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Engineering Mechanics 461
TRUSS BRIDGE ANALYSIS - TRUCK WEIGHTS
SUBMITTED BY: HAZIM AL KHUSAIBI DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING PENNSYLVANIA PENNSYLVANIA STATE STATE UNIVERSITY UNIVERSIT Y EMCH 461 FINAL PROJECT SUBMITTED TO DR. I. SMID
• H a z i m A l K h u s a i b i • E m a i l ; H s a 5 0 0 6 @ p s u . e d u
Table of Contents Background
1
Finite Element Analysis
1
Truss Bridge
1
Introduction
2
General Introduction to Project
2
Geometry
2
Approach & Formulation
4
Assumptions
4
Program Selection & Other ANSYS Assumptions
5
Problem Formulation
5
Analysis
6
Part 1: Control Analysis:
6
Part 2: Analysis After 75 year Cycle:
7
Results
8
Reaction Forces:
8
Deflection:
9
Axial Stress:
9
Discussion:
10
Conclusion
10
Results & Improvements to Model:
10
Finite Element Methods Discussion:
11
Appendix
12
List of Figures
12
List of Tables
12
Glossary
13
Bibliography & Programs Used
14
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Background Finite Element Analysis
Finite Element Method can be defined as the numerical method for solving problems of engineering and mathematical physics. Fields usually frequented by the finite element method range from structural analysis, mass transport, fluid flow and heat transfer. For complex cases and geometries it is also possible to obtain an analytical mathematical solution but this will not be emphasised much on this project. Developed in the 1940s by Structural engineers (Hrennikoff & McHenry) the finite element method increasingly evolved with the aid of computer programming, from being a lattice of single dimensional analysis to an enormous and advantageous application in solving complicated engineering programs from structural engineering to bioengineering.1 Truss Bridge
Truss structures are composed of members that are connected to form a rigid frame of steel, this broad application can be used in many areas, such as roof structures rail road and other transportation bridges. The individual members of a Truss Bridge are the load carrying components of the structure, they are arranged in a triangular manner resulting in the loads carried to become either in tension or compression. Today bridge trusses are mainly used for short span distances, since suspension and
other advanced bridges with modern concrete & steel standards.
Typical Short Span Truss Bridge used in project
Figure 1
1
Logan, Daryl L. A First Course in the Finite Element Method . Detroit: Cengage-Engineering, 2006. Print.
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Introduction General Introduction to Project
As a senior in the Civil Engineering program with an emphasis in Structural Engineering, Bridges play an important role in the fundamentals of Structural Design. Especially since bridges undergo a variety of loads, such as wind, snow and the transient loads due to the vehicular traffic utilising the bridge. Today, in the United States alone, thousands of aged bridges are in active service, challenging many municipalities and state governments to spend millions and hire many engineers to evaluate the structural integrity of the bridge. Avoiding disasters such as the collapse of the I-35 W Mississippi River Truss-Arch Bridge in Minnesota. (Date of Incident: Wednesday, August, 1st 2007) My project’s aim is to highlight the affect of vehicular transient loads, mainly the loads due to heavy duty trucks utilising a short span truss bridge, by emphasising the results of deflection due to loads of a Truss Bridge before and after ageing 75 years. The properties I found very important to consider after this time are: Fatigue, accumulation of rust, cross bracing distortion and the reduction of redundancy at the connection points of the girders. Geometry
The bridge chosen for this project, is a Howe Truss Configuration bridge, consisting of cross braced deck truss and a multi steel girder spans. The bridge geometric properties are as follows:
1
Short spanned bridge that is 40 m (~130 ft) long
2
Base Girders that are 5 m each (W21x44)
3
Diagonal truss beam are 9.43 m each (W14x22)
4
The hight of the Truss Girder is 8 m Table 1
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The geometry combined results in the following arrangement in the finite element analysis software, ANSYS. The base girders and beams are all connected via gusset plates and are cross braced on the top as well as the bottom where the pavement sits, the bridge carries a two way, four-lane road that serves about 7,500 trucks per day.
