Problem Statement: Consider the 2D truss structure show in Figure 1. Assume that all
of the elements have the same modulus and cross sectional area and that the distance
between nodes 1 and 5 is L. Determine the following components of the global stiffness
matrix:
Figure 1: Truss Element Node Set Up
a) i=1, j=1
b) i=3, j=12
c) i=9, j=12
Solution Summary (to Four significant figures):
a) ½ + 1/√2 ~ 1.207
b) 0
c) -½
Physical Meaning of the K(i, j) :
The physical meaning of the K(i,j)th component of the global stiffness matrix is the
resulting force acting on the ith Degree of Freedom (DOF) (on the same node in the same
direction) due to a unit displacement of the jth DOF while all other DOFs are fixed to
zero.
Thus, our problem comes down to determining a specific force (the ith) as a result of a
unit displacement of the jth DOF (while all other DOFs are fixed. Right away, we know
that K(i,j) is non-zero if and only if the ith force is connected through an element to the
jth DOF.
The rest of the problem is done by hand.