Mechanics of Materials
CIVL 3322 / MECH 3322
Statics Review
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Statics Review
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Statics Review
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Statics Review
A Quiz
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Statics Review
A Quiz
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Statics Review
A Quiz
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Statics Review
A Quiz
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Statics Review
A Quiz
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Statics Review
A Quiz
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Statics Review
Stress and Internal Forces
¢  In
Statics, we spent most of our time
looking at reactions at supports
¢  Two variations from this were when
we considered the forces in trusses
and
¢  The shear and moment at a point in a
beam (you may or may not have
looked at this)
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Statics Review
Stress and Internal Forces
¢  In
Mechanics of Materials, it is these
internal forces and how they affect the
behavior of the system that will be
critical to our analysis
¢  Depending on the loading pattern,
there can vary greatly through the
beam
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Statics Review
Stress and Internal Forces
¢  At
any point in a continuous system,
we can look at the internal forces
acting on the system by modeling the
point we are looking at in the system
as a fixed end support.
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Statics Review
Stress and Internal Forces
¢  This
means that at any point in a
continuous member, we will have a
force parallel to the member, a force
perpendicular to the member and a
resistive moment.
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Statics Review
Stress and Internal Forces
¢  The
force that acts parallel to the cut
we make to separate the member is
known as the axial force or the normal
force
¢  The force that acts perpendicular to
the cut is known as the shear force
¢  The moment is known as the bending
moment
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Statics Review
Stress and Internal Forces
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Statics Review
Stress and Internal Forces
¢  The
dark blue arrows along the axis of
the beam are the axial forces
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Statics Review
Stress and Internal Forces
¢  The
axial force is considered as a
positive axial force if it would cause
the section under consideration to be
in tension.
¢  The axial force is considered as a
negative axial force if it would cause
the section under consideration to be
in compression.
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Statics Review
Stress and Internal Forces
¢  This
shear force is always normal to
the axis of the cut face of the beam
and is typically labeled as V.
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Statics Review
Stress and Internal Forces
¢  The
force acting on the plane of the
cut generates a stress on that plane
¢  If the force is normal to the plane, the
stress is a normal stress or an axial
stress
¢  If the force is parallel to the plane, the
stress is a shear stress
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Statics Review
Stress and Internal Forces
¢  The
magnitude of the stress is the
ratio of the magnitude of the applied
force to the area of the cross section
¢  For normal stress, the expression is
σ avg
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F
=
A
Statics Review
Stress and Internal Forces
¢  This
expression assumes that the
force is equally distributed across the
cut face
¢  To determine the axial stress at a
point required an ability to divide the
force according to some function
σ avg
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F
=
A
Statics Review
Stress and Internal Forces
¢  Units
of stress are similar to units of
pressure
l  Lbf/ft2
l  N/m2
•  A N/m2 is given the unit of Pa (Pascal)
σ avg
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F
=
A
Statics Review
Stress and Internal Forces
¢  Pressure
is a scalar, stress is a vector
so they are not exactly the same
¢  Usually you don’t see Pa by itself, the
units are KPa, MPa, GPa
σ avg
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F
=
A
Statics Review
Stress and Internal Forces
¢  Pressure
is a scalar, stress is a vector so
they are not exactly the same
¢  Usually you don’t see Pa by itself, the units
are KPa, MPa, GPa
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Statics Review
A solid 0.5 in diameter steel hanger
rod is used to hold up one end of a
walkway support beam. The force
carried by the rod is 5,000 lb.
Determine the normal stress in the
rod. (Disregard the weight of the rod).
E01
Rigid bar ABC is supported by a pin at A and axial member (1), which has a cross
section of 540 mm2. The weight of the rigid bad ABC can be neglected.
(a)  Determine the normal stress in member (1) is a load P=8kN is applied at C.
(b)  If the maximum normal stress in member (1) must be limited to 50 Mpa, what is
the maximum load magnitude P that may be applied to the rigid bar at C?
A 50-mm-wide steel bar has axial loads applied at points B, C, and D. If the normal
stress magnitude in the bar must not exceed 60 MPa, determine the minimum
thickness that can be used for the bar.