By Prof L S Srinath
This publication is designed to supply a very good starting place in Mechanics of Deformable Solids after an introductory direction on energy of Materials. This version has been revised and enlarged to make it a complete resource at the topic. Exhaustive remedy of crucial themes like theories of failure, strength equipment, thermal stresses, rigidity focus, touch stresses, fracture mechanics make this a whole providing at the topic.
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Iii) What is the plane on which the tangential or shear stress is a maximum and what it is its magnitude? Answers to these questions are very important in the analysis of stress, and the next few sections will deal with these. pmd 14 7/3/2008, 5:27 AM Analysis of Stress 15 direction cosines nx, ny and nz on which the stress is wholly normal. Let s be the magnitude of this stress vector. e. 9), n T x = sx nx + txy ny + txz nz n T y = txy nx + sy ny + tyz nz n T z = txz nx + tyz ny + sz nz Subtracting Eq.
If such Qs are marked for every plane passing through P, then we get a surface S. This surface determines the normal component of stress on every plane passing through P. This surface is known as the stress surface of Cauchy. This has a very interesting property. Let m S Q be a point on the surface, Fig. 20(a). By the previous definiQ tion, the length PQ = R is such that R n the normal stress on the plane whose n T n normal is along PQ is given by T σ = 12 P (b) (a) Fig. 51) R If m is a normal to the tangent plane to the surface S at point Q, then this normal m is parallel to the n resultant stress vector T at P.
26 Advanced Mechanics of Solids t D p Q(s, t) * E C s3 B s2 0 Fig. 16 F A s1 s Mohr's stress plane (ii) The maximum shear stress is equal to 1 (s1 – s3) and the associated nor2 mal stress is 1 (s1 + s3). This is indicated by point D on the outer circle. 2 (iii) Just as there are three extremum values s1, s2 and s3 for the normal stresses, there are three extremum values for the shear stresses, these σ − σ3 σ 2 − σ3 σ − σ2 , and 1 . The planes on which these shear being 1 2 2 2 stresses act are called the principal shear planes.