# Maximum deflection of a beam, fixed in one end and concetrated load at free end [closed]

A 2 m long beam fixed in one side with a 2000 kg concentrated load at free end. Profile of the beam is HEB100 material S235.

I would like to know if the beam will break under this load. If yes, what is the maximum load it can handle and how do you calculate it?

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– Wasabi
Aug 24, 2016 at 10:22
• What do you mean when you say "break"? Do you mean shear? Bending stress that takes the material to plastic deformation? Aug 24, 2016 at 15:34

Bending moment at the fixed end for a cantilever with point load at free end is given by: $PL$ where $P$ is the concentrated load and $L$ is the beam's length.

$$M = 2000\ \text{kg} \cdot \dfrac{0.01\ \text{kN}}{1\ \text{kg}} \cdot 2\ \text{m} = 40\ \text{kNm}$$

The maximum stress is $\sigma = \dfrac{M}{Z}$, where $Z$ is the section modulus ($Z = \dfrac{I}{y}$). $$\sigma = \frac{40\ \text{kNm}\times10^6}{89.9\ \text{cm}^3\times10^3} = 444\ \text{N/mm}^2$$

This stress is well above the the yield of the beam and it will deform plastically.

In fact, it is above the plastic yield too, so it will break.

This doesn't account for lateral torsional buckling because the further calculation is only required if the beam passes this simple test.

• Thank you for your answer, what is the maximum weight this beam can handle ? Aug 24, 2016 at 10:40
• @denis that is easily found by working backwards with the equations presented. Get the steel's maximum allowable stress and use that to find the maximum allowable bending moment, from which you can then find the maximum allowable force. Also, this answer doesn't take into consideration things like factors of safety which must always be used in real applications (which is fine for this answer since insufficient information was given to include factors of safety).
– Wasabi
Aug 24, 2016 at 10:44
• Except you will need to account for lateral torsional buckling which reduces the capacity of the beam. Also, this does not have any safety factors in it either. Aug 24, 2016 at 11:02
• I wanted to know what can i do to reinforce the beam so it can hold this kind of load ? Aug 24, 2016 at 13:09
• As the applied stress is double the stress capacity, you could look at adding another beam of the same type. However, we are not here to provide design services so you would be best places to seek a professional engineer. Aug 24, 2016 at 13:11

To know whether the beam will break or not, you need to calculate the maximum stress in it and compare it to the maximum stress that your material can bear. For S235, it will be most likely 235MPa.

In your case, the maximum stress is located in the section where the beam is fixed. If it breaks, it will break there. To calculate it, start by calculating the bending momentum $M$ in this point then calculate the stress using $\sigma = \frac{M*y}{I}$ where $I$ is the section modulus. It should be given for your HEB100. And $y$ is the half the height of the beam.

Once you have the maximum stress in your beam, compare it to 235MPa.