Simply supported beam with two equal point loads: A beam of span L carries two equal concentrated loads W placed at distances L/3 from each support (i.e., at x = L/3 and x = 2L/3). What is the maximum bending moment in the beam?

Introduction / Context:
Finding the location and value of maximum bending moment for beams with symmetric point loads is a standard analysis task. The shear sign change and zero-shear region pinpoint the maximum moment zone.

Given Data / Assumptions:

• Simply supported beam, span L.
• Two equal loads W at x = L/3 and x = 2L/3.
• Static, linear analysis; self-weight ignored for clarity.

Concept / Approach:
By symmetry, reactions are equal: R_A = R_B = W. Between the two loads, the shear becomes zero, implying a constant bending moment there and indicating the maximum value occurs anywhere in that region.

Step-by-Step Solution:
Reactions: R_A = R_B = (2W)/2 = W.For a section at x in [L/3, 2L/3]: V(x) = R_A − W = 0 → moment is constant.Take x = L/3 or x = L/2 for convenience.At x = L/2: M = R_A * (L/2) − W * (L/2 − L/3) = W * L / 2 − W * L / 6 = W * L / 3.

Verification / Alternative check:
Compute at x = L/3: M = R_A * (L/3) − W * 0 = W L / 3. Same value confirms a constant maximum between loads.

Why Other Options Are Wrong:
WL/6, WL/4, WL/8: correspond to different loading configurations.2WL/3: not consistent with equilibrium and internal actions here.

Common Pitfalls:
Forgetting that zero shear implies constant moment and hence the maximum lies in that zone.

Final Answer:
W L / 3.