Question

Member (1) is a solid 50 mm diameter cylinder made from magnesium. The modulus of elasticity is 44.7 GPa and the thermal coefficient of expansion is 26 x 106/°C. The cylinder is placed in a clamp when the temperature is 20℃ Two stainless steel carriage bolts (2) hold the cylinder snug with negligible force against the rigid jaws of the clamp. Each bolt has a diameter of 10 mm, modulus of elasticity of 193 GPa, and a coefficient of thermal expansion of 17 x 101"c. a) The temperature increases from 20 C to 130 C. Write the equilibrium and compatibility equation(s) needed to solve the problem along with supporting sketches. Calculate the internal forces in members (1) and (2) in kN. Indicate tension or compression. [Ans. to Check: Fi0.904 kN] Calculate the normal stress in MPa in members (1) and (2). b) c) L1 100 mm a) L2-150 mm

Answer 1

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0.2 86- P As the γe is no externa Gorce 2- fre body diog om 6 balt head 10g, h[o.olaia 3] 0 005ら PO.DU5 5 2 0. 012 13 3 mem ber Nature Force CP) (k 1) 6-40364Compression 65 036 963.5 203.61N A 16.539 451 52 rm2 7. 539 tenrile 5:15 -lm,1レ