example calculation for reduced depth timber needed

huangyhg

example calculation for reduced depth timber needed
hi. i have a contractor who wishes to reduce the depth of the rafters over a stairwell as he hasn't left sufficient headroom. the stairwell is 900mm wide and there are 2 rafters equally spaced which are 46 x 220 tr26. the span on plan is 4018mm and he wishes to reduce the depth to 150mm, 1168mm from  the end. shear and bending are fine, i'm struggling to know how to check the deflection given the now non-uniform depth. any ideas?
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model it with a computer and let the machine do the work.  to ensure that you are seeing a reasonable result i would further hand calculate considering the point where the beam begins to taper as the support point for two back to back cantilevers.  split the beam at that point and treat each separately under the known load.  you are then calculating the deflection of a tapered cantilever, and you should be able to simply split the difference of the two results, in ratio to their lengths.  can't say i've ever seen a design procedure for this, however it feels quite rational and were it to agree to within 20% of the fem, i'd use it.
very interesting question; please post to let us know what you do!
good luck,
ys
b.eng (carleton)
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