Part 1: Limit Load Analysis

A frame is loaded with two proportional loads, as shown in Fig. 1a. The relative plastic moment values in different frame members are shown in the figure, with Mp = 86 kNm.

(1) For the frame shown in Fig. 1a, find the value of the load factor λ at collapse and prove that the yield condition is satisfied for the corresponding collapse mechanism.

(2) If boundary conditions at A and D are fixed supports, as shown in Fig. 1b, find the value of the load factor λ at collapse.

(3) If plastic moment of beam BC is 0.5Mp, as shown in Fig. 1c, find the value of the load factor λ at collapse.

(4) From the results obtained from (1)-(3), discuss on the influence of load, boundary conditions and section sizes on the collapse load and mechanism of a frame.

 

Part 2: Displacement Method

Figs 2a and 2b show a suspended teahouse designed by David Jameson. The teahouse is made of bronze and glass and is in the form of a Japanese lantern. It hangs from two planar steel frames through four vertical steel bars. The two steel frames are laterally braced at the top and aside for stability. Note that the stairs are not attached to the teahouse.

Please answer the following questions:

(1) What is the load path of the structure?
(2) Assume that the total weight of the teahouse is 200 kN, and universal beam sections UB 533×210×109 and UB 457×152×82 are used for the horizontal and vertical frame members, respectively.

i) Use Slope-Deflection Equations to analyse one of the two frames, and calculate end moments of all frame members under the self-weight of the teahouse. Young’s modulus of steel is 200 GPa. Fixed boundary conditions are assumed. The self-weight of frame members can be neglected. The dimensions of the frame are given in Fig. 2c, and the UB section table is provided in Appendix A. Note that all frame members bend about their major axes.

ii) Use moment distribution method to prove that the end moments of all frame members calculated in i) are correct.

iii) Draw bending moment diagram and shear force diagram of one steel frame, corresponding to the self-weight of the teahouse