Fundamentals of Structural Analysis
Fundamentals of Structural Analysis
5th Edition
ISBN: 9780073398006
Author: Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher: McGraw-Hill Education
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Chapter 4, Problem 43P
To determine

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

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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.

Fundamentals of Structural Analysis, Chapter 4, Problem 43P , additional homework tip  1

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

MA=0Ey(20)8(15)16(10)16(5)=020Ey12016080=0Ey=18kN()

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

+Fy=0Ay16168+Ey=0Ay40+18=0Ay=22kN()

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

+Fx=0Ex=0

Consider the joint E;

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

Fundamentals of Structural Analysis, Chapter 4, Problem 43P , additional homework tip  2

Resolve the vertical component of forces.

+Fy=018YIE=0YIE=18kN

Use the proportion:

XIE5=YIE2=FIE29XIE5=182=FIE29XIE=45kNFIE=48.47kN(C)

Resolve the horizontal component of forces.

+Fx=0FDE+XIE=0FDE+45=0FDE=45kN(T)

Consider the joint D;

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

Fundamentals of Structural Analysis, Chapter 4, Problem 43P , additional homework tip  3

Resolve the vertical component of forces.

+Fy=0FID=0

Resolve the horizontal component of forces.

+Fx=0FCD+45=0FCD=45kN(T)

Consider the joint A;

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

Fundamentals of Structural Analysis, Chapter 4, Problem 43P , additional homework tip  4

Resolve the vertical component of forces.

+Fy=022YAF=0YAF=22kN

Use the proportion:

XAF5=YAF2=FAF29XAF5=222=FAF29XAF=55kNFAF=59.24kN(C)

Resolve the horizontal component of forces.

+Fx=0FABXAF=0FAB55=0FAB=55kN(T)

Consider the joint B;

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

Fundamentals of Structural Analysis, Chapter 4, Problem 43P , additional homework tip  5

Resolve the vertical component of forces.

+Fy=0FFB=0

Resolve the horizontal component of forces.

+Fx=055+FBC=0FBC=55kN(T)

Consider the joint F;

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

Fundamentals of Structural Analysis, Chapter 4, Problem 43P , additional homework tip  6

Resolve the vertical component of forces.

+Fy=022+YFC16YFG=0YFGYFC=6        (1)

Resolve the horizontal component of forces.

+Fx=055XFGXFC=0XFG+XFC=55        (2)

Use the proportion:

XFG5=YFG2=FFG29XFG=0.928FFGYFG=0.371FFG

XFC5=YFC2=FFC29XFC=0.928FFCYFC=0.371FFC

Substitute 0.371FFG for YFG and 0.371FFC for YFC in Equation (1).

0.371FFG0.371FFC=6        (3)

Substitute 0.928FFG for XFG and 0.928FFC for XFC in Equation (2).

0.928FFG+0.928FFC=55        (4)

Solve equation (3) and (4).

FFG=37.70kN(C)FFC=21.54kN(C)

Consider the joint C;

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

Fundamentals of Structural Analysis, Chapter 4, Problem 43P , additional homework tip  7

Resolve the horizontal component of forces.

+Fx=055+45+20XCI=0XCI=10kN

Use the proportion:

XCI5=YCI2=FCI29105=YCI2=FCI29YCI=4kNFCI=10.77kN(C)

Resolve the vertical component of forces.

+Fy=08YCI+FCG=084+FCG=0FCG=12kN(T)

Consider the joint H;

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

Fundamentals of Structural Analysis, Chapter 4, Problem 43P , additional homework tip  8

Resolve the horizontal component of forces.

+Fx=0XGH=0

Use the proportion:

XGH5=YGH2=FGH2905=YGH2=FGH29YGH=0FGH=0

Resolve the vertical component of forces.

+Fy=0YGH+FIH8=00+FIH8=0FIH=8kN(C)

Consider the joint G;

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

Fundamentals of Structural Analysis, Chapter 4, Problem 43P , additional homework tip  9

Resolve the horizontal component of forces.

+Fx=035XGI=0XGI=35kN

Use the proportion:

XGI5=YGI2=FGI29355=YGI2=FGI29FGI=37.7kN(C)

Show the forces in the bars of the truss as in Figure 10.

Fundamentals of Structural Analysis, Chapter 4, Problem 43P , additional homework tip  10

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