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Theory of Structures

Theory of Structures
A truss containing j joints and m members, will be a simple truss if

m = 2j – 3
j = 2m – 3
j = 3m – 2
m = 3j – 2

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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

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

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Theory of Structures
A cantilever of length 2 cm and depth 10 cm tapers in plan from a width 24 cm to zero at its free end. If the modulus of elasticity of the material is 0.2 × 106 N/mm², the deflection of the free end, is

5 mm
3 mm
4 mm
2 mm

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Theory of Structures
A steel bar 20 mm in diameter simply-supported at its ends over a total span of 40 cm carries a load at its centre. If the maximum stress induced in the bar is limited to N/mm², the bending strain energy stored in the bar, is

411 N mm
511 N mm
711 N mm
611 N mm

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Theory of Structures
The maximum magnitude of shear stress due to shear force F on a rectangular section of area A at the neutral axis, is

F/2A
F/A
2F/3A
3F/2A

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Theory of Structures
The ratio of the maximum deflections of a simply supported beam with a central load W and of a cantilever of same length and with a load W at its free end, is

1/10
1/8
1/16
1/12

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