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.