What Is Moment? How Is It Calculated? Moment Lesson

For a moment to occur, the line of action of the force acting on the body must pass outside the pivot point. Otherwise no moment occurs.

We observe that at point (A) the door closes easily when pushed with force F1, rotating around the hinge. At point B it’s a bit harder, at point C it’s even harder, and at point D (the hinge point itself) we find that no matter how hard we push, we can’t close it at all.

The reason is that the highest moment occurs at point A. Even though the magnitude of the force is the same, the moment arm (distance to the hinge) is at its maximum at point A.

A system formed by two forces that are opposite in direction, parallel to each other, and equal in magnitude is called a “couple.”

A couple, as long as its elements and value stay constant, can be replaced by another couple.

A couple can be shifted to another location within its own plane. A couple can also be moved to a different plane parallel to the one it’s in.

Elements that carry a load in a horizontal position are called beams, and the systems that carry those beams are called supports.

Pinned support: fixed by a pin, it cannot move in the x or y direction. Consequently, it can carry two forces, along the x and y axes.

At the supports, opposing forces (reactions) arise according to how the beam is being acted on.

Under the basic principles of statics, action = reaction.

The directions of the reactions Ax and Ay can initially be chosen arbitrarily, or in either direction. If solving the equations ΣFx = 0 and ΣFy = 0 gives a positive (+) value, the direction was chosen correctly.

Roller support: since it can slide, it can only carry a load in the vertical direction.

Depending on how it’s acted on;
if a force comes in the x direction, the beam slides and the system’s equilibrium is disturbed. A vertical reaction Ay occurs.

A fixed support is supported at one end while the other end is free; since it prevents rotation as well as translation from where it’s fixed, reactions Ax, Ay, and M all occur.

Since the cylinder is perpendicular to plane N, force F cannot directly produce a turning effect.

The component of force F that’s parallel to (or lying in) plane N — that is, its projection — is what’s effective.

Moment = force x distance to the axis of rotation
M = Fx . r
M = F. cos α . r

Application problem: The nut shown in the figure is being tightened with an open-end wrench. Find the resulting moment.

Solution:
M = force . moment arm
M = F . r   
M = 200 . 0.3
M = 60 Nm

The forces acting on the pulley shown, which has a diameter of D = 500 mm, are shown in the figure. Find the resulting moment.

Solution: since both forces act in the clockwise direction, we add the effects of the forces together to find the total moment.

∑M = 100 . 0.25 + 100 . 0.25
∑M = 25 + 25
∑M = 50 Nm

Application problem: The system shown in the figure is in equilibrium. Find the force the cube exerts on the system.

cos 70⁰ = 0.342      sin 70⁰ = 0.94 

Solution:
∑MA=0
-G .2 – 8000 . 3 + 30000.sin70 . 4.5 =0
-G .2 – 24000 +30000 .0.94 . 4.5 =0
24000 +126900 = 2 G
102900 = 2 G
G = 51450 N

Problem: For the reaction at support B of bar AB, which is connected at point A with a frictionless pin, to be 600 N, how far from end A (x = ?) must a force of 1000 N be applied?

Problem: In the pinned lever arm system shown in the figure, what is the value of force F1?

Solution:  From the equation ∑ MA = 0
F1 . 400 – 100. 160 = 0
F1 .400 – 16000 =0
F1 .400 = 16000
F1 = 16000 / 400
F1 = 40 N