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EG1109 (Part II) - Mechanics of Materials ib-Tutorial 4 EG1109: STATICS and MECHANICS OF MATERIALS INQUIRY-BASED TUTORIAL 4 Question 1 A rectangular...

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EG1109 (Part II) – Mechanics of Materials ib-Tutorial 4 EG1109: STATICS and MECHANICS OF MATERIALS INQUIRY-BASED TUTORIAL 4 Question 1 A rectangular block is subjected to the resultant forces shown; the loads are applied uniformly over the surfaces indicated. The material has a Young’s modulus E = 25 GPa and a Poisson’s ratio ν = 0.2. x z y 120 kN 180 kN 60 kN 50 kN 200 mm 100 mm 50 mm 100 kN (a) Following the Cartesian coordinate axes illustrated, determine the values of the stress and strain components describing the state of the material, and write them down according to the matrix layout below: [] = zz zy zx yz yy yx xz xy xx σ τ τ τ σ τ τ τ σ σ [] = zz zy zx yz yy yx xz xy xx ε γ γ γ ε γ γ γ ε ε [Note that the shear modulus can be calculated from the relationship between Young’s modulus, shear modulus and Poisson’s ratio: E = 2 G (1+ ν ).] (b) What is the ratio of the final to the original (unloaded) volume of the block (calculate to 4 decimal places)? Also, calculate to 4 decimal places the sum of the three normal strain components and compare this value with the ratio of the final to the initial volume; what can you deduce about the significance of this quantity? (c) What single force acting on the x -face would generate the same change in length in the x -direction as that experienced by the loaded block? 1
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EG1109 (Part II) – Mechanics of Materials ib-Tutorial 4 Question 2 A pair of 12 mm thick, stiff rubber brake pads is used to stop a moving wheel. When the brakes are applied, the rubber is deformed, its profile becomes parabolic and follows the equation x = Cy 2 , where C = 3.645 m -1 . Where is the shear strain in the brake pad the largest and what is its value? (Remember to use consistent units in your calculations.) 12 mm F y x Brake Pad Wheel 2
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