Truss Design Project

1
Truss Design Project

• Kevin LaBeau
• Thao Lai
• EGR 209
• Dr. Reffeor
• October 27, 2003

2
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

3
Final Truss Bridge Design
Results and Analysis

• Bridge Cost 2169.51

4
Tensile and Compressive Strengths

• Strengths related to
• Material High-Strength Low-Alloy Steel
• Size of member
• Solid Bars Vs. Hollow Tubes

5

• 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
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Self-weight of truss members
W ?s Am L where, ?s the density of the
material Am the cross-sectional area of the
member L the length of the member
Sample Calculation for Member AB
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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
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• Self weight on any joint

• Total factored dead load on any joint

Load factor 1.25 for self weight given by WPBD
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Sample Calculations for Joint A
Member identification

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Dead load diagram
11
Situation 1

• Live load over Joint B.

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Situation 2

• Live load over Joint C.

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Situation 3

• Live load over Joint D.

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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
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Structural Adequacy
Member Factor of Factor of Factor of
  Safety Safety Safety
  Situation 1 Situation 2 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
CI 2.367 1.600 3.329
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
FG 4.172 2.965 2.299
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

• Average Factor of Safety
• 4.122

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Bolt Size

• Bolt grade 10.9
• Tensile strength 1040 MPa
• Shear stress .5tensile strength
• 520MPa
• minimum bolt diameter 55mm
• standard bolt diameter 56mm

where, V the shear force A the
cross-sectional area of the bolt
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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
18
Geometric Stability
Discussion

• Triangle most stable truss formation
• evenly distributes forces through members
• vertical forces unevenly distributed on the
  square.
• squares can also pivot and collapse

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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

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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