# Expression for Torsion Constant of Varying Thickness Box Section

• Engineering01
In summary, the conversation revolves around finding an expression for the torsion stiffness constant of a rectangular hollow section with varying wall thicknesses. The person has done some research but has not found any resources or proofs for four varying thicknesses. It is suggested that a torsional shear analysis can be done on the section if the wall thicknesses are considered "thin" in relation to the section's dimensions. A link is provided for more information on the calculation.
Engineering01
Hello Everyone,

I am after an expression for the torsion stiffness constant of a rectangular hollow section (RHS) with varying wall thickness. I have done some research into finding an expression that allows for four varying wall thicknesses but have not found anything as of yet. The only expressions that are published are of RHS's with two varying thicknesses (Roark's 7th ed, Wiki etc).

If anyone could point me to a resource or present a proof I would greatly appreciate it.

Attached is a sketch of the general shape (excuse the huge image).

Thanks.

Last edited:

## 1. What is the expression for the torsion constant of a varying thickness box section?

The expression for the torsion constant of a varying thickness box section is given by:
C = ∫(t^3)dA
Where t is the thickness of the section and A is the area enclosed by the section.

## 2. How is the torsion constant affected by varying thickness in a box section?

The torsion constant is affected by varying thickness in a box section as it takes into account the change in thickness throughout the section. The thicker portions of the section will have a greater contribution to the torsion constant compared to the thinner portions.

## 3. Can the torsion constant be calculated for any shape of box section?

Yes, the torsion constant can be calculated for any shape of box section as long as the thickness of the section remains constant along its length.

## 4. How is the torsion constant used in engineering applications?

The torsion constant is used in engineering applications to determine the torsional stiffness of a structure. It is also used in the design of various structural components such as beams, columns, and shafts to ensure they can withstand torsional forces.

## 5. Is the expression for the torsion constant of varying thickness box section applicable to both symmetric and asymmetric sections?

Yes, the expression for the torsion constant of varying thickness box section is applicable to both symmetric and asymmetric sections. However, for asymmetric sections, the torsion constant will be different for clockwise and counterclockwise torsional loading.

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