By Prof L S Srinath

This e-book is designed to supply a very good origin in Mechanics of Deformable Solids after an introductory path on power of Materials. This version has been revised and enlarged to make it a finished resource at the topic. Exhaustive therapy of crucial themes like theories of failure, power equipment, thermal stresses, pressure focus, touch stresses, fracture mechanics make this an entire delivering at the topic.

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20(b). Analysis of Stress 35 n We shall now show that the normal m to the surface S is parallel to T , the resultant stress vector. Let Pxyz be the principal axes at P (Fig. 21). n is the normal to a particular plane at P. 52) Substituting these in the above equation for s n x P s R2 = s1x2 + s2 y2 + s3z2 From Eq. 51), we have sR2 = ±1. The plus sign is used when s is tensile and the minus sign is used when s is compressive. Hence, the surface S has the equations (a surface of second degree) z Fig.

The pressure of water on face OB is also shown. With the axes Ox and Oy, as shown in Fig. 12 γ tan 2 β tyz = 0, tzx = 0, ⎞ ⎛ γ ⎞ − ρ ⎟⎟ y ⎟⎟ x + ⎜⎜ 2 ⎠ ⎝ tan β ⎠ x sz = 0 Check if these stress components satisfy the differential equations of equilibrium. Also, verify if the boundary conditions are satisfied on face OB. Solution The equations of equilibrium are ∂σ x ∂τ xy + + γx = 0 ∂x ∂y and ∂σ y ∂τ xy + + γy = 0 ∂y ∂x Substituting and noting that gx = 0 and gy = r, the first equation is satisifed.

63a) 40 Advanced Mechanics of Solids In the xy plane, the maximum shear stress will be τ max = 1 (σ 1 − σ 2 ) 2 and from Eq. 64) DIFFERENTIAL EQUATIONS OF EQUILIBRIUM So far, attention has been focussed on the state of stress at a point. In general, the state of stress in a body varies from point to point. One of the fundamental problems in a book of this kind is the determination of the state of stress at every point or at any desired point in a body. One of the important sets of equations used in the analyses of such problems deals with the conditions to be satisfied by the stress components when they vary from point to point.

### Advanced mechanics of solids by Prof L S Srinath

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