Question

TutorBin Question The frame shown in Fig. Q1 is fully fixed at A and E and has a pin at B. All members have a uniform plastic moment of resistance, Mp = 30kNm. (a) Determine the number of possible hinges and the number of hinges required for complete collapse. [4 marks] (b) Determine the collapse load factors that correspond to the following two independent elementary mechanisms. 1. Sway mechanism. 2. Beam mechanism. (Hint: Assume that the hinge at C forms at a distance x from point B and show that the value of x that minimises the load factor is x = 1.66m) [10 marks] (c) Consider a combined mechanism with hinges at A, C and E and calculate its collapse load factor. (Hint: Assume that the hinge at C forms at a distance x' from point B and show that the value of x ' that minimises the load factor is x' = 2.14m) [10 marks] (d) For the mechanism with the lowest collapse load factor calculated in parts (b) and (c) show the locations on the frame where plastic hinges have formed and complete the bending moment via a static check. Hence, state whether the lowest collapse load factor found is an upper bound or the exact value of the true collapse load factor. [10 marks] 10% (kN/m) 202 (kN) B C D x 2m (or x') 4m E TTTT V A TTTT 4m -

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