Question

A truss is loaded as shown in the figure. Determine the displacement of node 3 in the vertical direction using the strain energy method. The elastic modulus of the material is 200 GPa and the cross sectional area is 400mm?. [8] L1=3m L3=2m 10kN

Please show all working using the below formula.

Answer 1

. Given data, * Elastic modulus of material = 200 Gpa. *. Cooss - Sectional area = 400mm * Force 10 AN. 423m 23:2m TOEN forces * For is in each membee due to external forces, pie tension force is the and fol compression are force considered. point methood can be weed, for node - 3 Sfx zo -Fis - Faza cos 0 =0. Fis + 2 e 3 =0. TE &

fisog Veste Efy to -p+ f23 sino ao Es so mo Smo no- For node-sir s fy so. >> fix - y psimo 20. 0 squad -cy Strain Energy dere to axial force of U= EL CAE

f = External arial force A = Cooes - Seetioral area. E , Elastic modelul Total Strain - Energy stored in trues can be written, 2A US 3+ 46+ 4] - Deffection in veltical direction is. from Equation in Substitute Paloxios A = 400 x 10-6m? E = 200x109 pa

=> do ( * d = 10x103 .8 +13/13 3+ 900 x160x r09 5:1.13781010m. (82) To = 1.137mm) The deflection in vertical direction, d = 1.137mm