0Eg Problem:
A Beam Subjected Simultaneously to axial force and bending Moment:
Analysis:-
1. Superimposing of the stresses & strains caused by each load separately (provided - Stresses and strains are linearly dependent on loads applied and the material follows hooke's law)
2. Select critical cross section (the C/s prone to fail first) from the superimposed values of Stresses against allowable loads.
3. FOr the critical cross sections following formulas can be used:
a) Axial stresses - P/A (for tensile or compressive force P across C/s area A), My/I (in case of bending of beams by bending moment M), pr/t (for cylindrical shell structures like pressure vessels (of radius r and thickness t, subjected to internal pressure p), pr/2t (for spherical shell structures like pressure vessels (of radius r and thickness t, subjected to internal pressure p)
b) Shear Stresses - Tr/I (For circular shaft/beam of intermediate radius r and Polar Moment of Inertia I, subjected to torque T), VQ/Ib (V= shear force on the beam, Q is first moment of area of elemental strips of C/s area about neutral axis/plane, I is Moment of inertia of the c/s about Neutral Plane, b is width of beam)
4. We get resultant stresses in the form of Axial forces in X and Y axis directions and shear force in XY plane.
5. From the above find the principle stresses and max shear stress and their orientations (critical points on critical C/s) . Find strains at the critical points.