Figure 2: ANSYS model showing member and nodal assignment
Table 2
This table to the right illustrates how the key1
2
3
4
5
6
7
8
0, 0
5, 0
10, 0
15, 0
20, 0
25, 0
30, 0
35, 0
9
10
11
12
13
14
15
16
40, 0
35, 8
40, 8
25, 8
20, 8
15, 8
10, 8
5, 8
points are assigned to the coordinate system (x,y) in ANSYS forming the truss shown in the image above. Please refer to the text input attached to the Glossary section for more information and the (.txt) file used to execute the command. The following material properties and element type were used to model the truss bridge configuration into ANSYS. ELEMENT USED TO R EPRESENT (GIRDERS & BEAMS)
LINK 1
POISSON’S RATIO
0.29
MODULUS OF ELASTICITY
200 GPa
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Approach & Formulation Assumptions
To make this FEA problem much simpler, several basic assumptions have been made. The assumptions made concern the properties of the steel girders, the type of connections of the steel girders and beams, the amount of live load due to the transient load and finally the location of the load between the two cases. 1. Girder - Beam Connections:
The girder-beam connections used in an actual Truss Bridge uses gusset
plates, for simplification, the gusset plates were omitted from the finite element analysis and instead, simply line connections converging to a point were used instead. As illustrated below. Simplification
Gusset Plate
Figure 3
Figure 4
2. Beam-Girder Cross Sectional Area: The average cross-sectional area is assumed as (3250 mm 2).
3. The
(ADT): The Average Daily Traffic will be assumed as 15,000 trucks in both directions, as the
bridge is mainly a cargo route. 4. Predicted
Average Life: The predicted average life at a typical live-load stress of 138 MPa, is between
20,000 and 40,000 cycles. 5. Lane Loading:
The Lane loading is set using the maximum AASHTO legal limit of 356 kN, at a
spacing of 38 m. A single point load of 356 kN will be used at the mid point of the span for maximum deflection calculation. The ANSYS model assumes 10,000 significant load cycles per day. Final Project
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6. Truss Deterioration Assumption:
Many factors play into the deterioration of a Truss Bridge, most
notably Fatigue, Fatigue cracking at gusset plate connections, excessive truck loading and a lack of redundancy in the mainframe of the truss bridge. To simplify and summarise all these factors in ANSYS, the Modulus of Elasticity (E) will be reduced by, modelling the reduction in Stiffness (E I). Program Selection & Other ANSYS Assumptions
The truss bridge will be modelled using the (ANSYS 11.0) finite element analysis software. The type of element used for this Analysis is the structural mass (LINK1 --> 2D spar) element for all the beams and girders in the truss assembly. Metric units were used in Metres (m) for distances and spans and Newtons (N) for loads. • Constraints: The Truss Bridge assembly is fixed in all degrees of freedom at Keypoint #1, bridge is pinned at Keypoint #9. • The Control Modulus of Elasticity used is 200 GPa, and a Poisson's ratio of (0.29). • The Modulus of Elasticity after 75 years of deterioration assumed as 0.02 GPa. • Force due to truck loading: Simplified to point load of 356 kN. • Total Dead Load (Self Weight) of the truss assembly is (818.24 kN) distributed equally at Nodes (1 through 9) as (90.9 kN) Point Loads. • ANSYS Analysis Type: Static Truss Analysis. Problem Formulation
Before beginning the ANSYS analysis, hand calculations were used to solve for t he internal reactions of the beam-Girder configuration (By method of sections), and beams and girders are labeled according to their reactions being in compression or tension. The loading used was strictly the dead loads of the Final Project
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beams, and the results are used to stimulate where the weakest connection point in the truss configuration may be present. Once these calculations were complete the Dead loads (Self weight) will be simplified to the nodes numbered (1 - 9). The ANSYS analysis of the Truss is done twice as follows: 1. The first part
analysis, calculates the nodal deflection, reaction forces and stress for the Truss
configuration used. These results are to be used as a fixed control, to compare later with the results due to 75 years of service. 2. The second part of the analysis, models the excessive loading after 75 years of service cycles,
nodal deflection, reaction forces and the stress for the truss configuration measured will be compared to the control results.
