Finite Element Analysis of Truss Structure using MATLAB

Introduction
Truss is a structure that consists of two-force members only, where the members are organized
so that it behaves as a single object. It is assumed to comprise of long, thin members like wood,
steel or concrete joined and bound together in a triangular shape at their endpoints by welding or
gussets. Trusses are either simple, compound or complex, are triangular in shape and bear only
axial force. They are commonly used in bridge construction. Newton's Laws apply to the
structure as a whole, as well as to each node or joint. In order for any node that may be subject to
an external load or force to remain static in space, the following conditions must hold: the sums
of all horizontal forces, all vertical forces, as well as all moments acting about the node equal
zero. Analysis of these conditions at each node yields the magnitude of the forces in each
member of the truss. These may be compression or tension forces. Trusses that are supported at
more than two positions are said to be statically indeterminate, and the application of Newton's
Laws alone is not sufficient to determine the member forces. In order for a truss with pin-
connected members to be stable, it must be entirely composed of triangles. In mathematical
terms, there is necessary condition for stability:
M +R ≥ 2j
M =total number of truss members
j=total number of joints
r=number of reactions (equal to 3 generally)
When m = 2j − 3, the truss is said to be statically determinate, because the (m+3) internal
member forces and support reactions can then be completely determined by 2 j equilibrium
equations.
Some structures are built with more than this minimum number of truss members. Those
structures may survive even when some of the members fail. They are called statically
indeterminate structures, because their member forces depend on the relative stiffness of the
members, in addition to the equilibrium condition described. In a statically indeterminate truss,
static equilibrium alone cannot be used to calculated member force. If we were to try, we would
find that there would be too many “unknowns” and we would not be able to complete the
calculations. Instead we will use a method known as the flexibility method, which uses an idea
know as strain energy.
Objective
● The main motive of this experiment is to figure the forces on each joint by the help of
engineering structure by using finite element method.
● To develop a finite element model using MATLAB software to calculate the nodal
displacements, axial force, strain and stress in each member and their validation with
experimental results;

Result
Computed Stress Computed strain
-1.0278 -0.4894
-1.0278 -0.4894
-1.0278 -0.4894
0.5139 0.2447
0.5139 0.2447
1.0278 0.4894
1.0278 0.4894
Nodal Force Nodal displacement
0 0
250 0
0 0.0069
0 -0.0119
0 0
0 -0.0119
0 0.0069
250 0
0 0.0034
500 -0.0218
The values in the experimental force was too different from theoretical values. This can be
happened due to several reasons. As the equipment were not equipped and maintained properly.
There may be some environmental effects on this, as the device is extremely sensible with wind
and noise.