By Prof L S Srinath
This ebook is designed to supply an excellent 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 entire resource at the topic. Exhaustive remedy of crucial themes like theories of failure, power tools, thermal stresses, tension focus, touch stresses, fracture mechanics make this an entire providing at the topic.
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Additional resources for Advanced mechanics of solids
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.
7. Choosing Oxyz coinciding with n1, n2 and n3, the stress vector on any arbitrary plane n has value s, the direction of s coinciding with n. Hence, every plane is a principal plane. Such a state of stress is equivalent to a hydrostatic state of stress or an isotropic state of stress. 15 RECAPITULATION The material discussed in the last few sections is very important and it is worthwhile to put it in the form of definitions and theorems. 20 Advanced Mechanics of Solids Definition n For a given state of stress at point P, if the resultant stress vector T on any plane n is along n having a magnitude s, then s is a principal stress at P, n is the principal direction associated with s, the axis of s is a principal axis, and the plane is a principal plane at P.
Analysis of Stress 27 Choose the coordinate frame of reference Pxyz such that the axes arenalong the principal axes. 42) Since nx2 , n 2y and nz2 are all positive, the right-hand side expressions in the above equations must all be positive. Recall that we have arranged the principal stresses such that s1 ≥ s2 ≥ s3. There are three cases one can consider. Case (i) s1 > s2 > s3 Case (ii) s1 = s2 > s3 Case (iii) s1 = s2 = s3 We shall consider these cases individually. Case (i) s1 > s2 > s3 For this case, the denominator in Eq.