Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition
Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition
5th Edition
ISBN: 9781259820960
Author: Leet, Kenneth
Publisher: McGraw-Hill Education
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Chapter 4, Problem 51P
To determine

Find the force in each bar and mention the force is tension or compression of the bars in the truss.

Expert Solution & Answer
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Explanation of Solution

Assumptions:

  • Consider the state of bars as tension (T) where the force is pulling the bar and as compression (C) where the force is pushing the bar.
  • The sign of the force in the bar is positive when the force is in tension and negative when the force is in compression.
  • Consider the force indicating right side as positive and left side as negative in horizontal components of forces.
  • Consider the force indicating upward is taken as positive and downward as negative in vertical components of forces.
  • Consider clockwise moment as negative and anti-clock wise moment as positive wherever applicable.

Show the free-body diagram of the entire truss as in Figure 1.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  1

Find the horizontal reaction at point A by resolving the horizontal component of forces.

+Fx=0Ax+20(35)+20(35)=0Ax+12+12=0Ax=24kN()

Find the vertical reaction at point G by taking moment about point A.

MA=0Gy(16)60(8)20(45)(4)20(35)(6)20(35)(3)=016Gy480647236=0Gy=40.75kN()

Find the vertical reaction at point A by resolving the vertical component of forces.

+Fy=0Ay20(45)20(45)60+Gy=0Ay161660+40.75=0Ay=51.25kN()

Consider the joint G;

Show the forces acting at the joint G as in Figure 2.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  2

Resolve the horizontal component of forces.

+Fx=0XGH=0

Use the proportion:

XGH4=YGH3=FGH504=YGH3=FGH5YGH=0FGH=0

Resolve the vertical component of forces.

+Fy=0YGHFFG+40.75=00FFG+40.75=0FFG=40.75kN(C)

Consider the joint F;

Show the forces acting at the joint F as in Figure 3.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  3

Resolve the vertical component of forces.

+Fy=040.75YEF=0YEF=40.75kN

Use the proportion:

XEF4=YEF3=FEF5XEF4=40.753=FEF5XEF=54.33kNFEF=67.92kN(C)

Resolve the horizontal component of forces.

+Fx=0XEFFHF=054.33FHF=0FHF=54.33kN(T)

Consider the joint E;

Show the forces acting at the joint E as in Figure 4.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  4

Resolve the vertical component of forces.

+Fy=040.75FEH=0FEH=40.75kN(T)

Resolve the horizontal component of forces.

+Fx=0FDE54.33=0FDE=54.33kN(C)

Consider the joint H;

Show the forces acting at the joint H as in Figure 5.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  5

Resolve the vertical component of forces.

+Fy=040.75YDH=0YDH=40.75kN

Use the proportion:

XDH4=YDH3=FDH5XDH4=40.753=FDH5XDH=54.33kNFDH=67.92kN(C)

Resolve the horizontal component of forces.

+Fx=0FIH+54.33+XDH=0FIH+54.33+54.33=0FIH=108.66kN(T)

Consider the joint I;

Show the forces acting at the joint I as in Figure 6.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  6

Resolve the vertical component of forces.

+Fy=060+FDI=0FDI=60kN(T)

Resolve the horizontal component of forces.

+Fx=0FIJ+108.66=0FIJ=108.66kN(T)

Consider the joint D;

Show the forces acting at the joint D as in Figure 7.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  7

Resolve the vertical component of forces.

+Fy=060+YDJ+40.75=0YDJ=19.25kN

Use the proportion:

XDJ4=YDJ3=FDJ5XDJ4=19.253=FDJ5XDJ=25.67kNFDJ=32.08kN(C)

Resolve the horizontal component of forces.

+Fx=0FCD+XDJ54.3354.33=0FCD+25.67108.66=0FCD=83kN(C)

Consider the joint C;

Show the forces acting at the joint C as in Figure 8.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  8

Resolve the horizontal component of forces.

+Fx=083+20(35)+XBC=0XBC=71kN

Use the proportion:

XBC4=YBC3=FBC5714=YBC3=FBC5YBC=53.25kNFBC=88.75kN(C)

Resolve the vertical component of forces.

+Fy=020(45)FCJ+YBC=016FCJ+53.25=0FCJ=37.25kN(T)

Consider the joint J;

Show the forces acting at the joint J as in Figure 9.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  9

Resolve the vertical component of forces.

+Fy=037.2519.25YAJ=0YAJ=18kN

Use the proportion:

XAJ4=YAJ3=FAJ5XAJ4=183=FAJ5XAJ=24kNFAJ=30kN(T)

Resolve the horizontal component of forces.

+Fx=0FBJXAJ25.67+108.66=0FBJ2425.67+108.66=0FBJ=59kN(T)

Consider the joint A;

Show the forces acting at the joint A as in Figure 10.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  10

Resolve the vertical component of forces.

+Fy=051.25+18FAB=0FAB=69.25kN(C)

Show the forces in the bars of the truss as in Figure 11.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 4, Problem 51P , additional homework tip  11

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Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition

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