Concept explainers
7.35 and 7.36 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment.
Fig. P7.35
(a)
The shear and bending-moment diagrams.
Answer to Problem 7.35P
The shear diagram is drawn in figure 6 and bending momentum is drawn in figure 7.
Explanation of Solution
Refer Figure 1.
Refer Figure 2.
Write an expression to calculate the net counter clockwise moment at point C along AC.
Here,
Write an expression to calculate the net vertical force along AC.
Here,
Refer Figure 3.
Write an expression to calculate the net counter clockwise moment at point D along CD.
Here,
Write an expression to calculate the net vertical force along CD.
Refer Figure 4.
Write an expression to calculate the net counter clockwise moment at point E along DE.
Here,
Write an expression to calculate the net vertical force along EB.
Refer Figure 5.
Write an expression to calculate the net counter clockwise moment at point B along EB.
Here,
Write an expression to calculate the net vertical force along EB.
Conclusion:
Refer Figure 2 and equation (II). Calculate the net vertical force.
Here,
Rearrange the equation to calculate
Refer Figure 2 and equation (I). Calculate the net counter clockwise moment at point C.
Here,
Rearrange the equation to calculate
Refer Figure 3 and equation (IV). Calculate the net vertical force.
Rearrange the equation to calculate
Refer Figure 3 and equation (III). Calculate the net counter clockwise moment at point D.
Rearrange the equation to calculate
Refer Figure 4 and equation (VI). Calculate the net vertical force.
Rearrange the equation to calculate
Refer Figure 4 and equation (V). Calculate the net counter clockwise moment at point E.
Rearrange the equation to calculate
Refer Figure 5 and equation (VIII). Calculate the net vertical force.
Rearrange the equation to calculate
Refer Figure 5 and equation (VII). Calculate the net counter clockwise moment at point E.
Rearrange the equation to calculate
Thus, draw the shear diagram.
Thus, draw the bending-moment.
(b)
The maximum absolute value of the shear and bending moment.
Answer to Problem 7.35P
The maximum absolute value of the shear force is
Explanation of Solution
Determine the maximum absolute shear from diagram 2. The maximum absolute value of bending moment is at maximum shear force.
Conclusion:
Refer figure 6. Determine the maximum absolute value of shear force.
Here,
Refer figure 7. Determine the maximum value of the bending moment at position B.
Here,
Thus, the maximum absolute value of the shear force is
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Chapter 7 Solutions
Vector Mechanics for Engineers: Statics
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