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Torsion Confusion

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.
 

RE: Torsion Confusion

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

RE: Torsion Confusion

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 ...

RE: Torsion Confusion

(OP)
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.
 

RE: Torsion Confusion

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

RE: Torsion Confusion

(OP)
I'm looking for the maximum angle of rotation.

RE: Torsion Confusion

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).

RE: Torsion Confusion

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.

RE: Torsion Confusion

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).

RE: Torsion Confusion

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  

RE: Torsion Confusion

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

BA

RE: Torsion Confusion

(OP)
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.
 

RE: Torsion Confusion

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

RE: Torsion Confusion

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.

RE: Torsion Confusion

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

BA

RE: Torsion Confusion

(OP)
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.
 

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