Course Review, part 2
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Topics to be covered:
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Screws
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Frames
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Machines
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3D Rigid Bodies
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Particle Equilibrium
Others as time permits
Course evaluation today (end of period 1,
beginning of period 2)
Screws
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In general, we treat screws in a similar way to a
block sliding on an inclined plane.
There are two angles of importance:
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The Lead angle which is found by the inverse
tangent of L, the Lead, or amount the screw moves
in one turn, divided by the circumference of the
screw. This angle is usually designated α.
The friction angle, which is found by the inverse
tangent of the coefficient of friction. This angle is
usually designated as ϕ.
Screws (cont)
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Te resultant force, R, acts on the thread at a
total angle of (α + ϕ) for upward motion of a
jack, for example, and an angle of ( ϕ - α) for
downward motion.
We must consider the total force exerted by all
of the threads, ΣR.
The moment of R about the axis of the screw is
Rrsin (α + ϕ) and the total moment due to all
reactions of the screw threads is ΣRrsin (α + ϕ)
Screws (cont)
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This is illustrated below:
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The moment then becomes :
Pa= [rsin (α + ϕ)]ΣR
Screws (cont)
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Equilibrium of forces in the axial direction
requires:
W = ΣR [cos (α + ϕ)]
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Dividing Pa by W gives:
Pa = W tan (α + ϕ)
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To lower the jack requires a moment:
Pa = W tan (ϕ – α) if ϕ > α
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If the reverse were true, the screw would
unwind by itself and require a moment to keep it
from unwinding of:
Pa = W tan (α - ϕ)
Screws (cont)
1. A square threaded screw jack is used to lower a 7000 pound load. A normal force of 80
pounds applied to the end of a 20 inch long jack handle is required for impending motion.
The screw has 6 threads per inch and a mean diameter of 1.5 inches. Determine the
coefficient of friction in the threads.
Free body diagram of the unwrapped thread...
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You were asked to determine the friction
coefficient given that M is 1600 lb-in to lower
the jack, and the screw radius is 0.75 in.
Screws (concluded)
Frames—Example Problem
3. Determine the horizontal component of the reaction at Pin A of the pin connected frame
shown below. (25 points)
Another Frame Example
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A two foot diameter cylinder weighs 500 pounds
and is cradled between a fixed surface and a
rigid bar AB, which is pinned at A. A rope, CB,
supports the rigid bar. All surfaces are
frictionless. Determine the tension in rope CB.
6 feet
B
C
60o
60o
A
Example (cont)
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500 lb
FBD of cylinder:
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Rl sin 30 + Rr sin 30 = 500
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Rl = Rr = 500 lb
Rl
Rr
1/tan 30 = 1.73
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FBD of bar AB
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Σ Ma = 0
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Tcb (5.20) = 1.73(500)
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Tcb = 166 lb
Tcb
500
1.73'
6 cos 30=5.20 ft
Machines
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Machines transmit and modify forces..
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Identify the parts of the machine
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Make each a free body
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Identify two force members, consider these first
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Next, consider the multi-force members
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Solve the equations of equilibrium
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Reassemble the machine
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Check your results by means of an equation of
equilibrium that you have not already used...
Machines
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Machines transmit and modify forces..
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Identify the parts of the machine
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Make each a free body
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Identify two force members, consider these first
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Next, consider the multi-force members
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Solve the equations of equilibrium
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Reassemble the machine
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Check your results by means of an equation of
equilibrium that you have not already used...
Three Dimensional Rigid Bodies
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There are now six equations of equilibrium:
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Σ Fx = 0 , Σ Fy = 0 , Σ Fz = 0
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Σ Mx = 0 , Σ My = 0 , Σ Μz = 0
Remember that there are different reaction
forces associated with different mounting
methods
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A roller on a rail or rough surface has two forces
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A ball and socket has three forces
3D Rigid Bodies (cont)
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A fixed support has three forces and three
couples
Always remember to look for axes about which
to compute moments that will simplify the
problem
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Usually passing axes through mount points does
this by removing many of the unknown forces from
consideration.
Remember, rigid bodies can have couples
acting on them... the moment vector is movable
and can be placed anywhere on the body...
Particle Equilibrium
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Remember, when the resultant of all forces
acting on a particle is ZERO, the particle is in
equilibrium!
Remember, always sketch a FREE BODY
DIAGRAM ! Example:
Additional Topics
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You will be responsible for knowing how to
perform vector operations in three dimensions
The calculation of centroids of composite areas
will be expected
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The theorems of Pappas Guldinas should be part of
your tool kit
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Friction in its many manifestations
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Supports in two and three dimensions
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Conditions for statically determinate supports
Additional Topics (cont)
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Moments and force couples
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A moment vector is a free vector and can be placed
anywhere on the body
The sign convention...counterclockwise is positive,
clockwise is negative
The rules governing equivalent systems of
forces
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Forces with the same line of action can be moved
anywhere on the body, along that line of action
Final Exam--reminder
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First part of the exam will cover the recent
material
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Beams and cables
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Moments of Inertia
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Friction
The second part of the exam will cover the
entire course content