Analysis
Figure 5: ANSYS model showing mesh distribution and Nodal loading (Self Weight & Truck)
Part 1: Control Analysis:
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Figure 6: ANSYS model showing exaggerated deflection of the truss configuration 6
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Figure 7: ANSYS model showing Nodal Deflection Solution with the Red Colour indicating the max value
Figure 8: ANSYS model Axial Stress and the stress distribution along the Truss configuration
Part 2: Analysis After 75 year Cycle:
Figure 9: ANSYS model showing exaggerated deflection of the truss configuration
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Figure 10: ANSYS model showing Nodal Deflection Solution with the Red Colour indicating the max value
Figure 11: ANSYS model Axial Stress and the stress distribution along the Truss
Results Reaction Forces:
THE FOLLOWING X,Y,Z SOLUTIONS ARE IN THE GLOBAL COORDINATE SYSTEM
CONT OL REA TIONS
REACTIONS
NODE
FX
FY
NODE
FX
FY
1
2.33E-09
5.87E+05
1
-6.46E-09
5.87E+05
5.87E+05
9
1.17E+06
Total
9 Total
2.33E-09 Table 3
5.87E+05 -6.46E-09
1.17E+06
Table 4
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Deflection: Deflection:
Control Deflection: THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN
THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN
THE GLOBAL COORDINATE SYSTEM
NODE 1
UX
UY
0.0000
0.0000
THE GLOBAL COORDINATE SYSTEM
UZ
USUM
NODE
0.0000
0.0000
1
UX
UY
0.0000
0.0000
UZ
USUM
0.0000
0.0000
2 0.23856E-08-0.36154E-07 0.0000
0.36232E-07
2 0.23856E-04-0.36154E-03 0.0000
0.36232E-03
3 0.67197E-08-0.66371E-07 0.0000
0.66711E-07
3 0.67197E-04-0.66371E-03 0.0000
0.66711E-03
4 0.12565E-07-0.88218E-07 0.0000
0.89108E-07
4 0.12565E-03-0.88218E-03 0.0000
0.89108E-03
5 0.19485E-07-0.10255E-06 0.0000
0.10439E-06
5 0.19485E-03-0.10255E-02 0.0000
0.10439E-02
6 0.26405E-07-0.88218E-07 0.0000
0.92084E-07
6 0.26405E-03-0.88218E-03 0.0000
0.92084E-03
7 0.32250E-07-0.66371E-07 0.0000
0.73792E-07
7 0.32250E-03-0.66371E-03 0.0000
0.73792E-03
8 0.36585E-07-0.36154E-07 0.0000
0.51435E-07
8 0.36585E-03-0.36154E-03 0.0000
0.51435E-03
9 0.38970E-07 0.0000
0.0000
0.38970E-07
9 0.38970E-03 0.0000
0.0000
0.38970E-03
10 0.69198E-08-0.30047E-07 0.0000
0.30833E-07
10 0.69198E-04-0.30047E-03 0.0000
0.30833E-03
11 0.93055E-08-0.61383E-07 0.0000
0.62085E-07
11 0.93055E-04-0.61383E-03 0.0000
0.62085E-03
12 0.13640E-07-0.84348E-07 0.0000
0.85444E-07
12 0.13640E-03-0.84348E-03 0.0000
0.85444E-03
13 0.19485E-07-0.97053E-07 0.0000
0.98989E-07
13 0.19485E-03-0.97053E-03 0.0000
0.98989E-03
14 0.25331E-07-0.84348E-07 0.0000
0.88070E-07
14 0.25331E-03-0.84348E-03 0.0000
0.88070E-03
15 0.29665E-07-0.61383E-07 0.0000
0.68175E-07
15 0.29665E-03-0.61383E-03 0.0000
0.68175E-03
16 0.32050E-07-0.30047E-07 0.0000
0.43932E-07
16 0.32050E-03-0.30047E-03 0.0000
0.43932E-03
MAXIMUM ABSOLUTE VALUES NODE
9
5
0
MAXIMUM ABSOLUTE VALUES 5
VALUE 0.38970E-07-0.10255E-06 0.0000
NODE
0.10439E-06
9
5
0
5
VALUE 0.38970E-03-0.10255E-02 0.0000
0.10439E-02
Axial Stress: Control Axial Element Stress: Element Axial Stress
1
2
95.4 173
Element
16
17
Axial Stress
138
-81
3
4
5
6
234
277
277
234
18
19
20
21
7
8
9
10
11
12
13
14
173 95.4 -180 153 -147 125 -114 96.7 22
23
24
96.7 -114 125 -147 153 -180 -95
25
26
27
28
-173 -234 -234 -173
15 -81
29 -95
Table 5
Axial Element Stress: Element Axial Stress
1
2
95.4 173
Element
16
17
Axial Stress
138
-81
3
4
5
6
234
277
277
234
18
19
20
21
7
8
9
10
11
12
13
14
173 95.4 -180 153 -147 125 -114 96.7 22
23
24
96.7 -114 125 -147 153 -180 -95
25
26
27
28
-173 -234 -234 -173
15 -81
29 -95
Table 6
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Discussion:
The results are most interesting, with a large reduction in the Modulus of Elasticity (Assumed with the deterioration of the truss assembly), the FEA program ANSYS yielded relatively the exact same Axial Stresses in both cases, a small variation in the reaction force at Node #1. The most notable difference, that this project aims to highlight, is the significant change in deflection. The deflection of the truss assembly is initially (-0.10255 x 10-6 m) and went up several orders of magnitude to (-0.10255 x 10 -2 m), at the middle of the span (Refer to Node #5). This large change in magnitude would suggest a predication for a significant failure at multiple points for the truss bridge assembly.
