanced deterioration of primary structural elements.
1 "Imminent" Failure Condition: major deterioration or section loss present in critical structural components or obvious vertical or horizontal movement affecting structure stability.
0 Failed Condition: out of service, beyond corrective action.
Table 1.2. Code descriptions from the NBIS rating system (Hartle, et al. 1991).
The United States Army Corps of Engineers (USACE) also classifies corrosion
based on visual inspection (Greimann, et al. 1990). In a system developed to rate the
operating equipment of lock and dam structures, corrosion is measured based on it's
severity (see Table 1.3).
4


Level Description
0 New condition.
1 Minor surface scale or widely scattered small pits.
2 Considerable surface scale and/or moderate pitting.
3 Severe pitting in dense pattern, thickness reduction in local areas.
4 Obvious uniform thickness reduction.
5 Holes due to thickness reduction and general thickness reduction.
Table 1.3. Levels of corrosion from the USACE's rating system.
However, these types of inspection methodologies fall short when dealing with
tubular steel structural members. By the simple physical geometry of a tube
member, it is impossible to visually inspect the inside wall of a sealed or long
member. Therefore, if there was any corrosion forming on the inside of a tubular
steel member, it would go undetected by visual inspection alone. Even if it were
possible to see the corrosion (as would be the case for external corrosion of a tubular
steel member), if the thickness of the member is unknown, how could the corrosion
be quantified based on the amount of section loss?
As mentioned before, various problems were found by CCD employees during a
routine inspection of pedestrian bridges. Among these problems were complete
section loss of various members (see Photographs 2 through 4 and 8 through 10 in
Appendix B), disfigured and rounded members (see Photographs 5, 11 and 12 in
Appendix B) as well as cracking and splitting of members (see Photographs 6, 11
and 12 in Appendix B). Because of these problems, a research team at the
University of Colorado at Denver (UCD) along with CCD staff agreed that a more
detailed inspection method for tubular steel pedestrian bridges needed to be
5


developed rather then the visual inspection rating system of the Pontis program
currently used by the CCD. It was also decided that some form of non-destmctive
evaluation (NDE) may prove useful with the inspections of this type of structure. In
fact, Noqueria (1998) makes a reference to the importance of NDE techniques to
supplement any visual inspection. This is especially important when the inspection
of various structural components cannot be evaluated by use of visual inspection
alone. Even Parsons Brinkerhoff (1993) states that unknown and difficult to
measure steel thickness' can be measured by using an ultrasonic thickness device.
One of the key items to be incorporated into the modified inspection system was the
need to quantify a rating for structural rated items. In other words, a more accurate
method of measurement needed to be utilized to make it possible to determine bridge
safety. It was also decided that the new inspection system would have to remain
simple to allow anyone (regardless of technical competence) to inspect and rate any
of the structures.
In order to keep the inspection simple, the newly added measurement must be
conservative. This would allow the new measurement to raise a "red flag" prior to
any structural failure. Whenever a potential problem is encountered, the inspector
(or governing agency) would make the decision to further analyze the problem, fix
the problem, or do nothing. Regardless of the decision made, the potential problem
would be identified prior to any failure.
In summary, the purpose of this thesis is as follows:
1. Gather data on a set of existing pedestrian bridges in the City and County
of Denver. This data is to include the various distresses associated with
this type of bridge.
6


2. Measure the in-situ geometry of the bridges so they can be modeled and
analyzed.
3. Apply loads as per the AASHTO Guide Specifications for the Design of
Pedestrian Bridges to the models.
4. Analyze the structural capacity of these modeled bridges based on the
applied loads and varying distresses found associated with the bridges.
5. From the analysis results, develop a conservative rating system that can
be used on the bridges to determine if public safety is jeopardized.
6. Analyze the in-situ condition of each bridge to determine their modeled
conditions.
7. Compare the modeled conditions to the rating system conditions to
determine if modifications are needed on the rating system.
The following chapters of this thesis will explain how an analysis study was
completed on a group of 43 different tubular steel pedestrian bridges (38 in the city
and county of Denver, CO and the remaining five in Estes Park, CO). From this
study, graphs were created to correlate the thickness of a given member to the
member stresses. The same method was also used to determine the relationship
between cracked and/or rounded members and member stresses. These graphs
allowed similar structures to be grouped and mathematical functions developed.
These functions would allow the inspector to calculate the given stress for each
member based on the geometry and members sizes as well as visual inspection and
thickness measurement of each member. By knowing the stress of each member of
the structure, a given agency could determine what, if any, maintenance or repair
work is needed.
7


2. Literature Review
2.1 History of Inspections and Bridge Management Systems
Due to various bridge structure failures, in 1968 the Federal Highway
Administration (FHWA) ordered a review and inventory of all highway structures by
January, 1970. In addition to this, all structures were to be inspected every 2 to 5
years depending on the importance of the structure. Shortly thereafter, congressional
hearings began to establish the need for a permanent inspection program to ensure
public safety (White, 1981). These inspection programs stemmed from the fact that
structural components of bridges deteriorate over time. This deterioration process
can lead to the failure of a bridge member, which in turn can lead to the failure of the
bridge.
Following these congressional hearings, the American Association of State Highway
and Transportation Officials (AASHTO) and the FHWA developed the Manual for
Maintenance Inspection of Bridges (MMIB) in 1970. Shortly thereafter in 1971,
congress enacted the NBIS. From this, it was determined that periodic bridge
inspections can reduce and/or eliminate the chance of failures. These inspection
needs spawned the various types of inspection rating systems discussed previously in
Chapter 1.
While these inspection rating systems may function for rating the bridge on a
national level for federal funds distribution, they can sometimes fall short in
describing the problems associated with the structure (Noqueria, 1998). For
example, a condition rating of 7 refers to a description of "Good Condition some
8


minor problems" as per the NBIS (see Table 1.2). While this type of method may
help in quantifying the condition of the structure, it lacks information needed to
determine the quality of the staicture. In addition to this, the visual ratings
associated with these systems are subjective to the inspectors opinion. Therefore,
two separate people could rate the same structure differently.
While these inspection rating systems are used nationally by the FHWA to determine
the distribution of federal funds for rehabilitation and/or replacement of bridges, the
FHWA does allow some flexibility to the various agencies to develop their own
bridge selection procedures. Therefore, in an effort to develop a bridge management
system of their own, in April of 1986 the Indiana Department of Highways sent a
questionnaire to all fifty states, the District of Columbia, and Puerto Rico (Saito and
Sinha, 1987). By July of 1986, 44 of the 52 surveys were returned (85%). From
these 44, only 10 (23%) reported using these ratings to determine their own
priorities. In fact, while 31 states (70%) responded that improvements to the system
are necessary, 40 states (91%) listed structural strength as an attribute that should be
used in setting priorities.
16 states (36%) reported that they do have, or are developing, their own form of
priority setting procedures for bridge replacement and rehabilitation. Of these 16,
seven have established procedures to set priorities on bridges by assigning weighting
factors. These procedures require the agency to assign an importance factor (IF) to
the areas of concern (i.e., structural integrity, traffic safety, cost of improvements,
etc.). It should be noted that the sum of all the importance factors should equal 100
to represent 100%. The next step would be to assign a numerical rating (NR) to each
of the areas based on inspection and/or other acquired data. The third step would be
to multiply each importance factor to the associated numerical rating for a weighted
numerical rating (WNR). The fourth step would be to add all the WNR's for each
9


bridge. The final step would be to prioritized the bridges based on all the sums as
given by equation 2.1.1.
WNR = ^(IF)i(NR)i <2.1.1 >
i=i
Weighted systems are not isolated to bridge ratings only. A research team from
Iowa State University, along with a member from the United States Army
Construction Engineering Research Laboratories developed a weighted system used
by the USACE to rate the operating equipment of lock and dam structures. The title
of this research program is Repair, Evaluation, Maintenance and Rehabilitation
(REMR).
The program was developed to not only establish a base line associated with the
operating equipment used in lock and dam structures, but to also monitor the
deterioration of the equipment as well (Stecker, et al. 1997). Over time, the USACE
could use this information to budget for and plan maintenance and rehabilitation
work on various lock and dam components prior to failure. This future planning
would not only help to create an efficient maintenance program, it would also help to
maintain uninterrupted service to the public.
While the inspection process of the REMR program may not be pertinent to the
topics discussed in this thesis, the development of the rating system is. The first step
in this development was to determine how the operating equipment would be
measured. A Condition Index (Cl) for this program was developed and was based
on a numerical scale from 0 to 100. This Cl would indicate the need for repair
and/or replacement, due to deteriorating parts. In addition to identifying areas in
need of immediate repair, these numerical values could be used help to monitor the
changing condition of the equipment over time (see Table 2.1.1).
10


Zone Condition Index Condition Description Recommended Action
1 85 to 100 Excellent: No noticeable defects. Some aging or wear may be visible. Immediate action is not required.
70 to 84 Good: Only minor deterioration or defects are visible.
2 55 to 69 Fair: Some deterioration or defects are evident, but function is not significantly affected. Economic analysis of repair alternatives is recommended to determine appropriate action.
40 to 54 Marginal: Moderate deterioration. Function is still adequate.
3 25 to 39 Poor: Serious deterioration in at least some portions of the structure. Function is inadequate. Detailed evaluation is required to determine the need for repair, rehabilitation, or reconstruction. Safety evaluation recommended.
10 to 24 Very Poor: Extensive deterioration. Barely functional.
0 to 9 Failed: No longer functions. General failure or complete failure of a major structural component.
Table 2.1.1. Condition index scales and zones (Stecker, et al. 1997).


Once the Cl scales and zones were established, the next step was to determine how
to calculate the Cl for a given piece of equipment. In order to do this, the team
developed a method to assign an initial condition index (Cf) to each component of
the given piece of equipment. For this, the following equation was utilized where X
is the actual measurement of the particular component being inspected and Xmax is
the measurement of the same component where it would require immediate repair or
a more thorough inspection and evaluation (i.e., it is the limiting value).
Cl, =100(0.40)c^ <2.1.2>
As shown in Figure 2.1.1, when X=Xmax, CIj=40 which corresponds to a
marginal/poor rating on the Cl scales and zones listed in Table 2.1.1.


