Torsion Confusion
Torsion Confusion
(OP)
I am having a tough day today.
I have a tube that is subjected to uniform torsion. Currently I am figuring the supports to be fixed. Going back to my mechanics of materials book I find that T=G*Ip*[d(phi)/dx]. To find the twist I just have to write the torsion equation and integrate (simple enough). The problem I have is finding Ip. This problem is further complicated by the book saying that Ip (the polar moment of inertia) can sometimes be confused with J. This is what has me confused now. How do I find Ip?
This should be simple and it's not aaarrrggghhh.
I have a tube that is subjected to uniform torsion. Currently I am figuring the supports to be fixed. Going back to my mechanics of materials book I find that T=G*Ip*[d(phi)/dx]. To find the twist I just have to write the torsion equation and integrate (simple enough). The problem I have is finding Ip. This problem is further complicated by the book saying that Ip (the polar moment of inertia) can sometimes be confused with J. This is what has me confused now. How do I find Ip?
This should be simple and it's not aaarrrggghhh.






RE: Torsion Confusion
RE: Torsion Confusion
don't forget about warping ...
RE: Torsion Confusion
AISC design guide 9 has T=GJ (phi)' this would lead me to believe that in the AISC steel manual J=Ip, frustrating. Using J=Ip I calculate my twist to be approx 0.0023 radians quite small in this instance.
RE: Torsion Confusion
Are you trying to find the twist, or the shear stress? Because if you just need to know the shear stress, use the formula rb1957 listed.
DaveAtkins
RE: Torsion Confusion
RE: Torsion Confusion
RE: Torsion Confusion
RE: Torsion Confusion
RE: Torsion Confusion
RE: Torsion Confusion
Calculate the angle of twist theta with the formula given by graybeach.
This is correct for pure St. Venant torsion
RE: Torsion Confusion
BA
RE: Torsion Confusion
I just find it confusing that J does not equal Ip but then they use the term J my AISC design guide #9. Unfortunately the equations graybeach and miecz provided do not agree. I was calculating .0023 radians of deflection which was approx 1/64" where the load was being applied. Even if my use of J in the equation is wrong how much more rotation could I expect... 2x the calculated deflection (1/32")? I can live with 1/64" additional deflection due to torsion. Now, if I could only get the fabricator and erector to adhere to such tolerances.
RE: Torsion Confusion
RE: Torsion Confusion
I think this is what you need to find the twist angle.
RE: Torsion Confusion
BA
RE: Torsion Confusion
My mechanics of materials book lists the following equation:
T=G*Ip*[d(phi)/dx]
Therefore to get the phi (what I am calling the angle of twist) you have to integrate the following equation:
[d(phi)/dx]=T/(G*Ip)
Maybe I have no idea what I am doing.
Interestingly enough shapebuilder lists Ip=3.844 for this particular section which is very close to the Blodget number.
RE: Torsion Confusion
You are in good company. Navier made the same mistake. Attached is the expression for angle of twist for a rectangular HSS.
BA