ENGR 210 lecture 11: Mechanical Equilibrium Conditions and 2D Applications

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ENGR 210 lecture 11 Mechanical Equilibrium
Conditions and 2D Applications

• Conditions for Mechanical Equilibrium
• Forces must be balanced
• Moments must be balanced

Note Point O can be on or off the body. This
is true for 2D or 3D equilibrium   Note Up to 6
equations and 6 unknowns for each FBD can now be
written
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2D (Planar) Equilibrium Conditions
Forces all act in xy plane Moments all act on
z-axis
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2D (Planar) Equilibrium Conditions Special Notes
Particle All forces on the particle must be
concurrent (pass through the same point) 2-Force
Member Equilibrium No couples can be present on
the member The two forces must have equal
magnitude The two forces must have opposite
directions 3-Force Member Equilibrium No
couples can be present on the member Forces are
either 1. Concurrent (pass through same point)
and , 2. Parallel (F1, F2 in one dir., F3 in
opposite dir.), and F1F2 F3 Frictionless
Pulley A rope or cable on a frictionless pulley
has constant magnitude tension A rope or cable
on a frictionless pulley can change direction
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2D (Planar) Equilibrium Conditions FBD Notes

• Isolate the Rigid Body
• Sketch given externally applied forces and
  moments on the object
• Include appropriate geometry information about
  external forces and moments
• Analyze support locations by connection type
• Sketch reaction forces and/or moments for that
  connection type
• assume directions for unknown force or moment
  reactions
• negative signs in final answer indicate opposite
  direction to assumption

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Example Problem7.2.6Find the forces in cables
AC and AB if the cylinder is in equilibrium and
has a mass of 15kg.
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Example Problem 7.2.31Forklift of weight W2
lifts crate of weight W1 with front wheels able
to turn and rear wheels locked. What are the
loads created at A and B.
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Example Problem 7.2.48Student does arm curls
with upper arm fixed as shown and lower arm able
to change angle. Find Fmuscle as a function of W
and ?. Plot the results for 0? ??90.