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 7.87P
The equation for shear curve is
Explanation of Solution
Refer Fig P7.87.
Write the equation for the distributed load.
Here,
Write the equation for change in shear moment with distance.
Here,
Write the equation for change in bending moment with distance.
Here,
Conclusion:
Calculate the change in shear moment with distance using equation (II) and thus, find the equation for the shear moment curve.
Calculate the change in bending moment with distance using equation (III) and thus find the equation for the bending moment curve.
Apply boundary condition to find
At
Apply boundary condition to find
At
Use equation (V) to find the equation for shear curve.
Use equation (VI) to find the equation for bending moment curve.
Therefore, the equation for shear curve is
(b)
The magnitude and location of the maximum bending moment.
Answer to Problem 7.87P
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.
Write the equation to find the maximum bending moment.
Conclusion:
Calculate the location of the maximum bending moment.
Calculate the maximum bending moment.
Therefore, the magnitude of the maximum bending moment is
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Chapter 7 Solutions
VECTOR MECHANICS FOR ENGINEERS: STATICS
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