Module 1.1
Oscillatory Motion
Dr. A.K. Khosrovaneh
EME5213
Dr. A.K. Khosrovaneh
Harmonic Motion
Periodic Motion
When the motion is repeated in equal interval of
time t
Period of oscillation
The repetition time t is called the period of oscillation
Fr
Do not write on this equation sheet!
EME3013 Mechanics of Materials
Exam #3 - Equation Sheet
Chapter 8. Stress in Thin-Walled Pressure Vessels & Combined Loading
These pressure vessels must have
!
"
10
or r 10t for the following equations to be valid.
C
Review for Final Exam
EME3013 Mechanics of Materials
Chapter 12. Deflection of Beams and Shafts (by Integration)
Find M(x) by analyzing the beam and loading.
M(x) = internal bending moment
=
( )
.
E = Youngs modulus of elasticity
I = moment of inertia of
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Torsion of Prismatic Bars
Bars with noncircular
cross-section warp.
Prandtls Stress Function, (x,y)
Equilibrium equations are satisfied with:
Compatibility equation,
Poissons equation:
Boundary condition:
Prof. P. Sitaram
Prof. P. Sitaram
1
7/1
7/15/2015
Curved Beams
Curved Beam
Due to curvature of the beam, normal strain does not vary
linearly with depth as in the case of a straight beam.
Therefore NA will not pass through the centroid. The
variation of stress over the cross-section is hyperb
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Unsymmetrical Bending
Bending in two planes (xy and xz.)
Neutral axis does not coincide with the principal axes of cross-section
If the cross-section has an axis of symmetry, this axis must be the principal axis.
Therefore the product of ine
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Failure Theories
For ductile materials, failure is specified by initiation
of yielding
For brittle materials, failure is specified by fracture
For ductile materials, the popular yield theories are:
Tresca criterion
von Mises criterion
For
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State of Stress At a Point:
6 Things Are Needed
Magnitude
Plane on which it acts (because stress at the same
point will have different values on different
planes)
Direction
Distribution over the cross-section (Uniform, or
Linear, or Parabolic
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State of Stress: 3D
If we know the stresses on any 3 mutually perpendicular planes through a point, then we can
determine the stresses on any inclined plane
through the same point
Consider a tetrahedron element at a point.
Three of the four fa
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Mohrs Circle
Mohrs circle is a graphical method for solving
stresses, strains, moments of inertia, on
arbitrary planes.
It is an alternate method to the
transformation equations discussed in the
previous section.
Therefore we can determine, pr
Mechanics of Materials: Review
Problem_2:Determine the state of stress at A
Mechanics of Materials: Review
FBD of AB
Mechanics of Materials: Review
FBD of CA
Mechanics of Materials: Review
State of Stress at A