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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 5, Problem 52P

Textbook Problem

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Draw the shear and bending moment diagrams for the reinforced concrete footing subjected to the downward column loading of 22 kN/m and the upward soil reaction of 6 kN/m, as shown in the figure.

To determine

Plot the shear and bending moment diagram.

Given information:

The downward column loading is 22 kN/m.

The upward soil reaction is 6 kN/m.

Calculation:

Sign conversion:

Apply the following sign convention for calculating the shear and bending moments.

- When the portion of the beam considered is left of the section, then the external force acting to the left are considered as positive.
- When the portion of the beam considered is right of the section, then the external force acting to the right are considered as positive.
- When the portion of the beam considered is left of the section, then the external force acting upward are considered as positive.
- When the portion of the beam considered is right of the section, then the external force acting downward are considered as positive.
- When the portion of the beam considered is left of the section, then the clockwise moments are considered as positive.
- When the portion of the beam considered is right of the section, then the counterclockwise moments are considered as positive.

Calculation:

Show the free-body diagram of the entire beam as in Figure 1.

Shear diagram:

Point *A*:

Point *B*:

Point *C*:

Point *D*:

Plot the shear force diagram of the beam as in Figure 2.

Refer to the Figure 2, the area of the section is mentioned in the shear diagram.

The maximum bending moment occurs where the shear is zero.

Show the shear diagram of the section *BC* as in Figure 3.

Use the similar triangle method to find the location of the maximum bending moment.

Structural Analysis

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