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?

  • 1
    $\begingroup$ Welcome to Engineering! This looks like a "homework question" (notice the quotation marks). In order for such questions to be answered in this site, we need you to add details describing the precise problem you're having. What have you tried to solve this yourself? Please edit your question to include this information. $\endgroup$ – Wasabi Aug 24 '16 at 10:22
  • $\begingroup$ What do you mean when you say "break"? Do you mean shear? Bending stress that takes the material to plastic deformation? $\endgroup$ – Chuck Aug 24 '16 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.

  • $\begingroup$ Thank you for your answer, what is the maximum weight this beam can handle ? $\endgroup$ – denis Aug 24 '16 at 10:40
  • $\begingroup$ @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). $\endgroup$ – Wasabi Aug 24 '16 at 10:44
  • $\begingroup$ 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. $\endgroup$ – Rob GT Aug 24 '16 at 11:02
  • $\begingroup$ I wanted to know what can i do to reinforce the beam so it can hold this kind of load ? $\endgroup$ – denis Aug 24 '16 at 13:09
  • $\begingroup$ 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. $\endgroup$ – Rob GT Aug 24 '16 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.


Not the answer you're looking for? Browse other questions tagged or ask your own question.