Bending Moment in two directions

[shauntur]

Not Really a homework question but it will help with how i go about the homework.

So i have a beam coming out of the wall and it has force acting on it like this:
Woops, that 20 on the side view should be a 10 :P

What i want to find is the total moment at the mid point. I know how to find the moment in each direction but I am not sure if I am aloud to add them together or use pythag??
heres my solution for each direction:

Can i just go sqrt(10^2+10^2) to give me 10?
Thanks
Shaun

 

[PhanthomJay]

Can i just go sqrt(10^2+10^2) to give me 10?
Thanks
Shaun

Hi Shaun, welcome to PF!
Moments are vectors and as such, have both magnitude and direction. So aside from the fact that sqrt(10^2+10^2) = 10(sq root 2) , its magnitude, there is a direction associated with the moment also (what is it?). Sometimes it is best to leave the moment in its component form...M = M_x + M_y.

 

[shauntur]

thanks heaps mate, probably shouldn't be doing engineering if i can't use pythag properly :tongue:
really appreciate ur help

 

[pongo38]

In your M diagrams, the horizontal one shows an assumed hinge at the wall, whereas the vertical one assumes moment-fixity. This may not affect your answer to the moment at midpoint of the beam.

 

[DeeNos]

I would first clarify that the concept of bending moment is a measure of the internal forces within a beam or structure that cause it to bend or deform. It is typically represented by the symbol M and is measured in units of force multiplied by distance, such as Nm or ft-lb.

In this scenario, it appears that the beam is being subjected to a force of 10 units in one direction and another force of 10 units in a perpendicular direction. To find the total bending moment at the mid point, we must consider the moments in both directions.

To answer your question, yes, you can use the Pythagorean theorem to find the total moment at the mid point. This is because the bending moments in each direction act perpendicular to each other, making them independent of each other. Therefore, we can use the Pythagorean theorem to find the total moment at the mid point, which would be √(10^2+10^2) = 14.14 units.

However, if the forces were not acting perpendicular to each other, we would need to use vector addition to find the resultant moment at the mid point. This involves breaking down the forces into their components and then adding them together using vector addition principles.

In summary, to find the total bending moment at the mid point, you can use the Pythagorean theorem if the forces are acting perpendicular to each other, but if they are not, you would need to use vector addition. It is important to always consider the direction and magnitude of the forces when calculating bending moments in a structure.