Project ForgeA simply-supported beam of length 3L carries an upward point load P at distance L from the left support and a downward point load P at distance 2L. Given P=1 N, L=1 m, E=200 GPa, and a 10mm×10mm square cross-section, the bending stress (in Pa) at point A (top surface) located at 1.5L from the left end is __________ (compressive negative, tensile positive).
Explanation
Reactions (upward positive): summing moments about the left support gives R_right=P/3, R_left=-P/3. Bending moment at x=1.5L (using forces to the left): M = R_left(1.5L) + P(1.5L-L) = (-P/3)(1.5L) + P(0.5L) = -0.5PL+0.5PL = 0. Zero bending moment means zero bending stress at A.
Source: GATE ME 2016 Set-1 (2016)
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