ENGR 210 lecture 7: Moments in Equivalent Loads

1
ENGR 210 lecture 7 Moments in Equivalent Loads

• What is an equivalent load an equivalent load
  is a single force and single moment applied at
  a single point that produce the same result as a
  system of forces and moments applied at multiple
  locations

• Procedure for analysis of equivalent loads
• Define the moment center
• Determine the resultant force for the system
• Find vector components for each force
• Add x,y,z force components to get equivalent
  force resultant
• Determine the resultant moment at the moment
  center
• Find the position vector for each force
• Calculate the moment at the MC due to each force
• Find vector components for any applied moments
• Add x,y,z moment components to get equivalent
  moment resultant
• Apply equivalent resultant force and moment at MC

2
Couples

• What is a couple two forces of equal mag but
  opposite dir
• What is a couple moment a moment produced by a
  force couple
• MFD, where D perpendicular distance between
  forces
• MrF1F2 x F2
• Note a couple moment has the same magnitude and
  direction for ANY moment center on the object

Proof of MC independence
3
Example Problem5.4.8For the cantilever beam at
A, show the equivalent loading a) in vector
formb) as a diagram
4
Example Problem 5.4.24 Lug wrench has parallel
and opposite forces applieda) describe in a
sentence the effect of the forces on the wheel
b) determine the equivalent loading at Ac)
repeat step (b) for moment centers at B and Cd)
what does this tell you about a couple?