Beams find many uses in construction and machinery. Beams must be strong and flexible enough to support huge amounts of weight in sometimes adverse conditions. One way to measure this flexibility is the torsional warping constant, which is the amount the geometry of a beam is deviated from it's standard geometry when acted on by a torsional force (that is, the twisting of an object). You can calculate this constant for a standard geometry in a few short steps.
Things You'll Need
- Pen or pencil
Multiply the torque applied to the beam by the beam length. For example, if a torque of 500 Newton meters (Nm) is applied to a beam 1 meter (m) in length, the product will be 500 Newton meters squared (Nm^2). Call this product result A.
Multiply the angle of the beam's twist (in radians) by the shear modulus of the material. As an example, assume a steel beam, with a shear modulus of 79.3 gigapascals (GPa) is twisted by 0.2 radians. The product of these two numbers is 15.86 GPa. Call this result B.
Divide result A by result B. In our example, dividing 500 Nm^2 by 15.86 GPa (15 times 10 to the 9 Pa, or 15 x 10^9 Pa) gives 3.15 times 10 to the negative 8 (3.15 x 10^(-8) ). This dimensionless number is the torsional warping constant.
Tips & Warnings
- This method applies to a beam of uniform cross-section across it's length. For other geometries, this equation may not apply.
- "Roark's Formulas for Stress & Strain, 6th Edition"; Warren C. Young, 1989
- Photo Credit pile of l-beams image by Mikhail Tischenko from Fotolia.com
How to Calculate Torsion Constant
The torsional constant is a physical property of a material. It is most commonly used to describe metal beams and is denoted...
How to Calculate Torsion Bar Rates
Torsion bars function as springs in off-road vehicles and some sprint cars. They are connected to the base of the vehicle, and...
How to Calculate Maximum Torsion in a Round Bar
Round bars, otherwise known as shafts and axles, transmit torque and rotational power as well as carry radial and thrust loads when...
How to Calculate Wooden Beam Spans
The distance over which a wood beam bears a load when used for support is its span. The span of any wood...
How to Calculate Forces Acting on Beams
Beam equations are an essential part of mechanics and a great way to hone your math and physics skills. The ability to...