I wonder if anyone can point me in the direction of a formula for
calculating the maximum span of a joist?
The 'knowns' are these (I'm in the UK, by the way, so everything is in SI
load per unit length (kN/m)
fibre stress of timber (N/mm2)
breadth of joists (mm)
depth of joists (mm)
The 'unknown' is what maximum span would result for a given set of
parameters - I assume it would be possible to derive it from the data
joists centres: 353mm
load per unit length: 0.9kN/m
fibre stress of timber: 7.5N/mm2
breadth of joist: 47mm
depth of joist: 200mm
span of joist: ?
The reason for this is that I'm (trying to) draw up a set of tables for
preliminary joist sizing (UK span tables only provide metric spacing - I'm
doing a set with imperial spacing for use with alterations of old
Hope somebody can help with this one!
There are three parts to your question: bending strength,shear strength
and deflection limitations.
For floor joists with normal floor loading we can generally ignore the
shear calculation, so that leaves flexure and deflection.
For flexure, the bending formula is fb = M/Sx or
fb = (wl^2)/8Sx where Sx = (bd^2)/6
fb = (6wl^2)/(8bd^2)
L = sqrt[(8bd^2)*fb/(6w)] make sure your units are compatible
For deflection of floors:
L/360 = (5wL^4)/(384EI) where I= (bd^3)/12
I will leave you to work out the math.
Your "maximum" span is the smaller of the two L's
Bob Morrison, PE, SE
R L Morrison Engineering Co
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