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# Answer to Question #128722 in Mechanics | Relativity for Ariyo Emmanuel

Question #128722
(1) A rectangular block of metal of 50 mm x 25 mm cross-section and 125 mm length carries a tensile load of 100 kN along its length, a compressive load of 1.0 MN on its 50 x 125 mm faces and a tensile load of 400 kN on its 25 x 125 mm faces. If E = 208 GN/m² and Poisson’s ratio = 0.3, Find (a) change in volume of bar (b) increase required in 1.0 MN load to produce no change in volume.
1
2020-08-18T10:09:16-0400

(a)

"\\sigma_x=\\frac{F_x}{a\\cdot b}=\\frac{100}{25\\cdot50}=80(N\/mm^2)"

"\\sigma_y=\\frac{F_y}{h\\cdot b}=-\\frac{1000}{125\\cdot50}=-160(N\/mm^2)"

"\\sigma_z=\\frac{F_y}{h\\cdot a}=\\frac{400}{125\\cdot25}=128(N\/mm^2)"

"V=125\\cdot25\\cdot50=156250(mm^3)"

"\\frac{dV}{V}=\\frac{(\\sigma_x-\\sigma_y+\\sigma_z)(1-2u)}{E}=\\frac{(80-160+128)(1-2\\cdot0.3)}{208\\cdot10^3}="

"=9.23\\cdot 10^{-5}"

"\\Delta V=V\\cdot 9.23\\cdot 10^{-5}="

"=156250\\cdot9.23\\cdot 10^{-5}=14.42(mm^3)"

(b)

"\\sigma_x-\\sigma_y+\\sigma_z=0"

"\\sigma_y\\cdot h\\cdot b=F_y\\to"

"F_y=208\\cdot125\\cdot50=1300000(N)=1300(kN)"

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