Home Work #4 Due Date: 18 Mar, 2010 (Turn in your assignment at the mail box of S581 outside the ME general office) The solutions must be written on A4 papers only.

HW 4-Problem #1 A flat bar of rectangular cross section, length L, and constant thickness t is subjected to tension by forces P. The width of the bar varies linearly from b 1 at the smaller end to b 2 at the larger end. Assume that the angle of taper is small. a)Derive the following formula for the elongation of the bar: b)Calculate the elongation, assuming L=5 ft, t= 1.0 in., P=25 k, b 1 =4.0 in., b 2 =6.0 in., and E=30×10 6 psi.

HW 4-Problem #2 A rigid bar of weight W=800 N hangs from three equally spaced vertical wires, two of steel and one of aluminum. The wires also support a load P acting at the midpoint of the bar. The diameter of the steel wires is 2 mm, and the diameter of the aluminum wire is 4 mm. What load P allow can be support if the allowable stress in the steel wires is 220 MPa and in the aluminum wire is 80 Mpa?

HW 4-Problem #3 A copper bar AB of length 25 in. is placed in position at room temperature with a gap of in. between end A and a rigid restraint. Calculate the axial compressive stress σ c in the bar if the temperature rises 50ºF. For copper, use α=9.6×10 -6 /ºF and E=16×10 6 psi.

HW 4-Problem #4 A tension member is to be constructed of two pieces of plastic glued along plane pq. For purpose of cutting and gluing, the angle θ must be between 25˚ and 45˚. The allowable stresses on the glued joint in tension and shear are 5.0 Mpa and 3.0 Mpa, respectively. Determine the angle θ so that the bar will carry the largest load P. (Assume that the strength of the glued joint controls the design.) Determine the maximum allowable load P max if the cross-sectional area of the bar is 225 mm 2.