Consider an isotropic material subjected to a combined state of biaxial compression and simple shear, as shown in Fig. 2 and described by the stress state σij = T 0 Calculate the von Mises and Tresca yield criteria as a function of o and 7 and plot the curves in the σ- 7 plane. Calculate the values of o and 7 at which each of the yield functions intersect the σ and 7 axes. Note that your answer should not change if o positive or negative. ko 4x2 T 0 0 -ko 0 0 ka 1 T x1

Please solve d through g

Derive the following equation for computing shear stress in a solid bar along an oblique plane with angle B with respect to the vertical plane. The bar is subjected to centric axial loading. sin 0 cos 0 T = Ao

For a given homogeneous, isotropic, linearly elastic material, E = 15e6 psi and v = 0.3. Solve for the shear modulus. 2.1.1 Homogeneous, isotropic, linearly elastic materials For specimens undergoing small deformations, the stress-strain diagram often ex- hibits a linear behavior. Although this is a very crude approximation to the behavior of actual materials, it is a convenient assumption that is often used for preliminary evaluation. A linear relationship between stress and strain can be expressed as 01 = E €1, (2.1) where the coefficient of proportionality, E, is called Young's modulus or modulus of elasticity. Since strains are non-dimensional quantities, this coefficient has the same units as stress quantities, i.e., Pa. This linear relationship is known as Hooke's law. The elongation of a bar in the direction of the applied stress is accompanied by a lateral contraction that is also proportional to the applied stress. The resulting defor- mations for this uniaxial state of stress…