Truss Design Project

Truss Design Project

Kevin LaBeau

Thao Lai

EGR 209

Dr. Reffeor

October 27, 2003

Problem Statement

• Apply Math and Science skills to:



 Create a 24m bridge in West Point Bridge Designer

(WPBD)

 Costs around $1500-$2500

 Compute tensile and compressive strengths

 Calculate internal forces for the bridge

 Calculate the factors of safety

 Find a standard hex bolt to withstand the forces

Results and Analysis

• Final Truss Bridge Design









• Bridge Cost: $2169.51

• Tensile and Compressive Strengths



 Strengths related to



• Material – High-Strength Low-Alloy Steel



• Size of member



• Solid Bars Vs. Hollow Tubes

• Tensile and Compressive Strengths

Member Member Size (mm) Length (m) Compressive Strength (kg) Tensile Strength (kg)

AB 170 x 170 x 8 4.0 1235 1699

AH 65 x 65 5.5 77.20 1385

BC 170 x 170 x 8 4.0 1235 1699

BH 120 x 120 x 6 2.9 647.4 896.7

CD 170 x 170 x 8 4.0 1235 1699

CH 120 x 120 x 6 4.3 463.4 896.7

CI 120 x 120 x 6 4.3 464.4 896.7

DE 170 x 170 x 8 4.0 1235 1699

DI 120 x 120 x 6 4.3 464.4 896.7

DJ 120 x 120 x 6 4.3 464.4 896.7

EF 170 x 170 x 8 4.0 1235 1699

EJ 120 x 120 x 6 4.3 464.4 896.7

EK 120 x 120 x 6 4.3 463.4 896.7

FG 170 x 170 x 8 4.0 1235 1699

FK 120 x 120 x 6 2.9 647.4 896.7

GK 65 x 65 5.5 77.20 1385

HI 65 x 65 5.3 81.40 1385

IJ 65 x 65 4.0 145.3 1385

JK 65 x 65 5.3 81.40 1385

• Self-weight of truss members

W = γs Am L

where,

γs = the density of the material

Am= the cross-sectional area of the member



L = the length of the member



Sample Calculation for Member AB:





 kN 

 

W AB   76.98 3  0.0052m 2 4.00m

 m 

W AB  1.601kN

• Self-Weight of Members

Member Self-Weight (kN)

AB 1.601

AH 1.775

BC 1.601

BH 0.592

CD 1.601

CH 0.885

CI 0.883

DE 1.601

DI 0.883

DJ 0.883

EF 1.601

EJ 0.883

EK 0.885

FG 1.601

FK 0.592

GK 1.775

HI 1.727

IJ 1.294

JK 1.727

• Self weight on any joint



1 

W   Wi 

2 i 



• Total factored dead load on any joint





D  1.25W  Dext / int



Load factor = 1.25 for self weight given by WPBD

• Sample Calculations for Joint A





W A  W AB  W AH 

A 1

AB

2

W A  1.601kN  1.775kN 

AH 1

2

W A  1.688kN

Member identification









D A  1.25W A   Dext

D A  1.251.688kN   68.18kN

D A  70.29kN

• Dead load diagram

• Situation 1



• Live load over Joint B.

• Situation 2



• Live load over Joint C.

• Situation 3



• Live load over Joint D.

• Member Forces

• (T): Tension (C): Compression

• All forces in kN

Member AB AH BC BH CD CH CI



Situation 1 880.0 (C) 1017 (T) 785.0 (C) 360.8 (C) 701.1 (C) 11.01 (C) 196.2 (C)



Situation 2 1051 (C) 1214 (T) 967.0 (C) 318.6 (C) 940.0 (C) 143.6 (C) 290.3 (C)



Situation 3 930.2(C) 1075 (T) 892.4 (C) 143.8 (C) 1045 (C) 286.6 (C) 139.5 (C)





DE DI DJ EF EJ EK FG FK

600.1 (C) 28.28 (T) 186.4 (C) 333.8 (C) 67.03 (T) 307.5 (C) 296.0 (C) 143.8 (T)

786.2 (C) 61.26 (T) 265.5 (C) 454.4 (C) 110.4 (T) 366.7 (C) 416.5 (C) 143.8 (T)

950.7 (C) 96.96 (C) 298.5 (C) 574.9 (C) 107.6 (T) 425.9 (C) 537.1 (C) 143.8 (T)





GK HI IJ JK Ax Ay Gy

342.0 (T) 807.7 (T) 687.8 (T) 578.8 (T) 5.10E-14 748.5 241.6

481.3 (T) 1096.0 (T) 911.2 (T) 747.5 (T) 5.56E-14 678.6 311.4

620.6 (T) 1131 (T) 1091 (T) 916.2 (T) 8.44E-14 608.8 381.2

Member Factor of Factor of Factor of



• Structural Adequacy Safety

Situation 1

Safety

Situation 2

Safety

Situation 3

AB 1.403 1.175 1.328

AH 1.362 1.141 1.288

BC 1.573 1.277 1.384

BH 1.794 2.032 4.502

CD 1.762 1.314 1.182

CH 42.089 3.227 1.617

Strength

• Factor of Safety = CI 2.367 1.600 3.329

Force DE 2.058 1.571 1.299

DI 31.708 14.638 4.790

DJ 2.491 1.749 1.556

EF 3.700 2.718 2.148

EJ 13.378 8.122 8.334

EK 1.507 1.264 1.088

• Average Factor of Safety

FG 4.172 2.965 2.299

4.122 FK 6.236 6.236 6.236

GK 4.050 2.878 2.232

HI 1.715 1.264 1.225

IJ 2.014 1.520 1.269

JK 2.393 1.853 1.512

• Bolt Size



• Bolt grade = 10.9

• Tensile strength = 1040 MPa

• Shear stress = .5*tensile strength

• 520MPa







V where,

 V = the shear force

A A = the cross-sectional area of the bolt







• minimum bolt diameter = 55mm

• standard bolt diameter = 56mm

• Bridge Costs (minus cost of bolts)





Type of Cost Product Cost Calculation Cost



Material Cost High Strength Steel Bars (851.2 kg) x ($0.48 per kg) = $408.60



High Strength Steel Tubes (1647.1 kg) x ($0.72 per kg) = $1,185.91



Connection Cost (11 Joints) x ($25.00 per Joint) = $275.00



Product Cost 8 - 120 x 120 x 6 High-Strength ($100.00 per Product) = $100.00



Low-Alloy Steel Tubes



6 - 170 x 170 x 8 High-Strength ($100.00 per Product) = $100.00



Low-Alloy Steel Tubes



5 - 65 x 65 High-Strength ($100.00 per Product) = $100.00



Low-Alloy Steel Bars



Total Cost $2,169.51

Discussion

• Geometric Stability

F

F





Ffelt







Ffelt Ffelt



Ffelt









• Triangle: most stable truss formation

• evenly distributes forces through members

• vertical forces unevenly distributed on the square.

• squares can also pivot and collapse

• Geometric Stability



• Arches



• High resistance to the forces that will put stress on the bridge



• The force will act in the direction of the member and on the joint

itself



• Stronger bridge structure = smaller members = lower costs

Conclusion

• Designs based on mathematical and physical concepts

• Triangles are stronger than squares.

• Arches evenly distribute forces for more stability.



• Real life issues: costs & materials account for the design

process

• Important to keep costs at a minimum, but essential to never

compromise safety



• Engineers apply physical and mathematical models to

design and build projects suitable for lives to use.



• While working on this project, Kevin understands why

SHEER STRESS = Thao