St Venant's torsion constant

In summary, the calculation of St Venant's torsion constant involves solving a partial differential equation using advanced strength of materials methods. For thin-wall cross sections, approximate formulas and methods can be used, while for open sections commonly found in construction, there are specific formulas available. These formulas may not give exact values but are validated against measurements. For non-standard sections, a finite element model can be used. A recommended formula for open sections is J = bt^3/3, with a factor k to be multiplied for better accuracy.
  • #1
derryck1234
56
0
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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  • #2
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
 
  • #3
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:
 
  • #4
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
 
  • #5


Hello Derryck,

St Venant's torsion constant, also known as the warping constant, is a measure of a structure's resistance to torsion or twisting. It is an important parameter in structural engineering, especially for steel sections, as it helps determine the design and behavior of the structure under torsional loading.

To calculate St Venant's torsion constant, you will need to have the cross-sectional properties of the steel section, such as its area, moment of inertia, and section modulus. These can be obtained from the section's manufacturer or by using structural analysis software.

Once you have the cross-sectional properties, you can use the following formula to calculate St Venant's torsion constant:

C = (G * Iw) / L

Where:
C = St Venant's torsion constant
G = Shear modulus of elasticity of the material
Iw = Warping moment of inertia of the section
L = Length of the section

You can also find tables or charts that provide the values of St Venant's torsion constant for standard steel sections. However, for non-standard sections, it is best to calculate it using the above formula.

I hope this helps. Good luck with your calculations.

Best regards,
 

What is St Venant's torsion constant?

St Venant's torsion constant, also known as the torsion modulus or warping constant, is a geometric property of a cross section that measures its resistance to torsional stress.

How is St Venant's torsion constant calculated?

St Venant's torsion constant is calculated by taking the integral of the product of the cross-sectional area and the distance from the centroid to the point of interest squared, divided by the polar moment of inertia. This can also be expressed as the integral of the cross-sectional area times the square of the radius of gyration.

What is the importance of St Venant's torsion constant?

St Venant's torsion constant is an important parameter in the design of structural elements such as beams, shafts, and columns. It helps determine the level of torsional stress a cross section can withstand without failing.

What factors affect St Venant's torsion constant?

The main factors that affect St Venant's torsion constant are the cross-sectional shape, size, and material properties. The shape and size of the cross section can significantly impact the value of the torsion constant, while the material's elastic modulus and shear modulus also play a role.

Can St Venant's torsion constant be used for non-circular cross sections?

Yes, St Venant's torsion constant can be used for non-circular cross sections, as long as the cross section is symmetric about its centroid. However, in these cases, the calculation of the torsion constant may be more complex and may require numerical methods.

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