Stability and Tipping - Examples & Applications

Example

A rigid block weighs 300 kN300\text{ kN} and has a rectangular base width B=3.0 mB=3.0\text{ m}. A horizontal force H=60 kNH=60\text{ kN} acts at a height h=2.0 mh=2.0\text{ m} above the base. Determine the base-reaction eccentricity and whether the full base can remain in compression.

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Example

A machine weighs 180 kN180\text{ kN} on a 2.4 m2.4\text{ m}-wide base. The coefficient of friction at the interface is μ=0.40\mu=0.40. A horizontal force is applied 1.5 m1.5\text{ m} above the base. Determine whether sliding or tipping occurs first as the horizontal force is increased.

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Example

A simplified retaining-wall section has a total stabilizing vertical load of 420 kN420\text{ kN} whose resultant acts 1.10 m1.10\text{ m} from the toe. The lateral earth-pressure resultant is 110 kN110\text{ kN} acting 1.80 m1.80\text{ m} above the base. Determine the overturning moment ratio about the toe.

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Key Takeaways
  • Eccentricity follows directly from moment equilibrium: e=M/Ve=M/V.
  • The middle-third check concerns full compression; it is not the same as complete overturning.
  • Sliding and tipping thresholds must be evaluated independently.
  • Stability calculations are equilibrium checks, not substitutes for structural or geotechnical design.