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Default Shed project: Shearwall design

In a free-standing garage, where one wall is almost entirely absent to make
a door opening, what parts of the structure prevent the door wall from
racking?

I am second-guessing myself about my shed plan. One wall, a gable end wall,
is non-load-bearing but is a shear wall. Its plan has an 8x8 door opening
in a 12' wide by 9' high wall. I don't have the background to determine
whether such a wall will have sufficient shear strength. I'm using
conventional 2x4 framing 16" OC with APA-rated 7/16 OSB sheathing, no
interior sheathing is planned.

The obvious things would be to reduce the door opening, to use heavier
sheathing, and/or sheathe it inside and out. But first I would like to hear
any advice this august group has to offer, and with my thanks.

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Default Shed project: Shearwall design

wrote:
In a free-standing garage, where one wall is almost entirely absent to make
a door opening, what parts of the structure prevent the door wall from
racking?

I am second-guessing myself about my shed plan. One wall, a gable end wall,
is non-load-bearing but is a shear wall. Its plan has an 8x8 door opening
in a 12' wide by 9' high wall. I don't have the background to determine
whether such a wall will have sufficient shear strength. I'm using
conventional 2x4 framing 16" OC with APA-rated 7/16 OSB sheathing, no
interior sheathing is planned.

The obvious things would be to reduce the door opening, to use heavier
sheathing, and/or sheathe it inside and out. But first I would like to hear
any advice this august group has to offer, and with my thanks.


Traditional way, in addition to stiff sheathing, was to cut in angle
braces on all the corners. Try to create as many triangular sections at
right angles to each other as you can. A large header, corner post to
corner post, helps as well. On the addition to my house down south, we
actually used about 35 feet of glue-lam all the way from the original
house, over the open carport bay, and tied into the far corner of the
new garage beyond. It has worked out real well- no movement in 2
hurricanes since then. Carports in Louisiana hate hurricanes almost as
much as mobile home in Arkansas hate tornadoes.

I'd bump up the walls to 2x6 (so you can hang shelves on the walls), use
thicker sheathing (real plywood beats OSB), consider using adhesive and
nails on the sheathing, and use all recommended tie straps for your
area. Truss or stick-frame roof? If you aren't finishing the inside at
all, you can face-apply the triangular braces mentioned above on the
inside, including tying the adjacent walls together at the level of the
ceiling joists. That will make for very stiff corners.

Standard disclaimer- I'm not an engineer, but that is how I saw it done
as a wee lad, and how I would do it.

--
aem sends...

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Default Shed project: Shearwall design

In article 4a47884e.691334325@localhost,
wrote:

In a free-standing garage, where one wall is almost entirely absent to make
a door opening, what parts of the structure prevent the door wall from
racking?


The back wall.
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Default Shed project: Shearwall design

On Jun 28, 5:18*pm, "benick" wrote:
"Smitty Two" wrote in message
In article 4a47884e.691334325@localhost wrote:


In a free-standing garage, where one wall is almost entirely absent to
make
a door opening, what parts of the structure prevent the door wall from
racking?


The back wall.


You've NEVER seen a garage...LOL...Sorry about laughing but that was
funny...Once all 4 walls are up it will be fine...No extra thick sheathing
required..Use a 2X8 header with half inch sheating in the middle to make 3
1/2 inches for the wall thickness if using 2X4's.......


What does the header have to do with racking resistance? A header
doesn't contribute to shear resistance. Only connections and
construction that are designed to handle moments can resist the
racking.

Likewise one wall without the required shear strength will compromise
the entire building structurally. You see shoddy construction all
over the place, and buildings that clearly don't have the structure to
handle the required present day shear loads, yet they are still
standing. That doesn't mean that people should ignore the
requirements.

In the OP's case there is enough wall remaining in the door wall to
handle the shear. The Simpson Strongwall is a more expensive
solution, but it works. The diagonal bracing also works, but should
be let in to the studs as that increases its shear strength
considerably.

Sheathing either side of the door opening, inside and out, with glued
and nailed sheathing of at least 1/2" (nails not overdriven) would
probably be the easiest and strongest way to handle the shear load.
The specifics will depend on the local codes and design shear load.

R
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Default Shed project: Shearwall design

On Jun 28, 5:38*pm, wrote:
On Sun, 28 Jun 2009 17:18:21 -0400, in alt.home.repair, "benick"





wrote:

"Smitty Two" wrote in message
news
In article 4a47884e.691334325@localhost,
wrote:


In a free-standing garage, where one wall is almost entirely absent to
make
a door opening, what parts of the structure prevent the door wall from
racking?


The back wall.


