Calculate mass needed on ceiling for it to collapse

[Rei]

I've been working on something and I need to calculate how much mass I could put on the 10cm thick concrete ceiling of a 5x5 m^2 room before it collapses. I'm pretty stuck on it, tried many things, but none worked.  Any ideas?

Edited April 26, 2018 by Rei
title mistake

[Bender]

It depends on the reinforcement. Do you have any idea about which steel bars are inside, and at which position?

Do you have any background/education on mechanics/strength of materials/bending of beams under load?

The 3D scenario is relatively complex to calculate, but there could be online calculators once you know the stiffness matrix of the ceiling.

A much easier first approximation for the lower boundary would be to ignore two sides and approach the problem as a simple clamped beam.

 This belongs in engineering.

Edited April 26, 2018 by Bender

[studiot]

Gosh this really is a piece of string question.

 

What country are you in?
This is relevant because in some places they build to the codes, in some places they ignore them.

 

You need to provide a lot more information about what you really want to do, and, as Bender says, about the ceiling, walls and so on.

[J.C.MacSwell]

Are you trying to predict a point of collapse or trying to decide what is safe?

A conservative approach, at least for any possible failure of the ceiling itself, would be to assume a simply supported beam.  As Bender mentioned where the steel is incorporated is important, and also whether it is prestressed. I do this all the time for steel, other alloys or composites (usually grp/frp), sometimes wood, but rarely for concrete. I would expect picking safety factors would take a bit of experience, similar in some respects to composites (which it actually is)

[studiot]

9 minutes ago, J.C.MacSwell said:

Are you trying to predict a point of collapse or trying to decide what is safe?

No I think the question being asked is equivalent to greedy shipowners in the past asking

How many sacks of coal will sink my boat?