Deflection Comparison — Effect of Breadth on Beam Stiffness Two simply supported beams 'A' and 'B' have the same span length l and depth d. Beam 'A' has breadth b, while beam 'B' has breadth 2b. Both carry the same central point load W. The midspan deflection of beam 'B' will be __________ compared with beam 'A'.

Introduction:
This question evaluates your understanding of how the second moment of area influences deflection in beams under a central point load.

Given Data / Assumptions:

• Both beams are simply supported with equal span l and depth d.
• Same central point load W and same material modulus E.
• Breadth of B is 2b; breadth of A is b.

Concept / Approach:
For a simply supported beam with a central point load: δ = W * l^3 / (48 * E * I) For a rectangle: I = b * d^3 / 12 Thus deflection is inversely proportional to breadth b if depth is constant.

Step-by-Step Solution:
I_A = b * d^3 / 12I_B = (2b) * d^3 / 12 = 2 * I_Aδ_B / δ_A = (1 / I_B) / (1 / I_A) = I_A / I_B = 1/2Hence δ_B = (1/2) * δ_A.

Verification / Alternative check:
Deflection scales as 1/I. Doubling I halves the deflection, confirming the result.

Why Other Options Are Wrong:

• one-fourth, four times, double: These correspond to incorrect scaling with breadth.

Common Pitfalls:
Confusing changes in breadth with changes in depth (deflection is far more sensitive to depth, proportional to d^3).

Final Answer:
one-half