TRUSS DEFLECTION BY STRAIN ENERGY

INTRODUCTION

A loaded structure deforms under the applied loads resulting in the point of application of each load been displaced some distance. Thus, the loads are said to have done some work. This is the work done by the loads in deforming the structure, by straining the individual members.

If the member strains are all in the elastic range, the structure will return to its original shape once the loads are removed. Again, work is done in returning the structure to its original shape. Thus, the original work done by the loads must have been stored in the strained members as energy, and it is this energy that does work in returning the structure to its initial shape. This energy is referred to as the strain energy.

The strain energy concept may be used as a theoretical means to predict structure deflections under load. If there is only one applied load and it is the deflection at the load point that is of interest, direct strain energy equations can be used to determine the deflection. For cases where there are multiple loads or$/$and the deflection required is not at the load point, Castigliano's first theorem uses strain energy considerations to provide a means of determining the deflection. This experiment covers the use of Castigliano's first theorem in calculating deflections in trusses.

The course notes on 'Strain Energy' $-$ Structural Analysis $3$A may be taken as the required theoretical background for this experiment.

All members $25252mm$ thick SHS

Data: Area $=183m{m}^2$

$E=200$GPa

APPARATUS

The model truss shown above is made from a $25252$ square hollow section with welded connections. It is supported at A by a pinned $($hinge$)$ support, and on rollers at E$.$ The truss is placed in a load frame testing rig so that it can be loaded with downward forces at $C$ and $F$ or $H,$ as shown under the two load cases.

Each group of students, under the guidance of the laboratory technician, will be required to load