Is the force in a tilted beam affected by the angle of tilt?

[megavolt818]

If I have a beam tilted at an angle with a weight hagning off of one end and it is fixed on the other (see attachment), my teacher says that I need to resolve the force to find the force in the beam. However, it does not make sense to me that the force in the beam increases as the angle decreases. At an angle of 1 degree the beam has a very large internal force that "goes away" once the angle becomes zero. The way I am determining the force in the beam is: since the weight creates a force in the y-direction the force in the beam is the weight divided by the sine of the angle. This just doesn't sense. What am I missing?

 

[Studiot]

Your post seems a trifle muddled.

You say that you are calculating a force that equals a constant divided by the sine of an angle.
Yet you also express surprise that the calculation grows yields an increasing result as the angle decreases.

Since the sine is always less than 1 and decreases with decreasing angle why is this suprising?

I am not sure how you are modelling your beam.
Have you considered any other load imposed on the beam as a result of the geometry, in particular have you considered moment equilibrium?

 

[megavolt818]

I understand that there will be a moment applied to this beam due to the weight hanging off the end.

It seems counterintuitive that the compression in the beam increases as the angle decreases. I know what the math shows; it just doesn't seem correct that at a 90 degree angle the compression would be 100 lbs (assume the weight is 100 lbs), but at an agle of 1 degree the compression would be 5729.8 lbs. 100 divided by sine of 1 degree. Am I truly solving for the compression in the member correctly? The compression increases by 57 times the original? In my mind the compression of the beam should decrease as the angle approaches 0.

 

[john.phillip]

Draw a free body diagram for the tip of the beam, decomposing W and check where is theta.

 

[alphy]

I would like to clarify that the force in a tilted beam is indeed affected by the angle of tilt. The internal force in the beam is a result of the weight hanging off of one end and the fixed support on the other end. The angle of tilt affects the distribution of this force along the beam.

At a smaller angle of tilt, the weight is more perpendicular to the beam and therefore creates a larger force along the beam. As the angle of tilt increases, the weight becomes more parallel to the beam and the force along the beam decreases.

Your method of determining the force in the beam by dividing the weight by the sine of the angle is correct. This is known as resolving the force into its components. However, it is important to keep in mind that this method gives you the force along the beam, not the internal force within the beam.

To determine the internal force within the beam, you will need to use equations that take into account the angle of tilt and the distribution of forces along the beam. This may be what your teacher is referring to when they say you need to resolve the force.

Overall, it is important to remember that the force in a tilted beam is affected by the angle of tilt and cannot be simply calculated by dividing the weight by the sine of the angle. It is a more complex phenomenon that requires the use of specific equations and considerations of different factors.