Choosing correct steel beam for a span

[roldy]

TL;DR Summary

Determining correct steel beam size for a span while considering self loading with distributed loading

I have a weight of 30,000 lbs distributed across a span of 100' and supported at the ends. If I have 3 beams to support this load, each beam would then need to hold 10,000 lbs, and with a F.S of 1.6 each beam would need to hold 16,000 lbs. If I assume my max deflection at 1", then I can find the moment of inertia about the x-axis and then look up a steel beam that at a minimum has this value. I then would solve for the max stress to check if it exceeds 36,000 psi. The self weight of the beam would additionally add to the distributed weight of 16,000 lbs which would then change the moment of inertia etc. How can I include self weight of the beam in the distributed loading if I don't initially know what beam I am looking for? I'm not concerned about number calculations. I just need a process check about how to include self weight of the beam.

I solve for I from this:
$\delta _{max}=\frac{5wL^{4}}{384EI}$

I check for stress limit from this:
$\sigma_{max}=\frac{M_{y}}{I}$

 

[Dr.D]

You can solve this problem iteratively. Pick a beam that you think might work, find out its weight per length to be used in your calculations and then crunch. If the result is safe, you can stop. If not, pick another beam, rinse, and repeat.

 

[berkeman]

Summary:: Determining correct steel beam size for a span while considering self loading with distributed loading

I have a weight of 30,000 lbs distributed across a span of 100' and supported at the ends. If I have 3 beams to support this load, each beam would then need to hold 10,000 lbs, and with a F.S of 1.6 each beam would need to hold 16,000 lbs.

What is the application? You don't live in Florida near the beach, do you?

 

[roldy]

What is the application? You don't live in Florida near the beach, do

You can solve this problem iteratively. Pick a beam that you think might work, find out its weight per length to be used in your calculations and then crunch. If the result is safe, you can stop. If not, pick another beam, rinse, and repeat.

As I was creating my spreadsheet for calculations I was contemplating about using Excel's optimization tool to possibly solve for this.

 

[roldy]

What is the application? You don't live in Florida near the beach, do you?

The application is basically a water bypass bridge. The bridge would hold 24" diameter polymer based pipes up over an area needed to be kept clear. Unfortunately I don't live near in Florida or close to a beach. I get where you're coming from with that question in regards to ground conditions.

 

[berkeman]

The application is basically a water bypass bridge. The bridge would hold 24" diameter polymer based pipes up over an area needed to be kept clear.

Is this for a public works project? Or is it something you are building on your own property? What kind of permits do you need to build something like this? Are there any inspections/approvals/insurance required?

 

[roldy]

Is this for a public works project? Or is it something you are building on your own property? What kind of permits do you need to build something like this? Are there any inspections/approvals/insurance required?

This is a conceptual problem. Not a project of any kind.

 

[Dr.D]

This problem probably does not satisfy the necessary conditions for optimization by Excel. For one thing, steel beams are available only in discrete sized, not continuously variable.

 

[roldy]

This problem probably does not satisfy the necessary conditions for optimization by Excel. For one thing, steel beams are available only in discrete sized, not continuously variable.

Very true. I was hoping to get a value and find a beam close to it.