TRUSS PROBLEMQ. Consider a truss structure shown below. Assume that the stiffness of all the members is equal to unity. Write a finite element program to solve for the axial forces in the members labelled A, B, C. Verify the output of program by comparing with analytical solution.

P=1NL12CB

5A43L

Given,Stiffness of all members (k) =1;Load (P) =1N;Assumptions:Let the length of each element (L) =1 m; Area (A) =1;Youngs Modulus (E) =1;Analytical solution:Reaction forces will be, R5=3/4 N; R3=1/4 N;Lets solve this problem by method of jointJoint5:Joint1:

FC600FA600 R5FCFB

From this well get FA= 0.4330 N; FB=-0.2887 N; FC=-0.866 N;FEM solution:

P=1N1127542

56433

The nos given at nodes are node nos and the nos given at the middle are the element nos.So, there are 5 nodes and 7 elements and each node has 2 degrees of freedom say U1 to U10.Boundary condition:Node 5 is fixed so there will be no displacement and Node 3 has a roller joint so there will be no vertical displacement. i.e. U9=0; U10=0; U6=0;There is only one force applied at Node1 in ve y direction, so F2=-1 N;Now the height of the structure is = = 0.866 m.After solving well getnode1122334455

directionxyxyxyxyxy

displacement0.5052-1.290.22-0.540.57700.433-100

Elements12345=FB6=FA7=FC

Force-0.29-0.290.14430.29-0.28870.4330-0.866