8/11/2019 Thermal Stress and Torsion
1/17
Thermal & Torsion stresses
Daniel D. Dasig, Jr.
8/11/2019 Thermal Stress and Torsion
2/17
Thermal stresses
Temperature causes bodies to expand or contract.Change in length due to increase in temperaturecan be expressed as
L= L..t
Where, L is the length, (/o
C) is the coefficient oflinear expansion, and t(oC) is the temperaturechange.
8/11/2019 Thermal Stress and Torsion
3/17
When the temperature deformation is
prevented, thermal stress developed due to
temperature change can be given as:
= E..t
8/11/2019 Thermal Stress and Torsion
4/17
8/11/2019 Thermal Stress and Torsion
5/17
Example 1
A steel rod with a cross-sectional area of 0.25
in2is stretched between two fixed points. The
tensile load at 70F is 1200 lb. What will be
the stress at 0F? At what temperature will the
stress be zero? Assume = 6.5 10-6in/(inF)and E = 29 106psi.
8/11/2019 Thermal Stress and Torsion
6/17
For the stress at 0F:
8/11/2019 Thermal Stress and Torsion
7/17
For the temperature that causes zero stress
8/11/2019 Thermal Stress and Torsion
8/17
Example 2
A steel rod is stretched between two rigid
walls and carries a tensile load of 5000 N at
20C. If the allowable stress is not to exceed
130 MPa at -20C, what is the minimum
diameter of the rod? Assume =
11.7 m/(mC) and E = 200 GPa.
8/11/2019 Thermal Stress and Torsion
9/17
Solution
8/11/2019 Thermal Stress and Torsion
10/17
TORSIONTORSIONAL SHEARING
STRESS,
For a solid or hollow circular shaft
subject to a twisting moment T, the
torsional shearing stress at a
distance from the center of the shaftis
whereJ is the polar moment of inertia
of the section and r is the outer radius.
8/11/2019 Thermal Stress and Torsion
11/17
For solid cylindrical shaft
8/11/2019 Thermal Stress and Torsion
12/17
For hollow cylindrical shaft
8/11/2019 Thermal Stress and Torsion
13/17
ANGLE OF TWIST
The angle through which the bar length L will twist is
whereT= is the torque in Nmm,
L= is the length of shaft in mm,
G= is shear modulus in MPa,
J= is the polar moment of inertia in mm4,Dand d= are diameter in mm, and
r= is the radius in mm.
8/11/2019 Thermal Stress and Torsion
14/17
POWER TRANSMITTED BY THE SHAFT
A shaft rotating with a constant angular velocity (in radians per
second) is being acted by a twisting moment T. The power
transmitted by the shaft is
Where
T= is the torque in Nm
f= is the number of revolutions per second, andP= is the power in watts.
8/11/2019 Thermal Stress and Torsion
15/17
Example 1
A steel shaft 3 ft long that has a
diameter of 4 in is subjected to a
torque of 15 kipft. Determine themaximum shearing stress and the
angle of twist. Use G = 12 106psi.
8/11/2019 Thermal Stress and Torsion
16/17
Example 2
A steel marine propeller shaft 14 in. in
diameter and 18 ft long is used to
transmit 5000 hp at 189 rpm. If G = 12 106psi, determine the maximum
shearing stress.
8/11/2019 Thermal Stress and Torsion
17/17
QUIZ 2
1. A copper rod of 15 mm diameter, 800 mmlong is heated through 50C. (a) What is its
extension when free to expand? (b) Suppose
the expansion is prevented by gripping it at
both ends, find the stress, its nature and the
force applied by the grips when one grip yields
back by 0.5 mm.
Top Related