Assignment_1 - MAE157 Lightweight structures(Winter 09...

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1 MAE157 – Lightweight structures (Winter 09) Homework Assignment #1 Due in the drop box by 1pm on Friday, January 23, 2009 Solve the five following problems. For each problem, provide a detailed explanation of all the steps involved. Problem 1 The two trusses of Fig. 2 ((a) and (b)) are subject to the same external loads. For both, a=15cm, F=1000N and all the members have circular cross-section, with diameter, d=7mm . All members of both trusses are made of an Aluminum alloy, with yield strength ! Y = 300 MPa (assumed the same in tension and compression) and Young’s modulus, E = 70 GPa . Calculate the internal forces in the members and check whether trusses (a) and (b) are able to resist the applied load without yielding or buckling. [ Ans : Truss (a) fails by buckling; truss (b) resists] Problem 2 Fig. 4 is a unit-cell of a plane truss composed of two families of members (denoted 1 and 2 in the figure). It is loaded in a biaxial state, through identical forces F=10N applied at the nodes A, C, and E. Members of families 1 and 2 have cross-sectional area
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