Please help me for part (a) and (b) At room temperature (70 degree F) and with n

Question

Please help me for part (a) and (b)

At room temperature (70 degree F) and with no axial load (P=0) the extensional strain of a prismatic bar (Figure 1) in the axial direction is zero, that is, epsilon x = 0. Subsequently, the bar is heated to 120 degree F and a tensile load P is applied. The material properties of the bar are: E = 10 times 103 ksi alpha = 13 times 10-6/ degree F Area of cross section of the bar is 1.8 in2 For the latter load/temperature condition, the extensional strain is found to be epsilonx =900 times 10-6 Determine the value of the axial tensile load P. Determine the normal stress and shear stress on the oblique plane NN' (at an angle of 25 degree to normal plane). (Note: The total strain is the sum of strain associated with normal stress sigma x, and the strain due to change of temperature Delta t) Figure 1: Problem 2

Explanation / Answer

Due to Temperature , strain=alpha*delta T

delta T = 120 - 70 - 50 F

alpha = 13*10^-6

strain = 13*10^-6*50 = 650*10^-6

So strain due to tensile load = total strain - thermal strain = 900*10^-6 - 650*10^-6 =250*10^-6

Strain = Stress/E

so stress = 10*10^3 * 250*10^-6 =2.5 ksi ;

a) P = Stress * area =2.5*1.8 = 4.5 kilopounds = 4500 pounds

b) Normal Stress = 2.5*cos 25 = 2.2657 ksi = 2265.7 psi ;

Tangential stress = 2.5 sin 25 = 1.0565 ksi = 1056.5 psi ;

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