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HW6 - ABC can be considered rigid When a force F = 10 N is...

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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 1. Determine the strain components ε x , ε 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 1

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2. 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 30 100 70 5 kN all dimensions in mm Figure 2 3. A steel wire of length 50 meters is required to transmit a 10 kN tensile load. Determine the smallest diameter wire that can be used if the tensile stress must not exceed 150 MPa and the elongation of the wire must not exceed 25 mm. ( E steel = 210 GPa). 2
4. In Figure 4, the bar
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Unformatted text preview: ABC can be considered rigid. When a force F = 10 N is applied at C , the wire BD is observed to increase in length by 1 mm. If the wire diameter is 0.6 mm, estimate Young’s modulus for the material of the wire. If it is also known that the wire material has Poisson’s ratio ν = . 25, find the change in diameter of the wire due to the load and hence find the percentage change in the total volume of wire. 500 900 F A C 1000 B D all dimensions in mm. Figure 4 5. The Young’s modulus for aluminum is E = 70 GPa and Poisson’s ratio = . 34. The following strains are measured on the surface of an aluminum part: ε x = 350 × 10 − 6 ; y = 900 × 10 − 6 ; γ xy = 700 × 10 − 6 . Calculate the in-plane stress components and the out-of-plane strain z . (The surface is perpen-dicular to the z-direction, and there are no tractions applied to it.) 3...
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