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expression to calculate the twist angle of hollow-box beams under torsional loads

expression to calculate the twist angle of hollow-box beams under torsional loads

expression to calculate the twist angle of hollow-box beams under torsional loads

(OP)
Hello All,

I am doing some calculations, and I am calculating the torsional deflection of an internally reinforced rectangular section hollow-box beam. After looking at some websites and books, I have found that the twist angle is: T*L/(J*G), where
T is the torque
L is the length of the beam
J is the polar inertia moment
G is the Transversal Elasticity Modulus


However, I also found another expression:

(Mt*lt*L)/(4*G*A0^2*t)
where

Mt is the torsion moment
lt is the mean line perimeter
L is the length
A0 is the mean line area
t is the thickness
G is the Transversal Elasticity Modulus


Does anyone know the validity of each of these equations: Type of support, type of section. And what expression shall I use for a thin-walled, but reinforced beam of arbitrary section?

regards,
Miguel Silva, MSc.

RE: expression to calculate the twist angle of hollow-box beams under torsional loads

use the 2nd one, for closed thin walled sections.

Quando Omni Flunkus Moritati

RE: expression to calculate the twist angle of hollow-box beams under torsional loads

What rb said. The first equation is only valid for round bars, for any other shape the "J" is replaced by a value called "K", the torsional stiffness constant - see Roark's.

RE: expression to calculate the twist angle of hollow-box beams under torsional loads

What do you mean by "internally reinforced"? If the reinforcements add to the torsional stiffness then the above equations would be off by a bit.

RE: expression to calculate the twist angle of hollow-box beams under torsional loads

Even the second equation has problems. It may work for well behaved sections, reentrant sections and the like, not so much. If your section is reasonably regular then I am sure that Roark will cover it.

Cheers

Greg Locock


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