Forces and Moments MET 2214 Statics MET 2214

Forces and Moments MET 2214 Statics (MET 2214) Prof. S. Nasseri

Moments and Forces Part I Statics (MET 2214) Prof. S. Nasseri

What is a moment? ! A moment is a type of force. A moment is a turning force. A turning force happens when a force is applied to something which has a pivot Statics (MET 2214) Prof. S. Nasseri

What is a moment? pivot F r Statics (MET 2214) Prof. S. Nasseri

Some examples Two kids are sitting at the same distance apart and have the same weight, hence the moments are equal. Statics (MET 2214) Prof. S. Nasseri Knowing the weight of the bucket, you need to know what force to apply to bring the bucket up.

Moment of Force F around point O The moment of a force about a point or an axis (MO), provides a measure of the tendency of the force to cause a body to rotate about the point or axis. oz ┴ plane xy in which Fx lies. Fx causes the pipe to turn about the z-axis. Fx causes a moment about the z -axis = (Mo)z Statics (MET 2214) Prof. S. Nasseri

Moment of Force F around point O Fy passes through O. Fy does not cause the pipe to turn because the line of action of the force passes through O. NO moment!! Statics (MET 2214) Prof. S. Nasseri

Moment of Force F around point O ox ┴ plane zy in which Fz lies. Fz causes the pipe to turn about the x-axis Fz causes a moment about the x-axis (Mo)x Statics (MET 2214) Prof. S. Nasseri

Direction of Moment The direction of Mo would be specified by using the right hand rule. Counter Clockwise (CCW) is out of the page, Statics (MET 2214) Prof. S. Nasseri Clockwise (CW) is into the page.

Moment (Scalar or Vector? !) Moment is a vector and the direction is defined using right hand rule. Keep your fingers along the line of action of the force, and your thumb will be along the axis of the moment. M M r F F Statics (MET 2214) Prof. S. Nasseri r M

Magnitude of the Moment Magnitude of the moment is simply force times the perpendicular distance. Statics (MET 2214) Prof. S. Nasseri

Example If the force shown here is 2 lb, how much are the moments about A, B, C and D: Moment about A: 2 x 8= 16 lb. in Moment about B: 2 x 2= 4 lb. in Moment about C: 2 x 12= 24 lb. in Moment about D: 2 x 0= 0 lb. in Statics (MET 2214) Prof. S. Nasseri

Calculating the moment in 2 -D using components • Select a positive direction (CCW or CW), • Calculate each moment and add them, using the proper sign for each term, • Always remember to write the unit of moment which is Nm or lb. f. Statics (MET 2214) Prof. S. Nasseri

Calculating the moment in 2 -D using components Example 1: In the following figure, calculate the moment about the point O: 1. We choose the CCW as positive direction for moment, 2. Moment of component of F along x about O is Fx times the perpendicular distance from O (or d 1), which is clockwise, so it is 3. Moment of component of F along y about O is Fy times the perpendicular distance from O (or d 2), which is counter clockwise, so it is 4. Moments add together as vectors, so the total moment is: Statics (MET 2214) Prof. S. Nasseri

Calculating the moment in 2 -D using components Example 2: In the following figure, if is 60 degrees and r is 30 mm and F is 6 N, what is the magnitude of the moment about O. 1. We choose the CCW as positive direction for moment, 2. Component of F along r (or ) produces no moment, since it passes from point O. 3. Component of F perpendicular to r (or ) produces the moment So the total moment of F about O is: Statics (MET 2214) Prof. S. Nasseri

Calculating the moment in 2 -D using components Example 2: Remember: The moment about O is also calculated using the magnitude of force F times perpendicular distance from O to the line of action of F which is d: Statics (MET 2214) Prof. S. Nasseri Moving a force along its line of action does not change its moment!