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A 3 m long simply supported beam of uniform cross section is subjected to a uniformly distributed load of w = 20 kN/m in the central 1 m as shown in the figure. If the flexural rigidity (EI) of the beam is 30 × 10⁶ N·m², the maximum slope (expressed in radians) of the deformed beam is

1. 0.681 × 10⁻⁷
2. 0.943 × 10⁻⁷
3. 4.310 × 10⁻⁷
4. 5.910 × 10⁻⁷

Correct answer: 5.910 × 10⁻⁷

Solution

The maximum slope of a beam under a uniformly distributed load can be calculated using beam deflection formulas, which take into account the load distribution, length of the beam, and its flexural rigidity. In this case, the calculations yield a maximum slope of 5.910 × 10⁻⁷ radians, confirming that option D is correct.

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