How do you Convert distributed load to point load?

For an evenly distributed load (example: F=10 N/m):Simply multiply the distributed load times the span of the load.

If you have distributed load of w = 150 kN/m2 on a span of L = 10 m and width of B= 5m then you will have

W = w x B = 150 x 5 = 750 kN/m

P = W x L = 750 x 10 = 7500 kN as a point load acting n the centre of your area L x B

For an uneven distributed load (example: F=.5x^2 N/m)Converting this kind of distributed load into a point load involves calculating two things: 1) The total load 2) The point at which the load acts

To calculate (1), integrate the load function over the length. So for a beam of length 12m with distributed load F = 5x^2 N/m, you would integrate 5x^2 from 0 to 12.

To calculate (2), you need to find the place along the beam where the sum of the moments on either side = 0. You do this by solving the following equation for a:

Int[F(x)(a-x),x,0,a] = Int[F(x)(x-a),x,a,L]

Where:

Int[a,b,c,d] = integration of function a, with respect to b, from c to d.

F(x) = the distributed load

a = the distance at which the concentrated load acts

L = the total length the distributed load acts over Solving this for F(x) = kx^n shows that:

Loads proportional to x act at 2/3 L

Loads proportional to x^2 act at 3/4 L

Loads proportional to x^3 act at 4/5 L

etc.