Question 2 A rigid bar of weight W=1,200 N hangs from three equally spaced vertical wires as shown in Figure Q2. The wires also support a concentrated load P acting on the bar. The diameter of the steel wires is 6 mm while the diameter of the aluminium wire is 15 mm. Assume the modulus of elasticity of steel and aluminium are E, 200 x 103 N/mm² and Ea = 80 x 103 N/mm² respectively. (a) Set up the equilibrium and compatibility equations for the system shown. [7 marks] (b) What load Pallow can be supported at mid-span of the bar if the allowable stress in the steel wire is 210 N/mm² and that in the aluminium wires is 70 N/mm². You are expected to show all calculations or checks for both aluminium and steel wires. [15 marks] (c) What will be the change in length of each wire when the load Pallow is acting? [3 marks] A 950 mm S A S = Steel 250 mm 250 mm A Aluminium → W Figure Q2

A uniform bar AB of weight W = 25 N is supported by two springs, as shown in the figure. The spring on the left has a stiffness k[= 300 N/m and natural length Lt=250 mm. The corresponding quantities for the spring on the right are k2= 400 N/m and L^ = 200 mm. The distance between the springs is L = 350 mm, and the spring on the right is suspended from a support that is a distance it = SO mm below the point of support for the spring on the left. Neglect the weight of the springs. (a) At what distance x from the left-hand spring (figure part a) should a load P = 18 N be placed in order to bring the bar to a horizontal position? (b) If P is now removed, what new value of k{is required so that the bar (figure part a) will hang in a horizontal position underweight If? (c) If P is removed and kt= 300 N/m. what distance b should spring ktbe moved to the right so that the bar (figure part a) will hang in a horizontal position under weight II"? (d) If the spring on the left is now replaced by two springs in series (kt= 300 N/m, kt) with overall natural length Lt= 250 mm (see figure part b). what value of k; is required so that the bar will hang in a horizontal position under weight IF?

*16 A prismatic bar AB of length L, cross-sectional area A, modulus of elasticity E, and weight Changs vertically under its own weight (see figure). (a) Derive a formula for the downward displacement Scof point E. located at distance It from the lower end of the bar. (b) What is the elongation SBof the entire bar? (c) What is the ratio £ of the elongation, of the upper half of the bar to the elongation of the lower half of the bar? (d) If bar A B is a riser pipe hanging from a drill rig at sea. what is the total elongation of the pipe? Let L = 1500 m, A - 0.ol57 m2, and E = 210 GPa. See Appendix 1 for weight densities of steel and sea water. (See Probs. 1.4-2 and J.7-13 for additional figures.)

The L-shaped arm ABCD shown in the figure lies in a vertical plane and pivots about a horizontal pin at A. The arm has a constant cross-sectional area and total weight W. A vertical spring of stiffness k supports the arm at point B. (a) Obtain a formula for the elongation of the spring due to the weight of the arm. (b) Repeat part (a) if the pin support at A is moved to D.