EBK STRUCTURAL ANALYSIS
EBK STRUCTURAL ANALYSIS
6th Edition
ISBN: 9780357030974
Author: KASSIMALI
Publisher: VST
Question
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Chapter 5, Problem 1P
To determine

Find the axial force, shear, and bending moment at points A and B of the beam.

Expert Solution & Answer
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Answer to Problem 1P

The axial force at point A is 50kN_.

The shear at point A is 91.7kN_.

The moment at point A is 1,333.6kN-m_.

The axial force at point B is 0_.

The shear at point B is 194.9kN_.

The moment at point B is 584.7kN-m_.

Explanation of Solution

Sign conversion:

Apply the sign convention for calculating the equations of equilibrium as below.

  • For the horizontal forces equilibrium condition, take the force acting towards right side as positive (+) and the force acting towards left side as negative ().
  • For the vertical forces equilibrium condition, take the upward force as positive (+) and downward force as negative ().
  • For moment equilibrium condition, take the clockwise moment as negative and counter clockwise moment as positive.

Apply the following sign convention for calculating the axial forces, shear and bending moments.

  • When the portion of the beam considered is left of the section, then the external force acting to the left are considered as positive.
  • When the portion of the beam considered is right of the section, then the external force acting to the right are considered as positive.
  • When the portion of the beam considered is left of the section, then the external force acting upward are considered as positive.
  • When the portion of the beam considered is right of the section, then the external force acting downward are considered as positive.
  • When the portion of the beam considered is left of the section, then the clockwise moments are considered as positive.
  • When the portion of the beam considered is right of the section, then the counterclockwise moments are considered as positive.

Calculation:

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

EBK STRUCTURAL ANALYSIS, Chapter 5, Problem 1P , additional homework tip  1

Find the horizontal reaction at point C by resolving the horizontal equilibrium.

+Fx=0Cx+100cos60°=0Cx=50kN

Find the vertical reaction at point C by taking moment about the point D.

+MD=0Cy(20)+120(15)+200(10)+100sin60°(5)=020Cy+1800+2000+433.01=0Cy=211.7kN

Find the vertical reaction at point D by resolving the vertical equilibrium.

+Fy=0Cy120200100sin60°+Dy=0211.732086.60+Dy=0Dy=194.9kN

Pass the sections aa and bb at points A and B respectively.

Show the sections aa and bb as in Figure 2.

EBK STRUCTURAL ANALYSIS, Chapter 5, Problem 1P , additional homework tip  2

Consider section aa:

Consider the left side of the section aa for calculation of internal forces.

Show the free-body diagram of the left side of the section aa as in Figure 3.

EBK STRUCTURAL ANALYSIS, Chapter 5, Problem 1P , additional homework tip  3

Find the axial force at point A by resolving the horizontal equilibrium.

+Fx=050QA=0QA=50kN

Find the shear at point A by resolving the vertical equilibrium.

+Fy=0211.7120SA=0SA=91.7kN

Find the moment at point A by taking moment about the section aa.

+M=0211.7(8)120(3)MA=01693.6360MA=0MA=1,333.6kN-m

Thus, the axial force at point A is 50kN_.

Thus, the shear at point A is 91.7kN_.

Thus, the moment at point A is 1,333.6kN-m_.

Consider section bb:

Consider the right side of the section bb for calculation of internal forces.

Show the free-body diagram of the right side of the section bb as in Figure 4.

EBK STRUCTURAL ANALYSIS, Chapter 5, Problem 1P , additional homework tip  4

Find the axial force at point B by resolving the horizontal equilibrium.

+Fx=0QB+0=0QB=0

Find the shear at point B by resolving the vertical equilibrium.

+Fy=0SB194.9=0SB=194.9kN

Find the moment at point B by taking moment about the section bb.

+M=0MB+194.9(3)=0MB=584.7kN-m

Thus, the axial force at point B is 0_.

Thus, the shear at point B is 194.9kN_.

Thus, the moment at point B is 584.7kN-m_.

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Chapter 5 Solutions

EBK STRUCTURAL ANALYSIS

Ch. 5 - Prob. 11PCh. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - Draw the shear and bending moment diagrams for the...Ch. 5 - For the beam shown: (a) determine the distance a...Ch. 5 - For the beam shown: (a) determine the distance a...Ch. 5 - Prob. 55PCh. 5 - Prob. 56PCh. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - Prob. 59PCh. 5 - Prob. 60PCh. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Prob. 63PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - Prob. 66PCh. 5 - Prob. 67PCh. 5 - Prob. 68PCh. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Prob. 71P
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