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Theory of Structures

Theory of Structures
For a strongest rectangular beam cut from a circular log, the ratio of the width and depth, is

0.303
0.404
0.505
0.707

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Theory of Structures
In case of a simply supported I-section beam of span L and loaded with a central load W, the length of elasto-plastic zone of the plastic hinge, is

L/4
L/3
L/5
L/2

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Theory of Structures
The maximum deflection due to a load W at the free end of a cantilever of length L and having flexural rigidity EI, is

WL3/2EI
WL3/3EI
WL²/3EI
WL²/2EI

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Theory of Structures
If E, N, K and 1/m are modulus of elasticity, modulus of rigidity. Bulk modulus and Poisson ratio of the material, the following relationship holds good

(3/2)K (1 – 2/m) = N (1 + 1/m)
All of these
E = 3K (1 – 2/m)
E = 2N (1 + 1/m)

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Theory of Structures
A masonry dam (density = 20,000 N/m³) 6 m high, one metre wide at the top and 4 m wide at the base, has vertical water face. The minimum stress at the base of the dam when the reservoir is full, will be

75000 N/m²
75 N/m²
7500 N/m²
750 N/m²

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Theory of Structures
A lift of weight W is lifted by a rope with an acceleration f. If the area of cross-section of the rope is A, the stress in the rope is

[W (1 + f/ G)]/ A
[W (2 + g/f)]/A
(1 – g/f)/A
[W (2 + f/G)]/A

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