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- Welcome to the presentation on moments so just if you were wondering I have already covered moments you just may not have recognized it because I covered it in mechanical advantage in torque but I do realize that when I covered it in mechanical advantage in torque I think I may be over complicated it and if anything I didn't cover some of the most basic moment of force problems that you see in.
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What is a Moment?
The Moment of a forceis a measure of its tendency to cause a body to rotate about a specificpoint or axis. This is different from the tendency for a body to move, ortranslate, in the direction of the force. In order for a moment to develop,the force must act upon the body in such a manner that the body would beginto twist. This occurs every time a force is applied so that it does notpass through the centroid of the body. A moment is due to a force not havingan equal and opposite force directly along it's line of action.
Imagine two people pushing on a door at the doorknob from opposite sides.If both of them are pushing with an equal force then there is a state ofequilibrium. If one of them would suddenly jump back from the door, thepush of the other person would no longer have any opposition and the doorwould swing away. The person who was still pushing on the door created amoment.
The magnitude of the moment of a force acting about a point or axis isdirectly proportinoal to the distance of the force from the point or axis.It is defined as the product of the force (F) and the moment arm (d). Themoment arm or lever arm is the perpendicular distance betweenthe line of action of the force and the center of moments.
Moment = Force x Distance or M= (F)(d)
The Center of Moments may be the actual point about which theforce causes rotation. It may also be a reference point or axis about whichthe force may be considered as causing rotation. It does not matter as longas a specific point is always taken as the reference point. The latter caseis much more common situation in structural design problems.
A moment is expressed in units of foot-pounds, kip-feet,newton-meters, or kilonewton-meters. A moment also has a sense; A clockwiserotation about the center of moments will be considered a positive moment;while a counter-clockwise rotation about the center of moments will be considerednegative. The most common way to express a moment is
The example shows a wrench being applied to a nut. A 100 pound force isapplied to it at point C, the center of the nut. The force is applied atan x- distance of 12 inches from the nut. The center of moments could bepoint C, but could also be points A or B or D.
Key Moments Chauvin Trial
Moment about C
The moment arm for calculating the moment around point C is 12 inches. Themagnitude of the moment about point C is 12 inches multiplied by the forceof 100 lbs to give a total moment of 1200 inch-lbs (or 100 ft-lbs).
Moment Arm (d) = 12 inches
Magnitude (F) = 100 lbs
Moment = M = 100 lbs x 12 in. = 1200 in-lbs
Similarly, we can find the moments about any point in space.
| Moment @ | A | B | D |
| Moment Arm | 8 inches | 2 inches | 0 inches |
| Magnitude of F | 100 pounds | 100 pounds | 100 pounds |
| Total Moment | 800 in- pounds | 200 in- pounds | 0 in- pounds |
A moment causes a rotation about a point or axis. If the moment is tobe taken about a point due to a force F, then in order for a moment to develop,the line of action cannot pass through that point. If the line of actiondoes go through that point, the moment is zero because the magnitude ofthe moment arm is zero. Such was the case for point D in the previous wrenchpoblem. The total moment was zero because the moment arm was zero as well.
As another example, let us assume that 200 pound force is applied to thewrench as indicated. The moment of the 200 pound force applied at C is zerobecause:
M = F x d = 200 lbs x 0 in = 0 in-lbs
In other words, there is no tendency for the 200 pound force to causethe wrench to rotate the nut. One could increase the magnitude of the forceuntil the bolt finally broke off (shear failure).
The moment about points X, Y, and Z would also be zero because they alsolie on the line of action.
A moment can also be considered to be the result of forces detouring froma direct line drawn between the point of loading of a system and its supports.In this case, the blue force is an eccentric force. In order for it to reachthe base of the column, it must make a detour through the beam. The greaterthe detour, the greater the moment. The most efficient structural systemshave the least amount of detours possible. This will be discussed in moredetail in Lecture 37 andlater courses.
There are cases in which it is easier to calculate the moments of thecomponenets of a force around a certain point than it is to calculate themoment of the force itself. It could be that the determination of the perpendiculardistance of the force is more difficult than determining the perpendiculardistance of components of the force. The moment of several forces abouta point is simply the algebraic sum of their component moments about thesame point. When adding the moments of componenets, one must take greatcare to be consistant with the sense of each moment. It is often prudentto note the sense next to the moment when undertaking such problems.
CombinedMoments
Momentson a Beam
When adding the moments of componenets, one must take great care to be consistantwith the sense of each moment. It is often prudent to note the sense nextto the moment when undertaking such problems.
Frequently Asked Questions
Any difficulty with calculating a moment can usually be traced to one ofthe following:
- The center of moments has not been correctly established or clearly understood.
- The assumed moment arm is not the PERPENDICULAR distance between the line of action of the force and the center of moments.
- The direction, or sense, of the rotation has been ignored or misunderstood.
Questions For Thought
What is the moment about point B and about point D for both of the casesshown in the wrench example above? How could adding an extension to theend of the wrench help turn a rusted bolt? What kind of structural systemswould have the least number of 'detours?'
Problems
Moments In Women's
Associated Readings
Moment's Silence Lyrics
Shaeffer, R.E. Elementary Structures for Architects and Builders.pp. 33-39.
Copyright © 1995, 1996 by Chris H. Luebkeman andDonald PetingMoments Game
Copyright © 1996, 1997, 1998 by Chris H. Luebkeman