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Department of Mechanical Engineering
ENGR 0135
Chapter 6-1
Department of Mechanical Engineering
Today’s topicsDefinition of equilibriumFree-body diagramApplied forces and reactions Idealized Supports and Connections
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Equilibrium
A system of forces and moments is said to be in equilibrium when their force and moment resultants are zeros
0kjiC
0kjiR
=++=
=++=
∑∑∑∑∑∑
zyx
zyx
MMM
FFFVector notation
000
000
===
===
∑∑∑∑∑∑
zyx
zyx
MMM
FFFScalar notation
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Forces (and Moments)External forces
– Applied forces (including weights) - given– Support Reactions – prevent bodies to “rigidly
move”
Internal forces– lead to stresses– Exposed when a loaded body is “cut”
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Free body diagrams
Inside the FBD– A portion of the body of interest or– A full body of interest or– A group of bodies of interest– Body forces
On the boundary of the FBD– “Replacement” forces/distributed forces
FBD
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How to make the FBD Select and draw bodies or parties of interest to be
shown in the FBD Identify and draw the body and surface forces applied
on the bodies Discard contacting bodies that are not wanted and
replace them with the forces they exert to the body of interest
Cut the body parts that are not wanted and replace them with internal forces they exert to the body of interest
Locate the coordinate system
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Discarded bodies and the replacement forces
Contacting bodies
String/cable/axially loaded members
Body parts
Supports and connections
Forces normal and/or tangential to the FBD surfaces
Forces with lines of actions that coincide with the member axis
Distributed forces called stress
Support reactions
New!!
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Reaction forcesThe task of a support is to prevent rigid
body motion in some directionsThe prevented motion/displacement
transforms into reaction forces/momentsSo the reactions are exposed when supports
and connections are not included in the FBD
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Flexible cord, rope, chain, or cable
Only motion in the axis of the cable (extension) is prevented only tension reaction forceTension = leaving out the FBD
Compression is not prevented.
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Rigid link
Similar to tension, but the compression is prevented as well.So the reaction R is either tension or compression.
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Ball, Roller, or Rocker
This support does not allow vertical motion (in most cases compression).
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Smooth Surface
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Rough Surface
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Smooth Pin
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Pin in a smooth guide
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Ball and socket
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Hinge
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Ball Bearing
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Journal Bearing
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Thrust Bearing
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Smooth Pin and Bracket
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Fixed support
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Example: Draw FBD
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Example
Department of Mechanical Engineering
Example: Draw FBD
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Smooth contacts
Smooth pins
FBD of the pin C
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Example: Draw FBD of the curved bar
Ball and socket
Pin and bracket
Flexible cable
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06_23
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Example: Draw FBD of the curved bar
Fixed support
Department of Mechanical Engineering
Example: Draw FBD of the curved bar
Fixed support