By Prof L S Srinath

This ebook is designed to supply an exceptional beginning in Mechanics of Deformable Solids after an introductory path on energy of Materials. This version has been revised and enlarged to make it a complete resource at the topic. Exhaustive therapy of crucial subject matters 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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**Extra resources for Advanced mechanics of solids**

**Sample text**

X¢ plane and y¢ plane, are stress free. 16 THE STATE OF STRESS REFERRED TO PRINCIPAL AXES In expressing the state of stress at a point by the six rectangular stress components, we can choose the principal axes as the coordinate axes and refer the rectangular stress components accordingly. 30) Analysis of Stress 25 On any plane with normal n, the components of the stress vector are, from Eq. 35) MOHR’S CIRCLES FOR THE THREE-DIMENSIONAL STATE OF STRESS We shall now describe a geometrical construction that brings out some important results.

The point Q lies on the circle BEC. Case (iii) s1 = s2 = s3 This is a trivial case since this is the isotropic or the hydrostatic state of stress. Mohr’s circles collapse to a single point on the s axis. See Appendix 1 for the graphical determination of the normal and shear stresses on an arbitrary plane, using Mohr’s circles. 19 PLANES OF MAXIMUM SHEAR From Sec. 17 and also from Fig. 16 for the case s1 > s2 > s3, the maximum 1 1 shear stress is (s1 – s3) = t2 and the associated normal stress is (s1 + s3).

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. While the planes on which the principal normal stresses act are free of shear stresses, the principal shear planes are not free from normal stresses.