Conclusion The ANSYS analysis for this Truss Bridge is very insightful, even with many factors being omitted in the analysis. The results are very interesting in that the exaggerated change in (E) did not yield any changes in the Axial Stress nor the Reaction forces of the Truss configuration, neither does this changes the internal forces of the beams and girders. The change was most notable in the value of deflection, which is an important value to study in bridge failures. Results & Improvements to Model:
I am very satisfied with the results I have yielded with this analysis, and if I had more time, given more time and properties, I could have incorporated many more properties into the analysis, such as the geometry of the steel beams and girders used, the presence of the gusset plates at each connection point, as well as the affect of the cross bracing truss members that contribute to the general stiffness of the over all truss configuration. I would also incorporate the entire 3-Dimensional configuration of the Final Project
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truss bridge, along with properties for the concrete pavement and girders used to form the four-lane road. Finite Element Methods Discussion:
The Finite Element analysis software used for this project is ANSYS 11.0, and was run directly using the university’s server & HAMMER (interactive login cluster) on my personal computer at home. Most of the assumptions used for this analysis were attained using the help of Dr. Edward Gannon (
[email protected]), a professor in the Civil Engineering Department, whose input was important in helping simply the Truss configuration for me and making it workable on ANSYS. In reference to my results formulation on ANSYS, the truss configuration was meshed once only, since the important factor in my results, deflection, did not get affected my increasing the mesh size, nonetheless, as simple as the truss configuration I used, meshing any more would not have yielded any difference in results. The text INPUT used to formulate my project is attached below in the Glossary section, the text file does not include however the different varying solutions I have sought for the results of my project. The accurate results of an FEA model is very impressive and forms the basis of other softwares used more specifically for Civil Engineering purposes such as SAP2000 and STAADpro.
ELEMENT USED
TIME ELAPSED FOR ANALYSIS
LICENSE USED
LINK 1
~ 15 seconds
ANSYS 11.0
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Appendix 8. Figure 7: ANSYS model showing Nodal Deflection
Hand Calculations:
Solution with the Red Colour indicating the max value
The hand calculations performed for this projected included: 1. Self Weight of the 2-D
9. Figure 8: ANSYS model Axial Stress and the stress
distribution along the Truss configuration
truss assembly, using
approximate AISC beam sizes. 2. The force reactions due to the self weight
10. Figure 9: ANSYS model showing exaggerated
deflection of the truss configuration
plus the
weight of truck loading.
11. Figure 10: ANSYS model showing Nodal Deflection
Solution with the Red Colour indicating the max value
3. The internal reactions of the truss members using the
method of sections.
12. Figure 11: ANSYS model Axial Stress and the stress
distribution along the Truss configuration. (After 75
4. AASHTO Bridge typical weight approximates for
Years Cycle)
truss bridges of varying spans.
List of Tables
5. Axial Stress using (F/A)
1. Table 1: Geometric
Properties Table (summary)
List of Figures 2. Table 2: Nodal (Keypoint) assignment t
1. Cover image: Walh Truss Bridge. [Online image]
the
coordinate system.
Available http://www.dcctrain.com/images/ walh_corner_bridge.jpg , Dec 1, 2009.
