Concept explainers
(a)
Write the equations for shear force and bending moments based on singularity function.
(a)
Answer to Problem 110P
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 E 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 shear force function as follows;
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 normal stress due to bending using the singularity function.
(b)
Answer to Problem 110P
The maximum normal stress due to bending is
Explanation of Solution
Refer to Equation (2).
Point A
Substitute 0 m for x in Equation (2).
Point B
Substitute 0.75 m for x in Equation (2).
Point C
Substitute 1.5 m for x in Equation (2).
Point E
Substitute 2.25 m for x in Equation (2).
Point E
Substitute 3 m for x in Equation (2).
Point F
Substitute 3.75 m for x in Equation (2).
Refer to the calculated bending moment values, the maximum bending moment occurs at point C.
The maximum bending moment in the beam is
Refer to Appendix C “Properties of Rolled-Steel Sections” in the textbook.
The section modulus (S) for
Determine the maximum normal stress
Substitute
Therefore, the maximum normal stress due to bending is
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Chapter 5 Solutions
Mechanics of Materials, 7th Edition
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