Average and standard deviation of the bending moment in the beams

[Erwin1998]

Hello all,


I have a question about determining the average and standard deviation of the following ( homework mathematics) :

Given: - a diverse number of beams
- the average length of a beam is 11 meters with a standard deviation of 0.5m
- the average bending moment with a beam of 11 meters 110 kn /m


Asked: Determine the mean and standard deviation of the bending moment in the beams.


How do I handle this to start? Which formula can I use for this?

 

[Erwin1998]

Hello all,


I have a question about determining the average and standard deviation of the following ( homework mathematics) :

Given: - a diverse number of beams
- the average length of a beam is 11 meters with a standard deviation of 0.5m
- the average bending moment with a beam of 11 meters 110 kn /m


Asked: Determine the mean and standard deviation of the bending moment in the beams.


How do I handle this to start? Which formula can I use for this?

I have calculated that the minimum bending moment is 105 kn / m. (beam L = 10.5 m)
And that the maximum bending moment is 115 kn / m. (beam L = 11.5 m)


How can I determine the average and the standard deviation of the bending moment? Because the assignment does not indicate how many beams there are.

 

[j-astron]

Hello all,


I have a question about determining the average and standard deviation of the following ( homework mathematics) :

Given: - a diverse number of beams
- the average length of a beam is 11 meters with a standard deviation of 0.5m
- the average bending moment with a beam of 11 meters 110 kn /m


Asked: Determine the mean and standard deviation of the bending moment in the beams.


How do I handle this to start? Which formula can I use for this?

Hi Erwin1998, welcome to the forum.

It's been a while since I've had to think about bending moment (Introductory Mechanics, basically). But having researched it a little bit, it seems like there isn't enough information about the physics of the situation in order to solve the problem. For instance, around what point along the beam is the bending moment being computed? At what point along the beam is the force that is causing the bending moment being applied?

You need to know the answers to these questions. I suspect that the problem has been set up in such a way that the bending moment ends up being a fairly simple function of the beam length L. I.e. M = f(L). But I do not know what that function is.

Once you figure out what f(L) is, you know that L is a random variable with mean 11 m and standard deviation 0.5 m. What are the mean and standard deviation of a function of a random variable M = f(L)? One way to think about it is that you need to propagate the measurement error of the beam lengths L through the calculation, so that you end up with the resulting error in f(L). Perhaps you have been given some error propagation formulae for this purpose?

Look forward to hearing back from you with more information that is needed to enable us to help you.

 

[Erwin1998]

Hi Erwin1998, welcome to the forum.

It's been a while since I've had to think about bending moment (Introductory Mechanics, basically). But having researched it a little bit, it seems like there isn't enough information about the physics of the situation in order to solve the problem. For instance, around what point along the beam is the bending moment being computed? At what point along the beam is the force that is causing the bending moment being applied?

You need to know the answers to these questions. I suspect that the problem has been set up in such a way that the bending moment ends up being a fairly simple function of the beam length L. I.e. M = f(L). But I do not know what that function is.

Once you figure out what f(L) is, you know that L is a random variable with mean 11 m and standard deviation 0.5 m. What are the mean and standard deviation of a function of a random variable M = f(L)? One way to think about it is that you need to propagate the measurement error of the beam lengths L through the calculation, so that you end up with the resulting error in f(L). Perhaps you have been given some error propagation formulae for this purpose?

Look forward to hearing back from you with more information that is needed to enable us to help you.

Hi j-astron , thanks !


All beams are loaded by a q-load of 20 kn / m. The q-load engages in the middle of beam. The q-load only works over a length of 4 meters.

I do not have a standard formula for this. I determined the moment by calculating reaction and transverse forces.


Should we search with the data minimum moment and maximum moment? I determined this by calculating the shortest beam and the longest beam.

In samples, all kinds of formulas are known to determine the mean and the standard deviation. But this is not a sample. And we do not know how many beams there are in total.


thanks in advance for your response