Deflection of a simply supported steel beam – midspan point load A simply supported steel beam of span L carries a concentrated load W at its centre. What is the central deflection in terms of W, L, E, and I (second moment of area)?

Introduction / Context:
Deflection control is a key serviceability criterion in beam design. The classical elastic curve solution for a simply supported beam under a central point load is a staple result, used to check deflection limits against code-prescribed span ratios.

Given Data / Assumptions:

• Beam is prismatic with constant E and I.
• Boundary conditions: simple supports at both ends (no end fixity).
• Loading: a single concentrated load W at midspan.
• Small deflections and linear elastic behavior.

Concept / Approach:
Use the standard integration of the Euler–Bernoulli beam equation: E * I * d^2y/dx^2 = M(x). For a central point load, the bending moment diagram is triangular, peaking at W * L / 4 at midspan. Integrating twice with appropriate boundary conditions yields the closed-form deflection at midspan.

Step-by-Step Solution:

Verification / Alternative check:
Compare with tabulated deflection coefficients: for central point load on simply supported beam, coefficient = 1/48, matching the derived expression.

Why Other Options Are Wrong:
1/24 overestimates deflection by a factor of 2; (W * L^2)/(8 * E * I) has wrong dimensions; 5/384 corresponds to uniformly distributed load, not point load; (W * L)/(4 * E * I) is dimensionally inconsistent.

Common Pitfalls:
Mixing up the coefficient with that for uniformly distributed loads; forgetting to use consistent units for E and I.

Final Answer:
δ = (W * L^3) / (48 * E * I)