ME 221 Statics

1
ME 221 StaticsLecture 22Section 5.5
2
Homework 8

• Chapter 9 problems
• 42, 43, 50 55
• Chapter 5 problems
• 11, 13, 16, 20, 24 25
• See Angel for additional information
• Due Friday, October 24

3
Quiz 5

• Friday, October 24

4
Last Lecture

• Equilibrium equations

• Free body diagrams

• Modeling supports

5
Equilibrium Equations

• When the force system is replaced by a resultant
  force and moment that are zero, the rigid body is
  in equilibrium.

The equilibrium conditions may be expressed as
6
Supports for Rigid Bodies
If a rigid object is subjected to some set of
forces but does not move, then its motion could
be restrained by a normal force exerted by the
ground, a wall or from fixing the object with
some support.
If the support prevents translation in a given
direction, then a force is developed on the
member in that direction. Likewise, if a
rotation is prevented, then a couple moment is
exerted on the member.
7
Free Body Diagram

• Draw the body separate from all other bodies
  (including ground).

• Draw the magnitudes and directions of all
  external forces acting on the body.

• Include applied loads, reactions due to
  supports, and the weight of the object.

• Include necessary dimensions of the body

• Dimensions are needed for summing moments

• Draw the positive sense of the coordinate system
  used to write out equilibrium equations

8

• Special Cases
• Equilibrium of Rigid Bodies
• - 2D 3D
• Two- and Three-Force Members
• Special Supports

9
Two- and Three-Force Members
Two-Force Members
When the member is not subjected to a couple and
the forces are applied only at two points, the
member is said to be two-force member.
These forces will maintain equilibrium if
(FA and FB must be collinear)
10
Two- and Three-Force Members
Three-Force Members
If the member is subjected to three coplanar
forces, then it is necessary that the forces are
either concurrent or parallel if the member is to
be in equilibrium.
?
11
Note

• It should be noted that single bearing, single
  pin and single hinge supports can support both
  forces and couples. Most often, however, these
  supports are used in conjunction with other
  bearings, pins or hinges to hold the body in
  equilibrium. In this case, the force reaction at
  the support may be adequate.

12
Chapter 5 Equilibrium Examples