Condition Index (Cl)
x/x
max
Figure 2.1.1. Condition Index related to X/Xmax (Stecker, et al. 1997).
The next step in determining the overall Cl for a given piece of equipment was to
assign a numerical ranking (R) to each component. This ranking is a measurement
used to identify the importance of the component to the equipment. In order to
normalize these rankings and assign a weighted value (W) from 1 to 100 to them, the
following equation was used where the Rj represents the ranking of a given
component.
W =
R.
I*.
(100)
<2.1.3>
13


These weighting factors can be assigned to the Cf for each component being
analyzed such that the total weighted condition index (CIw) is as follows.
<2.1.4>
7 = 1
By calculating CIw, the varying significance of each component was accounted for
in the overall Cl of the equipment.
Before assigning the value of CIw to the particular piece of equipment, the
components were also analyzed to determine which were deemed as critical to the
operation of the equipment. In the case where a particular component will
drastically affect the overall performance of the equipment, the Cf for that
component could govern the overall Cl for the equipment. Therefore, it was
determined the overall Cl would be based on the following equation where CIimin is
the minimum Cl, of all the critical components.
Cl = Minimum(CI imm,CI w) <2.1,5>
Once the overall Cl is determined, the inspector can refer to the values shown in
Table 2.1.1 to determine what, if any, further steps are needed. As shown, the
process for determining the Cl for the equipment not only analyzes each component
of the equipment, but also how critical the component is to the function of the
equipment.
2.2 Survey Data Analysis
As stated in Chapter 1 of this thesis, a survey was submitted to various agencies in
the United States and Canada (see Appendix A). This was completed in an attempt
to determine if the problems encountered by the CCD with respect to tubular steel
14


pedestrian bridges was localized to the Denver area or if it was widespread and
related to the type of material used. In other words, is the section loss, rounding, and
splitting of square tube members localized in Denver, or is it a common problem
with square tubes exposed to weather? While 50 of the 77 agencies responded
(65%), only 12 of the responses contained useful data (24% of those who responded,
16% overall). When the survey was originally mailed during the summer of 2000, it
contained a cover letter explaining the intent of the survey. Many of the returned
surveys were unanswered and contained the comment "We do not have any of these
types of structures in our inventory...". In an attempt to gather more useful
information, a second letter was mailed explaining we were looking for feedback on
what we were doing and any information would be helpful. Similarly, negative
responses followed.
Questions 1 and 2 of the survey which respectfully states, "We regularly maintain
and inspect our tubular steel pedestrian bridges" and "We feel regular inspections
and maintenance is needed on tubular steel pedestrian bridges" relate to the
inspection practices of the agencies. Although there were few responses with
measurable data, it was evident from the 12 responses containing useful information
that those agencies with this type of structure do regularly inspect them (59%). Even
more feel regular inspections and maintenance on pedestrian bridges is needed
(75%). Based on the limited amount of data collected from the survey, this type of
response enforces the fact that an inspection and rating system is needed for this type
of structure.
Question 3 states, "We have used non-destructive evaluation (NDE) in the inspection
of our tubular steel pedestrian bridges." This question deals more with the methods
of inspection used by the agencies. Only 25% of the 12 responses answered 'YES' to
this question. That can be viewed two ways. The first is that the agency feels NDE
15


is not warranted for the inspection of this type of structure. Noqueria (1998)
addresses this topic by saying that visual inspections account for 80% of the defects
found during bridge inspections. However, he goes on to say that the use of NDE is
likely to provide more information about a defect already suspected. Parsons
Brinckerhoff (1993) adds to this by discussing the use of more advanced equipment
and testing methods to accommodate the growth of specialized inspections.
Therefore, the use of NDE should not be viewed as the only tool used in inspections,
rather an aid to visual inspections.
The second view to the minimal use of NDE by the various agencies is they do not
feel they have enough qualified personnel to operate the various equipment nor the
time and resources it would take to train an individual. If this is the case, these
agencies should be respected for knowing their limitations. In fact, it is very
important to understand the functions and limitations of what NDE equipment can
do so erroneous data is not the result of an inspection (Noqueria, 1998). However,
the additional information gathered from NDE could prove to be of great importance
when determining an agencies future needs.
Questions 4 and 6 dealt primarily with moisture inside the tubular steel members.
While question 4 ("Moisture inside the members of a tubular steel pedestrian bridge
is a problem that we have encountered.") addresses the problem directly by asking if
moisture inside the members are a problem, question 6 ("Internal corrosion of the
members of a tubular steel pedestrian bridge is a problem that we have encountered.)
indirectly refers to it by asking about internal corrosion. Based on the 12 agencies
that responded, over half neither agree nor disagree or are not sure (84% for question
4 and 59% for question 6).
16


This item falls back to the need for NDE in the inspection process. As discussed in
Chapter 1, visual inspection alone deals with only items that can be seen.
Photographs 2 through 4 and 8 through 10 in Appendix B show members subjected
to complete section loss. If these members corroded from the inside out, it is
obvious how this corrosion could have gone undetected until complete section loss
was visible.
Some of the additional comments written on the returned surveys stated that the
various agencies did not have a problem with corrosion because the tubular steel
pedestrian bridges were constructed with weathering steel. However, problems have
developed on various structures due to a false sense of security incorporated with
weathering steel (Heidersbach, 1987). The most common cause of section loss to
weathering steel is improper drainage. Based on this, one could claim the addition
of weep holes in the tubular steel members could allow drainage and prevent this
internal corrosion. However, drainage alone will not solve the problem.
Heidersbach (1987) talks about the corrosion from the inside out resulting in
complete section loss of an exterior wall panel on a university building in Illinois.
Here the problem was not drainage but the build up of condensation.
Question 5 states, "External corrosion of the members of a tubular steel pedestrian
bridge is a problem that we have encountered." While this type of distress on a
tubular steel member can be detected during a visual inspection, as discussed in
Chapter 1, the extent of the corrosion can not be measured from access to only one
surface without advanced inspection techniques such as ultrasonic, NDE equipment.
One could also claim that painting the structure could help to eliminate external
corrosion. While this is true, this could be a complicated and costly task, especially
from a maintenance perspective. As shown in Photographs 16 and 17 of Appendix
17


B, unless the corrosion is completely removed, the corrosion will continue to
advance. An abrasive blasting method should be used to remove the exterior
corrosion. Power tool cleaning to bare metal is not an effective method to remove
the chlorides and other containment's (which will accelerate the corrosion and paint
degradation) from the steel (SSPC, 1992). Also, depending on the location of the
painted area, as well as various climate related issues, special paints and/or coatings
might be needed.
Questions 7 and 8 could also be associated with internal moisture. Question 7 states,
"Rounding or disfiguration of the square members of a tubular steel pedestrian
bridge is a problem that we have encountered" and question 8 states, "Cracking or
splitting of the members of a tubular steel pedestrian bridge is a problem that we
have encountered." It is possible that these distresses are caused by the freeze/thaw
cycle of contained moisture in a sealed member. They may also be the result of the
sun heating the moisture inside the members thereby creating hoop stresses similar
to pressure vessels. Regardless of the cause, these are distresses that could
jeopardize the structural integrity and safety of the bridge.
Another important topic to note about question 7 and 8 is that every agency that
responded to the survey stated these items were not a problem. As a result of this
survey, one of the agencies that did respond contacted the author of this thesis and
extended and invitation to include the 5 tubular steel pedestrian bridges in the town
as part of the study. During the inspection of the 5 bridges, a structural member on
one of the bridges was found to be rounded and split. Until that time, the agency
was unaware of any distress. It is important to note that while this type of distress is
valuable information to analyze the structure, it can easily go undetected.
i
i
18


Question 9 which states, "Bolt failure at spliced connections of a tubular steel
pedestrian bridge is a problem that we have encountered" does not deal directly with
the research for this thesis. While every reporting agency listed this as not a problem
area, it is a distress found on one of the bridges inspected. The bridge it was found
on was Structure D-l l-GG-140, Goldsmith Gulch at the north end of Tamarac
Square in Denver, CO. The various other distresses found on this structure (see
Photographs 8 to 12 in Appendix B) could have contributed to the bolt failure found.
19


3. Analysis
The City and County of Denver has 38 tubular steel pedestrian bridges that were
inspected for this thesis. These, along with 5 other from the town of Estes Park,
Colorado made up the sample group of bridges that were inspected and analyzed. As
mentioned previously, the analysis was used to determine a relationship between the
thickness of an individual member and the overall structure stress. In addition, the
relationship between rounded and/or split members and the associated stress was to
be determined. To develop these relationships, the following procedure was
followed:
Obtain geometry measurements of the sample bridges.
Determine the various loads to be used on each member of each bridge.
Analyze the structure based on changing section properties for the
various members.
Record and plot the stress in each member based on the section property
modifications.
3.1 Geometry Measurements
As built plans for the majority of the structures analyzed were unavailable.
Therefore, in order to maintain a consistent form of measuring, the in-situ geometry
of each bridge was measured.
The geometry measurements consisted of field measuring and recording all data
needed to model and analyze the bridge (see Figure 3.1.1). These measurements
20


consisted of length, width, bay spacing, truss orientation, member size, and camber.
For member sizes, only the outside dimensions of the tubes were measured at this
time. The thickness measurements would be determined during the analysis portion
of the study. It should be noted that camber measurements were taken by stretching
a string across one side of the bridge and measuring the distance from the string to
the top chord. While this method did not account for elevation differences at the
abutments, it did provide a moderately accurate in-situ camber measurement.
4X.5 TUBE fOP CHORDS
/
4X3 luBL RA;u

I
El EVATlON V W
PLAi\
Figure 3.1.1. Typical geometry measurements.
3.2 Load Calculations
Before any analysis can be completed on the structure, various loads have to be
determined. The dead load of the structure was simply the self weight of the steel
members and the weight of the deck on the structure. Wooden decks were assumed
to have a weight equivalent to saturated oak with the measured deck thickness. To
21


calculate the weight of saturated oak, a specific gravity for oak (Goak) of 0.73 was
used (NDS, 1997). Also found in the NDS (1997) was the Fiber Saturation Point
(FSP) of 32.5%. Assuming the moisture content (MC) of saturated oak = FSP and
knowing the weight of water = 62.4 pcf, the density (p)of the oak timbers could be
calculated from the NDS equation:
Therefore, to determine the area weight of the saturated oak timber, the thickness of
the timbers in feet was multiplied by 60.36pcf. For example, the weight of a 4" thick
deck would be:
The weight of concrete decks were calculated by the same method except, 150pcf
was assumed the density for normal weight concrete. Therefore, the weight of a 4"
thick concrete deck would be:
The live loads and wind loads used for the structures were taken from the American
Association of State Highway and Transportation Officials (AASHTO) Guide
Specifications for the Design of Pedestrian Bridges. In this publication, AASHTO
states that the pedestrian live loads may be taken as 85psf on the part of the structure
that produces the maximum stress to the member being designed. Based on the
geometry measurements of the structure, tributary areas to the supporting members
of the deck were calculated and multiplied by 85psf. This generated the equivalent
live load acting on the supporting members.
<3.1>
<3.2>
<3.3>
22


