Elastic (bending) strength comparison of two rectangular beams with identical width b and depth d: Beam A has length l; Beam B has length 2l. For the same material and cross-section, how does the elastic strength in bending of Beam B compare with Beam A?

Introduction:
"Elastic strength in bending" refers to the maximum bending stress capacity governed by material yield/allowable stress and section modulus, not by member length. This question checks whether you distinguish strength (stress capacity) from deflection (stiffness).

Given Data / Assumptions:

• Both beams: same rectangular section (b by d) and same material.
• Only length differs: l vs 2l.
• Strength reference is section capacity in the elastic range.

Concept / Approach:
For bending, maximum normal stress σ_max = M_max / Z, where Z = bd^2/6 for a rectangle. Strength capacity depends on Z and material limit; it does not directly depend on span. Span affects M_max only for a specific loading pattern, but the intrinsic elastic strength (capacity per unit bending moment) is unchanged by length if b and d are fixed.

Step-by-Step Solution:

Verification / Alternative check:
If both are subjected to the same bending moment at a section, the computed stress σ = M/Z is identical because Z is identical.

Why Other Options Are Wrong:

• one-half / one-fourth / one-eighth: These imply strength scaling with length, which is incorrect for intrinsic bending strength.
• greater than Beam A: No increase without a change in section or material.

Common Pitfalls:
Confusing strength with deflection or moment due to a particular load case; span affects deflection and internal M for a given load pattern, but not the intrinsic section strength.

Final Answer: