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ESO 202A/204: Mechanics of Solids (2016-17 II Semester)
Assignment No. – 4 4.1 The piece of rubber is originally rectangular and subjected to the deformation shown
by the dashed lines. Determine (a) the average shear strain at A and (b) the average
normal strain along the diagonal DB and side AD (Fig. 4.1).
4.2 The state of plane strain on an element is
εxx = -300×10-6, εyy = 0, γxy = 150×10-6
Use the strain-transformation equations to determine the equivalent state of strain
which represents (a) the principal strains, and (b) the maximum in-plane shar strain
and the associated average normal strain. Specify the orientation of the
corresponding elements for these states of strain with respect to the original element
(Fig. 4.2).
4.3 The state of strain at a point on a wrench has components
εxx = 120×10-6, εyy = -180×10-6, γxy = 150×10-6
Use Mohr’s circle to determine (a) the in-plane principal strains and (b) the
maximum in-plane shear strain and average normal strain. In each case specify the
orientation of the element and show how the strains deform the element within the
x-y plane.
4.4 The strain rosette of configuration shown in Fig. 4.4 is mounted on a beam. The
following readings are obtained for each gauge:
εa = 200×10-6 , εb = -450×10-6, εc = 250×10-6
Determine (a0 the in-plane principal strains and (b) the maximum in-plane sear
strain and average normal strain. In each case show the deformed element due to
these strains. Fig. 4.1
Fig. 4.2 Fig. 4.4
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