Because of the many different members used to make up these structures, it is
unlikely that one distinct load pattern will generate the maximum stress in each
member. Therefore, ten different loading patterns were developed in which the live
load was applied to:
1. The first third of the bridge span on a pre-determined left side of the
structure. This was done to represent a structure loaded near one of the
supports (see Figure 3.2.1).
2. The middle third of the bridge span on a pre-determined left side of the
structure. This simulates a structure loaded near mid-span with a torsion
type load (see Figure 3.2.2).
3. The first third of the bridge span on a pre-determined right side of the
structure. This produced a symmetrical type load to that generated from
number 1 above (see Figure 3.2.3).
4. The middle third of the bridge span on a pre-determined right side of the
structure. This produced a symmetrical type load to that generated from
number 2 above (see Figure 3.2.4).
5. The first and last third of the bridge span on the left side as well as the
middle third on the right side. This was done to simulate a true torsion
type load on the structure (see Figure 3.2.5).
6. The first and last third of the bridge span on the right side as well as the
middle third on the left side. This produced a symmetrical type load to
that generated from number 5 above (see Figure 3.2.6).
7. The first third of the structure across the entire width. This simulated a
bridge fully loaded near one end (see Figure 3.2.7).
8. The left side of the structure across the entire span length. This simulated
a bridge fully loaded on one side (see Figure 3.2.8).
23


9. The right side of the structure across the entire span length. This
produced a symmetrical type load to that generated from number 8 above
(see Figure 3.2.9).
10. The entire structure. This simulated a bridge being loaded to its full
capacity (see Figure 3.2.10).
Figure 3.2.1. Plan view of bridge with load pattern 1.
24


Figure 3.2.2. Plan view of bridge with load pattern 2.
Figure 3.2.3. Plan view of bridge with load pattern 3.
25


Figure 3.2.4. Plan view of bridge with load pattern 4.
Figure 3.2.5. Plan view of bridge with load pattern 5.
26


Figure 3.2.6. Plan view of bridge with load pattern 6.
Figure 3.2.7. Plan view of bridge with load pattern 7.
27


Figure 3.2.8. Plan view of bridge with load pattern 8.
Figure 3.2.9. Plan view of bridge with load pattern 9.
28


Figure 3.2.10. Plan view of bridge with load pattern 10.
For consistency, AASHTO was also referred to for vehicle loading. The document
states that pedestrian bridges should be designed for the occasional loading of a
maintenance vehicle, provided vehicular access is not physically prevented. As per
AASHTO guidelines, the following vehicle loads were applied to each structure.
Structures with a clear deck width of less then six feet need not be
designed for a maintenance vehicle.
Structures with a clear deck width from six feet to ten feet should be
designed for a 10,000 lb. (H-5 Truck) maintenance vehicle.
Structures with a clear deck width greater the ten feet should be designed
for a 20,000 lb. (H-10 Truck) maintenance vehicle.
Wind loading from the AASHTO Guide Specifications for the Design of Pedestrian
Bridges was also used. For open truss bridges where wind can readily pass through
the trusses, AASHTO allowed for the structure to be designed for a wind load
29


equivalent to a horizontal load of 35psf applied to the full vertical projected area of
the structure, as if enclosed. This force, along with being allowed to neglect the
wind on live load force and longitudinal wind force simplified the wind load
calculations.
Given a bay on the structure, which was bound by the top chord, bottom chord and
two rail posts, the wind force applied to the bounding members calculated to a
uniform linear load (w) equal to the 35psf force times the ratio of the area to the
perimeter of the bay.
w=(3WW <34>
Perimeter
It should be noted that when dealing with a member separating multiple bays (i.e., a
rail post at mid-span), the total uniform load applied to the member is equivalent to
the addition of the uniform loads calculated from each bay. It should also be noted
that these calculations resulted in four different wind load patterns.
1. Wind directed towards the structure on the left.
2. Wind directed away from the structure on the left.
3. Wind directed toward the structure on the right.
4. Wind directed away from the structure on the right.
After calculating the individual dead load, live loads and wind loads, load
combinations could be determined. As per AASHTO Guide Specifications for the
Design of Pedestrian Bridges, the following load combinations were considered. It
should be noted that Live Load (LL) and Wind Load (WL) in the load combinations
groups represent the applied loads based on the various load patterns and wind
direction. For example, the Group II Loading will produce four separate load
combinations. While the Dead Load (DL) remains constant throughout the analysis,
30


the applied wind loads for each of the four combinations is consistent with the four
separate wind load patterns.
Group I (DL + LL)
Group II (DL + WL) / 1.25
Group III (DL + LL + 0.3WL) / 1.25
3.3 STAAD Model
Once the geometry of the structure, member sizes, and individual loads were
determined, the structure was modeled and analyzed using STAAD III1 for Windows
(STAAD). The use of a structural analysis program simplified and quickened the
analysis process for each section property modification which will be discussed later.
The typical STAAD model included the following input to accurately model and
analyze the structure. For an example of the input commands, see Appendix C.
The 'Joint Coordinates' represents the location of every point where
members are connected. These joint coordinates are based on the
Cartesian coordinate system and may be in feet or inches.
The 'Member Incidences' used to identify the start joint and end joint of
each member.
The 'Member Property' of each member. For tubular steel members, this
consisted of the depth, width and thickness of the member.
Various 'Constants' for each of the members. This normally consisted of
the modulas of elasticity, density, poisons ratio and thermal coefficient
of the material used to construct the member.
1 STAAD III for Windows, Research Engineers, Inc., Yorba Linda, CA. 92687
31


!
i
I
I
I
i
i
j Which members are to be considered 'Truss Members' (i.e.,
I
j tension/compression only members).
! Which joints are to be used as 'Supports' and what type of support is to
be used (i.e., pinned, fixed, etc.).
j The various 'Load' conditions and 'Load Combinations' previously
discussed in Section 3.2.
i The Structural Code and/or standard reference used to analyze the
i structure. For the purpose of this study, the ninth edition of the
American Institute of Steel Construction Allowable Stress Design
! (AISC-ASD) was used for analysis instead of the AASHTO code. The
reasons for this will be discussed latter.
The 'Yield Strength' of the steel used. It is unknown what grade steel
was used for the various bridges inspected, therefore, 46ksi steel was
used for analysis. This is typically the lowest grade steel available for
tubular steel members and therefore, would be conservative for anything
larger.
The 'Deflection' limits to be used in the analysis. For the purpose of this
study, the AASFITO recommendation of span length/500 was used.
Once the structure was modeled properly, STAAD was able to check the
various members for stressed based on the applicable 'Code'
recommendations input.
As mentioned above, AASHTO was used to determine the loads for the structure and
AISC-ASD was the standard reference used to analyze the structure. This is
consistent and/or conservative to the Special Specifications for Prefabricated Bridges
(Continental Bridge, 1998), a publication written by Continental Bridge Co., one of
the widely used manufacturers of prefabricated tubular steel pedestrian bridges.
32


Both publications specify a live load of 85psf applied to the area of the bridge that
produces the maximum stress in the member being designed, or in the case of this
research project, the member being analyzed. AASHTO states this type of load
represents an average person occupying 2 square feet of bridge deck area and is
considered reasonably conservative. Although Continental specifies 25psf wind
load, AASHTO requires 35psf applied to the full vertical projected area of the
structure. This method is offered for design simplicity in lieu of computing forces
on the individual truss members. The AISC-ASD standard reference was used in
lieu of the AASHTO Standard Specifications for Highway Design primarily because
the bridges inspected were not part of highway facilities. Another reason was that
AASHTO states pedestrian bridges designed for the 85psf live load and the
AASHTO service load allowable stress are designed for an overload capacity.
Instead of an overload capacity, these bridges were analyzed based on normal
service loads.
3.4 Section Property Modifications
As discussed previously, various types of problems pertaining to tubular steel
members were found during a routine inspection of local tubular steel pedestrian
bridges. Among these problems were complete section loss of various members,
disfigured and rounded members, and cracking and splitting of members. Therefore,
any type of analysis performed would need to account for these distresses.
It became apparent that section loss would probably be the most critical of these
problems, mainly due to the fact that it was the most likely of the problems to go
undetected by a visual inspection. STAAD can accommodate section loss in the
analysis by inputting the thickness of the member in the member property section.
However, this would generate a member of uniform thickness on all four walls of the
33


tubular steel member. While this would not be an accurate description of the
member, it would error on the conservative side. Because of the unlimited
possibilities that could be found pertaining to the thickness of each of the four walls,
as well as the thickness locations along the axis of the member, this conservative
approach would satisfy the requirements addressed in Chapter 1 (i.e., the method
needs only to raise red flag for questionable areas, therefore keep it simple and
conservative).
Rounded members could also be addressed in the member property section of the
input. Square members were input as pipes with a given thickness and rectangular
members were entered as elliptical shaped hollow members. While STAAD did
allow for pipe sections to be input, section properties needed to be calculated for
elliptical shaped members and input manually. By assuming the depth of the
rectangular tube equal to the long dimension of the ellipse (x) and the width of the
tube equal to the short dimension of the ellipse (y), and assuming a thickness of t,
the formulas used to calculate Ix and Iy for the elliptical members were as follows.
a: a~2 <3.5>
a, =a0-t <3.6>
h -Z 0 2 <3.7>
ja- il l <3.8>
4 <3.9>
j na\b0 ~ xa)bi y 4 <3.10>
34


These formulas allowed for moments of inertia (Ix and Iy) to be calculated as the
moments of inertia of the whole section as if it were solid minus the moment of
inertia of the hollow portion.
Split members were also accommodated in the member property section of the input.
To simulate a member that was split, the member was input as two angles rotated
180 from each other to form a box section. It should be noted that the legs of the
angles as well as the thickness were comparable to the actual tubular member.
While this type of analysis simulates a member split the entire length on two
opposite sides, this method produces a simple and conservative result for any type of
crack in a member.
It should be noted that the members of each structure were separated into seven
different member groups to analyze the various members of the structure. These
groups were as follows:
1. Top Chords are the members spanning longitudinally across the top of
each side of the bridge as well as the turned down members at the ends.
2. Lower Chords are the members spanning longitudinally across the bottom
of each side of the bridge.
3. Rail Posts are the vertical members spanning between the top and lower
chords.
4. Truss Members are the diagonal members spanning from the top of one
rail post to the bottom of the adjacent rail post.
5. Floor Beams are the members spanning laterally between the lower
chords.
6. Floor Trusses are the diagonal members spanning from one side of a floor
beam to the opposite side of an adjacent floor beam.
35


