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

[silvamat]

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.

 

[rb1957]

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

Quando Omni Flunkus Moritati

 

[btrueblood]

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.

 

[BrianE22]

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.

 

[GregLocock]

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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