For a following loading that has generated the strain state below in the limit of isotropic elasticity, ?(epsilon) = 0.001    0.001        0                     0.001 −0.002     0.0005                     0            0.0005     0 Find out how the stress state relates to yielding using a) Tresca criteria b) Von-Mises criteria If an experiment has shown that the yielding stress is 25 MPa. E=200 GPa  and G=90 GPa.

The stresses on the surface of a hard bronze component are shown in the figure below. The yield strength of the bronze is σY = 345 MPa.a) What is the factor of safety predicted by the maximum-shear-stress theory of failure for the stress state shown? Does the component fail according to this theory?b) What is the value of the Mises equivalent stress for the given state of plane stress?c) What is the factor of safety predicted by the failure criterion of the maximum-distortion energy theory of failure? Does the component fail according to this theory?

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…

A bar BD is held in a horizontal position when there is no load by the steel wire AB. When a weight Wis added at C, also hanging from a steel wire CE, then point C is displace down by 0.025in. The cross-sectional area of the wires is 0.002in². The wires are made of a steel alloy with E = 29000ksi and σy = 70ksi. Calculate the strain in both wires, and the weight W. B A N E Parameter ft L_1 4 L_2 1 L_3 2 L_4 4 The strain in AB is € AB = The strain in CE is ECE = The weight W = 30 W cc 080 BY NO SA 2021 Cathy Zupke Xlb D in./in. in./in.