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# Beam calculator - beam with excess length under single load

This is a free beam calculator. Data about sections and further bending specific parameters can be found in the profile assistant.

Calculate the deflection of a beam with excess length under single load.

## Example deflection calculation

A beam with a span of 3 m and a protruding end of 1 m should support a unit with a weight of 5 t, which is attached to the outside of the beam. The deflection of the beam should be limited to 1/200. The beam should be made of steel.

The Young's modulus for steel is 210 GPa (or 210,000 N / mm²), the resulting weight load of the unit is simplified to 10 m/s² * 5,000 kg = 50 kN.

The values ​​are entered into the deflection calculator. The moment of resistance against bending (section modulus) is not relevant for this first estimate; the value for the area moment of inertia is assumed to be 10,000 cm4.

The result for the deformation between the supports is f = 1.37 mm and for the deformation at the free end of the beam 3.17 mm.

The first estimate was very close to the target size of 1000mm / 200 = 5mm. The required geometrical moment of inertia is now adjusted by the rule of three to 10,000 cm 4 / 5 mm * 3.17 mm = 6,340 cm 4 and the calculation is carried out again - and now results in a deflection of 5.01 mm at the free end of the beam.

With this value the profile assistant can be called.

The profile assistant now searches for suitable steel beams with a tolerance of ± 20%. For the case just calculated, 6 suitable profile types are output, e.g. an IPE A 300 or an HE 180 M could be used.

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