Overturning and Sliding Stability Calculator

What is an overturning and sliding check?

A horizontal force (wind, earth thrust, impact) can move a body in two ways: it can push it along its base or tip it about its front edge. The two are checked separately.

Overturning: if the horizontal force acts at height h above the base, the overturning moment is M_d = H × h. The weight of the body resists it. With the centre of gravity at a distance x_W from the tipping edge, the resisting moment is M_r = W × x_W. The factor of safety is FS_d = M_r / M_d.

Sliding: friction at the base resists sliding. The friction resistance is μ × N and the factor of safety is FS_k = μ × N / H, where N is the total vertical force.

Example

A block 1.5 m wide weighing 30 kN is pushed by 10 kN at 1.2 m above its base. The overturning moment is 10 × 1.2 = 12 kN·m, the resisting moment 30 × 0.75 = 22.5 kN·m and the factor of safety against overturning 1.875. With a friction coefficient of 0.5 the friction resistance is 15 kN and the factor against sliding is 1.5. If the force grows, the block starts to slide at 15 kN and to tip at 18.75 kN: it slides first.

Does it slide or tip first?

The body starts to tip when H × h = W × x_W and to slide when H = μ × W. A high point of application and a narrow base favour tipping. A low point of application and a slippery surface favour sliding. The calculator reports both threshold forces.

Where the resultant falls

The resultant of the vertical and horizontal forces crosses the base at a distance e from its middle. Once that distance exceeds B / 6, the heel of a base resting on soil lifts off and the bearing pressure at the toe rises quickly. For structures on soil, bearing pressure is therefore checked separately even when the overturning factor is adequate.

Limits

This is static equilibrium only. Earth pressure on a retaining wall, passive resistance, water pressure and seismic action are outside this tool. The value 1.5 is a common lower bound, but it does not hold for every standard or every type of structure.