Strength of materials – deflection comparison For beams of the same length L and flexural rigidity EI, what is the ratio of the maximum deflection of a simply supported beam with a central point load W to that of a cantilever carrying the same load W at its free end?

Introduction / Context:
This question assesses recall and application of standard deflection formulas from elementary beam theory. Comparing deflections for common boundary conditions (simply supported vs cantilever) helps engineers quickly estimate stiffness and serviceability under identical loads.

Given Data / Assumptions:

• Both members have the same span L and flexural rigidity EI.
• Simply supported beam has a single central point load W.
• Cantilever has a single point load W at the free end.
• Small-deflection, linear-elastic behavior is assumed; shear deformation is neglected.

Concept / Approach:
Use the standard closed-form deflection expressions for prismatic beams under classic loads. For a central point load on a simply supported beam, and for an end load on a cantilever, the maximum deflection expressions are well known and depend only on W, L, E, and I.

Step-by-Step Solution:
Maximum deflection of simply supported beam with central load: delta_ss = WL^3 / (48EI)Maximum deflection of cantilever with end load: delta_cant = WL^3 / (3EI)Form the ratio: R = delta_ss / delta_cantR = (WL^3 / (48EI)) / (WL^3 / (3EI)) = (1/48) / (1/3) = 3/48 = 1/16

Verification / Alternative check:
Numerically, set W = 1, L = 1, E*I = 1. Then delta_ss = 1/48 and delta_cant = 1/3. The ratio (1/48)/(1/3) equals 1/16, confirming the result without units.

Why Other Options Are Wrong:
(1/8) and (1/12) are larger than the correct ratio and would imply the simply supported system deflects relatively more than it truly does; (1/24) is too small; 'None of these' is incorrect because a correct ratio, 1/16, is provided.

Common Pitfalls:
Mixing the formulas for distributed loads and point loads; forgetting that cantilevers are much more flexible under the same load and span; canceling terms incorrectly when forming the ratio.

Final Answer:
1/16