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Beam calculator – central load

This is a free beam calculator, to be used to determine the deflection of a beam under central load. The beam is on a fixed bearing and a floating bearing, the load is located in the middle.

Some notes

Two tips and examples for converting units for the modulus of elasticity and the geometrical moment of inertia.

The E-Modulus of steel is 210000 N/mm² respectively 210 GPa.

The area moment of inertia for an IPB-beam with a flange width of 100 mm according DIN 1025 is Iy = 167 cm4, this equals 1670000 mm4.

The deflection is calculated on the basis of the Bernoulli beam deflection.

If you are looking for section properties of I-beams, H-beams or similiar, try out the Profile Assistant. Or you can use the online calculation tools for mechanical properties of sections.

Example calculation

If we want to find the maximum acceptable load on the IPB section mentioned above, we can use the “deflection calculator for central load” to get the value by iteration (two steps). Let’s assume we want to allow a maximum deflection of l/200 and our beam length is l = 3000 mm. This means we have a maximum deflection of 15 mm.

The first approach is to type in the geometrical values and a guessed load of F = 1000 N. The result is a deflection of 1.60 mm. To get the maximum load we use the rule of three: 15 mm / 1.60 mm * 1000 N = 9375 N.

If we do the calculation again with the maximum load, the deflection calcutor gives a result of 15.04 mm. That’s close enough!