Experiments show that if a bar is lengthened by axial tension, there is a reduction in the transverse dimensions. Simeon D. Poisson showed in 1811 that the ratio ϑ the unit dimensions or strain in these directions is constant for stresses within the proportional limit. V= - = …………. (6) Where: V: Poisson ratio ϵx = strain in x-direction ϵy = strain in y-direction ϵz = strain in z-direction Note; minus sign indicates a decrease in transverse dimension positive as in the case ϑ tensile elongation. Tensile stress in x and y direction thus; (biaxial) ϵx = – V ……... (7) ϵy = – V ……… (8) or σx = ; σy = ; ……(9) Tensile stress in x, y, and z (triaxial tension stress); ϵx = [σx – V (σy+σz)] ϵy = [σy – V (σz+σx)] ϵz = [σz – V (σx+σy)] ……… (10) G = …… (11) for a given material Where:
Experiments show that if a bar is lengthened by axial tension, there is a reduction in the transverse dimensions. Simeon D. Poisson showed in 1811 that the ratio ϑ the unit dimensions or strain in these directions is constant for stresses within the proportional limit. V= - = …………. (6) Where: V: Poisson ratio ϵx = strain in x-direction ϵy = strain in y-direction ϵz = strain in z-direction Note; minus sign indicates a decrease in transverse dimension positive as in the case ϑ tensile elongation. Tensile stress in x and y direction thus; (biaxial) ϵx = – V ……... (7) ϵy = – V ……… (8) or σx = ; σy = ; ……(9) Tensile stress in x, y, and z (triaxial tension stress); ϵx = [σx – V (σy+σz)] ϵy = [σy – V (σz+σx)] ϵz = [σz – V (σx+σy)] ……… (10) G = …… (11) for a given material Where:
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