Section D: Long Problems You must attempt all questions (3 questions) from this section 1- (35 pts) The below figure shows a stepped bar structure that consists of three elements. The structure is fixed in the left-hand side. A 20 (kN) load is applied at the position of 100 (mm) from left and a 10 (kN) load is applied at the end right-hand side. Develop a finite element model to find the below: a) Using direct stiffness method, determine the nodal displacement of stepped bar. Elastic Modulus of the material (E) is 200 (GPa). b) Determine reaction at the support and c) Determine the stresses in each element. Please note that you must solve the problem by using the Partition Method. 100 mm A=200 mm 200 mm 20kN A=100 mm 10 kN www 150 mm W mK 2- (30 pts) The circular rod shown in the below figure has an outside diameter of 60 (mm), length of 1 (m), and is perfectly insulated on its circumference. The left half of the cylinder is aluminium, for which thermal conductivity kx1 = 200 and the right half is copper having thermal conductivity kx = 389 The extreme right end of the cylinder is maintained at a temperature of 80 (C), while the left end is subjected to a heat input rate 4000 Using four equal-length elements, determine the steady-state temperature distribution in the cylinder. W mK Please note that you must solve the problem by using the Deletion Method. Al 9in 1 Cu Yout 3 4 4 5 12 2 3 +0.25 m 0.25 m 0.25 m 0.25 m |