# How much load could the ceiling hold

I am replacing the ceiling in my flat with some soundproofing materials and since these are heavier than usual materials used I want to check if the new materials would pose a problem.

The room I want to apply this to is 3.3x4 metres.

Joists Height: 22.2 cm / 8.85 inch; Width: 5 cm / 2 inch; Length: 330 cm / 130 inch

30 cm spacing between these; 13-14 joists

What I want to know is how I can calculate the maximum load that the ceiling could hold.

Any ideas?

• This is a job that belongs to the architect or structural engineer.
– r13
Jan 5, 2022 at 15:24
• That is true. I am almost certain it will hold the weight but I want to double-check my logic. The ceiling already has plasterboard which would be removed and hence reduce the weight on it so it would only be the difference in weight between materials Jan 5, 2022 at 16:31
• Caution: Our church sprayed some sound proofing foam on a large drywall ceiling, The weight of the product pulled down the ceiling, ( the joists were unhurt). In case you think about spraying instead of replacing. Jan 5, 2022 at 16:41
• Nope, in this case, it's replacing but with sturdier materials, hence it would really only be the difference in weights. Also since it would be directly attached to the joists it's unlikely it would collapse. It sounds like in your case the drywall was the one supporting the weight. Jan 5, 2022 at 16:59

You need to know what type of lumber is used in your ceiling to know its strength for moment and shear,$$F_b \ , V_{allowable}$$ and its elastic modulus, E. but for illustration assume a lower range of

$$F_b=1000psi \ and\ V=100psi$$

$$M=\omega l^2/8= \omega*(11*12)^2/8=2178\omega$$

you beam elastic module $$S_x$$ is $$S_x=bh^2/6=2*8.8^2/6=25.80in^3$$

$$\sigma x=F_b=1000=M/S_x=2178\omega/25.8=84.4\omega$$ $$\omega= 1000/84.4=11.8lbs/ft^2$$

This is the allowable load per square foot your ceiling joist can support.

Usually, Fb is in the range 1500-1800psi for Douglas fir and similar structural lumber, implying your ceiling can support approximately 16-17lbs.ft^2. then we have to check for deflection and shear as well. Deflection $$\delta$$ should be smaller than l/360

$$\delta=\frac{5 \omega l^4}{384EI}$$

• Thanks for the really thorough response. The calculations themselves are way beyond my high school physics education :D but the idea is that it would be able to support ~16lbs per square foot? So for a room of 140 square foot then it could hold about 2240 lbs? Jan 5, 2022 at 16:26
• yes. something like that if the joist are not cut and look ok. Jan 5, 2022 at 16:35