write mechanics of material lab (Torsion Tests of Metal specimens lab & Concrete lab)

Objective:

The objective of this lab was to determine and draw the torsion vs. angle of twist and shear stress vs. shear-strain diagrams for steel and aluminum specimens tested. Also, to calculate the shear modulus for the steel and aluminum specimens.

Equipment:

Tinius Olsen Torsion tester

Steel rod specimen

Aluminum rod specimen

Ruler

Micrometer

Theory:

Where:

= the shear stress (psi)

T = torsion (in-lb)

= distance from axis of shaft to

where the stress is acting (in)

J = polar moment of inertia with

respect to the longitudinal axis (in4)

Where:

= shear strain (rad)

= distance from axis of shaft to

where the stress is acting (in)

L = length of the metal specimen (in)

= angle of twist (rad)

Where:

G = modulus of rigidity (psi)

L = length of the metal specimen (in)

= angle of twist (radians)

T = torsion (in-lb)

J = polar moment of inertia with

respect to the longitudinal axis (in4)

= maximum shear strain (radians)

= the shear stress (psi)

Procedure:

Place the rod in the Tinius Olsen Torsion Tester and secure each end in machine. Start applying twisting load on the specimen. Record the torque (in-lb.) on the specimen at various points during the experiment according to how many degrees the specimen has been twisted. Repeat this process for each specimen.

Data:

Discussion and Conclusion

After conducting the torsion test for both the aluminum and the steel specimens, the values for the modulus of rigidity for each specimen was found to be for the aluminum and for the steel specimen. These results are conflicting with the standard modulus of rigidity for aluminum and steel (based on the table of typical properties of materials used in engineering found in Appendix B of the book used in Mechanics of Materials course) being 11.2 x 106 psi for steel and 4 x 106 psi for aluminum. We also noticed that there was a slippage while twisting the steel specimen at the angles 4 and 5 because we got the same T value for both. These results could be fixed by making sure that the torsion tester machine is perfectly calibrated and that the manual rotation of the machine is being done accurately.

Steel calculation:

Then do the same process for Aluminum.

Torsion vs Angle of Twist (Aluminum)

Angle of twist (degrees)

Torsion (in-lb)

Shear Stress vs. Shear Strain (Aluminum)

Shear Strain (rad)

Shear Stress (psi)

Torsion vs Angle of Twist (Steel)

Angle of twist (degrees)

Torsion (in-lb)

Shear Stress vs. Shear Strain (Steel)

Shear Strain (rad)

Shear Stress (psi)