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N/m2

The principal stresses are found from

Substituting gives

<n,o-2 = {5(10.43+ 0.43) ± ^[(10.43 - 0.43)2 + 4 x 2.922]}106 N/m2 = (5.43 ± 5.79)106 N/m2

giving ox — 11.22 MN/m2 (T) and cr2 = 0.36 MN/m2 (C) The directions are found from substituting gives

The required principal stresses for element b are therefore a, = 11.22 MN/m2 (T) and <72 = 0.36 MN/m2 (C) and are illustrated in Fig. 9.49.

Problems

9.1 Figure 9.50 shows a support structure in the form of a pin-jointed plane frame, all three members of which are steel, of the same uniform cross-sectional area and length, such that ae/l = 200 kN/m, throughout, (a) Using the displacement based finite element method and treating each member as a rod, determine the nodal displacements with respect to global coordinates for the frame shown in Fig. 9.50.

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