TGPSC HMWSSB Manager 2015 Paper 2 · Question 114
Question 114 of the TSPSC Manager (Engineering), HMWSSB, 2015: Paper 2 (Civil Engineering) (1 November 2015). Try it first, then open the answer and explanation.
A simply supported beam of span L and flexural rigidity EI carries a UDL of intensity w/unit run all along its span. The beam is supported at its centre by a linear spring of stiffness k. The force carried by the spring is ______.
- 5kwL⁴/(kL³+8EI)
- 5kwL⁴/8(kL³+48EI)
- 5wL⁴/8(kL³+8EI)
- 5wL⁴/8(kL³+48EI)
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Answer: (2) 5kwL⁴/8(kL³+48EI)
The UDL alone deflects mid-span by 5wL⁴/384EI and the spring force R lifts it back by RL³/48EI; the spring compresses by the net deflection, so R = k(5wL⁴/384EI − RL³/48EI). Multiplying by 48EI gives R(48EI + kL³) = 5kwL⁴/8, so R = 5kwL⁴/8(kL³ + 48EI).