How Is St Venant's Torsion Constant Calculated for Non-Standard Steel Sections?

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Discussion Overview

The discussion focuses on the calculation of St Venant's torsion constant for non-standard steel sections, addressing both theoretical and practical approaches. Participants explore methods for determining this constant, particularly in the context of structural engineering applications.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that the calculation of St Venant's torsion constant (J) for arbitrary cross-sections typically involves solving a partial differential equation, often using finite element methods.
  • Another participant mentions that various approximate formulas exist for calculating J for thin-walled cross-sections, particularly in the context of aircraft or ship structures.
  • A suggestion is made to use specific formulas for open sections commonly found in construction, referencing an external article for detailed methods.
  • It is highlighted that the mathematical notion of a torsion constant is an approximation, especially for complex shapes, and that values in structural steel tables may be validated against experimental measurements.
  • One participant proposes a specific formula for open sections, indicating that it provides a good approximation under certain conditions, while cautioning that the formula may not hold when the ratio of dimensions is not favorable.
  • Another participant suggests creating a finite element model to determine the torsion constant for non-standard sections if existing formulas do not apply.

Areas of Agreement / Disagreement

Participants express varying views on the methods for calculating the torsion constant, with some advocating for theoretical approaches and others suggesting practical modeling techniques. No consensus is reached on a singular method for all non-standard sections.

Contextual Notes

Limitations include the dependence on specific assumptions regarding cross-section shapes and the applicability of various formulas, which may not be universally valid for all geometries.

derryck1234
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Hello

I am a Junior Structural engineer and need to know how St Venant's torsion constant is calculated. It appears in structural steel tables, but without knowing how to calculate it, I cannot find its value for non-standard steel sections.

Please, can somebody help.

Regards

Derryck
 
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This is a topic which is covered in advanced strength of materials courses. The general calculation of J for an arbitrary cross-section involves solving a partial differential equation, usually by means of a finite element method.

For thin-wall cross sections, various approximate formulas and methods have been developed to calculate J for closed and open sections. These methods are usually covered in texts dealing with aircraft or ship structures.

For open sections of the type usually found in construction, the formulas in the attached article may be used:

http://www.cisc-icca.ca/files/technical/techdocs/updates/torsionprop.pdf
 
This might help. http://www.cisc-icca.ca/files/technical/techdocs/updates/torsionprop.pdf

Bear in mind that the mathematical notion of a torsion constant is only an approximation to the real behavior of the object (except for circular sections) and the formulas for complicated shapes are approximate.

One might hope that the values quoted in structural steel tables for standard sections were validated against measurements, not just calculated theoretically, so don't worry too much the formulas don't give exactly the same values as the tables.

If the shape of your non-standard sections don't match any of the formulas, probably the easiest way would be to make a finite element model of a length of section, apply some loads to twist it, and find the displacements.

EDIT: That must be a good reference if two people recommended it independently :smile:
 
If you have an open section (e.g. I-beam, parallel flanged changed, equal angle i.e. with a closed flow of shear flows within the walls of a section) this formula will give you a good enough approximation:

J = bt^3/3 where b is the always the longer side. e.g. for a rectanngle

J = breadth * depth^3/3

For an I-beam or indeed other section you can simply add all the bt^3/3 i.e. for an I-beam,

J = (1/3)*(bTF*tTF^3+dweb*tweb^3 + bBF*tTF^3)

It should be noted that the formulaa begins to break down where b isn't >> t. To get a better approximate there are various tables that give you a factor k to multiply the torsion constant with that's a function of b/t
 

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