Concept explainers
The beam AB supports a uniformly distributed load of 480 lb/ft and two concentrated loads P and Q. The normal stress due to bending on the bottom edge of the lower flange is +14.85 ksi at D and +10.65 ksi at E. (a) Draw the shear and bending-moment diagrams for the beam. (b) Determine the maximum normal stress due to bending that occurs in the beam.
Fig. P5.63
(a)
Draw the shear and bending-moment diagrams for the beam.
Explanation of Solution
Given information:
The normal stress due to bending at the point D is
The normal stress due to bending at the point E is
Refer to Appendix C “Properties of Rolled-Steel Sections” in the textbook.
The section modulus (S) for
Determine the bending moment at point D
Here, the normal stress at point D is
Substitute 14.85 ksi for
Determine the bending moment at point E
Here, the normal stress at point E is
Substitute 10.65 ksi for
Show the free-body diagram of the region DE as in Figure 1.
Determine the vertical reaction at point D by taking moment about point E.
Show the free body diagram of the region ACD as in Figure 2.
Determine the magnitude of the load P by taking moment about the point A.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Show the free body diagram of the entire beam as in Figure 3.
Determine the magnitude of the load P by taking moment about the point B.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Shear force:
Show the calculation of shear force as follows;
Show the calculated shear force values as in Table 1.
Location (x) ft | Shear force (V) kips |
A | 24.54 |
C (Left) | 23.82 |
C (Right) | –2.01 |
F (Left) | –4.41 |
F (Right) | –13.12 |
B | –13.84 |
Plot the shear force diagram as in Figure 4.
Bending moment:
Show the calculation of the bending moment as follows;
Show the calculated bending moment values as in Table 2.
Location (x) ft | Bending moment (M) kips-ft |
A | 0 |
C | 36.27 |
F | 19.77 |
B | 0 |
Plot the bending moment diagram as in Figure 5.
Refer to Figure 5;
The maximum absolute bending moment is
(b)
The maximum normal stress due to bending.
Answer to Problem 63P
The maximum normal stress due to bending is
Explanation of Solution
Given information:
Refer to Appendix C “Properties of Rolled-Steel Sections” in the textbook.
The section modulus (S) for
The maximum absolute bending moment is
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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