2. Two aluminum rods AB and BC hinged to rigid supports are pinned together at 3m B to carry a vertical load P= 20 KN. Each 50 30 2m rod has a cross- sectional area of 400 mm and E = 70,000 MPa, compute the elongation P= 20KN of each rod.
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- Solve the preceding problem for an aluminum column with b = 6,0 in., t = 0.5 in., P = 10 kips, and E = 10.6 × 106 ksi. The defied ion at the top is limited to 2.0 in.A steel column ( E = 30 X 103 ksi) that is fixed at the base and free at the top is constructed of a W8 x 35 wide-flange member (sec figure). The column is 9.0 ft long. The force P acting at the top of the column has an eccentricity e = 1.25 in. If P = 40 kips, what is the maximum compressive stress in the column? If the yield stress is 36 ksi and the required factor of safety with respect to yielding is 2.1, what is the allowable load Pallow?A steel pad supporting heavy machinery rests on four short, hollow, cast iron piers (see figure). The ultimate strength of the cast iron in compression is 400 MPa. The total load P that may be supported by the pad is 900 kN. Using a factor or safely 3.0 with respect to ultimate strength, determine the outer diameter of the pier if the thickness, is of the cross section is 12 mm.
- Column AB has a pin support at A,a roller support at B, and is compressed by an axial load P (see figure). The column is a steel W12 × 35 with modulus of elasticity E = 29,000 ksi and proportional limit pl = 50 ksi. The height of the column is L = 12 ft. Find the allowable value of load P assuming a factor of safety n = 2,5.A square aluminum bar with pinned ends carries a load P = 25 kips acting at distance e = 2,0 in. from the center (sec figure). The bar has a length E = 54 in. and modulus of elasticity E = 10,600 ksi. If the stress in the bar is not to exceed 6 ksi, what is the minimum permissible width bminof the bar?AW310 × 74 wide-flange steel column with length L = 3.8 m is fixed at the base and free at the top (see figure). The load P acting on the column is intended to be centrally applied, but because of unavoidable discrepancies in construction, an eccentricity ratio of 0.25 is specified. Also, the following data are supplied: E = 200 GPa, y = 290 MPa, and P = 310 kN. What is the maximum compressive stress max in the column? What is the factor of safety n with respect to yielding of the steel?
- A steel bar has a square cross section of width b = 2.0 in. (sec figure). The bar has pinned supports at the ends and is 3.0 ft long. The axial forces acting at the end of the bar have a resultant P = 20 kips located at distance e = 0,75 in, from the center of the cross section. Also, the modulus of elasticity of the steel is 29,000 ksi. Determine the maximum compressive stress max, in the bar. If the allowable stress in the steel is 18,000 psi, what is the maximum permissible length Lmaxof the bar?A pinned-end column with a length L = 18 ft is constructed from a W12 x 87 wide-flange shape (sec figure). The column is subjected to a centrally applied load P1=180 kips and an eccentrically applied load P2=15 kips. The load P2acts at a distance s = 5.0 in. from the centroid of the cross section. The properties of the steel arc E = 29,000 ksi and y = 36 ksi. Calculate the maximum compressive stress in the column. Determine the factor of safety with respect to yielding.A pinned-end strut of aluminum (E = 10,400 ksi) with a length L = 6 ft is constructed of circular tubing with an outside diameter d = 1 in. (sec figure). The strut must resist an axial load F = 4 kips with a factor of safety n = 2.0 with respect to the critical load. Determine the required thickness t of the tube.