7. Floor Stringers are the members spanning longitudinally below the deck
and between the lower chords.
3.5 Stress Relationship Based On Section Properties
Once the STAAD model was created with the proper geometry, member sizes,
member properties, and load conditions, as well as a method for modifying the
member section properties, the structure was analyzed for code compliance. As
mentioned previously, AISC-ASD was the governing structural steel standard
reference used to analyze these structures. STAAD provides a code check in the
analysis of the structure and prints the stress ratio of each member along with the
dictating forces and locations (see Appendix D). To determine the stress found in
various members based on the properties of a given member, several models were
analyzed. The analysis results for each model was then plotted to determine the
relationship between the two.
The first section property modification to be analyzed was the thickness of the
members to develop a relationship between stress and corrosion. As mentioned
before, several models were analyzed. The first analysis was completed to
determine a baseline. Here, all the members were given a thickness of 1/2". From
this benchmark, the thickness of a member group was decreased by 1/8" while the
thickness of each of the other member groups were kept at 1/2". This resulted in a
total of 22 STAAD models for corrosion for each bridge (the baseline model plus
three other models for each of the seven member groups). This was completed to
determine the stress ratio of each member based on the section loss of every other
member. Figures 3.5.1 and 3.5.2 show graphical relationships between the stress in
a member associated with the thickness of the same member and the stress in a
36


member associated with the thickness of another member. Refer to Graphs 1 to 49
in Appendix E for all the stress vs. thickness relationships.
LOWER CHORD STRESS FROM LOWER CHORD THICKNESS
Figure 3.5.1. Lower chord stress from lower chord thickness.
37


L0V\4ER CHORD STRESS FROM TOP CHORD THICKNESS
1.200
cr 1.000
w

a>
0.800
p
o
.c
o
- 0.600
0.1000 0.2000 0.3000 0.4000 0.5000
Top Chord Thickness (in.)
Figure 3.5.2. Lower chord stress from top chord thickness
0.6000
The next section property modification was that which simulated a cracked or split
member. As was done for the corrosion analysis, several analyses were performed
on each structure. After approximately ten structures were analyzed, it became
apparent the same type of uniform graphs were not going to develop. As seen in
Figures 3.5.3 and 3.5.4, there was no uniform stress distribution from one bridge to
another. Because of this, and due to the fact that this promotes internal corrosion
(i.e., water is allowed to penetrate the member), this type of distress needs to be
examined in a different manner. Of the ten structures that were analyzed, the worst
case found a stress increase of 100% of allowable for the members subjected to the
crack and 75% for all others. This percentage is based on the stress derived from the
model which simulated a cracked member with a thickness 'f minus the stress
derived from the model simulating corrosion on a member with the same thickness
'f. This was completed to prevent the thickness based stress from being figured into
38


the equation twice. Because of the large increase in stress stemming from a split or
cracked member, it should be noted that any such distress should flag the structure as
failing until a more in-depth analysis can be performed. This topic will be discussed
in more detail in the Stress Calculation Formulas and Recommendations for Future
Study sections.
LOWER CHORD STRESS FROM SPLIT LOWER CHORD
Lower Chord Thickness (in.)
Figure 3.5.3. Lower chord stress from split lower chord.
39


TOP CHORD STRESS FROM SPLIT LOWER CHORD
Lower Chord Thickness (in.)
Figure 3.5.4. Top chord stress from split lower chord.
The final section property to be modified was that which simulated rounded
members. Again, several analysis's were performed on each structure to determine a
stress relationship to this type of distress. As was found with the cracked member
analysis, the stress graphs did not display a similar type of uniformity as those
produced by the corrosion analysis (see Figures 3.5.5 and 3.5.6). However, after
deriving the stress by the same method as was done for the cracked members (i.e.,
subtracting the thickness induced stress from the STAAD calculated stress for a
rounded member), the maximum stress found in the bridges analyzed were much
lower then the stresses from the analysis on the cracked members. The maximum
stress increase for a member subjected to a rounding type distress was found to be
0.15% of allowable and the 0.05% for all other members.
40


LOWS? CHORD STRESS FROM ROUND LOWER CHORD
Lower Chord Thickness (in.)
Figure 3.5.5. Lower chord stress from rounded lower chord.
TOP CHORD STRESS FROM ROUND LOWER CHORD
Lower Chord Thickness (in.)
Figure 3.5.6. Top chord stress from rounded lower chord.
41


4. Field Investigations
The collection and organization of field data is perhaps the most critical part of any
type of inspection. The inspection process should be planned ahead of time. A well-
planned sequence will provide the inspector with a means of more efficiently
utilizing time at the bridge site and will help to make a more systematic inspection.
Many vital decisions about the maintenance and repair work needed on a structure
are not made during the time of the inspection nor by the inspectors. A notebook, or
any other form of record keeping, should be able to communicate to other
individuals an assessment of the conditions observed during the inspection of the
bridge (White et al. 1981). Therefore, the data should be recorded in a manner that
can be easily reviewed and understood by another party at a later time.
4.1 Bridge Alignment and Description
The first objective is to lay out the structure in a manner so that distress locations can
be identified and found at a later time. These locations could also prove to be useful
if any type of analysis is completed on the structure in the office. For example, the
person doing the analysis may need to know if the distress is located at mid-span or
closer to one end. The efficient use of sketches of the bridge and surrounding
structures could prove to be a beneficial tool used to convey this type of information
(White et al. 1981).
42


All the pedestrian bridges used for this study span across a waterway. Therefore, for
the purpose of this study and consistency, the following method was used to
determine the alignment of the bridge.
Bent number one of the structure (i.e., the abutment at the start of the
span) was the left most abutment in an elevation view of the bridge facing
downstream.
The bents were numbered consecutively from left to right starting with
bent one. Therefore, the end abutment would be bent two for a single
span bridge, bent three for a two-span bridge, etc.
Center line of the bridge was the line down the center of the bridge deck.
The forward direction of the centerline was that as seen by facing bent
two while standing on bent one.
The left and right sides of the bridge were determined by the forward
direction of the center line.
A bay was defined as the area of the bridge bounded by the left and right
lower chords and two consecutive floor beams. This area was projected
vertically, usually along the rail posts joined to the floor beams and lower
chords, to include truss members, any portion of the top chord, and any
member below the floor beam or lower chords.
Bays were numbered in the same manner as the bents. Starting with bay
number one being the left most bay as facing downstream, the bays were
numbered consecutively from left to right.
43


A general description of the components that make up the structure is also needed.
To accurately measure the severity of a distress, the type and size of the distressed
member is just as important as its location. Some of the information required for an
accurate description of the structure include the following.
Does the structure have a concrete or timber deck?
What is the size and spacing of the members?
What type of foundation supports the structure?
Is the bridge bearing on steel bearing plates or neoprene bearing pads?
Appendix F contains a report which was submitted to the CCD recommending the
permits for two structures be revoked. The General Description section of the report
lists items that are needed to help communicate to other individuals an assessment of
the conditions observed during the inspection of the bridge.
4.2 Visual Inspection
The second step of the inspection sequence should develop some sort of visual
inspection of the bridge. Valuable information can be seen during a visual
inspection. As mentioned previously, the problems found during a visual inspection
prompted the need for this study.
Before performing any visual inspections, make sure all the needed tools for the
inspection are available. Remember, the primary objective associated with any type
of inspection is to record as much information as possible about the structure and of
any distress. Also, inspection documentation is often used to convey information to
another party. Therefore, a camera could possibly be the most important tool used
on a visual inspection.
44


Photographs can be used to not only complement the sketches of the structure, they
can be used to identify problem areas or distresses. When documenting a distress
with photographs, it is good practice to take several photographs from different
perspectives. The first photograph should be taken of the distressed area showing
how it relates to the structure and surrounding members (see Photograph 13 in
Appendix B). The others should be a close up of the problem area (see Photograph
14 and 15 in Appendix B). The photo should be able to clearly show the details of
the problem as well as an identifiable object used to give a reference to size if
needed (i.e., a penny, pencil, ruler, etc.) (Parsons Brinckerhoff, 1993). As with all
recorded areas of distress, the photographs should be documented in such a way that
the areas of distress can be located at a later date.
While this study is primarily concerned with the structural members of a tubular
steel pedestrian bridge, all elements of the structure should be examined. As
mentioned earlier, one of the critical distresses to look for is cracks or splits in a
member. If a cracked or split member is found, its location should be documented so
it can be readily found at a latter date if needed.
Another distress previously mentioned is the rounding of members. The location of
these members, if any, should be documented as well. While this type of distress
may not be as critical as the cracked or split members, it is important to know the
location if any analysis is to be completed on the structure. It could also help with
future inspections to determine when the distress occurred.
Other areas of concern include, but are not limited to, bridge deck, foundation, and
bearings. For example, it should be noted if a wooden deck contains any rotted
timbers. It should also be documented if an abutment shows signs of advanced
45


deterioration. As seen in Photographs 13 to 15, Structure D-l l-GG-150 has a
deteriorated abutment with exposed reinforcement and a bearing pad showing signs
of corrosion. The Obsemed Visual Distresses section of the report in Appendix F
list typical items of a visual inspection.
4.3 Thickness Measurements
As shown in section 3.5, the thickness of each member is an important property used
to determine the stress in each member of the structure. Therefore, a method for
measuring the thickness of tubular steel members must be utilized. For the purpose
of this study, a Panametrics Epoch III Flaw Detector (Epoch III) was used. The
Epoch III is an hand-held, portable ultrasonic device used to measure the thickness
of steel as well as locate any flaws in a steel sample (i.e., cracks, pits, porosity, etc.).
For more detailed information on what the Epoch III is and how to use it, refer to
Appendix G.
As stated at the beginning of this chapter, proper organization of inspection data is
critical. Therefore, to help efficiency, the inspector should develop a method for
gathering thickness readings prior to the inspection. The decrease in thickness of a
member is primarily caused by corrosion, corrosion is normally caused by moisture,
and moisture generally rests at the lowest point on a member. Therefore, the
following locations were determined to be typical areas for thickness measurements:
Top Chords The four sides of the base on the downward sloping
member of the top chords at the ends of the structure as well as the
bottom of the top chords at the half points between each rail post (i.e.,
three points per bay).
Rail Posts The four sides around the base of each rail post.
46


Diagonal Truss Members The four sides around the base of each truss
member.
Lower Chords The bottom of the lower chords at the half points
between each rail post as well as the sides of the lower chords at the half
points of the end bays .
Main Floor Supports The bottom of each floor beam at the quarter
points (i.e., five points per floor beam).
Floor Truss Members The bottom of each floor truss at the quarter
points.
Floor Stringers The bottom of each floor stringer at the half points of
each bay.
While each of these points were considered to be typical locations to take thickness
measurements, elevation and the waterway constraints below the structure, not all of
the points could be easily accessed on each structure. The inspector was then forced
to decide if the particular points in question could be ignored or if further measures
needed to be taken so that measurements could be taken. This decision was
primarily based on visual inspection of the said locations and the thickness of similar
points already measured. It should also be noted that additional thickness (other than
the typical locations listed above) were sometimes taken due to visual inspection and
as a result of other thickness readings. These additional readings were generally
taken in problem areas of known section loss. Referring again to Appendix F, the
Analysis Performed section shows an example of the measurement locations for a
given structure.
Once the locations of measurements were determined, a sequential method for
recording the data needed to be developed so the inspection could be performed
47


efficiently and data could be reviewed at a later date if needed. To help with this,
additional functions of the Epoch III as well as the Epoch Ill's interface program
were used. These additional functions allows the user to store thickness readings
(and/or waveforms used for flaw detection) in a self-contained database file that can
be downloaded to a personal computer for later review.
Prior to any thickness measurements, a blank database was developed and stored in
the Epoch III for each bridge inspected. This database was developed using a
Windows based interface program created by Panametrics for the Epoch III. The
program allows the creation of a list of pre-determined ID numbers for each
thickness measurement. Because it is a Windows based program, anyone familiar
with Microsoft Windows should be able to navigate through the menus with little or
no problems.
Figure 4.3.1 shows the main, working screen of the program. Once the program is
started, the user can create a new database by selecting |FILE| and |NEW|. The
Create Database dialog box (see Figure 4.3.2) can be seen in the main screen of the
program. From here, the various tabs can be used to create a database.
48


