Please excuse me for starting a fresh thread on the subject but I got a lot
more info on how the floor is constructed.

We removed an old whirlpool made by Jacuzzi. Jacuzzi says the floor needs
to be 55 lbs/ sq ft. For some reason the new Sanijet tub recommends 100
lbs/sq ft. The latter number seems to make more sense.

So I want to strengthen the floor and plan on using a sheet of 3/4" plywood
on top of the old floor.

Here is the new information. The portion of the floor with the tub is
cantilevered out 2 feet. There is basically a box made up of 10 inch
joists that are 8 feet long with the last 2 feet of them sticking out the
side of the house to make the cantilever. That means that some of the tub
will be sitting on the sill plate. That is good, I would think. However
the parallel joists that make up the cantilever portion terminate at a
single perpendicular joist which is fastened to another long joist which is
part of the main floor system. So imagine a house of parallel joists with
a box attached to the middle of one joist consisting of one parallel joist
for the attachment and perpendicular joists that stick out beyond the sill
plate 2 feet.

The part on the sill plate should be plenty strong. I am worried about the
part that attaches to the long joist in the main part of the floor system.
I am thinking all of the weight is on that one joist (except for what is on
the sill plate). I cannot put posts underneath. I am thinking of sistering
that joist and bolting all 3 joists together (the joist that is the end of
the box, the joist that the box is attached to, and the new sister joist.)
I will probably have an engineer look at it but I know you guys have great
ideas, and I rather verify your ideas with the engineer rather than asking
him to come up with a fix.

Thanks again for your assistance.

On Jul 12, 8:37 pm, "Art" wrote:
Please excuse me for starting a fresh thread on the subject but I got a lot
more info on how the floor is constructed.

We removed an old whirlpool made by Jacuzzi. Jacuzzi says the floor needs
to be 55 lbs/ sq ft. For some reason the new Sanijet tub recommends 100
lbs/sq ft. The latter number seems to make more sense.

So I want to strengthen the floor and plan on using a sheet of 3/4" plywood
on top of the old floor.

Here is the new information. The portion of the floor with the tub is
cantilevered out 2 feet. There is basically a box made up of 10 inch
joists that are 8 feet long with the last 2 feet of them sticking out the
side of the house to make the cantilever. That means that some of the tub
will be sitting on the sill plate. That is good, I would think. However
the parallel joists that make up the cantilever portion terminate at a
single perpendicular joist which is fastened to another long joist which is
part of the main floor system. So imagine a house of parallel joists with
a box attached to the middle of one joist consisting of one parallel joist
for the attachment and perpendicular joists that stick out beyond the sill
plate 2 feet.

The part on the sill plate should be plenty strong. I am worried about the
part that attaches to the long joist in the main part of the floor system.
I am thinking all of the weight is on that one joist (except for what is on
the sill plate). I cannot put posts underneath. I am thinking of sistering
that joist and bolting all 3 joists together (the joist that is the end of
the box, the joist that the box is attached to, and the new sister joist.)
I will probably have an engineer look at it but I know you guys have great
ideas, and I rather verify your ideas with the engineer rather than asking
him to come up with a fix.

Thanks again for your assistance.

Art-

Quick answer....if I'm understanding the existing conditons

you've got 8 ft 2x10 joist that span ~6ft & cantilever ~2ft and a
"rim" joist that collects the ends of the cantilevers

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

Of course the actual loading (edge of tub or a real distributed load)
depends on how the tub bears on the floor


anyway based on my rough calcs (assuming worst case 100 psf
distributed load all concentrated at the end) the 2 ft cantilever
looks ok stress ~300 psi & deflection 1/64"

the 6ft span (again with all the 100 psf distributed load concentrated
at midspan..assumed worst case) again looks ok stress ~660 psi &
deflection 1/16"

looks ok as is, no mods needed

sistering the rim joist IMO won't really do much,

but if you WANT to stiffen the floor, sister the 8 ft joists, use
glue & small dia (.113 to .131) nails..forget the bolts, you want
good shear transfer & its hard to beat glue & lots of small nails (~4"
oc)

Your joist to sill bearing loads (~100psi) look ok so the sisters
don't really have to bear on the sill. Non-bearing sisters will be
easier to install & they'll be there just to stiffen the spans

I spent more time typing than doing the design or calcs...so hopefully
someone will check my concepts.
Its all about checking the load path so if I'm not understanding the
existing condition...oops!

cheers
Bob

"BobK207" wrote in message
ups.com...
On Jul 12, 8:37 pm, "Art" wrote:
Please excuse me for starting a fresh thread on the subject but I got a
lot
more info on how the floor is constructed.

We removed an old whirlpool made by Jacuzzi. Jacuzzi says the floor
needs
to be 55 lbs/ sq ft. For some reason the new Sanijet tub recommends 100
lbs/sq ft. The latter number seems to make more sense.

So I want to strengthen the floor and plan on using a sheet of 3/4"
plywood
on top of the old floor.

Here is the new information. The portion of the floor with the tub is
cantilevered out 2 feet. There is basically a box made up of 10 inch
joists that are 8 feet long with the last 2 feet of them sticking out the
side of the house to make the cantilever. That means that some of the
tub
will be sitting on the sill plate. That is good, I would think. However
the parallel joists that make up the cantilever portion terminate at a
single perpendicular joist which is fastened to another long joist which
is
part of the main floor system. So imagine a house of parallel joists
with
a box attached to the middle of one joist consisting of one parallel
joist
for the attachment and perpendicular joists that stick out beyond the
sill
plate 2 feet.

The part on the sill plate should be plenty strong. I am worried about
the
part that attaches to the long joist in the main part of the floor
system.
I am thinking all of the weight is on that one joist (except for what is
on
the sill plate). I cannot put posts underneath. I am thinking of
sistering
that joist and bolting all 3 joists together (the joist that is the end
of
the box, the joist that the box is attached to, and the new sister
joist.)
I will probably have an engineer look at it but I know you guys have
great
ideas, and I rather verify your ideas with the engineer rather than
asking
him to come up with a fix.

Thanks again for your assistance.

Art-

Quick answer....if I'm understanding the existing conditons

you've got 8 ft 2x10 joist that span ~6ft & cantilever ~2ft and a
"rim" joist that collects the ends of the cantilevers

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

Of course the actual loading (edge of tub or a real distributed load)
depends on how the tub bears on the floor


anyway based on my rough calcs (assuming worst case 100 psf
distributed load all concentrated at the end) the 2 ft cantilever
looks ok stress ~300 psi & deflection 1/64"

the 6ft span (again with all the 100 psf distributed load concentrated
at midspan..assumed worst case) again looks ok stress ~660 psi &
deflection 1/16"

looks ok as is, no mods needed

sistering the rim joist IMO won't really do much,

but if you WANT to stiffen the floor, sister the 8 ft joists, use
glue & small dia (.113 to .131) nails..forget the bolts, you want
good shear transfer & its hard to beat glue & lots of small nails (~4"
oc)

Your joist to sill bearing loads (~100psi) look ok so the sisters
don't really have to bear on the sill. Non-bearing sisters will be
easier to install & they'll be there just to stiffen the spans

I spent more time typing than doing the design or calcs...so hopefully
someone will check my concepts.
Its all about checking the load path so if I'm not understanding the
existing condition...oops!

cheers
Bob


Thank you for your response. I guess what worries me is that the short rim
joist attaches to the middle of a long parallel joist (lets call that long
joist, joist "A") which is part of the regular floor system. The middle of
the joist "A" is holding all of the weight of the tub except that portion
which is being held by the sill plate. Seems like Joist "A" is being asked
to do a lot. So are the nails between joist "A" and the rim joist.

On Jul 13, 12:28 am, "Art" wrote:
"BobK207" wrote in message

ups.com...



On Jul 12, 8:37 pm, "Art" wrote:
Please excuse me for starting a fresh thread on the subject but I got a
lot
more info on how the floor is constructed.

We removed an old whirlpool made by Jacuzzi. Jacuzzi says the floor
needs
to be 55 lbs/ sq ft. For some reason the new Sanijet tub recommends 100
lbs/sq ft. The latter number seems to make more sense.

So I want to strengthen the floor and plan on using a sheet of 3/4"
plywood
on top of the old floor.

Here is the new information. The portion of the floor with the tub is
cantilevered out 2 feet. There is basically a box made up of 10 inch
joists that are 8 feet long with the last 2 feet of them sticking out the
side of the house to make the cantilever. That means that some of the
tub
will be sitting on the sill plate. That is good, I would think. However
the parallel joists that make up the cantilever portion terminate at a
single perpendicular joist which is fastened to another long joist which
is
part of the main floor system. So imagine a house of parallel joists
with
a box attached to the middle of one joist consisting of one parallel
joist
for the attachment and perpendicular joists that stick out beyond the
sill
plate 2 feet.

The part on the sill plate should be plenty strong. I am worried about
the
part that attaches to the long joist in the main part of the floor
system.
I am thinking all of the weight is on that one joist (except for what is
on
the sill plate). I cannot put posts underneath. I am thinking of
sistering
that joist and bolting all 3 joists together (the joist that is the end
of
the box, the joist that the box is attached to, and the new sister
joist.)
I will probably have an engineer look at it but I know you guys have
great
ideas, and I rather verify your ideas with the engineer rather than
asking
him to come up with a fix.

Thanks again for your assistance.

Art-

Quick answer....if I'm understanding the existing conditons

you've got 8 ft 2x10 joist that span ~6ft & cantilever ~2ft and a
"rim" joist that collects the ends of the cantilevers

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

Of course the actual loading (edge of tub or a real distributed load)
depends on how the tub bears on the floor

anyway based on my rough calcs (assuming worst case 100 psf
distributed load all concentrated at the end) the 2 ft cantilever
looks ok stress ~300 psi & deflection 1/64"

the 6ft span (again with all the 100 psf distributed load concentrated
at midspan..assumed worst case) again looks ok stress ~660 psi &
deflection 1/16"

looks ok as is, no mods needed

sistering the rim joist IMO won't really do much,

but if you WANT to stiffen the floor, sister the 8 ft joists, use
glue & small dia (.113 to .131) nails..forget the bolts, you want
good shear transfer & its hard to beat glue & lots of small nails (~4"
oc)

Your joist to sill bearing loads (~100psi) look ok so the sisters
don't really have to bear on the sill. Non-bearing sisters will be
easier to install & they'll be there just to stiffen the spans

I spent more time typing than doing the design or calcs...so hopefully
someone will check my concepts.
Its all about checking the load path so if I'm not understanding the
existing condition...oops!

cheers
Bob

Thank you for your response. I guess what worries me is that the short rim
joist attaches to the middle of a long parallel joist (lets call that long
joist, joist "A") which is part of the regular floor system. The middle of
the joist "A" is holding all of the weight of the tub except that portion
which is being held by the sill plate. Seems like Joist "A" is being asked
to do a lot. So are the nails between joist "A" and the rim joist.

Art-

Its all about relative stiffness.......stiffer elements (stiffer load
path) take more load than more flexible load path.


I have an idea about how your floor is framed but without a picture or
a sketch I'm really not 100% sure that I'm clear on the framing
scheme.

Based on my understanding of your description

The joists cantilever over the sill ~2', the ends of these joists
frame into a "rim joist" which frames into another joist (a long
joist that is parallel to the cantilevers)

if this is correct..... then the rim joist just stabilizes the ends of
the cantilevers & not much load finds it way out the end of the
cantilevers thru rim to the parallel joist. So the parallel joist
really isn't being loaded through it's connection to the rim joist

my premise is that the cantilevers (cuz' they are so short & stiff)
are bringing all their load back to the sill thus the rim joist along
with joist A are doing virtually nothing to support the load on the
cantilevers.

If the connection from the rim to joist A went away would the
performance of the cantilevers suffer?

think of your cantilvers like a series of parallel diving boards, add
a rim joist to the ends of the diving boards.

Now add another LONG diving board but support its far end AND frame
the rim joist into this long diving board.

Put a 100 lbs at the end of each short diving.....what supports the
majority 100's of pounds of load?

the short boards? or the long board?

My premise is that because of the stiffness of the cantilever sill
support vs the rim connection most (nearly all) of the load exists the
cantilver thru the sill support.

cheers
Bob

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 Whitney" wrote in message
...
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

The position of the tub with respect to the sill plate certainly is key and
I should have included that in my original post:

The portion of the bottom of the tub that holds water is 29 inches wide.
Towards the top the tub widens to 44 inches wide plus figure a 5 inch
surround. So the heavy part of the tub starts 12 inches from the inside
wall which is 4 inches thick. So the heavy part of the tub starts 17 inches
inside from the cantilever joists. So 7 inches of the tub is cantilevered,
6 inches are sitting on joists directly above the sill plate (which is on a
concrete foundation wall), and 16 inches are on the other side of the sill
plate putting its weight on the joists that lead to the rim joist that
connects to a long joist which is part of the main floor system.

On 2007-07-13, Art wrote:

So 7 inches of the tub is cantilevered, 6 inches are sitting on
joists directly above the sill plate (which is on a concrete
foundation wall), and 16 inches are on the other side of the sill
plate

I am not an engineer, but I would say that since your tub is less
sitting on top of a strong support (the concrete wall), the bending
moments induced in the 2x10 floor joists, even at 100 psf load, are
comparitively small. So there is certainly no need to strengthen the
floor system as far as bending of the joists goes; you should check
the bearing area to be sure the joists won't crush over the wall. It
would be a very different situation if you had your tub in the middle
of a 16' span, say.

Cheers, Wayne

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"

"BobK207" wrote in message
oups.com...
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"



Thanks for all the info. Here is the exact tub. Note that they say the
base is structural. I am not sure whether that means it spreads out the
weight of the water. I did question them about the 100 psf but they said
that is their recommendation... they would not budge on it:

http://www.sanijet.com/downloads/Model360_42x60_D6.pdf

On Jul 13, 10:00 pm, "Art" wrote:
"BobK207" wrote in message

oups.com...



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"

Thanks for all the info. Here is the exact tub. Note that they say the
base is structural. I am not sure whether that means it spreads out the
weight of the water. I did question them about the 100 psf but they said
that is their recommendation... they would not budge on it:

http://www.sanijet.com/downloads/Model360_42x60_D6.pdf

Art-

750 lbs of water, 250 lbs of person, 150 lbs of machine total 1150
lbs

~3.5' x ~5' foot print

~65 psf ...............sounds like the 100 psf is a "cover their
butt" requirement

I did question them about the 100 psf but they said
that is their recommendation... they would not budge on it

of course not, they're not doing or paying for the framing mods

cheers
Bob

On 2007-07-14, BobK207 wrote:

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

Well, since we were talking about a tub, I was considering constant
total load. But you are right that the 6' beam deflection is still
greater than the 2' cantilever deflection, the constants in the
deflection equations are much less for the beam but not by a factor of
3^3 = 27.

Cheers, Wayne