EMA 3702L: MECHANICS AND MATERIALS
SCIENCE LAB
TORSION OF A
ROD
Objectives
To understand the relationship between a torsion load and
angular deflection of a rod. To determine the shear modulus of
elasticity of the different testing materials by performing the torsion test on
them.
Introduction
A
circular rod is subjected to a torque T loading at one end. The angular deflection q of the rod is measured by a
dual test indicator. It is proportional to the torque T applied on the rod. Also it is proportional to the length of specimen L,
and inverse proportional to the polar area moment of inertia J of the rod.
where: G is the shear modulus of
elasticity.
The
maximum shear stress tmax
and shear strain on the cylindrical surface g are:
where: D is the diameter of the rod.
The
relationship of the shear can be represented as Hooke’s law:
The
following formula can be used to convert the testing data, applied force F and
displacement Dy,
to a torque load T and the angular deflection q.
where: R1 = 3.96", distance between the center of
the rod and point of the applied load.
R2 =
2.01", distance between the center of the rod and the dial indicator.
Check the distances of R1 and R2, correct them if necessary.
Procedures
Step 1. Measure diameter
of rod using a dial caliper. Note the material of the rod.
Step 2. Mount rod in apparatus and measure
the length of the rod between the stationary and movable grips. Check the
distances R1 and R2.
Step 3. Apply a preload to the rod (suggest
100g), zero the dial indicator.
Step 4. Increase the load, and record the
data of the load and displacement.
Step 5. Repeat the step 4, to obtain 6 to
10 samples.
Step 6. Use two other different material
rods, repeat the entire process.
Analysis and Discussion
Use
statistic method to process the experimental data and create a chart of shear
stress vs. strain for all tested materials. Use least squares linear
interpolation to determine the shear modulus of elasticity for tested materials
according to the experimental data. All the data and calculation results have
to be presented in a tabular form which is organized and clearly labeled. It
should include: A. The rod length, diameter and material, the distances of load
and displacement from the center of the rod. B. The applied load and
displacement. C. The calculations of the applied torque and the angle of twist,
maximum shear stress and shear strain for each testing load. Compare the
experimental results with the data from references.
Report Requirement
A
short version report must be submitted in both printed copy and electronic copy
on the due date.