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Theory of Structures

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

j = 2m – 3
j = 3m – 2
m = 2j – 3
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 = 2N (1 + 1/m)
E = 3K (1 – 2/m)
(3/2)K (1 – 2/m) = N (1 + 1/m)

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Theory of Structures
A simply supported beam which carries a uniformly distributed load has two equal overhangs. To have maximum B.M. produced in the beam least possible, the ratio of the length of the overhang to the total length of the beam, is

0.207
0.407
0.508
0.307

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

0.404
0.303
0.505
0.707

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Theory of Structures
The yield moment of a cross section is defined as the moment that will just produce the yield stress in

The fibre everywhere
The outer most fibre of the section
The neutral fibre of the section
The inner most fibre of the section

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Theory of Structures
constant, depth of a cantilever of length of uniform strength loaded with Keeping breadth uniformly distributed load varies from zero at the free end and

2w w l at the fixed end
w l) at the fixed end
l) at the fixed end
3w l at the fixed end

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