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A rod of length L is attached to wall. The load on the rod increases linearly (as shown by...

A rod of length L is attached to wall. The load on the rod increases linearly (as shown by the arrow in the figure) from zero at the left end to W newton per unit length at the right end. Find the shear force at a) the right end,  b) the center , and    c) the left and.

Step-by-Step Solution

Solution 1
Step #1 of 6

THINK:

To determine shearing force at the right end, at the center and at the left end, write the shearing force as an arbitrary function of distance from the wall.

Step #2 of 6

SKETCH:

Given situation is as shown below figure:

Step #3 of 6

RESEARCH:

The shearing force acting on a small part of the rod due to weight of the rod at a distance from the wall can be written as …… (1)

The shearing force acting on total length of the rod due to weight of the rod at a distance from the wall is …… (2)

SIMPLIFY:

Simplify equation (2), we get the equation for shearing force as follows

…… (3)

Step #4 of 6

CALCULATE:

(a)

Substitute in equation (3), we get the shearing force at the right end of the rod as

Step #5 of 6

(b)

Substitute in equation (3), we get the shearing force at the center of the rod as

Step #6 of 6

(c)

Substitute in equation (3), we get the shearing force at the left end of the rod as

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