Simple Tension Question 1: Finding Forces and Direction with Two Rigid Rods

[mpassman]

1. Two light rigid rods of equal length are fixed to a wall at one end and to a particle, of weight P, at the other end, as shown in attachments. The angles marked are both 40 degrees. Find the forces through the rods and state whether they are tensive or compressive.




3. I'm just confused by the whole thing. I know it's simple and I should be able to do it, but working out which direction the forces are acting is hard. I'm fairly sure both tensions are equal and that the lower one is in compression. So resolving vertically would give
2tcos45 = P ?


Thanks in advance for any help.

 

[FedEx]

Welcome to the forums.

Now is the angle 40 or is it 45.Second thing, try to draw a free body diagram.

The weight of the particle is acting downward. Now resolve the tension in both the rods.The system is in equlibrium.This is the key idea.

And what do you mean by the lower and the upper rods.

 

[TVP45]

Did you leave something out? How do you know there is no bending moment?

 

[FedEx]

Did you leave something out? How do you know there is no bending moment?

The rods are fiwxed at the wall and they both are inclined at the same angle and hence i don't think that they are in motion.

 

[mpassman]

Sorry, yes the angle is 45.
This is a statics question.

If the tension is equal both, and it is shown by T, is it correct, by resolving vertically to say that 2T*Cos45=P?

 

[TVP45]

"hence i don't think that they are in motion"
I agree they are not in motion; that is not what is meant by a bending moment. Depending on how the ends of these rods are attached, this can be an indeterminate problem. However, if we assume the questioner knew next to nothing about mechanics, then we can treat the rods as transmitting colinear forces. To be clear, all three joints should be free to rotate in the plane of the rods.

There is a fairly simple way to convince yourself of which way the forces act. Get a couple popsickle sticks and a couple pieces of string. Using the popsicle sticks, make a model of this problem, using any small weight hanging down. Connect all ends with a small hole and a bent paper clip, or something like that. Then try replacing each popsicle stick with a piece of string. If you can use string, it was in tension; if not, it was in compression.

 

[FedEx]

Sorry! It is bending moment i misunderstood it as bending movement in a hurry.And by the way for the example which you have given i feel it is not a correct demonstration. The strings will fall down to their own masses. We have to consider massless rods and hence massless strings.

 

[TVP45]

Actually, the example works very well. I've built fairly complicated trusses using this technique. The only "trick" is that the hanging down mass p should weigh at least 10 times what a popsickle stick does. You will not get extremely accurate tension or compression values with this technique but you will get the correct distinction between tension and compression.
Try it. A good starting project is a simple kingpost bridge truss.

 

[PhanthomJay]

1. Two light rigid rods of equal length are fixed to a wall at one end and to a particle, of weight P, at the other end, as shown in attachments. The angles marked are both 40 degrees. Find the forces through the rods and state whether they are tensive or compressive.




3. I'm just confused by the whole thing. I know it's simple and I should be able to do it, but working out which direction the forces are acting is hard. I'm fairly sure both tensions are equal and that the lower one is in compression. So resolving vertically would give
2tcos45 = P ?


Thanks in advance for any help.

While your solution may be correct in magnitude, it does not give you tension vs. compression info. Also, please show your work, you may have your sines and cosines mixed up, and you may not be properly applying Newton's law, I can't tell because of the symmetry and 45 degree angle used in this problem. In general, you need to isolate the joint at the load P,and apply Newton 1 in the x and y directions. If the member force points in toward the joint, it is in compression; if it points away from the joint, it is in tension. Using the string and popsicle stick model described above is helpful. Or try to visualize that the upper rod is being pulled (tension) while the lower rod is being squeezed (compression).