Empirical proportion between offset and depth of concrete bed Let a (in cm) be the plan offset (projection) of a concrete bed beyond the footing edge, and d (in cm) be the depth (thickness) of that bed. Choose the commonly used empirical relation between d and a.

Introduction / Context:
For PCC leveling beds and plain concrete projections beneath footings, simple empirical rules are often used at the estimation stage to size thickness relative to the bed’s plan offset a (the overhang beyond the footing). These rules roughly account for bending and shear in the projecting portion under soil pressure.

Given Data / Assumptions:

• a = plan offset (projection) in centimetres.
• d = depth (thickness) of concrete bed in centimetres.
• Rule-of-thumb proportion relates d to a for preliminary sizing.
• Final design should be checked by structural calculations and local codes.

Concept / Approach:
The projection behaves somewhat like a cantilever under upward soil reaction. A moderate fraction of the projection used as thickness offers a practical balance between strength and economy. The relation d ≈ 0.445 a is a commonly cited thumb rule for preliminary estimates, subject to verification.

Step-by-Step Solution:

Verification / Alternative check:
Comparative checks using simple cantilever bending under uniform reaction show that thickness proportional to projection provides acceptable preliminary stresses, which detailed design can fine-tune.

Why Other Options Are Wrong:

• d = 0.557 a or 0.775 a: overly conservative for typical PCC beds, inflating quantities.
• d = 0.250 a: too thin for many practical projections.
• none of these: incorrect since a standard thumb rule exists.

Common Pitfalls:
Treating thumb rules as final design; ignoring edge cases such as very high soil pressures or poor-quality concrete requiring thicker beds.

Final Answer:
d = 0.445 a