The normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression yy/3E where y = 2.9 lb/in.³ is the specific weight of the material, y = 0.5 in. is the distance from the free (i.e., bottom) end of the bar, L = 5 in. is the length of the bar, and E= 25000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar. (c) the maximum normal strain in the bar.

2. The stress-strain behavior of a ductile cast iron of diameter 15.8mm and a gauge length of 60.80mm is shown below, 400 300 200 100 0.00 0.10 Strain Determine the following: (a) the modulus of elasticity (b) yield strength at a strain offset of 0.002. Stress (MPa)

After load P is applied to the pin-connected structure, a normal strain of = +650 µe is measured in the longitudinal direction of member (1). The cross-sectional area of member (1) is A₁ = 0.6 in.2, its elastic modulus is E₁ = 31000 ksi, and its yield strength is 33 ksi. Assume a=6.25 ft, b=7.75 ft, c=4.5 ft, and d=3.75 ft. (a) Determine the axial force in member (1), the applied load P, and the resultant force at pin B. (b) The ultimate shear strength of the steel pins is 52 ksi. Determine the minimum diameter for the pin at B if a factor of safety of 2.2 with respect to the ultimate shear strength is required. (c) Compute the factor of safety for member (1) with respect to its yield strength. (1) a D Answer: 0₁ = 1.6377 B (a) Determine the axial stress o, in member (1). ksi. b

For the state of a plane strain with Ex, Ey and yxy components: (a) construct Mohr's circle and (b) determine the equivalent in-plane strains for an element oriented at an angle of 30° clockwise. Ex = 250 x 10-6 Ey = 310 x 10-6 Yxy = -100 × 10-6