Concept explainers
For the beam and loading shown, (a) write the equations of the shear and bending-moment curves, (b) determine the magnitude and location of the maximum bending moment.
(a)
To write the equations of the shear and bending moment curves.
Answer to Problem 7.86P
The equation for shear curve is
Explanation of Solution
Refer Fig P7.86 and figure 1.
Write the equation for the distributed load.
Here,
Write the condition used to find the reaction force B.
Here,
Write the condition used to find the reaction force A along y direction.
Here,
Write the equation for change in shear moment with distance.
Here,
Write the equation for change in bending moment with distance.
Here,
Conclusion:
Use equation (I) to calculate the reaction force at B.
Use equation (II) to calculate the reaction force at B.
Sketch the shear diagram.
Calculate the change in shear moment with distance using equation (IV) and thus find the equation for the shear moment curve.
Sketch the bending moment diagram.
Calculate the change in bending moment with distance using equation (V) and thus find the equation for the bending moment curve.
Therefore, the equation for shear curve is
(b)
The magnitude and location of the maximum bending moment.
Answer to Problem 7.86P
The magnitude of the maximum bending moment is
Explanation of Solution
The maximum absolute value of the bending moment can be found using the equation for the bending moment curve.
The distance of the maximum bending moment is measured from the left hand side.
Conclusion:
At
If
The magnitude of the maximum bending moment.
According to figure 2, find the location of the maximum bending moment.
Therefore, the magnitude of the maximum bending moment is
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