Formula for Uniform Torque
Formula for Uniform Torque
(OP)
I am working on a simple beam (L = 60 ft) with uniform Torque of say + 20 ft-k/ft. I am trying to find the torque at the pinned supports but I have not really found a reference for that.
I was trying to apply the same concept as a uniform load, but I am not sure if that is applicable. I was thinking that I would have a total torque of (20 ft-k/ft)(60 ft) = 1200 ft-k.
I also I am not sure if one reaction will take 0 Torque and the other reaction 1200 ft-k of torque. OR both take 1200 ft-k/2 = 600 ft-k of torque and in opposite direction.
Appreciate your feedback and comments on What Is the Proper way of distributing the torque to the reactions.
THANKS
I was trying to apply the same concept as a uniform load, but I am not sure if that is applicable. I was thinking that I would have a total torque of (20 ft-k/ft)(60 ft) = 1200 ft-k.
I also I am not sure if one reaction will take 0 Torque and the other reaction 1200 ft-k of torque. OR both take 1200 ft-k/2 = 600 ft-k of torque and in opposite direction.
Appreciate your feedback and comments on What Is the Proper way of distributing the torque to the reactions.
THANKS






RE: Formula for Uniform Torque
If one end is free (torsionally) and the other fixed, then 100% goes to the fixed end in a triangular diagram.
RE: Formula for Uniform Torque
I don't think either source addresses the reactions at the supports. I think you can decide how to apply the reactions, if you account for it in your detailing, much as you would ordinary reactions. For example, I've detailed a beam connection at one end with flange restraints (torsionally "fixed"), while leaving the other end "simple". I'd like to hear other people's thoughts.
RE: Formula for Uniform Torque
dealing with 1.2M ft.lbs. of torque, i'd hope that both ends of the beam can react torque. you'll have to be carefull with deflections too
RE: Formula for Uniform Torque
RE: Formula for Uniform Torque
RE: Formula for Uniform Torque
However, when it comes to the internal distribution of stress within the rod, warping and deflections are completely different. Warping and rotation are different displacements. As mentioned above, an I-shape may be approximated as two flanges acting to produce a resisting torque equal to the applied torque. This neglects the contribution of the shape acting as a rod without the warping, which is probably not too severe a compromise. With both ends of the flange restrained, it will produce an internal stress analagous to a fixed-fixed beam loaded with a uniform load. This is the fully restrained condition. If only one end is restrained it will act as a cantilever beam. The other condition, the one which permits warping, produces a condition analagous to a pinned support. With both ends restrained against rotation but free to warp, the flange will have an internal stress similar to a pinned-pinned beam. With one end torsionally fixed and the other end torsionally pinned, you will have a stress distribution in the flange similar to a propped cantilever beam.
This subject gets very confusing quickly (and I probably haven't helped) but comes up all the time. Good Luck
RE: Formula for Uniform Torque
Obviously if you have torsion you can't have a pinned-pinned connection in the usual sense because that would be unstable. Torsionally pinned is a connection which can resist torsion but does not restrain the member from deforming at the joint. One example of this would be a wide flange with a double-angle bolted connection to a column. The bolts can resist the torsion but the gap between the beam and the column allows the beam to deform by twisting. Torsionally fixed would mean basically the beam is welded to the column. Then the section next to the column cannot deform relative to the column.
RE: Formula for Uniform Torque
Also, does this apply to multi-span beam, so I still cannot apply torsion to say a 7 span beam with all pin connections?
THANKS, I really appreciate your feedback in helping me understand this concept.
RE: Formula for Uniform Torque
Secondly, the multi-span condition you describe where vertical loads are resisted via positive and negative moments means there is a level of fixity at the end supports of each of the 7 spans. Sometimes (many times?) the type of connection and/or fixity that is detailed to create a continuous span in-and-of-itself creates torsional restraint. Not always, but sometimes.
Lastly, if you use a wide-flange beam or channel, then the torsional rigidity of the section is very very low and very large torsional twists may occur which are not desired in any structure. Closed sections such as tubes or pipes are many times more torsionally rigid.
RE: Formula for Uniform Torque
1. I obtained all the forces about the center of the beam, so I have a beam with a vertical downward force, a horizotal force and a moment per ft.
2. Say my beam is 800 ft, I am thinking of putting piles at say 10 ft, which I plan to model as pin or fixed supports, this is something I am still looking at.
3. From my downard vertical force per feet (uniform), I am going to obtain a vertical reaction at each support. Plus a moment pointing in the horizontal direction.
4. From my horizontal force per feet (uniform), I am going to obtain a horizontal reaction at each support. Plus a moment pointing in the vertical direction.
5. My moment per feet (uniform), is actually a torque on the beam, and I am trying to find the reaction of that torque on the support.
So basically I am trying to transfer all the loadings on a multi-span beam to piles. From these loadings I envision a pile with vertical, horiztonal loadiding and biaxial bending and torque.
Hope this is not that confusing, appreciate your feedback.
THANKS
RE: Formula for Uniform Torque
If you have a load case where there is substantial influence on the piles due to torque, that would be unusual. Remember the pile group will also act to resist some torsional imbalance in the applied load.
Problems of this sort have caused me to reflect on the relative fixity of the top of the pile to the footing of the wall (is it pinned, fixed or something in between, and if it is in between ... how do I create a mathmatical model to capture it) and the interaction between the soil and pile to predice shear and bending in the pile accurately (or at least reasonably conservatively).
Good Luck.
RE: Formula for Uniform Torque
For item 3, I would not consider a moment acting in the horizontal direction acting on the piles. Although there is some moment, it is proportional to the rotation of the wall about a horizontal axis at the top of the pile. This is a small rotation and I believe it may be neglected.
Similarly for item 4, I would not consider a moment acting in the vertical direction acting on the piles. Although there is some moment, it is proportional to the rotation of the footing about a vertical axis at the top of the pile. This is a small rotation and I believe it may be neglected.
For Item 5, the nearly all of the overturning moment is taken by a couple between your rows of piles (if you have 2 rows). I believe you can ignore any small moment transferred to the top of the piles at the connection.