IgfrEpoch HI Interface (Ep3db1 : DATABASE!
,1 £dft £iedte View Epoch III look Window Help
WEFlssMl'jJlHPfcjaiii
jJSJjsJ
Figure 4.3.1. Main screen of the Epoch III interface program.
Create Database
2D
Manual
I 3D
Memo | T emplate
Boiler I
Sequential |
Manual ID
i
Close Apply
Figure 4.3.2. Create Database dialog box of the Epoch III interface program.
49


The Template tab shown in Figure 4.3.3 allows the user to create customized
formatted templates. The user can input various information used to distinguish this
particular database from others. For example, this information can be any one of or
all of the following:
The job name and/or number.
An identifying number of the structure being inspected.
The date of the inspection
The type of structure being inspected.
Create Database
20 | 3D |
Manual | Memo Template J
T emplate
Boiler ]
Sequential |
Close
Apply
Figure 4.3.3. The Template tab of the create database dialog box.
The Memo tab is similar to the Template tab but allows the user to input a comment
at any location within the database (see Figure 4.3.4). These comments can be
anything that will help the inspection process. For example, reminders can be
entered that help the inspector locate the predetermined measurement locations.
50


They can also be used to remind the inspector which members are next in the
inspection sequence.
Figure 4.3.4. The Memo tab of the create database dialog box.
The remaining tabs allow the user to set up identification numbers (ID) for data
collection. Each number can be up to 16 characters in length and will represent a
particular thickness measurement. After they are stored in the Epoch III, the
thickness measurements that are saved are attached to the ID numbers.
The Manual ID tab allows the user to enter only one ID point at a time into the
database (see Figure 4.3.2). The Sequential ID tab is used to create the databases
used in this study (see Figure 4.3.5). It allows the user to enter ID points in a
sequential order. The 2D and 3D tabs allows the user to create database constructed
of a 2-dimensional or 3-dimensional matrix respectively (see Figure 4.3.6 and 4.3.7).
2D
Manual
Memo J Template | Sequential
3D
Boiler
Memo
Close | Apply |
51


The Boiler tab is identical to the 3D tab except it is set up for creating a database
specifically for boiler tube inspection (see Figure 4.3.8).
Cieate Database
2D
Manual
Prefix
Start
I 3D |
Memo Template
Boiler
Sequential
Finish
Inc
r
Close
Apply
Figure 4.3.5. The Sequential tab of the create database dialog box.
52


Cieate Database
Manual | Memo | Template | Sequential
2D I 3D I Boiler
Prefix
Start Column End Column
Start Row End Row
r
Inc
r
Increment
| Column Jj
Pattern
| Standard *" 1
Close
Apply
Figure 4.3.6. The 2D tab of the create database dialog box.
1 Create Database BEST; 1*1
Manual | Memo | Template I Sequential )
2D 3D I Boiler {
Prefix ii
r Start Column End Column Inc
1 I r
Start Row End Row Inc
1 I r
Start Point End Point Inc
1 | r
1st Increment 2nd Increment Pattern
| Point | Row j | Standard
Close j | Apply
Figure 4.3.7. The 3D tab of the create database dialog box.
53


Cieate Database
Manual | Memo | Template
2D I 3D
Sequential
Boiler
Prefix
Start End Elevation
1 Start Tube 1 End Tube
1 Start Point 1 End Point
r
Inc
r
Inc
1 st 2nd Pattern
| Point 3 lTube 3 |Standard 3
Close I Apply
Figure 4.3.8. The Boiler tab of the create database dialog box.
Appendix H shows an example of a database that was created for thickness
measurements on Structure D-l l-GG-183 (Goldsmith Gulch at the north end of
Rosamund Park). Appendix I shows an example of the same database after
thickness measurements were collected and downloaded to a PC.
Throughout this chapter, the report found in Appendix F was referred to for
examples on how to document inspection data. It should be noted that Structure D-
11-GG-l 50 is one of the bridges listed in this report. As the Analysis Results section
of Appendix F show, several of the members were found to be deficient and in need
of repair and/or replacement. While the structures listed in the report are not owned
by CCD, they do span across a waterway that does. Therefore, they are inspected by
CCD personnel on a regular basis. Because of the findings on these structures
54


during the research for this thesis, CCD responded to the report found in Appendix F
by closing Structures D-l l-GG-140 and D-l l-GG-150 (see Appendix J) and notified
the owner of the required repair and/or replacement. The owner in turn responded
by committing to the repair of the structures. Photographs 18 through 28 of
Appendix B show the repair work that was performed by a company contracted by
the owner.
55


5. Condition Rating System
The first section of this chapter will discuss how similar bridges were grouped
together. The second section will show how the equations used for the rating system
were developed. The remaining sections will focus on the comparison between the
in-situ condition of the group of bridges and the condition of the bridges according
to the rating system. From that comparison, it can be determined if further
modifications are needed to the rating system.
5.1 Grouping of Structures
As mentioned previously, this inspection rating system is based on visual inspections
supplemented by an ultrasonic flaw detector to measure the thickness of the
members. Therefore, the parameters used to group the structures must be relatively
obvious to the naked eye. The reason the structures were grouped was so an
inspector could determine the safety of the structure based on data and formulas
from similar bridges.
It is important to note that while the original sample group of 43 bridges appears to
be large enough to prove various assumptions with, the grouping of the structures
created many smaller subgroups from one larger group. Many of the subgroups
contained three or fewer structures. Proving a hypothesis from a sample group of
that size was impractical. Therefore, the structures used to generate many of the
subgroups were discarded.
56


In grouping the structures, the obvious similarities between the sample group of 43
different tubular steel pedestrian bridges is that the majority of these bridges are
simply supported pony-truss structures (i.e., truss structure open at the top) with a U
or an H cross-sectional shape (see Figures 5.1.1 and 5.1.2). After recognizing this,
the nonconforming type bridges were discarded from the sample group.
Top Chord
I
F loor Bean
\
\
Figure 5.1.1. Section cut of U-shaped pony truss.
57


To: L'l-.' --------
v
i
Figure 5.1.2. Section cut of H-shaped pony truss.
Photographs 29 and 30 in Appendix B show a box truss structure. While this type of
structure is similar to a pony truss, the added members across the top of the bridge
help to stiffen the structure from applied wind loads. Because only one of this type
of structure exists in the sample group, it was discarded.
Photographs 31 and 32 in Appendix B show pony truss structures with a horizontal
curve. Because the structure in simply supported at the ends, the horizontal curve
adds a torsional stress to the lower chords not found in those without the horizontal
curve. Only two of this type of structure exist in the sample group, therefore they
were not used in the study.
Other structures removed from the group of sample bridges included a pair of 2-sapn
continuous pony truss bridges (see Photographs 33 and 34 in Appendix B), a tied
arch structure (see Photograph 40 in Appendix B), and two simply supported deck
58


structures with an attached railing (see Photograph 35 and 36 in Appendix B). The
welded connection at the center support shown on Photograph 34 in Appendix B
forces a continuous span condition. While these continuous span structures are still
truss type in nature, they generate a different type of stress in the top chords and
truss members than the normal stresses found in a simply supported truss. For
obvious reasons, the tied arch and the two simply-supported deck structures develop
different load paths then those found in a truss.
At first glance, Photograph 37 in Appendix B appears to show a simply-supported
pony-truss structure. However, a closer look at the support conditions shows the
structure supported by square bars cantilevered from a foundation below the water
surface (see Photographs 38 and 39 in Appendix B). Because of the allowed flexure
in the cantilevered bars, the support conditions actually resemble that of a roller with
a spring constant. Therefore, this structure was also eliminated from the sample
group.
Once the obvious unique structures were isolated, the remaining 34 structures were
grouped according to similar characteristics. The first noticeable difference was the
deck type (i.e., concrete vs. wood). Because the concrete deck generated more of a
dead load on the structure when compared to the wood deck (50psf for a 4" thick
concrete deck vs. 20psf for a 4" thick wood deck), an assumption could be made that
the members used to support a concrete deck were larger then those used to support a
wooden deck. It should also be noted that floor stringers were used to support a
wooden deck. These stringers rested on the main floor beams which were connected
to the lower chords. Structures built with a concrete deck did not have floor
stringers. Instead, the deck resembled a two way slab supported by the main floor
beams and lower chords. Because of these differences, the first grouping would be
based on the type of deck, namely concrete or wood.
59


The property modifications to the lower chords and top chords had a greater affect to
the overall performance of the structure then any other member type. For example,
the thickness of the lower chord typically affected six of the seven member types
where the thickness of the floor trusses only affected the floor trusses. In addition to
this, the stress ratios found in the lower chords and top chords were typically higher
then those found in other members (see the Graphs in Appendix E). It should also be
noted that this increase in stress was generally related to the length of the structure.
Therefore, the next parameter used for grouping would be based on length.
Based on the above mentioned parameters, the initial assumption was to divide the
34 remaining structures in the sample set into the following four subgroups:
Concrete Deck with Length <100'
Concrete Deck with Length > 100'
Wood Deck with Length < 100'
Wood Deck with Length > 100'
However, because of reasons that will be explained later, the typical pony-truss
structures would be grouped according to the following:
Concrete Deck with Length < 50' (2 Structures)
Concrete Deck with 50' < Length < 75' (2 Structures)
Concrete Deck with 75' < Length < 100' (2 Structures)
Concrete Deck with 100' < Length < 150' (1 Structure)
Wooden Deck with Length < 50' (11 Structures)
Wooden Deck with 50' < Length < 75' (10 Structures)
Wooden Deck with 75' < Length < 100' (3 structures)
Wooden Deck with 100' < Length < 125' (2 Structures)
Wooden Deck with 125' < Length < 150' (1 Structure)
60


