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Calculating the vertical distortion of a wooden beam with a load on-top of it

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Hi, so I am at dead-end with this, I have a rafter construction consisting of 466x140mm beams of laminated veneer lumber, now I have a terasse where there is a bout a 4420mm free span where some of the beams would be unsupported, the roof itself has a weight of around 1,15 kN/m², my question is, how do I find how much vertical distortion will occur if I keep the beams over the terasse unsupported?

Sincerely

Jonas P.

May 28, 2018
edited by SomeoneSomewhere  May 28, 2018

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I have found the equation needed for this, I needed to search for an equation for a cantilever beam with an evenly distributed load, which looks like this (see added picture).

ω = load in Newtons pr. m

l = length of the affectd area

E = is the elasticity of the beam (something that you need to look up)

i = is the inertia of the affected axis (in this case the x-axis, this is found by this formula 1/12*width of the beam*height of the beam³, to find the y-axis inertia simply switch the positions of the height, and width) May 29, 2018