Torsion Confusion

[SteelPE]

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.

 

[Lion06]

If I remember correctly, Ipolar is the sum of Ix and Iy.

 

[rb1957]

but ... you've got a tube in torsion ... shear flow (around the section) = T/(2*[A]) where [A] is the area enclosed by the tube (mid-thickness plane if you want to fuss it). and shear stress = shear flow /t

don't forget about warping ...

 

[SteelPE]

In this particular instance I don’t think I need to be so accurate as to consider warping.

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.

 

[DaveAtkins]

I don't think there is any warping with a tube.

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

 

[SteelPE]

I'm looking for the maximum angle of rotation.

 

[Lion06]

A closed circular section has no warping, and a closed tube has very little warping, certainly not enough to make a difference in the strength (at least not that I've ever encountered in my experience).

 

[DHKpeWI]

J and Ip are not the same. The formulas is Design Guide 9 use J. I can provide documentation later. Do you have ShapeBuilder? You can download it for free. It provides values for J and Ip.

 

[miecz]

I've attached a PDF of an old worksheet that may help. This was for a cantilever with a concentrated torque. For a unifom torsion and a simple span, I would look at Design Guide 9.

 

[graybeach]

Do you have Blodgetts Design of Welded Structures? Table 2 on Page 2.10-4 says that theta = TL/(Shear Modulus * R), and R = 2*t*b^2*d^2/(b+d).

 

[letrab]

For a circular hollow section the Torsion constant J for pure torsion is 0.5 Pi*(R out^4 -R inner^4)
Calculate the angle of twist theta with the formula given by graybeach.
This is correct for pure St. Venant torsion

 

[BAretired]

Are we assuming the tube is circular? It might be, but I don't think the OP has said so.

BA

 

[SteelPE]

Sorry guys, I didn't say that the tube in question is a square tube HSS 2-1/2 x 2-1/2 x 1/4".

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.

 

[rb1957]

graybeach's and letrab's posts look like Ip = Ix+Iy (round or sq tubes)

 

[ash060]

Check the steel spec section H3 for information. They list the Ip for rounds and a different equation for rectangles. They call it the torsional shear constant, C (for both, C for rounds is Ip).

I think this is what you need to find the twist angle.

 

[BAretired]

The polar moment of inertia is not the parameter needed to find the twist angle of a rectangular tube. Check out membrane analogy.

BA

 

[SteelPE]

BAretired,

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.

 

[BAretired]

SteelIPE,

You are in good company. Navier made the same mistake. Attached is the expression for angle of twist for a rectangular HSS.

BA