Page 23 - Finite Element Analysis with ANSYS Workbench

14 Chapter 2 Truss Analysis

  x 
x  0

where  is the truss axial stress.
x

2.1.2 Related Equations
The truss stress varies with the strain  by the Hook’s
x
law,
 x  E 
x
where E is the modulus of elasticity or Young’s modulus. The
strain  is related to the displacement according to the small
x
deformation theory as,
u 
 x  x 

where uu () is the displacement that varies with the distance x
x
along the length of the truss member. Thus, the stress can be
written in form of the displacement as,
u 
 x  E x 

The governing differential equation, for the case of constant
Young’s modulus, becomes,
 2 u
E  0
x  2

For a truss member that lies only in the x-direction, the
displacement distribution u  u () can be derived from the
x
differential equation above. This is done by performing integra-
tions twice and applying the problem boundary conditions. The
stress of the truss member can be then determined. However, if the
problem contains many truss members oriented in three
dimensions, it is not easy to determine their deformed shape and
member stresses. The finite element method offers a convenient
way to find the solution as explained in the following section.