For overall stability against overturning in structural engineering (e.g., retaining walls, shear walls, chimneys), the resisting weight or anchorage should provide a minimum restoring moment equal to what multiple of the overturning moment due to dead load alone?

Introduction / Context:
Designing for stability against overturning requires a safety margin between the restoring moment (from self-weight and anchorage) and the overturning moment (from dead, live, wind, or seismic actions). Codes and classical design practice prescribe minimum factors so that minor uncertainties in loading, construction tolerances, or deterioration do not compromise safety.

Given Data / Assumptions:

• We compare restoring (stabilizing) moment to the overturning moment due to dead load.
• We seek the minimum multiple that the resisting system (weight/anchorage) should provide.
• Target is a conservative, code-consistent value used in preliminary checks.

Concept / Approach:

A common benchmark for stability checks is to ensure that the available restoring moment comfortably exceeds the destabilizing effects. When evaluating only dead-load overturning, practice typically requires a restoring moment at least 1.4 times the dead-load overturning component, giving a margin above unity.

Step-by-Step Solution:

Verification / Alternative check:

Even when fuller factored load combinations are used, a separate serviceability-style stability check often preserves a margin >1.0. The 1.4 multiple aligns with conservative practice for dead-load-only comparisons.

Why Other Options Are Wrong:

• 1.2 times: Less conservative; smaller safety margin.
• Sum of (a) and (b): Not meaningful dimensionally for a single multiple.
• None of these / 1.0 times: Offers no safety margin; unacceptable.

Common Pitfalls:

• Using equality (M_r = M_o) with no reserve capacity.
• Mixing factored and unfactored moments inconsistently in a single check.

Final Answer:

1.4 times the minimum overturning moment due to dead load