Calculating Torque T & Q for I-Beams & Torsion

[Fantastic Fox]

You have two parallel I-beams. A trolley with 4 wheels runs on top, and carries a total load of say 10kN. How would you evaluate the torsion?

angle theta = TL/GK
where (for an I beam) K = [2bt^3 + (d - 2t)(thickness of web)^3] / 3
and t = thickness of flange
But, how would you calculate the torque T?
Say if the beams were 1m apart, if torque was simply 10kN x 0.5m, then the beam would roll over.


For the equation; tau = T/Q
how do you calculate Q for an I beam?

 

[FredGarvin]

This isn't an easy question to answer. If you are running a trolley on an I-beam, that would mean, most likely, that the beam is set on the ground, effectively constraining the bottom flange from any deflections. That means all of the deflections will be in the web and the upper flange. Combined with multiple point loads, off the top of my I'd say you really need a numeric solution. Then again, I don't have a copy of Roark's in front of me right now to see if this type of problem has a general solution already formulated. You could simplify it to have one point load at the center of the two beams, but you're still in a tough spot.

 

[oswaler]

To calculate the torque T, you would need to know the distance between the two parallel I-beams. This distance, along with the load of 10kN, would allow you to calculate the moment arm of the load. The moment arm is the perpendicular distance from the axis of rotation (in this case, the center of the I-beams) to the applied force. The equation for torque is T = F x d, where F is the applied force and d is the moment arm.

To calculate Q for an I-beam, you would need to know the moment of inertia of the cross-section of the beam. This can be calculated using the dimensions of the flanges and web of the I-beam. The equation for the moment of inertia of an I-beam is I = (1/12)bh^3 + (1/12)bd^3, where b is the width of the flange, h is the height of the flange, and d is the depth of the web. Once you have the moment of inertia, you can then calculate Q using the equation Q = I/G, where G is the shear modulus of the material.

To evaluate the torsion, you would need to compare the torque T to the maximum allowable torque for the I-beam. This maximum torque can be calculated using the ultimate strength of the material and the cross-sectional area of the beam. If the calculated torque is greater than the maximum allowable torque, then the I-beam would experience torsional failure and potentially roll over. If the calculated torque is less than the maximum allowable torque, then the I-beam would be able to withstand the torsional forces from the trolley and load.