Why Does Moment Act Perpendicular to Force?

[paddles069]

Hi all, please view the file I have attached which contains the diagram of the question. The picture is a cross section of a cantilever beam in which a force is applied downwards at the tip of the beam, as shown in the upper diagram. The solutions then conclude that the moment is acting in a perpendicular direction to the force, as shown in the bottom diagram. Why is this?

Thanks!

 

[SteamKing]

Think about what the vector r x F means in terms of its components.

As a memory aid: i j k | i j which means: i X j = k; j x k = i; k x i = j
got a right-hand coordinate system.

 

[Jupiter6]

That moment has nothing to do with that force. That looks like half of an illustration to draw stress squares and Mohr's circles. Where did you get that? What is it supposed to mean?

 

[nvn]

The solutions then conclude that the moment is acting in a perpendicular direction to the force, as shown in the bottom diagram. Why is this?

paddles069: The 10 kN force is applied at the cantilever tip, 10 m from the fixed support. Therefore, the bending moment at the fixed support is M = (10 m)*(10 kN) = 100 000 N*m, which is a twisting force about (around) an axis perpendicular to the applied force, and perpendicular to the moment arm.

By the way, straight moment vectors should always be drawn with a double arrowhead (not a single arrowhead). However, if the moment vector is normal to the page, then the moment symbol should be drawn curved, with a single arrowhead.

 

[DeeNos]

I can explain the reason behind the perpendicular direction of the moment acting on the cantilever beam. This phenomenon is governed by the principles of mechanics and is known as the "right-hand rule."

The right-hand rule states that when a force is applied at a point on a body, the resulting moment will act in a direction perpendicular to both the force and the line connecting the point of application to the pivot point of the body. In this case, the pivot point is the fixed end of the cantilever beam.

In the upper diagram, the force is acting downwards at the tip of the beam, and the point of application is the tip itself. The line connecting the tip to the pivot point is vertical, and the force is also acting in a vertical direction. According to the right-hand rule, the resulting moment will act in a direction perpendicular to both the force and the line connecting the tip to the pivot point. Hence, the moment will act in a horizontal direction towards the right, as shown in the bottom diagram.

This perpendicular direction of the moment is essential in balancing the force applied at the tip and preventing the beam from bending or breaking. If the moment acted in the same direction as the force, it would increase the bending effect and potentially cause the beam to fail.

In summary, the perpendicular direction of the moment acting on the cantilever beam is a result of the right-hand rule, which is a fundamental principle in mechanics. Understanding this concept is crucial in analyzing and designing structures to ensure their stability and safety. I hope this explanation helps clarify the reason behind the perpendicular moment in this scenario.