Concept explainers
(a)
Write the equations for shear force and bending moments based on singularity function.
(a)
Answer to Problem 109P
The equation of shear force as a singularity function is;
The equation of bending moment as a singularity function is;
Explanation of Solution
Show the free-body diagram of the beam as in Figure 1.
Determine the vertical reaction at point B by taking moment about point A.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Write the equation of the load function as follows;
The equation for shear force as a function of load is,
Integrate the equation (1) to find V;
The equation for bending moment as a function of shear force is,
Integrate the equation (1) to find M;
Therefore,
The equation of shear force as a singularity function is,
The equation of bending moment as a singularity function is,
(b)
The maximum bending moment using the singularity function.
(b)
Answer to Problem 109P
The maximum bending moment in the beam is
Explanation of Solution
Refer to Equation (2), find the location of maximum bending moment where the shear force changes sign. i.e.,
Point A
Substitute 0 ft for x in Equation (2).
Point C
Substitute 3 ft for x in Equation (2).
Point D
Substitute 7 ft for x in Equation (2).
Point E
Substitute 11 ft for x in Equation (2).
Point B
Substitute 14 ft for x in Equation (2).
Refer to the calculated shear force values, the shear force changes at point D.
Refer to Equation (3).
Substitute 7 ft for x in Equation (3).
Therefore, the maximum bending moment in the beam is
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Chapter 5 Solutions
Mechanics of Materials, 7th Edition
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