UCD FUND OF STRUCTURAL ANALYSIS 5E
UCD FUND OF STRUCTURAL ANALYSIS 5E
5th Edition
ISBN: 9781264843923
Author: Leet
Publisher: MCG
Question
Book Icon
Chapter 4, Problem 16P
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
Check Mark

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.

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  1

Find the horizontal reaction at point B by taking moment about point A.

MA=0Bx(6)60(9)+60(6)=06Bx540+360=0Bx=30kN()

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

+Fy=0Ay60=0Ay=60kN()

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

+Fx=0Ax+Bx+60=0Ax+30+60=0Ax=90kN()

Find the zero force bars in the truss.

By observation, the zero force bars are HG, GF, IF, KD, and LB.

Pass a section 1-1 as in Figure 1.

Consider the lower portion of the section 1-1.

Show the free-body diagram of the lower portion 1-1 as in Figure 2.

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  2

Find the force in the member EF by taking moment about the joint L.

ML=030(3)+60(3)60(9)+FEF(9)=090+180540+9FEF=0FEF=30kN(T)

Consider the joint E;

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

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  3

Resolve the vertical component of forces.

+Fy=0YKE+3060=0YKE=30kN

Use the proportion:

XKE1=YKE1=FKE2XKE1=301=FKE2XKE=30kNFKE=42.43kN(T)

Resolve the horizontal component of forces.

+Fx=0FDEXKE+60=0FDE30+60=0FDE=30kN(T)

Consider the joint D;

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

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  4

Resolve the vertical component of forces.

+Fy=0FKD=0

Resolve the horizontal component of forces.

+Fx=0FCD+30=0FCD=30kN(T)

Consider the joint F;

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

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  5

Resolve the vertical component of forces.

+Fy=0YHF30=0YHF=30kN

Use the proportion:

XHF1=YHF1=FHF2XHF1=301=FHF2XHF=30kNFHF=42.43kN(T)

Resolve the horizontal component of forces.

+Fx=0XHF+FKF=030+FKF=0FKF=30kN(C)

Consider the joint H;

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

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  6

Resolve the vertical component of forces.

+Fy=0YHJ30=0YHJ=30kN

Use the proportion;

XHJ1=YHJ1=FHJ2XHJ1=301=FHJ2XHJ=30kNFHJ=42.43kN(C)

Resolve the horizontal component of forces.

+Fx=0XHJ+30FIH=030+30FIH=0FIH=60kN(T)

Consider the joint I;

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

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  7

Resolve the vertical component of forces.

+Fy=0FIJ=0

Resolve the horizontal component of forces.

+Fx=0FAI+60=0FAI=60kN(T)

Consider the joint K;

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

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  8

Resolve the vertical component of forces.

+Fy=0YCK30=0YCK=30kN

Use the proportion;

XCK1=YCK1=FCK2XCK1=301=FCK2XCK=30kNFCK=42.43kN(C)

Resolve the horizontal component of forces.

+Fx=0XCK+3030FKJ=030FKJ=0FKJ=30kN(T)

Consider the joint C;

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

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  9

Resolve the vertical component of forces.

+Fy=0YCL30=0YCL=30kN

Use the proportion;

XCL1=YCL1=FCL2XCL1=301=FCL2XCL=30kNFCL=42.43kN(T)

Resolve the horizontal component of forces.

+Fx=0XCL+FBC30+30=030+FBC=0FBC=30kN(C)

Consider the joint J;

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

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  10

Resolve the vertical component of forces.

+Fy=0YAJ30=0YAJ=30kN

Use the proportion;

XAJ1=YAJ1=FAJ2XAJ1=301=FAJ2XAJ=30kNFAJ=42.43kN(T)

Resolve the horizontal component of forces.

+Fx=0XAJ+FLJ30+30=030+FLJ=0FLJ=30kN(C)

Consider the joint L;

Show the forces acting at the joint L as in Figure 11.

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  11

Resolve the vertical component of forces.

+Fy=0FAL30=0FAL=30kN(T)

Show the forces in the bars of the truss as in Figure 12.

UCD FUND OF STRUCTURAL ANALYSIS 5E, Chapter 4, Problem 16P , additional homework tip  12

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Structural Analysis
Civil Engineering
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:Cengage,
Text book image
Structural Analysis (10th Edition)
Civil Engineering
ISBN:9780134610672
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Principles of Foundation Engineering (MindTap Cou...
Civil Engineering
ISBN:9781337705028
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Cengage Learning
Text book image
Fundamentals of Structural Analysis
Civil Engineering
ISBN:9780073398006
Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:McGraw-Hill Education
Text book image
Sustainable Energy
Civil Engineering
ISBN:9781337551663
Author:DUNLAP, Richard A.
Publisher:Cengage,
Text book image
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning