On Jul 13, 9:25 am, Wayne Whitney wrote:
On 2007-07-13, BobK207 wrote:

On Jul 12, 8:37 pm, "Art" wrote:

Here is the new information. The portion of the floor with the tub
is cantilevered out 2 feet. That means that some of the tub will
be sitting on the sill plate.

Is the tub centered or nearly centered over the wall below? If so,
almost all the weight will be carried by the wall, and you need only
concern yourself with whether that wall is strong enough. Your 2x10
joists will be strong/stiff enough to carry the tub load to the wall.
[Imagine cutting through the joists at the edge of the tub over the 6'
span; the joists just have to be able to carry the weight back to the
wall as a cantilever on either side of the wall.] Sounds reasonable,
Bob?

since deflection goes as span^3 the 2 ft cantilever section is
actually stiffer than the 6 ft span section.

Hmm, that's not really true, is it? A unit point load at the end of
the 2' cantilever will induce a moment at the support of 2 ft-lbs. A
unit point load at the middle of the 6' span will induce a moment
there of 1.5 ft-lbs.

Cheers, Wayne

Wayne-

A unit point load at the end of
the 2' cantilever will induce a moment at the support of 2 ft-lbs. A
unit point load at the middle of the 6' span will induce a moment
there of 1.5 ft-lbs.

yes, what you wrote is true but there's more to it since we have a
"distributed load".....total load increases linearly with span length

thanks for asking, you made me double check my thinking...here's a
little more

deflection at the END of a cantilever for a distributed load is
P*L^3 / (8*E*I)
deflection at the beam mid span for a distributed load is 5 * P*L^3
(384*E*I)

E - material modulus
I - joist moment of inertia

working out the constants so we can compare
cantilver .125 * P*L^3 / (E*I)
beam .013 * P*L^3 / (E*I)

Yup, cantilevers look more flexible than beams

BUT the key is that L for our cantilever is 24" & L for the "beam"
span is 72"

& P in each case is the TOTAL of the distributed load for each

so the 6' span P would be 16"/12"*6ft *100 lbf/ft 800 lbf
& the 2' cantilever p would be 16"/12"*2ft *100 lbf/ft 267 lbf

Of course I simplified the situation since we really don't have a
cantilver or a simple beam span ....

we really have an "overhung beam" but I'm too lazy to do the analysis
& can only remember a few simple loading cases like simply supported
beam & cantilever both with distributed load or point load

good enough to do rough stiffness comparisons & I'm pretty sure
they'll give conservative results (ie calc more defection than the
real situation)

so if you play the numbers..... the 6' span gets a double whammy 3x
the load AND 3x the span

of course a cantilever is not a stiff as a simply supported
beam .....IF they're same length AND support the same load

BUT in our case the "beam" is 3x as long ...... that distributed load
AND the L^3 terms are killers

even with the .25 vs .013 factors in our formulae ( a ratio of about
20) the combined effect of increased load & length gives us an
"inverse" ratio of 81

so the 6 ft beam span deflects about 4x as much as the 2 ft cantilever
when exposed to the SAME distributed load,

even under the SAME point load, the 6 ft span deflection would be
~35% higher

your moment analysis is correct for the SAME point load BUT the beam
span sees an effective point load 3x the cantilever (because of the
distributed load) thus the ratio of 1.5 vs 2.0 is overwhelmed by the
load increase.


cheers
Bob


PS about the bearing stress....each joist sees 16/12 * 8 ft * 100psf
~1070 lbf

even if all of the load through the joist into the wall sill you've
got bearing area 1.5 * 3.5 = ~5 in^2

about 200 psi bearing even a conservative 400 psi (not the code ~600
psi) gives a really good margin

Art-

The Sanijet requiement of 100 psf seems REALLY high......what's the
total tub weight, how much water does it hold & what is the "foot
print"