Strength of Material (Part-3) (General Engineering) (SSC JE)

Column analogy method– It is a force method in which degree of freedom is more than static indeterminacy. And rest other method is displacement method.

Moment distribution is an iterative method of solving an indeterminate structure.
• Moment distribution method was first introduced by Hardy Cross in 1932.
• Moment distribution is suitable for analysis of all types of indeterminate beam and rigid frames.
• It is also called a relaxation method.

In the displacement method of analysis, the primary uknowns are the displacements. In this method, first force-displacement relations are computed and subsequently equations are written satisfying the equilibrium conditions of the structure. Difference between force and displacement methods–

Conjugate Beam Method–The conjugate beam method is a further extension of the method of integration, to simplify the computations of displacements at given sections in a beam. This method applies the moment area relationships discussed earlier.
• The conjugate beam is a notional beam with modified support conditions and loaded with the (M/EI) diagram corresponding to the given loading for the original beam.
The analogy between slope and deflection in a beam and SF and BM in the corresponding conjugate beam is utilized in this method.
Relation between the real beam and conjugate beam–

Column analogy method–This is a method of structural analysis of frames by considering an analogous column. The analogous column has a crosssection similar to the frame but with 1/EI as the width and loaded by bending moment diagram.

The analogous column is analyzed by the column formula for stresses the deflection of the frame are inter-related to the stresses of an analogous column.

Flexibility–Flexibility is inverse of stiffness. Flexibility is defined as the deformation produced due to unit load.
f = 1/k
Stiffness–It is the load required to produce unit deflection in the spring.

Castigliano’s 2ⁿᵈ theorem– • The first partial derivative of the total internal energy in a structure with respect to the force applied at any point is equal to the deflection at the point of application of that force in the direction of its line of action.

• The second theorem of Castigliano is applicable to linearly elastic (Hooke material) structure with constant temperature and unyielding supports.

For a two hinged arch, if one of the supports settles down vertically then the horizontal thrust is decreased.