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Theory of Structures

Theory of Structures
For beams of uniform strength, if depth is constant,

Width b M
Width b M 2
Width b 3 M
Width b 1/M

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Theory of Structures
Y are the bending moment, moment of inertia, radius of curvature, modulus of If M, I, R, E, F, and elasticity stress and the depth of the neutral axis at section, then

M/I = E/R = Y/F
M/I = R/E = F/Y
I/M = R/E = F/Y
M/I = E/R = F/Y

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Theory of Structures
If a solid shaft (diameter 20 cm, length 400 cm, N = 0.8 × 105 N/mm²) when subjected to a twisting moment, produces maximum shear stress of 50 N/mm 2, the angle of twist in radians, is

0.003
0.0025
0.001
0.002

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Theory of Structures
In a shaft, the shear stress is not directly proportional to

Length of the shaft
Modulus of rigidity
Angle of twist
Radius of the shaft

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Theory of Structures
The moment of inertia of a triangular section (height h, base b) about its base, is

bh²/12
b³h/12
b²h/12
bh³/12

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Theory of Structures
The ratio of lateral strain to axial strain of a homogeneous material, is known

Hooke’s ratio
Yield ratio
Poisson’s ratio
Plastic ratio

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