# How to calculate the supporting force exerted by a stationary object (cupboard) and support (brackets) for it?

I have a wall mounted Stuva Ikea cupboard, which measures 60x64x30cm. The base is 64x30cm. It is already supported by 2 holes at the back base, (64x60cm).

But I need to add in L shape brackets underneath for extra support. Only, the brackets can support a max load of 15kg only. The cupboard is 15kg, I need to load another 15kg of books on, making the total 30 kg.

Can anyone help to calculate the distance that I have to put the brackets as additional support?

15kg max load brackets (28cm x 2cm) base of cupboard (64x30cm) total weight to support (30kg) - alr 2 holes wall mounted on base-to-wall (60x64cm)

Appreciate any help.

How do I calculate F=ma, as the cupboard and brackets are stationary?

Cupboard frame 8.6kg http://www.ikea.com/sg/en/catalog/products/70165163/

Cupboard doors 5kg http://www.ikea.com/sg/en/catalog/products/90169103/

The cupboard backing board comes with 2 holes predrilled, and 2 plastic backing boards.the backing board is 2mm thick, doubt the screws i screwed in will actially hold it up. Ikea is no help at all! I hv two of this cupboards side by side (but not joined)

• Do you know how to do free-body diagrams? If so can you draw one and let us know what's still unclear? We can give more specific advice then. Commented Aug 22, 2014 at 2:35
• I echo what @paisanco is saying. Please draw a picture of a section through the cupboard and wall so we understand what you are trying to do. You need to worry about torque here - force acting as a lever - so it is important to mark (approximately) the distances between points where the cupboard might pivot (e.g. bottom edge against the wall) and where the supports are (screws in the wall, where the bracket is mounted on the cupboard, etc). You usually want to build in some safety factor - don't support 15kg of books plus 15 kg of cupboard with brackets that can carry 30kg. One more book... Commented Aug 22, 2014 at 2:40
• As a completely untrained professional, I would recommend just getting 4 such angle braces for each shelf and drill them in with appropriate screws. I've done it numerous times around the several apartments I've lived in. Commented Aug 22, 2014 at 2:45
• yup it's all about torque in practice Commented Aug 22, 2014 at 13:49

I'm not 100% sure about this but here goes. If your cupboard is in equilibrium, or not undergoing any changes in motion, the wall is pushing up on it with the same force it is pushing down on the screws/nails holding up the cupboard. That is to say $$ΣF = 0$$

Using: $$F = ma$$ and assuming you are near sea level, we can use the acceleration due to gravity at sea level in place of a. $$F=m(9.8m/s^2)$$ We can use the mass you mentioned $$F=(15Kg)(9.8m/s^2)$$ And since a Newton is 1Kg * m/s^2, we get $$F=147N$$ If it is already supported in two places then each one has about 73.5N on it. If you add another bracket(for a safety margin), it would be 49N on each one.

$$147N / 3\text{ Total brackets} = 49N/\text{Bracket}$$ Since the load and the cupboard and the books have the same mass, you can just double our force calculation. You would also double the number of brackets. $$(147N ⋅ 2) = (3\text{ Total brackets}) ⋅2$$ $$294N = 6\text{ Total brackets}$$ $$\text{Because:}$$ $$\frac{249N}{49N/\text{Bracket}}$$ $$\text{Cancel the Newtons, get the Brackets out of the denominator and divide the fraction:}$$ $$6\text{ Brackets}$$ 6 Brackets minus the two already in your cupboard, leaves you with 4 brackets to be evenly spaced along the bottom.