Chapter 9, Problem 5Q

A ground retaining wall is shown in Fig. 9-36a .The ground, particularly when wet, can exert a significant force F on the wall, (a) What force produces the torque to keep the wall upright? (b)Explain why the retaining wall in Fig. 9-36bwould be much less likely to overturn than that in Fig. 9-36a

To determine

(a)

What force produces the torque to keep the wall upright.

Answer to Problem 5Q

Solution:

The force that produces the torque to keep the wall upright on (a)is Weight (W)

Explanation of Solution

Given info:

The ground, particularly when wet, can exert a significant force F on the wall.

According to the figure the wall rest vertically. Assume that the pivot is placed on the lower left corner. When the ground is wet there is a significant ( $\overrightarrow{F}$ force that the ground exerts on the wall. However, the total torque on the wall is zero because the weight ( $\overrightarrow{W}$ )of the wall makes a torque ( ${\tau }_W$ )clockwise while the force ( $\overrightarrow{F}$ )of the ground makes a torque ( ${\tau }_F$ )counterclockwise. Therefore, the sum of these two torques results in zero and the wall remains vertical.

To determine

(b)

Explain why the retaining wall in (b)would be much less likely to overturn than that in (a).

Answer to Problem 5Q

Solution:

The weight of the wall increases and therefore the torque made by the weight increases and it is more easy to counteract the force F. Due to the geometry of the retaining wall of (b)the center of gravity is lower and displaced to the right than in the case of the retaining wall of (a), so the force made for the ground makes a smaller torque on the wall.

Explanation of Solution

Given info:

The ground, particularly when wet, can exert a significant force F on the wall.

For the retaining wall of (b), the center of gravity moves slightly to the right, the mass is greater, therefore the weight increases. In this way the torque made by the weight is greater and therefore it is easier to counteract the torque made by the force of the ground.