Continuum Mechanics, Assignment # 3 Due date: 16/10/1393

Continuum Mechanics, Assignment # 3
Due date: 16/10/1393
1-The stress distribution in a continuum is given by:
2- The stress vectors σx, σy act on planes x = constant, y = constant, where (x, y) are plane oblique
coordinates. Let (e x, ey) be unit vectors along axes (x, y). Then
σx = pxx ex + pxy ey
σy = pyx ex + pyy ey
(a) Compute the normal stress (σx, σy) and the shear stresses (τxy, τyx ) on planes
x = constant, y = constant in terms of p xx, pxy, pyx, pyy , and θ.
(b) Derive the relation between τxy and τyx.
(c) Derive the differential equilibrium equations for the element in terms of
pxx, pxy, pyy , pyx and ex , ey.
3- The stress array for the torsion problem of a circular cross-section bar of radius a and

Download Report