ENGR:2750 MECHANICS OF DEFORMABLE BODIES
THE UNIVERSITY OF IOWA
Professor Colby C. Swan, Ph.D.
4120 Seamans Center; 335-5831
Department of Civil & Environmental Engineering
Period #10: Calculation of Twist in Shafts
J 2 dA
Polar moment of inertia:
Period #9: Torsion
A torque is a moment applied to mechanical system that causes it to twist or
In the present circumstances, well be concerned with torsional moments
(torques) applied to long slender shafts as shown in the figure below
Period #1: Course Overview and Equilibrium
A. Course Overview:
This course addresses how mechanical systems respond when subjected to loads:
When loads are applied to a mechanical system what are the internal stresses?
What is stress?
How do we describe i
Period #6: Material Properties
We have introduced two concepts thus far:
Loads applied to structures result in internal stresses.
i.e. the stress tensor (Fig. 6.1)
Deformation on the material scale is quantified by strain.
i.e. the strain tenso
Period #12: Bending Behavior
A. Next Topic
Chapter 4 dealt with axial loading of axial members (rods)
Chapter 5 dealt with torsional loading of axial members (shafts)
Chapters 6 and 7 deals with transverse loading of axial members (beams).
Our goal in stu
Period #11: Statically Indeterminate Shafts
B. Statically Indeterminate Shafts
Cannot simply use the equations of static equilibrium to calculate reactions or
Period #2 : Average Normal Stresses
A. Review of Statics
When external loads are applied to a restrained deformable body, internal forces are generated
to keep the body in equilibrium.
The internal forces in a body can be examined using methods of section
Period #3 : Average Shear Stresses
A. Review of Stresses Thus Far
At a point in a body, the state of stress is generally
represented with a stress tensor.
xx xy xz x xy xz
yx yy yz yx y yz
zx zy zz zx zy z
Period #7: Axially Loaded Members
For now, we confine our attention to axial members in tension or compression in
the linear, elastic regime of behavior.
Thus it is assumed that the magnitudes of axial stresses in the members are less
Period #8: Axial Load/Deformation in Indeterminate Members
We are considering axial members in tension or compression in the linear, elastic
regime of behavior. Thus the magnitudes of axial stresses in the members are less
than the material yiel
Period #4 : Allowable Stresses and Factors of Safety
A. Factors of Safety
All mechanical systems have loads at which the material yields or
fractures or at which the structure become unstable.
These are generally called the ultimate loads or failure loads
P R O P E R T Y TA B L E S A N D
CHARTS (ENGLISH UNITS)