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Theory of Structures

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

WL²/3EI
WL²/2EI
WL3/2EI
WL3/3EI

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Theory of Structures
Maximum shear stress theory for the failure of a material at the elastic limit, is known

Guest's or Trecas' theory
Haig's theory
Rankine's theory
St. Venant's theory

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

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Theory of Structures
For calculating the allowable stress of long columns σ0 = σy/n [1 - a (1/r)²]is the empirical formula, known as

Perry
Parabolic formula
Straight line formula
Rankine

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

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

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Theory of Structures
A short column (30 cm × 20 cm) carries a load P 1 at 4 cm on one side and another load P2at 8 cm on the other side along a principal section parallel to longer dimension. If the extreme intensity on either side is same, the ratio of P1 to P2 will be

3/2
2/3
8/5
5/8

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