(\'Unless Noted) Values Are For Room Temperature, 1 atm Ambient Pressure, and An

Question

('Unless Noted) Values Are For Room Temperature, 1 atm Ambient Pressure, and Annealed Mic Mpa Density g/cm3 7.87 Elastic Modulus, GPa Ultimate Tensile Strength, Yield Point, MPa 295 415 290 Poisson's Ratio 0.29 Tensile Strain at Failure % 26.5 17.7 50 Material 1020 Steel 316 Stainless Steel Nickel 8.00 2.81 8.88 4.5 19.3 200 193 207 395 580 317 0.27 0.33 0.31 7075 Aluminum T6 T 138 30 116 ungst 0.28 A cylindrical rod of titanium is stressed elastically in tension. The original diameter was 15 mm and a force of 48 kN was applied. Compute the diameter of the rod upon loading, in millimeters. Answer Format: X.XXX Unit: mm

Explanation / Answer

given
cylindrical rod of titanium is stressed elastically in tension

do = 15 mm
Fo = 48 kN

now, stress/strain = E
stress = Fo*4/pi*do^2
strain = dl/l
also, from the data
E = 116 GPa
hence
strain = stress/E = 0.00234158

now, poissions raio = v = -dr/dl
v*dl = -dr
dr = -v*dl = -v*strain*r
for titanium, v = 0.34
r = do
then
hence
dr = 0.0119421 mm

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