However, as mentioned earlier, grouping similar structures produced many
subgroups from the one larger group of 43. Because of the smaller groups, two of
the above parameters produced groups with more then 3 or less structures in them.
Therefore, the only groups that could legitimately be evaluated to generate a rating
system are the following:
11 Structures with Wooden Deck and Length < 50'
10 Structures with Wooden Deck and 50' < Length < 75'
5.2 Stress Calculation Formulas
Once the structures were grouped according to the parameters listed in the previous
section, equations were derived to calculate the pseudo stress for all the members
based on the properties of a given member. As mentioned in Chapter 3, split and
rounded members did not produce the same type of symmetrical stress curves as
those associated with section loss. Therefore, the following stress increases were
associated with the members of a structure:
100% of the allowable stress added to cracked or split members on a structure.
75% of the allowable stress added to all other members on a structure
containing a cracked or split member.
15% of the allowable stress added to rounded members.
5% of the allowable stress added to all other members on a structure containing
a rounded member.
These numbers are conservative based on the analysis performed on the given
structures. It should also be noted that these stress increases will raise a red flag for
structures containing cracked or split members.
I
61


Other then cracked, split, or rounded members, the other property modification that
was analyzed was section loss. As seen on Graphs 1 to 49 in Appendix E, the
relationships between stress and thickness of a member are fairly uniform. Using the
regression analysis functions built into Microsoft Excel (Excel), best-fit curves were
imposed onto these graphs to approximate the equations associated with the stress in
each structure.
The stress in the lower chords associated with the thickness of the lower chords (see
Graph 1 in Appendix E) were the first equations generated. Tables 5.2.1 and 5.2.2
list the Excel generated equations associated with the given lengths and widths of the
structures. It should be noted that in the tables, o refers to the calculated stress in the
member from a measured thickness of t. As shown in the tables, all of the stress
equations are of the form a = atb.
62


Lower Chord Stress from Lower Chord Thickness
Structure Number Length Width Equation R2
D-l l-GG-183 20.0' 6.3' a = 0.03 89/~'5783 0.9918
D-l l-GG-185 30.0' 6.3' a = 0.0995C04944 0.9673
D-Ol-CC-338 40.0' 6.4' o- = 0.1036r0 5429 0.9996
D-12-SG-050 44.0' 5.3 D-12-SG-060 44.0' 5.3' a = 0.0946r6033 0.9992
D-16-LG-110 44.0' 5.3' cr = 0.1 130/_0 5981 0.9992
D-16-LG-140 44.0' 5.3' cr = 0.1130/5981 0.9992
D-27-MP-065 48.0' 7.3 a = 0.1631C0'6933 0.9985
D-01-CC-336 20.0' 10.5' a = 0.0552/''5300 0.9974
D-01-CC-337 40.0' 8.3 a = 0.1164C0 5879 0.9953
D-10-HC-070 48.0' 11.5' <7 = 0.2155/_0 6701 0.9992
Table 5.2.1. Stress equations for wooden dec c with Length < 50'
63


Lower Chord Stress from Lower Chord Thickness
Structure Number Length Width Equation R2
D-10-HC-200 60.3' 4.4' cr = 0.1242/" 6541 0.9946
D-10-HC-210 60.5' 4.5 a = 0.1251C06525 0.9946
D-17-WG-068 64.7' 5.4' cr = 0.1499/ 06773 0.9996
D-10-HC-220 67.0' 4.9' a = 0.205/"0'6849 0.9946
D-16-LG-025 74.0' 5.4' a = 0.3124/-a6954 0.9968
D-10-HC-105 50.0' 10.3' a = 0.1754/-'7184 0.9981
D-10-HC-090 54.0' 11.5' a-= 0.2740/-0-5453 1.0000
D-10-HC-020 60.0 11.5 a = 0.3548/a5952 1.0000
Estes-16 60. r 8.4 cr = 0.2611/0 5828 0.9998
Estes-15 70.8' 10.4 a = 0.2716/-0 7096 0.9994
Table 5.2.2. Wooden Deck wit i 50' < Length < 75'.
As seen in tables 5.2.1 and 5.2.2, stress is calculated from the measured thickness
and two variables, a and b. It was assumed that a and b were functions of length and
width of the bridges. After closer examination, it was determined that these groups
could be broken down into smaller groups dependent on width. It appeared as
though the separating width would be approximately 7.5 feet. As seen in the tables,
for a width less then 7.5 feet, the variables generally increase as the length of the
structure increases. The same can be determined for structures with a width greater
then 7.5'. Therefore, the structures were separated once again into the following
groups.
Wooden Deck with Length < 50' and Width < 7.5'
Wooden Deck with Length < 50' and Width > 7.5'
64


Wooden Deck with 50' £ Length < 75' and Width < 7.5'
Wooden Deck with 50' < Length < 75' and Width > 7.5'
The variables a and b were then plotted as a function of length. From these plots, a
built in regression analysis program in Microsoft Excel was used to derive an
structure for the eight structures listed in Table 5.2.1 with a Length < 50' and a
Width < 7.5'. Also shown are the best fit curves and equations derived by the
regression analysis program built into Excel. By calculating the values for a and b
and by knowing the thickness of a given member, the stress in the given member can
be calculated.
equation for a and b. Figure 5.2.1 shows a plot of the a and b values vs. length of the
a & b Values for Stress Functions
0.3
a = 0.0000332x3 0.0033730x2 + 0.1120928x- 1.1197664
0.2

0.1
10
20
30
40
50
60
>
b = -0.0000061X3 0.0000868x2 + 0.0242720x 0.9798873
R2 = 0.9981405
LU
-O -0.4
06
03 -0.5
-0.6
-0.7
-0.8
Length
Figure 5.2.1. Equations to find a and b for Length < 50' and Width < 7.5'
65


Section 5.1 stated the initial assumption was to divide the structures into subgroups
based on Length < 100' and Length > 100'. By looking at the plot of data points
shown in Figure 5.2.2 it can bee seen why this assumption was rejected. While it is
not immediately evident in the data points for the variable a (those along the positive
y-axis), the data points for b (those along the negative y-axis) show an obvious break
point at a length of 50'.
a and b Values for Stress Equations
to
_0
.Q
ro
CD
>
C
o
ro
3
cr
HI
o
c
CD
CD
0.6
0.4
0.2
0
-0.2
a = -0.0000113x3 + 0.0015351 x2 0.0579209x + 0.6908929
R2 = 0.8916786
-0.4 |
-0.6
0 10
b = -0.0000103x3 + 0.0014429X2 0.0639278x + 0.2592219
R2 = 0.4348456
l
-0.8
Length
Figure 5.2.2. Equations to find a and b for Length < 100' and Width > 7.5.
80
As mentioned previously, this procedure was completed to determine the stress in
the same member subjected to section loss (i.e., lower chord stress from lower chord
thickness, top chord stress from top chord thickness, etc.). To calculate the pseudo
66


stress in a member due to the section loss in a different member, a different approach
was used. Later discussions will show how the total stress in a given member can be
calculated by adding various stress components together. For example, the total
stress in the lower chord with relationship to the thickness of each member of the
structure is a combination of the stress in the lower chord associated with the
following:
The thickness of the lower chords. This pseudo stress is that which can be
calculated by using the equations with the variables "a" and "b" discussed
previously.
The thickness of the top chords.
The thickness of the rail posts.
The thickness of the diagonal truss members.
The thickness of the floor beams.
The thickness of the floor trusses.
The thickness of the floor stringers.
As stated in Chapter 3, an initial thickness of 1/2 inch was given to each member to
establish a baseline stress. Also mentioned in Chapter 3, to determine the various
stress vs. thickness relationships, the thickness of a given member was modified
while keeping the others constant at 1/2 inch. Therefore, assuming the base-line
stress for each member is constant, the stress in each of the other members
associated with the thickness of a given member would be the total stress found in
each of the other members minus their associated base-line stress.
For example, suppose the base-line stress for floor stringers was 50% of the
allowable stress for that member. The stress found in the floor stringers due to a
thickness of 1/4 inch for the lower chords and 1/2 inch for all other members was
67


51% of the allowable. It would be incorrect to assume the stress in the floor
stringers associated with a 1/4" lower chord thickness was 51% because 50% of that
stress was due to the thickness of the floor stringers. However, it could be
determined that a lower chord thickness of 1/4" created 1% stress in the floor
stringers (51 %-50%= 1 %). Therefore, the stress found on the graphs shown in
Appendix E do not represent the stress in a given member due to the change in
thickness of a different member. The change in stress found on those graphs do
however represent the additional stress for a given member due to the thickness of a
different member.
With that in mind, the change in stress of a given member was plotted as a function
of the thickness of a different member. As was done previously, Excel was used to
generate a best-fit curve and equation for the plot (see Figure 5.2.3). This equation
was then used to calculate the additional stress (oadd) in a given member due to the
thickness of a different member (i.e., the additional stress in the floor stringers due to
the thickness of the lower chords).
68


Floor Stringer Stress from Lower Chord
Thickness
C/5
0
L_
-4*
U)
l
0
CD
C
CO
4_
o
o
LL
c
0
CD
C
co
.c
O
Figure 5.2.3. Equations for Floor Stringer Stress, Length < 50' and Width < 7.5'
It should be noted that this procedure was not completed for each individual case.
The additional stress in a member due to the thickness of another member was
generally low (less then 5% allowable stress increase). Therefore, the worst case
was typically used for all of the structures. On the occasions with a wider spread of
stress increases (i.e., one structure being less then 5% allowable stress increase and
another being greater then 10% allowable stress increase), the structures were broken
into the four groups previously mentioned and the worst case for each group was
used.
Stress in the diagonal truss members were directly related to the direction of the truss
members. In other words, if all of the truss members were angled down toward the
0.025
0.020
0.015
0.010
0.005
0.000
0.00
69


center of the span, they were all in tension for normal gravity loads. However, if any
of the truss members were angled downward toward the nearest abutment, that
member would be in compression and subjected to different stress limits. Therefore,
if any of the truss members were in compression, it was assumed all of the members
would be limited to compression stresses. This would error on the conservative side.
By completing these procedures for each case, the following equations were
developed to calculate the pseudo stress in a given member for structures with
wooden decks.
I. / < 50', w < 7.5', and Stress based on Lower Chord Thickness V
A. Lower Chord Stress
a = 2.77e~5/3 2.8le-3/2 + 9.43e2/ 0.944 <5.2.1>
b = -6.82e'0/3 -1,57e 5/2 + 2.20e 2/ 0.957 <5.2.2>
o = atb <5.2.3>
B. Additional Top Chord Stress
oADD = 0.0128/ + 0.0065 <5.2.4>
C. Additional Rail Post Stress

D. Additional Diagonal Truss Stress
cradd = 0 fr tension only members <5.2.6>
oadD = 0.688/2 0.653/ + 0.156 for compression <5.2.7>
E. Additional Floor Beam Stress
oADD = 0.432/2 -0.343/ + 0.0648 <5.2.8>
F. Additional Floor Truss Stress
^ADD ~ 0 <5.2.9>
70


