How to use the beam calculator
- Pick the support type and load from the pictures.
- Enter the modulus of elasticity E and the moment of inertia I. For I of a built-up or unusual shape, use the cross section calculator.
- Enter the load and the dimensions shown in the picture. The picture redraws to scale.
- Set a point of interest x to read the values at a particular spot, such as under a post.
Typical modulus of elasticity
| Material | E (ksi) | E (kPa) |
|---|---|---|
| Structural steel | 29,000 | 200,000,000 |
| Aluminum alloys | 10,000 | 69,000,000 |
| Normal-weight concrete, 4,000 psi | 3,600 | 25,000,000 |
| Douglas fir-larch lumber | 1,600 to 1,900 | 11,000,000 to 13,100,000 |
| Southern pine lumber | 1,400 to 1,800 | 9,700,000 to 12,400,000 |
Sign convention
Deflection is positive downward, the way beam tables usually give it. Bending moment is positive when the beam sags (tension on the bottom), so a cantilever's moment comes out negative. Shear is the rate of change of the moment along the beam, which makes the shear at the left end of a simply supported beam equal to the left reaction.
Questions
Does it include the beam's own weight?
No. Add the self weight to a uniform load q. In US units that's pounds per foot ÷ 12,000 to get kips per inch.
Why kips and inches?
Steel properties are tabulated in inches, so keeping every input in inches avoids mixing feet and inches. Switch to metric for meters and kilonewtons.
Can I combine two load cases?
Yes, for a linear elastic beam you can add the results of two cases on the same beam at the same x. For anything more involved, the shear and moment diagram tool takes any mix of loads.