Concept explainers
5.1 through 5.6 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the equations of the shear and bending-moment curves.
Fig. P5.2
(a)
To draw: The shear and bending-moment diagrams.
Explanation of Solution
Determine the reactions of the beam.
Show the free-body diagram of the entire beam as in Figure 1.
Determine the vertical reaction at point C by taking moment about point A.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Substitute
Determine the horizontal direction at point A by resolving the horizontal component of forces.
Show the free-body diagram of the section 1-1 and 2-2 as in Figure 2.
Section 1-1:
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Section 2-2:
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Show the free-body diagram of the section 3-3 and 4-4 as in Figure 3.
Section 3-3:
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
When the section 3-3 is at point B,
Section 4-4:
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Shear force and bending moment values:
Show the calculated shear force and bending moment values as in Table 1.
Location (x) | Shear force (V) | Bending Moment (M) |
1-1 | 0 | |
2-2 | ||
3-3 | ||
4-4 | 0 |
Plot the shear force and bending moment diagrams as in Figure 4.
(b)
The equations of the shear and bending-moment curves.
Answer to Problem 2P
The equation of shear force and bending-moment curves is:
For section AB;
For section BC;
Explanation of Solution
Determine the reactions of the beam.
Show the free-body diagram of the entire beam as in Figure 5.
Determine the vertical reaction at point C by taking moment about point A.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Substitute
Determine the horizontal direction at point A by resolving the horizontal component of forces.
Show the free-body diagram of the section 1-1 and 2-2 as in Figure 6.
Section 1-1:
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Section 2-2:
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Show the free-body diagram of the section 3-3 and 4-4 as in Figure 7.
Section 3-3:
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
When the section 3-3 is at point B,
Section 4-4:
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Therefore, the equation of shear force and bending-moment curves is:
For section AB;
For section BC;
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Chapter 5 Solutions
Mechanics of Materials, 7th Edition
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