Problem 2. A cylindrical rod is to be subjected to a tensile load of 24,500 N. T

Question

Problem 2. A cylindrical rod is to be subjected to a tensile load of 24,500 N. The original length and diameter of the rod are 190.0 mm and 10.0 mm, respectively. If the rod is to experience neither plastic deformation nor an elongation of more than 0.45 mm, which of the four metals or alloys listed below are possible candidates? Justify your choice(s).

Modulus of Elasticity (GPa)

70 100 110 207

Material

Aluminum alloy Brass alloy Copper
Steel alloy

Yield Strength (MPa)

255 345 250 450

Tensile Strength (MPa)

420 420 290 550

Explanation / Answer

load = P= 24,500 N

length of rod = L= 190 mm = 0.19 m

diameter of rod =d = 10 mm = 0.01 m

cross sectional area of rod = A= pi/4 (d)2 = pi/4 (0.01)2 = 7.85 *10^-5 m2

elongation = delta = 0.45 mm

we have the equation

delta = PL/AE

but elongation should be less than 0.45 mm = 0.45*10^-3 m

delta<0.45*10^-3

PL/AE < 0.45*10^-3

(24,500*0.19)/( 7.85 *10^-5 *E) < 0.45*10^-3

E> (24,500*0.19)/( 7.85 *10^-5 *0.45 *10^-3)= 131.77 GPa

so the modulus of elasticity E should be greater than 131.77 GPa

in the options only steel alloy has modulus of elasticity(youngs modulus) E = 207 GPa (which is greater than 131.77GPa)

Hence there is only one possible candidate I,e STEEL ALLOY

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