Question

Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the element stiffness matrix in global axis system [KG] of the members and assembled them to generate the overall stiffness matrix [K of the truss. Modify the stiffness matrix [K] in order to incorporate boundary conditions following the elimination technique of rows and columns. Take E 200 GPa and A 200 mm2 for all elements The nodal displacement vector of the structure is: X)-[0.0 0.0 0.0 0.0 -4.4993 -7.8128 10.415 -7.8123 -8.9988 -3.7996] - units are in mm. From this nodal displacement vector of the whole structure, extract the nodal displacement vector {XG) of element 5. Using transformation matrix [T] of this element, convert (Xg} in terms of nodal displacement vector of the element in its local axis system Xi). Use the stiffness matrix of the element in its local axis system [KL] (calculated earlier) and calculate member end forces of the element using [KL] and {XL). State the nature/type (tension or compression) of the axial force that will be carried by this element. For checking this result, you may apply the method of joint to calculate the force in member 5 4 4 100kN 4 4 3 2.4 m 2.4 m

Answer 1

Dy D8 10 D2 D, 7 Di to Do (ocal dis plecument node no Ih5 in Reetmle Jont no Co,o) Co, 6.4) 2.4, o u, 32)n 5

2 .4 2.4 i mi mode i modde elem ent no o-8 0 8 2 3 3 0 0-6 -O

elementul Stippnn) mubiX 0 IJ 13 aj im 2 D3 -7-3123 D to uis -7.8123D -. 488D /0

elementul Ship,essrnutM element - no S 5 Djo D6 0 OD 良x10 ,x200 o o78128 10 38 3.7996 I O

Stoegs h element le le ou xIu 一7-8113 -3.A -3749 よxto l Q.MX1u3 &.yme | | o o 311 miう