3B Scientific UE1090200 Apparatus for Measuring Young’s Modulus Instruction Manual
- June 7, 2024
- 3B Scientific
Table of Contents
3B Scientific UE1090200 Apparatus for Measuring Young’s Modulus
EXPERIMENT PROCEDURE
- Measure the deformation profile with loads in the center and loads away from the center.
- Measure the deformation as a function of the force.
- Measure the deformation as a function of the length, width, and breadth as well as how it depends on the material and determine the modulus of elasticity of the materials.
OBJECTIVE
Measurement of deformation of flat beams supported at both ends and
determination of modulus of elasticity
SUMMARY
A flat, level beam’s resistance to deformation in the form of bending by an
external force can be calculated mathematically if the degree of deformation
is much smaller than the length of the beam. The deformation is proportional
to the modulus of elasticity E of the material from which the beam is made. In
this experiment, the deformation due to a known force is measured and the
results are used to determine the modulus of elasticity for both steel and
aluminum.
REQUIRED APPARATUS
BASIC PRINCIPLES
A flat, level beam’s resistance to deformation in the form of bending by an
external force can be calculated mathematically if the degree of deformation
is much smaller than the length of the beam. The deformation is proportional
to the modulus of elasticity E of the material from which the beam is made.
Therefore the deformation due to a known force can be measured and the results
are used to determine the modulus of elasticity. For the calculation, the beam
is sliced into parallel segments which are compressed on the inside by the
bending and stretched on the outside. Neutral segments undergo no compression
or extension. The relative extension or compression ε of the other threads and
the associated tension σ depends on their distance z from the neutral segments
:
As an alternative to the radius of curvature ρ(x), in this experiment the deformation profile w(x), by which the neutral segments are shifted from their rest position, will be measured. This can be calculated as follows, as long as the changes dw(x)/dx due to the deformation are sufficiently small:
the deformation profile is obtained from this by double integration. A typical example is to observe a beam of length L, which is supported at both ends and to which a downward force F acts at point a. In a state of equilibrium the sum of all the forces acting is zero:
Similarly, the sum of all the moments acting on the beam at an arbitrary point
x is also zero:
No curvature or deformation arises at the ends of the beam, i.e. M(0) = M(L) = 0 and w(0) = w(L) = 0. This means that M(x) is fully determinable:
The deformation profile is obtained by double integration
In the experiment the shape of this profile is checked for load at the center of the beam (α = 0.5) and off-center (α < 0.5).
EVALUATION
When the load is in the center, then For a rectangle of width b and height d,
the following calculation is made:
Bending of Flat Beams | DEFORMATION OF SOLID BODIES | MECHANICS