G. Additional Floor Stringer Stress a add = 0.464/2 0.443/ + 0.106 <5.2.10>
/ < 50', w < 7.5', and Stress based on Top Chord Thickness '/' A. Additional Lower Chord Stress aAdd = 1.024/2 -0.978/+ 0.235 <5.2.11>
B. Top Chord Stress a = 3.22e"5/3 -3.18e 3/2 + 0.101/-0.955 <5.2.12>
6 = 1.17e"4/3 1,28e2/2 + 0.449/ 5.684 <5.2.13>
<7 = ath <5.2.14>
C. Additional Rail Post Stress add =0.064/2 -0.08/+ 0.024 <5.2.15>
D. Additional Diagonal Truss Stress a add = 0 fr tension only members <5.2.16>
add = 0.560/2 0.488/+ 0.105 for compression <5.2.17>
E. Additional Floor Beam Stress (7ADD =0.22412 -0.215/+ 0.052 <5.2.18>
F. Additional Floor Truss Stress ADD = ^ <5.2.19
G. Additional Floor Stringer Stress a add = 0.46912 0.431/ + 0.0989 <5.2.20>
III. / < 50', w < 7.5', and Stress based on Rail Post Thickness V
A. Additional Lower Chord Stress
add= 0 <5.2.21>
B. Additional Top Chord Stress
add= 0 <5.2.22>
71


C. Rail Post Stress
a = -1,32e~5/4 + 1,82e3/3 9.19e 2/2 + 1.99/ 15.37 <5.2.23>
b = -6.69e '74 + 9.44e4/3 4.82e2/2 + 1.05/ 8.79 <5.2.24>
a = ath D. Additional Diagonal Truss Stress <5.2.25>
& ADD = 0 E. Additional Floor Beam Stress <5.2.26>
ADD ~ 0 F. Additional Floor Truss Stress <5.2.27>
GADD ~ 0 G. Additional Floor Stringer Stress <5.2.28>
a add = 0.064/2 0.069/ + 0.019 IV. / < 50', w < 7.5', and Stress based on Diagonal Truss Thickness 7' A. Additional Fower Chord Stress <5.2.29>

a add = 0.36812 0.297/ + 0.057 for compression B. Additional Top Chord Stress <5.2.31>
G ADD = 0 C. Additional Rail Post Stress <5.2.32>
ADD ~ ^ <5.2.33>
72


D. Diagonal Truss Stress
a = -3.07e4/2 + 2.18e~2l -0.29 for tension members
a = -7.95e~5/3 + 7.97e3/2 0.24/ + 2.36 for compression
b = -2.11 l2 + 0.020/ -1.12 for tension members
b = -7.37e5/3 + 7.11 e"3/2 0.21/ + 1.34 for compression
a = atb
E. Additional Floor Beam Stress
ADD ^
F. Additional Floor Truss Stress
ADD 0
G. Additional Floor Stringer Stress
ADD ~ ^
V. / < 50', w < 7.5', and Stress based on Floor Beam Thickness V
A. Additional Fower Chord Stress
oADD = 0.368/2 -0.357/ + 0.087
B. Additional Top Chord Stress
oADD = 0.112/2 -0.101/+ 0.023
C. Additional Rail Post Stress
GADD ~ ^
D. Additional Diagonal Truss Stress
ADD ~ ^
E. Floor Beam Stress
a = 5.45eV -0.126w2 + 0.948vv-2.184
b = 5.03e3w3 -0.119vv2 +0.886w- 2.860
<7 = ath
<5.2.34>
<5.2.35>
<5.2.36>
<5.2.37>
<5.2.38>
<5.2.39>
<5.2.40>
<5.2.41 >
<5.2.42>
<5.2.43>
<5.2.44>
<5.2.45>
<5.2.46>
<5.2.47>
<5.2.48>
73


F. Additional Floor Truss Stress
0 add 0
G. Additional Floor Stringer Stress
= 0.368/2 0.344/ + 0.081
ADD
VI. / < 50', w < 7.5', and Stress based on Floor Truss Thickness V
A. Additional Lower Chord Stress
aadd ~ 0
B. Additional Top Chord Stress
ADD 0
C. Additional Rail Post Stress
GADD ~ 0
D. Additional Diagonal Truss Stress
G ADD ~ 0
E. Additional Floor Beam Stress
GADD ~ 0
F. Floor Truss Stress
a = -4.03e_2w3 + 0.869w2 6.166w+ 14.487
b = 0.44w4 11.97w3 +121.1 lw2 539.96w+894.03
<7 = ath
G. Additional Floor Stringer Stress
GADD ~
VII. / < 50', w < 7.5', and Stress based on Floor Stringer Thickness '/
A. Additional Lower Chord Stress
G ADD ~ ^
B. Additional Top Chord Stress
GADD ~ 0
<5.2.49>
<5.2.50>
<5.2.51>
<5.2.52>
<5.2.53>
<5.2.54>
<5.2.55>
<5.2.56>
<5.2.57>
<5.2.58>
<5.2.59>
<5.2.60>
<5.2.61>
74


c.
D.
E.
F.
G.
Additional Rail Post Stress
a ADD ~ 0
Additional Diagonal Truss Stress
ADD ~ ^
Additional Floor Beam Stress
ADD ~ 0
Additional Floor Truss Stress
G ADD ~ 0
Floor Stringer Stress
a = 5.49e'5/3 5.42e~3/2 + 0.168/ 1.517
b ~ -5.33e~5/4 + 7.70e3/3 -0.40/2 +8.96/-71.76
cr = ath
VIII. / < 50', w > 7.5', and Stress based on Fower Chord Thickness 7'
A. Fower Chord Stress
a = 3.33e4/2 1,69e~2l + 0.261
b = -2.64e4/2 + 1.29e~2! 0.683
cr = ath
B. Additional Top Chord Stress
aADD = 0.192/2 0.177/ + 0.041
C. Additional Rail Post Stress
oADD = -0.016/2 +0.0044?+ 0.0018
D. Additional Diagonal Truss Stress
a add = 0.688/2 0.653/+ 0.156 for compression
<5.2.62>
<5.2.63>
<5.2.64>
<5.2.65>
<5.2.66>
<5.2.67>
<5.2.68>
<5.2.69>
<5.2.70>
<5.2.71>
<5.2.72>
<5.2.73>
<5.2.74>
<5.2.75>
75


E. Additional Floor Beam Stress
oADD = 0.22412 0.18/ + 0.0035
F. Additional Floor Truss Stress
aADD ~ 0
G. Additional Floor Stringer Stress
aADD = 0.144/2 -0.145/ + 0.0368
IX. / < 50', w > 7.5', and Stress based on Top Chord Thickness V
A. Additional Fower Chord Stress
uADD = 1.024/2 0.977/ + 0.235
B. Top Chord Stress
a = 3.55e~4l2 -1,88e-2/+ 0.298
b = 1.03e-3/2 7.47e 2/ + 0.487
<7 = ath
C. Additional Rail Post Stress
D. Additional Diagonal Truss Stress
aadd = 0 fr tension only members
a add = 0.736?2 -0.671/+ 0.153 for compression
E. Additional Floor Beam Stress
aadd =0.096/2 -0.0856/+ 0.019
F. Additional Floor Truss Stress
a ADD ~ 0
G. Additional Floor Stringer Stress
ajnn = 0.469/2 -0.431/+ 0.0989
<5.2.76>
<5.2.77>
<5.2.78>
<5.2.79>
<5.2.80>
<5.2.81>
<5.2.82>
<5.2.83>
<5.2.84>
<5.2.85>
<8.2.86>
<5.2.87>
<5.2.88>
76


X. / < 50', w > 7.5', and Stress based on Rail Post Thickness 7'
A. Additional Lower Chord Stress
^ADD ~ 0 B. Additional Top Chord Stress <5.2.89>
G ADD = 0 C. Rail Post Stress <5.2.90>
a -1,23e~4/2 + 1,00e2/ 937e~2 <5.2.91 >
b = 1.03e3/2 6.05e'2/ + 9.37e'2 <5.2.92>
cr = atb D. Additional Diagonal Truss Stress <5.2,93>
17 ADD = ^ E. Additional Floor Beam Stress <5.2.94>
ADD ~ 0 F. Additional Floor Truss Stress <5.2.95>
ADD ~ 0 G. Additional Floor Stringer Stress <5.2.96>
aADD =0.064/2 -0.069/+ 0.019 XI. / < 50', w > 7.5', and Stress based on Diagonal Truss Thickness '/' A. Additional Lower Chord Stress <5.2.97>
a4DD = 0.432/2 0.394/ + 0.090 for tension only members <5.2.98>
cr add = 0.368/2 0.2977 + 0.057 for compression B. Additional Top Chord Stress <5.2.99>
ADD = 0 C. Additional Rail Post Stress <5.2.100>
ADD ~ 0 <5.2.101 >
77


D. Diagonal Truss Stress
a = -3.07e~AI2 + 2.18e~2l 0.29 for tension members
a = -7.95e~5/3 + 7.97e 3/2 0.24/ + 2.36 for compression
b = -2.77e4/2 + 0.020/ 1.12 for tension members
b = -7.37e5/3 + 7.11 e'3/2 0.21/ + 1.34 for compression
a = ath
E. Additional Floor Beam Stress
^ ADD = 0
F. Additional Floor Truss Stress
a ADD = ^
G. Additional Floor Stringer Stress
^ ADD = 0
XII. / < 50', w > 7.5', and Stress based on Floor Beam Thickness V
A. Additional Lower Chord Stress
aADD = 0.212t2 0.2221 + 0.044
B. Additional Top Chord Stress
C. Additional Rail Post Stress
ctadd =0.192/2 -0.222/+ 0.064
D. Additional Diagonal Truss Stress
G ADD = ^
E. Floor Beam Stress
a = 5.45 b = 5.03e^3u'3 0.118w2 + 0.886vr- 2.860
cr = atb
<5.2.102>
<5.2.103>
<5.2.104>
<5.2.105>
<5.2.106>
<5.2.107>
<5.2.108>
<5.2.109>
<5.2.110>
<5.2.111>
<5.2.112>
<5.2.113>
<5.2.114>
<5.2.115>
<5.2.116>
78


F. Additional Floor Truss Stress
ADD ~ 0
G. Additional Floor Stringer Stress
0.688/2 -0.626t +0.143
ADD
XIII. / < 50', w > 7.5', and Stress based on Floor Truss Thickness
A. Additional Lower Chord Stress
= 0
cr
ADD
B. Additional Top Chord Stress
0ADD ~ ^
C. Additional Rail Post Stress
a ADD 0
D. Additional Diagonal Truss Stress
^ADD ~ ^
E. Additional Floor Beam Stress
G ADD = 0
F. Floor Truss Stress
a = -4.03e~2w3 + 0.869w2 6.166w+ 14.487
b = 0.44w4 11.97w3 + 121.1 Ivt2 539.96w+ 894.03
a = atb
G. Additional Floor Stringer Stress
a ADD = ^
XIV. / < 50', w > 7.5', and Stress based on Floor Stringer Thickness V
A. Additional Lower Chord Stress
= 0
cr
ADD
B. Additional Top Chord Stress
a ADD 0
<5.2.117>
<5.2.118>
<5.2.119>
<5.2.120>
<5.2.121 >
<5.2.122>
<5.2.123>
<5.2.124>
<5.2.125>
<5.2.126>
<5.2.127>
<5.2.128>
<5.2.129>
79