3. Table 3: Table summarising ANSYS results for
the
Reaction forces in the X and Y directions (CONTROL)
2. Figure 1: Simple Span Truss Bridge. [Online image]
Available http://www.con-span.com/DYOBTruss/ ,
4. Table 4: Table summarising ANSYS results for
Dec 1, 2009
Reaction forces in the X and Y directions
3. Figure 2: ANSYS model showing member and nodal
5. Table 5: Table summarising ANSYS results for
assignment.
nodal deflection in the X and Y directions (CONTROL)
4. Figure 3: Gusset Plate simplification, drawn in Paint.
6. Table 6: Table summarising ANSYS results for
nodal deflection in the X and Y directions
5. Figure 4: Gusset Plates. [Online image] Available
http://images.publicradio.org/content/ 2007/08/09/20070809_gussetplate_2.jpg , Dec 1, 2009. 6. Figure 5: ANSYS model showing mesh distribution
and Nodal loading (Self Weight & Truck) 7. Figure 6: ANSYS model showing exaggerated
deflection of the truss configuration
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the
the
the
Glossary ANSYS Text Input as follows: /PREP7 ! preprocessor phase ! define keypoints K,1, 0,0 K,2, 5,0 K,3, 10,0 K,4, 15,0 K,5, 20,0 K,6, 25,0 K,7, 30,0 K,8, 35,0 K,9, 40,0 K,10, 35,8 K,11, 30,8 K,12, 25,8 K,13, 20,8 K,14, 15,8 K,15, 10,8 K,16, 5,8 ! define lines L,1,2 L,2,3 L,3,4 L,4,5 L,5,6 L,6,7 L,7,8 L,8,9 L,9,10 L,10,8 L,8,11 L,11,7 L,7,12 L,12,6 L,6,13 L,13,5 L,13,4 L,4,14 L,14,3 L,3,15 L,15,2 L,2,16 L,16,1
L,16,15
! /PNUM,TABN,0
L,15,14
! /PNUM,SVAL,0
L,14,13
! /NUMBER,0
L,13,12
!*
L,12,11
! /PNUM,ELEM,0
L,11,10
! /REPLOT
!*
!*
ET,1,LINK1
ANTYPE,0
!*
FLST,2,1,3,ORDE,1
R,1,3250, ,
FITEM,2,1
!*
!*
!*
/GO
MPTEMP,,,,,,,,
DK,P51X, , , ,0,ALL, , , , , ,
MPTEMP,1,0
FLST,2,1,3,ORDE,1
MPDATA,EX,1,,200e9
FITEM,2,9
MPDATA,PRXY,1,,0.29
!*
! /REPLOT,RESIZE
/GO
! /REPLOT,RESIZE
DK,P51X, , , ,0,UY, , , , , ,
! /REPLOT,RESIZE
FLST,2,1,3,ORDE,1
! /REPLOT
FITEM,2,5
! LPLOT
FLST,2,1,3,ORDE,1
! /PNUM,KP,1
FITEM,2,5
! /PNUM,LINE,1
FLST,2,1,3,ORDE,1
! /PNUM,AREA,0
FITEM,2,5
! /PNUM,VOLU,0
!*
! /PNUM,NODE,0
/GO
! /PNUM,TABN,0
FK,1,FY,-90.916e3
! /PNUM,SVAL,0
FK,2,FY, -90.916e3
! /NUMBER,0
FK,3,FY, -90.916e3
!*
FK,4,FY, -90.916e3
! /PNUM,ELEM,0
FK,5,FY, -446.916e3
! /REPLOT
FK,6,FY, -90.916e3
!*
FK,7,FY,- 90.916e3
!*
FK,8,FY,- 90.916e3
LESIZE,ALL, , ,1, ,1, , ,1,
FK,9,FY,- 90.916e3
FLST,2,29,4,ORDE,2
FINISH
FITEM,2,1
/SOL
FITEM,2,-29
!*
LMESH,P51X
ANTYPE,0
! /PNUM,KP,1
! /STATUS,SOLU
! /PNUM,LINE,0
SOLVE
! /PNUM,AREA,0
FINISH
! /PNUM,VOLU,0 ! /PNUM,NODE,1
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Bibliography & Programs Used 1. ANSYS-386/ED Reference Manual 2. American Association of State Highway and Transportation Officials. AASHTO LRFD Bridge Design Specifications, Washington (District of Columbia) 3. Truss Bridges: http://en.wikipedia.org/wiki/Truss_bridge 4. Logan, Daryl L. A First Course in the Finite Element Method. Detroit: Cengage-Engineering, 2006. Print. 5. Steel Construction Manual, 13th Edition (Book). New York: American Institute of Steel Construction, 2006. Print. 6. Geschwindner, Louis F. Unified Design of Steel Structures. New York: Wiley, 2007. Print.
Program used:
1. ANSYS Version 11.0 Workbench.
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