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Unformatted text preview: to the examination room. • Purposely exposing written papers to the view of other candidates. The plea of accident or forgetfulness will not be received. Question No. 1. 2. 3. 4. Total (%) Mark Time: 2.5 hours Name: Signature: Student Number: Marks (%) (25) 1. Three identical, uniform wires labeled 1,2, and 3 are made of an elastic-perfectly plastic material (elastic modulus E and yield stress σ y ) are attached to a support at the left-hand end and to a pin-connected rigid bar at the right-hand end as shown in Figure 1. Assume that each wire has cross-sectional area A, and length L. (a) If the magnitude of the load P acting at the upper end of the rigid bar (point D) is such that the wires behave elastically, determine the tensile forces T1, T2 and T3 in the wires in terms of P. (b) Determine the load Py at first yield (i.e. when the yield stress is first reached in any of the wires) and the corresponding displacement δ y at the point of application of the load (point D). (c) Determine the load P* at which a second wire yields and the corresponding displacement δ * at point D. (d) Determine the fully plastic load Pp and the corresponding displacement δ p at point D. (e) Draw a complete load-displacement diagram with the load P as ordinate and the displacement at point D as abscissa. Clearly label the diagram with your solutions to parts (a) to (d). D P a 3 C 2 B a a 1 A a O L Figure 1 Name: Signature: Student Number: Marks (%) (25) 2. A solid circular bar ABCD of length L = 3m and with fixed supports is subjected to the torques TB = 500 Nm and TC = 1000 Nm as shown in Figure 2. The material of the bar is steel [shear modulus, Gs = 80 GPa] and its di...
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