XV.
C. Additional Rail Post Stress
^ ADD ~ 0 <5.2.130>
D. Additional Diagonal Truss Stress
GADD ~ ^ <5.2.131 >
E. Additional Floor Beam Stress
a ADD ~ 0 <5.2.132>
F. Additional Floor Truss Stress
G ADD = 0 <5.2.133>
G. Floor Stringer Stress
a = 3.60e 4/2 2.20e'2/ + 0.359 <5.2.134>
b = 1.43e3/2 -9.00e~2/ + 0.536 <5.2.135>
a = atb <5.2.136>
50' < / < 75', w < 7.5', and Stress based on Lower Chord Thickness 7'
A. Lower Chord Stress
a = 9.23e4/2 0.11/ + 3.41 <5.2.137>
b = 1.88e~4/2 2.81c"2/ + 0.36 <5.2.138>
a atb <5.2.139>
B. Additional Top Chord Stress
add = 0.080/2 0.092/ + 0.026 <5.2.140>
C. Additional Rail Post Stress
aADD = 0.208/2 -0.203/ + 0.050 <5.2.141 >
D. Additional Diagonal Truss Stress
aadd ~ 0 fr tension only <5.2.142>
cjadd = 0.640/2 0.600/ + 0.141 for compression <5.2.143>
80


E. Additional Floor Beam Stress
XVI.
1
I
I
(Jadd = 0.784C 0.740/ + 0.175
F. Additional Floor Truss Stress
add = 0
G. Additional Floor Stringer Stress
crAdD = 0.960/2 0.990/ + 0.257
50' < / < 75', w < 7.5', and Stress based on Top Chord Thickness
A. Additional Lower Chord Stress
a add = 1.184/2 -1.127/ + 0.270
B. Top Chord Stress
a -1,23e3/2 + 0.17/ 5.54
b = 4.2 le4/2 6.54e~2/ + 1.75
cr = a th
C. Additional Rail Post Stress
= 0.544/2 -0.478/+ 0.104
a
ADD
D. Additional Diagonal Truss Stress
= 1.440/2 -1.228/+ 0.258
a
ADD
E. Additional Floor Beam Stress
0.848/2 -0.777/+ 0.178
ADD
F. Additional Floor Truss Stress
^add ~ 0
G. Additional Floor Stringer Stress
add ~ -440/'
.364/+ 0.325
<5.2.144>
<5.2.145>
<5.2.146>
'/'
<5.2.147>
<5.2.148>
<5.2.149>
<5.2.150>
<5.2.151 >
<5.2.152>
<5.2.153>
<5.2.154>
<5.2.155>


XVII. 50' < / < 75', w < 7.5', and Stress based on Rail Post Thickness 7'
A. Additional Lower Chord Stress
aADD = 0.36812 0.328/ + 0.073 B. Additional Top Chord Stress <5.2.156>
ADD ~ 0 C. Rail Post Stress <5.2.157>
a = 1,20e4/2 1.05e2/ + 0.259 <5.2.158>
b = -2.70e~4/2 + 4.16e2/ 2.30 <5.2.159>
<7 = atb D. Additional Diagonal Truss Stress <5.2.160>
^ ADD = 0 E. Additional Floor Beam Stress <5.2.161 >
a add =0.56012 -0.520/+ 0.121 F. Additional Floor Truss Stress <5.2.162>
ADD ~ ^ G. Additional Floor Stringer Stress <5.2.163>
ADD ~ 0 <5.2.164>
XVIII. 50' < / < 75', w < 7.5', and Stress based on Diagonal Truss Thickness 7'
A. Additional Lower Chord Stress
oADD = 0.816/2 0.728/ + 0.162 B. Additional Top Chord Stress <5.2.165>
ADD ~ ^ C. Additional Rail Post Stress <5.2.166>
oadd ~ 1 152/2 1.061/ + 0.245 for tension only <5.2.167>
aadd = 0 for compression <5.2.168>
82


Diagonal Truss Stress
a = 2.33e~4l2 2.48e~2/ + 0.727 for tension only <5.2.169>
a -5.62e~Al2 + 1.75e~2! 2.50 for compression <5.2.170>
b = -3.28e~4l2 +4.10^ 2/ 2.07 for tension only <5.2.171 >
b = 6.30e"4/2 9.39e 2l + 2.94 for compression <5.2.172>
a = atb <5.2.173>
Additional Floor Beam Stress
GADD ~ 0 <5.2.174>
Additional Floor Truss Stress
GADD = ^ <5.2.17 5>
Additional Floor Stringer Stress
oADD = 0.368/2 -0.341/+ 0.079 <5.2.176>
XIX. 50' < / < 75', h < 7.5', and Stress based on Floor Beam Thickness't'
A. Additional Lower Chord Stress
^ add = 0 <5.2.177>
B. Additional Top Chord Stress
cadd ~ 0 <5.2.178>
C. Additional Rail Post Stress
aADD =0.400/2 -0.404/+ 0.103 <5.2.179>
D. Additional Diagonal Truss Stress
ADD= 0 <5.2.180>
E. Floor Beam Stress
a = 5.27e4/2 6.3 le~2/ + 1.97
b = 2.66cC3/2 -0.344/+ 10.435
<7 = ath
<5.2.181 >
<5.2.182>
<5.2.183>
83


F. Additional Floor Truss Stress
XX.
XXL
ADD ~ ^
<5.2.184>
Additional Floor Stringer Stress
= 0.592/2 -0.608t + 0.157
cr
ADD
<5.2.185>
50' < / < 75', w < 7.5', and Stress based on Floor Truss Thickness V
A.. Additional Lower Chord Stress
= 0
a
ADD
B. Additional Top Chord Stress
& ADD ~ 0
C. Additional Rail Post Stress
add ^
D. Additional Diagonal Truss Stress
ADD ^
E. Additional Floor Beam Stress
aADD ~ 0
F. Floor Truss Stress
a = 5.56e 4!2 8.\4e~2l + 3.09
b = 1.41e"3/2 -0.199/+ 6.400
o = ath
G. Additional Floor Stringer Stress
ADD ~ 0
<5.2.186>
<5.2.187>
<5.2.188>
<5.2.189>
<5.2.190>
<5.2.191 >
<5.2.192>
<5.2.193>
<5.2.194>
50' < / < 75', w < 7.5', and Stress based on Floor Stringer Thickness V
A. Additional Lower Chord Stress
^ADD ~ ^
B. Additional Top Chord Stress
G ADD ~~ ^
<5.2.195>
<5.2.196>
84


C. Additional Rail Post Stress
^ ADD 0 D. Additional Diagonal Truss Stress <5.2.197>
a ADD = 0 E. Additional Floor Beam Stress <5.2.198>
& ADD ~ 0 F. Additional Floor Truss Stress <5.2.199>
ADD ~ 0 G. Floor Stringer Stress <5.2.200>
a = 2.86c*""4/2 3.03e2/ + 0.891 <5.2.201 >
b 4.26e3/2 0.550/ + 17.239 <5.2.202>

XXII. 50' < / < 75', w > 7.5', and Stress based on Lower Chord Thickness 7'
A. Lower Chord Stress
a = -5.65e6/3 -1,91e4/2 + 9.04e2/ + 3.16 <5.2.204>
b = 2.40e4/3 4.45e"2/2 + 2.72/ 55.67 <5.2.205>
o ath <5.2.206>
B. Additional Top Chord Stress aADD = 0.080/2 0.092/ + 0.026 C. Additional Rail Post Stress <5.2.207>
aADD = 0.208/2 -0.203/ + 0.050 D. Additional Diagonal Truss Stress <5.2.208>
a add = 0 fr tension only <5.2.209>
a 4DD = 0.640/2 -0.600/+ 0.141 for compression <5.2.210>
85


E. Additional Floor Beam Stress
a add = 0.784/2 0.740/ + 0.175 F. Additional Floor Truss Stress <5.2.211>
7ADD = 0 G. Additional Floor Stringer Stress <5.2.212>
a4Dd = 0.960/2 -0.990/ + 0.257 <5.2.213>
XXIII. 50' < / < 75, w > 7.5', and Stress based on Top Chord Thickness V
A. Additional Lower Chord Stress
aaDd = 2.096/2 -2.004/+ 0.481 B. Top Chord Stress <5.2.214>
// = -8.74e4/2 + 0.11/ 3.26 <5.2.215>
b -1,49e3/2 + 0.18/ 6.08 <5.2.216>
er = ath C. Additional Rail Post Stress <5.2.217>
(JADD =0.544/2 -0.478/+ 0.104 D. Additional Diagonal Truss Stress <5.2.218>
aAdD = 1.440/2 -1.228/+ 0.258 E. Additional Floor Beam Stress <5.2.219>
CJadd = 0.848/2 -0.777/ + 0.178 F. Additional Floor Truss Stress <5.2.220>
a ADD = 0 G. Additional Floor Stringer Stress <5.2.221 >
a add = 1.440/2 -1.364/+ 0.325 <5.2.222>
86


XXIV. 50' < / < 75', w > 7.5', and Stress based on Rail Post Thickness '?'
A. Additional Lower Chord Stress
a add = 0.368?2 0.328? + 0.073 B. Additional Top Chord Stress <5.2.223>
ADD ~ 0 C. Rail Post Stress <5.2.224>
a = 5.93c'5/3 -1.06e-2/2 +0.631/- 12.326 <5.2.225>
b = 1.00e"4/3 1.89e"2/2 + 1.186/ 25.156 <5.2.226>
a ath D. Additional Diagonal Truss Stress <5.2.227>
ADD = 0 E. Additional Floor Beam Stress <5.2.228>
aADD 0.560/2 + 0.520/ + 0.121 F. Additional Floor Truss Stress <5.2.229>
G ADD = ^ G. Additional Floor Stringer Stress <5.2.230>
aADD ~ ^ <5.2.231 >
XXV. 50' < / < 75', w > 7.5', and Stress based on Diagonal Truss Thickness 7'
A. Additional Lower Chord Stress
aaDd = 0.816?2 -0.728?+ 0.162 B. Additional Top Chord Stress <5.2.232>
& ADD = ^ C. Additional Rail Post Stress <5.2.233>
a WD = 1.152?2 1.061? + 0.245 for tension only <5.2.234>
add =0 for compression <5.2.235>
87