HW6+Solutions - HOMEWORK PROBLEMS Week 6: Due Friday 21...

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HOMEWORK PROBLEMS Week 6: Due Friday 21 October 1. The rectangular plate ABCD is homogeneously deformed into the shape A B C D as shown in Figure 1. Determine the strain components ǫ x y and γ xy . x y C A B D A B C D 0.007 0.006 0.004 0.002 0.002 0.002 0.001 0.004 15 20 all dimensions in inches [not to scale]. Figure 1 Solution The displacements of the corners are u A x = 0 . 001 ; u A y = 0 . 002 ; u B x = 0 . 006 ; u B y = 0 . 004 , 1
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u C x = 0 . 007 ; u C y = 0 . 002 ; u D x = 0 . 002 ; u D y = 0 . 004 . so the strains are ǫ x = u D x u A x L AD = 0 . 002 + 0 . 001 15 = 66 . 7 × 10 6 . ǫ y = u B y u A y L AB = 0 . 004 0 . 002 20 = 300 × 10 6 . γ xy = u D y u A y L AD + u B x u A x L AB = 0 . 004 0 . 002 15 + 0 . 006 + 0 . 001 20 = 116 . 7 × 10 6 . 2
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Figure 2 shows a rigid rectangular block which is attached to a rigid foundation through two (deformable) rubber blocks. The 5 kN force shown causes the rigid block to move downwards a distance 1.8 mm. Find the average shear strain γ and the average shear stress τ in each of the rubber blocks and hence estimate the shear modulus G for the rubber. rigid rigid rigid rubber 30 100 70 5 kN all dimensions in mm Figure 2 Solution Figure 2.1(a) shows the deformation of the rubber, from which we deduce that the shear strain is γ = 1 . 8 30 = 0 . 06 . 3
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This note was uploaded on 02/15/2012 for the course MECHENG 211 taught by Professor ? during the Fall '07 term at University of Michigan.

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HW6+Solutions - HOMEWORK PROBLEMS Week 6: Due Friday 21...

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