Advanced mechanics of solids by Prof L S Srinath

By Prof L S Srinath

This publication is designed to supply a superb beginning in  Mechanics of Deformable Solids after  an introductory path on energy of Materials.  This variation has been revised and enlarged to make it a complete resource at the topic. Exhaustive therapy of crucial themes like theories of failure, strength equipment, thermal stresses, pressure focus, touch stresses, fracture mechanics make this an entire delivering at the topic.

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Take another set of axes s and t. In this plane we can mark a point Q with co-ordinates (s, t ) representing the values of the normal and shearing stress on the plane n. For different planes passing through point P, we get different values of s and t. Corresponding to each plane n, a point Q can be located with coordinates (s, t ). The plane with the s axis and the t axis is called the stress plane p. (No numerical value is associated with this symbol). The problem now is to determine the bounds for Q (s, t) for all possible directions n.

The axis of the body is usually taken as the z axis. The two other coordinates are r and q, where q is measured counter-clockwise. 31(b). s r , sq and sz are called the r radial, circumferential and P axial stresses respectively. If z the stresses vary from point to point, one can derive the sz q appropriate differential equations of equilibrium, as in tzq Sec. 26. For this purpose, consider a cylindrical eletrq trz sq ment having a radial length tqz sr Dr with an included angle Dq and a height Dz, isolated from (b) the body.

21 THE STATE OF PURE SHEAR The state of stress at a point can be characterised by the six rectangular stress components referred to a coordinate frame of reference. The magnitudes of these components depend on the choice of the coordinate system. If, for at least one particular choice of the frame of reference, we find that sx = sy = sz = 0, then a state of pure shear is said to exist at point P. For such a state, with that particular choice of coordinate system, the stress matrix will be ⎡ 0 τ xy τ xz ⎤ ⎢ ⎥ ⎡⎣τ ij ⎤⎦ = ⎢τ xy 0 τ yz ⎥ ⎢ ⎥ ⎣⎢τ xz τ yz 0 ⎥⎦ For this coordinate system, l1 = sx + sy + sz = 0.

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