Problem 1 Consider two rectangular slabs of copper and one of steel of the same

Question

Problem 1

Consider two rectangular slabs of copper

and one of steel of the same dimensions

and drilled holes for pins as shown. The

copper slabs are cooled to a temperature

of -100*" F and the steel slab is heated to

a temperature of 200

Consider two rectangular slabs of copper and one of steel of the same dimensions and drilled holes for pins as shown. The copper slabs are cooled to a temperature of -100*" F and the steel slab is heated to a temperature of 200 degree F. The pins are inserted and the assembly allowed to come to room temperature 70 degree F. Calculate the stress in the copper and the stress in the steel when the assembly reaches room temperature

Explanation / Answer

1) For Copper

bulk strain = dV/V = dT*a

a = Volumetric Thermal Coefficient = 51*10^-6 /K

T2 = 70 oF = 294.261 K

T1 = -100 oF = 199.817 K

so,

bulk strain =  dT*a = (T2-T1)*a = (294.261-199.817)*51*10^-6 = 0.0048166

bulk stress = B*bulk strain

B = Bulk modulus = 140*10^9 Pa

so,

stress = 140*10^9*0.0048166 = 674324000 = 6.7432*10^8 Pa

2) For steel

bulk strain = dV/V = dT*a

a = Volumetric Thermal Coefficient = 36*10^-6 /K

T2 = 70 oF = 294.261 K

T1 = 200 oF = 366.483 K

so,

bulk strain = dT*a = (T2-T1)*a = (294.261-366.483)*36*10^-6 = -0.0026

bulk stress = B*bulk strain

B = Bulk modulus = 160*10^9 Pa

so,

stress = 160*10^9*-0.0026 =-416000000= -4.16*10^8 Pa

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