Strength of Material (Part-2) (General Engineering) (SSC JE)

Distortion energy theory–This theory is an important one because it comes closest of all to verifying experimental results. The derivation is based on the assumption that Hooke's law applies and so this theory is valid only for ductile materials, that is, materials that may yield.

• In the literature the distortion energy theory is also called the shear energy theory as well as the "Von Mises-Henky theory".

• It cannot be applied for material under hydrostatic pressure. • All theories will give same results if loading is uniaxial.

• A bar stressed to the elastic under the state of uniaxial stress as occurs in a simple tension/ compression test.

A beam of uniform rectangular cross-section is under a transverse load– The maximum shear stress developed in a beam of rectangular cross-section–
• It may be noted that the shear stress in a beam is uniformly distributed over the cross-section but varies from zero at outer fiber to a maximum at the neutral axis.

Maximum bending at the crown if the temperature increase is greater at the crown of the arch rib than at the hinges, there will be a maximum bending moment induced at the crown. This is because the arch rib expands more at the crown than at the hinges and this results in a maximum bending moment at the crown.

Parabolic arch subjected to UDC (w/per unit length) our entire span
H = wL²/8h
Two hinged parabolic arch subjected to uniformly distributed load on the half span.
• A two hinged parabolic arch carries a UDL of w per unit run on entire span then it is subjected to normal thrust alone.
Radial shear and bending moment at every point on arch is found to be zero.

The slope of fixed and will be zero using moment area theorem.

The ILD for thrust in parabolic arch horizontal thrust due to a concentrated load P at a distance x from X

Then ILD for horizontal thrust is parabolic.