Assigned 8-31-06; Due 9-7-06

Use the direct method we used in class for the truss element to derive the stiffness matrix for a torsional element. The torsional element is a line element with a node at either end. Loadings are a torque at each node, and displacements are the angles of twist at each node.

The element has a length L and torsional stiffness constant J. The material has a shear modulus G. From solid mechanics we know that if a torque T is applied, the angular twist of one end relative to the other is TL/GJ.