This experiment on asymmetrical bending was conducted with the main objective of comparing theoretical to experimental values, principal axes location and the reciprocal theorem verification were also on the agenda. Results were determined and tabulated for experimental and theoretical values.
These were very closely met in this successful experiment with results within reasonable engineering accuracy.
INTRODUCTION:-.
Bending is one of the most common forms of deformation in engineering structural studies. In this experiment we will be dealing with a ("L") Beam, which is the simplest component in an engineering structure subjected to bending. Bending causes deflections to occur in the beam structure, such deflections are one of the prime concerns of this experiment. The positions of the "Principal axes" are fundamental to such cases; in order to use in certain calculations. If a body has an axis of symmetry, then rotations about that axis will be dynamically balanced; in other words that axis is a principal axis; and the normal plane to this axis is also a principal axis. .
In this experiment we will be dealing with asymmetrical bending, where the deflection occurs normal to the neutral plane.
The main objectives of this experiment are to:-.
- Locate the position of the principal axes in the cross-section from experimental results and theory.
- Determine the deflections due to bending from experimental methodology and compare these to the theoretical values.
- Also to demonstrate the "Reciprocal theorem" in this experiment. .
THEORY:-.
To determine the principal axes from experimental results, we will use the formula,.
tanu = (u/v) = (U/V) {as explained on lab. Sheet}.
.
To compare to theoretical value, tan2u = 2Ixy/(Ix - Iy) {where Ixy ≠ 0}.
In order to obtain the theoretical values of, .
du/dV dv/dU du/dU dv/dV.
the following equations were derived, using general beam deflection theory (intermediate steps omitted):.