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# fa - ME 211 INTRODUCTION TO SOLID MECHANICS Practice Final...

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ME 211 INTRODUCTION TO SOLID MECHANICS Practice Final Examination Attempt all questions MULTIPLE CHOICE QUESTIONS 1. (2 points). Three strain gages are attached to a body with 0 o , 120 o , and 240 o orientation relative to the x -direction (i.e. gage ( a ) is aligned with the x -direction), as shown in Figure 1. The readings obtained are ǫ a = 1 . 6 × 10 - 3 ; ǫ b = 0 . 2 × 10 - 3 ; ǫ c = 2 . 0 × 10 - 3 . o 120 120 120 o o (a) (b) (c) Figure 1 The shear strain component γ xy is A B C D E F G H γ xy = ( × 10 - 3 ) 2 . 54 2 . 07 1 . 73 1 . 27 0 0 . 20 1.60 2.54 check one only

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2. (2 points). The stresses acting on an element of material are shown in Figure 2. 100 MPa 40 MPa 80 MPa 100 MPa 40 MPa 80 MPa Figure 2 The maximum in-plane shear stress is A B C D E τ in-plane max = (MPa) 40 100 10 50 41.2 check one only 3. (2 points). Figure 3 shows a cylinder of outside diameter D = 200 mm and wall thickness t = 8 mm. The left end of the cylinder is closed and at the right end, a gas-tight, frictionless piston is pressed in by an axial force F = 15 kN until it is in equilibrium with the internal gas pressure. D F t piston . A Figure 3 At the point A in the cylinder wall, the circumferential (hoop) stress is A B C D E F G σ = (MPa) 0 -0.57 2.2 3.4 6.8 8.7 14.1 check one only
4. (2 points). By sketching the shear force diagram for the beam of Figure 4 or otherwise, determine where the magnitude of the bending moment is a maximum.

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