Formula for weight resistance

Question

I want to know if there is a formula for calculating how much weight an object can hold. For example if I have a wooden plank I want to know if it could hold a 20kg object. by knowing the mass of the object and the size of the object I would know how much pressure or newtons it could hold

Answer 1

Yes there is.  This is a strength of materials problem. Look up the yield stress and ultimate stress of your chosen structural material (wood?).

 

Let

 

σ_y = yield stress of the material in N/m²

σ_u = ultimate stress of the material in N/m²  (σ_u > σ_y always)

A = vertical cross-sectional area of the structural member (assumed constant for a simple case)

 

The stress due to a weight mg evenly distributed over the area A is

 

σ = mg/A

 

Now compare σ to σ_y and σ_u.  If σ < σ_y, the structure will deform elastically, which keeps you in a safe range.  If σ ≥ σ_y but less than σ_u, the structure will permanently deform without breaking.  But if σ ≥ σ_u, the structure will break.  The question is, are you willing to let the structure deform permanently some without breaking, or do you require it to deform elastically?  That will determine whether you want to meet the more restrictive condition that 

 

mg/A < σ_y

 

or the less restrictive condition that

 

mg/A < σ_u.