Many of the structural calculations involved in construction are relatively simple. Naturally, there is no substitute for a professional engineer when you're faced with complicated or uncommon structural problems, but basic load-bearing calculations are well within the capabilities of many carpenters and homeowners. Most timber-framed systems can be analysed with the same general formulas. In the case of a floor, you can determine the load capacity fairly accurately with nothing more than the size, space and span of the floor joists.
Write down the beam strength formula: Maximum load in kilograms = FBd^2 / 9L.
Fill in the values for B, d and L. B is the breadth of the joist, in centimetres. If your floor system uses standard timber, this will be 3.75 cm (1.5 inches). The d is the depth of the joist in inches, which you will have to measure. L is the span, in metres. The span is the unsupported distance over which the joist must bear its load.
Determine the value for F, which stands for the fibre stress in bending of the wood. This may be difficult to find, because it depends on the species of tree that your joists came from. If the joists are relatively new, the F value may be stamped right on the piece of timber. If you know the species of the wood, you can refer to a timber manual to find the corresponding F value. If all else fails, you can safely use 1,000 for F, as almost all graded timber will have an F value of 1,000 or higher.
Calculate the maximum load in kilograms that one of your floor joists can support. For example, if you have joists spaced 40 cm (16 inches) on centre with a span of 4.2 metres (14 feet), the load would be 462 kg (1,019 lb) per joist.
Calculate the total area supported by one joist according to this formula: joist spacing (in metres) x span (in metres). Continuing the previous example, 0.41 m (1.333 feet) x 4.2 m (14 feet) = 1.72 square metres (18.7 sq feet).
Divide the maximum load of one joist by the area supported by one joist: 462 kg (1,019 lb) / 1.72 square metres (18.7 sq feet) = 269 kg per square metre (54.5 lb per square foot). This number tells you how much load your floor can support for each square metre of floor space.
Multiply the maximum load per square metre by the total area of the floor. If the example floor is 6 by 9 metres (20 by 30 feet), the total area is 54 square metres (600 square feet); 54 x 269 = 14,526 kg (32,024 lb). This number tells you the total load capacity of your floor.
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