Calculating the factor of safety for overturning.?

Question

A wall 2m high x 1.2m thick has a unit weight of 24kN/m3.
It is subject to a horizontal load of 10kN/m run at a height of 0.7m.

Calculate the factor of safety against sliding if the coefficient of friction = 0.45

....I'm having trouble with this question and would appreciate any help I can get. Cheers.

Answer 1

This is a classic gravity retaining wall calc.

Draw your picture with the forces. Assume the load acts right to left.

Calculate the weight of the wall per meter of length.

2m x 1.2m x 1m = 2.4 m^3
Thus the weight of the wall is 2.4 x 24 = 57.6 kN

To calc the overturning FS, find the moments of the Hz force and weight about the toe of the wall (lower left corner).

Overturning moment = 10 kN x 0.7 m = 7 kN m
Resisting moment (weight of wall) = 57.6 kN x 0.6 m (distance to center of mass from toe) = 34.56 kN m

FS overturning = 34.56/7 = 4.94 OK

Sliding force = 10 kN
Friction force = 0.45 x 57.6 kN = 25.92 kN

FS sliding = 25.92/10 = 2.59 OK

Select 2m x 1.2 m wall!

Answer 2

Overturning Moment

Answer 3

Some of these answers are close, but they define the concept in reverse. When given a simple problem, such as a bridge must support the weight equivalent of a dozen cement trucks at one time, the engineer will design the structure to withstand the weight of 60 cement trucks at one time, to have a static load factor of safety of 5 times. Most aircraft applications have a factor of safety of 2 to 2.5. I worked on a rocket program where the propellant tank had a factor of safety of only 1.5.