Effect of doubling beam width on central deflection A simply supported prismatic beam carries a single concentrated load at midspan. If the beam's width b is doubled (all other parameters unchanged), how does the central deflection change?

Introduction / Context:Deflection control is a key serviceability requirement. For rectangular sections, the flexural rigidity E * I depends on the geometry, so changing width or depth alters deflection in predictable ways.

Given Data / Assumptions:

• Simply supported beam, concentrated load P at midspan.
• Span L, Young’s modulus E, depth h remain constant.
• Rectangular section with width b.

Concept / Approach:For a midspan point load on a simply supported beam, the maximum deflection is:delta_max = P * L^3 / (48 * E * I)For a rectangle, the second moment of area is:I = b * h^3 / 12Therefore, delta_max is inversely proportional to b when h, E, L, and P are fixed.

Step-by-Step Solution:

Verification / Alternative check:Check dimensional consistency and observe that increasing section size increases stiffness, reducing deflection proportionally.

Why Other Options Are Wrong:

• Options a, b, c, e suggest larger deflections, which contradict stiffness increase when width increases.

Common Pitfalls:Confusing the stronger influence of depth (h appears as h^3) with width (linear effect). Doubling depth would reduce deflection by a factor of 8; doubling width only halves it.

Final Answer:It becomes 1/2 of the original deflection