Question 1 Consider the bar, shown in Figure 1, that undergoes axial displacement due to both a distributed load and a point force. The bar is of cross-sectional area A = 1.10-3 m², and has a modulus of elasticity E = 100 GPa. (x) = 5 kN/m 10 kN 4114 X x=0.0 x=2.0 2.0m Figure 1: Bar domain with varying distributed forces. form of the governing ddu(x) dx எ) dx What are the accompanying boundary conditions for this bar? 1 2 1 2 1m 1m Placement, u(x), is given by, Figure 2: Mesh of 2 elements. Elements are numbered with underlines. [6 marks] c) The general form of the element stiffness matrix system, with nodes indexed by i and j, is, AE L 1 {]{}={ * Ni (a) (a) dz } + { N; (2) ƒ (2) – N; (0)ƒ(0) N;(x)l(x)dx N;(2)f(2) - N,(0)f(0)) where f(2) and f(0) denote the boundary forces at positions x = 2 and x Evaluate the right hand side of equation 1 for element 2. = (1) 0, respectively. [18 marks]

A polyethylene tube (length L) has a cap that when installed compresses a spring (with under-formed length L1) by an amount ?? = (L1 = L). Ignore deformations of the cap and base. Use the force at the base of the spring as the redundant. Use numerical properties given in the boxes. (a) What is the resulting Force-in the spring, Fk? (b) What is the resulting Force in the tube, Ftl (c) What is the filial length of the tube, Lf? (d) What temperature change ?T inside the tube will result in zero force in the spring

Two steel wines support a moveable overhead camera weighing W = 28 lb (see figure part a) used For close-up to viewing of field action at sporting, events. At some instant, wire I is at an angle a = 22° to the horizontal and wire 2 is at angle fi = 40°. Wires I and 2 have diameters of 30and 35 mils, respectively. (Wire diameters are often expressed in mils; one mil equals 0.001 in.) (a) Determine the tensile stresses s and s2 in the two wires. (b) If the stresses in wires 1 and 2 must be the same, what is the required diameter of wire 1 ? (c) To stabilize the camera for windy outdoor conditions, a third wire is added (see figure part b). Assume the three wires meet at a common point coordinates (0, 0. 0) above the camera at the instant shown in figure part b. Wire I is attached to a support at coordinates (75 ft, 48 ft, 70 Ft). Wire 2 is supported at (-70 ft. 55 ft, 80 Ft). Wire 3 is supported at (-10 ft. -85 Ft, 75 ft). Assume that all three wires have a diameter of 30 mils. Find the tensile stresses in all three wires

A suspender on a suspension bridge consist of a cable that passes over the main cable (see figure) and supports the bridge deck, which is Far below. The suspender is held in position by a metal tie that is prevented from sliding downward by clamps around the suspender cable. Let P represent the load in each part of the suspender cable, and let represent the angle of the suspender cable just above the tie. represent the allowable tensile stress in the metal tie. (a) Obtain a formula for the minimum required cross-sectional area of the lie. (b) Calculate the minimum area if P = 130 kN, = 75°, and allow=80 .