Unformatted text preview: Mechanics of Materials Homework #3 – SOLUTIONS Problem 1: The column below is constructed from high‐ strength concrete (E = 29 GPa) and four A‐ 36 steel reinforcing rods (E = 200 GPa). If it is subjected to an axial force of 800 kN, determine the required diameter of each rod such that one‐fourth of the load is carried by the steel and three fourths by the concrete. Problem 2: A thermo gate consists of a 6061‐T6 aluminum plate AB (E = 68.9 GPa, coefficient of thermal expansion = 24 x 10‐6/°C) and an Am‐1004‐T61 magnesium plate CD (modulus of elasticity = 44.7 GPa, α = 26 x 10‐6/°C), each having a width of 15 mm. Both are fixed and supported at their ends, as shown below. If the gap between them is 1.5 mm when the temperature T1 = 25 °C, determine the temperature required to just close the gap. Also, what is the axial force in each plate if the temperature is raised to T2 = 100 °C? Assume bending or buckling will not occur. Problem 3: The C83400 red‐brass rod AB (modulus of elasticity = 14.6 x 106 psi, α = 9.8 x 10‐6/°F) and 2014‐ T6 aluminum rod BC (E = 10.6 x 106 psi and coefficient of thermal expansion of 12.8 x 10‐6/°F) are joined at the collar B and fixed connected at their ends. If there is no load in the members when T1 = 50 °F, determine the average normal stress in each member when T2 = 120 °F. Also, how far will the collar be displaced? The cross‐sectional area of each member is 1.75 in2. Problem 4: The aluminum block shown below has a rectangular cross section and is subjected to an axial compressive load of 8 kip. If the 1.5 in. side changed its length to 1.500132 in., determine Poisson’s ratio and the new length of the 2 in. side. The modulus of elasticity may be taken as 10 x 103 ksi. Problem 5: An element of aluminum (E = 10.4 x 106 psi, Poisson’s ratio = 0.33) in the form of a rectangular parallelepiped, shown below, has dimensions a = 5in., b = 4 in., and c = 3 in. It is subjected to triaxial stresses σx = 11,000 psi, σy = ‐ 5,000 psi, and σz = ‐1,500 psi acting on the x, y, and z faces, respectively. Determine (a) the maximum shear stress τmax in the material, (b) the changes in the dimensions of the element Δa, Δb, and Δc and (c) the change in volume ΔV. Problem 6: A rubber block is subjected to an elongation of 0.03 in. along the x axis, and its vertical faces are given a tilt so that Θ = 89.3°. Determine the strains εx, εy, and γxy. Take νr = 0.5. ...
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- Spring '10
- axial force, high‐ strength concrete, thermal expansion, axial compressive load, T6 aluminum rod, 6061‐T6 aluminum plate