You've NEVER seen a garage...LOL...Sorry about laughing but that was
funny...


Yeah, but it did make me stop and think. *I think he's partly right. *My
thinking did not take into account the roof structure and how it rigidly
ties all of the walls together. *It's certainly not the first "duh!" moment
I've had on this project, almost certainly not the last.

Thanks to all who have replied so far, you're giving me plenty to think
about.

--
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you want me to read your reply, be sure to include this line of text in
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will delete your email with all due prejudice. *Thanks!- Hide quoted text -

- Show quoted text -


But then I have seen, and currently have, a double car garage with 2
8' doors that _has_ racked. Mine is very old (don't know how many)
and has only about 1 ft between the door openings and the corners.

Harry K
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Default Shed project: Shearwall design

RicodJour wrote:
On Jun 28, 5:18 pm, "benick" wrote:
"Smitty Two" wrote in message
In article 4a47884e.691334325@localhost wrote:
In a free-standing garage, where one wall is almost entirely absent to
make
a door opening, what parts of the structure prevent the door wall from
racking?
The back wall.

You've NEVER seen a garage...LOL...Sorry about laughing but that was
funny...Once all 4 walls are up it will be fine...No extra thick sheathing
required..Use a 2X8 header with half inch sheating in the middle to make 3
1/2 inches for the wall thickness if using 2X4's.......


What does the header have to do with racking resistance? A header
doesn't contribute to shear resistance. Only connections and
construction that are designed to handle moments can resist the
racking.

Likewise one wall without the required shear strength will compromise
the entire building structurally. You see shoddy construction all
over the place, and buildings that clearly don't have the structure to
handle the required present day shear loads, yet they are still
standing. That doesn't mean that people should ignore the
requirements.

In the OP's case there is enough wall remaining in the door wall to
handle the shear. The Simpson Strongwall is a more expensive
solution, but it works. The diagonal bracing also works, but should
be let in to the studs as that increases its shear strength
considerably.

Sheathing either side of the door opening, inside and out, with glued
and nailed sheathing of at least 1/2" (nails not overdriven) would
probably be the easiest and strongest way to handle the shear load.
The specifics will depend on the local codes and design shear load.

R

If a header is strongly tied in to the wall corners, like with diagonal
bracing (or the gusseting of the corner sheathing), the whole wall can
be strong enough to resist racking. Almost like a bridge. If the header
is basically just sitting on the cripples at either end of the opening,
all it can do is catch weight from above. See my previous post about the
addition to my house down south- one continuous glue-lam header, from
original house wall, across added room, across carport bay, and all the
way across door wall of garage. Plywood sheathing on that end of garage.
Gone through 2 hurricanes so far- no twist, no sag, and overhead door
still operates with one hand.

Not that different from adding a 1x10 along the top back edge of cheap
pine shelving unit, to keep it from racking.
--
aem sends...


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Default Shed project: Shearwall design

On Jun 29, 12:02*am, aemeijers wrote:
RicodJour wrote:
On Jun 28, 5:18 pm, "benick" wrote:
"Smitty Two" wrote in message
In article 4a47884e.691334325@localhost wrote:


In a free-standing garage, where one wall is almost entirely absent to
make
a door opening, what parts of the structure prevent the door wall from
racking?
The back wall.


You've NEVER seen a garage...LOL...Sorry about laughing but that was
funny...Once all 4 walls are up it will be fine...No extra thick sheathing
required..Use a 2X8 header with half inch sheating in the middle to make 3
1/2 inches for the wall thickness if using 2X4's.......


What does the header have to do with racking resistance? *A header
doesn't contribute to shear resistance. *Only connections and
construction that are designed to handle moments can resist the
racking.


Likewise one wall without the required shear strength will compromise
the entire building structurally. *You see shoddy construction all
over the place, and buildings that clearly don't have the structure to
handle the required present day shear loads, yet they are still
standing. *That doesn't mean that people should ignore the
requirements.


In the OP's case there is enough wall remaining in the door wall to
handle the shear. *The Simpson Strongwall is a more expensive
solution, but it works. *The diagonal bracing also works, but should
be let in to the studs as that increases its shear strength
considerably.


Sheathing either side of the door opening, inside and out, with glued
and nailed sheathing of at least 1/2" (nails not overdriven) would
probably be the easiest and strongest way to handle the shear load.
The specifics will depend on the local codes and design shear load.



If a header is strongly tied in to the wall corners, like with diagonal
bracing (or the gusseting of the corner sheathing), the whole wall can
be strong enough to resist racking. Almost like a bridge. If the header
is basically just sitting on the cripples at either end of the opening,
all it can do is catch weight from above. See my previous post about the
addition to my house down south- one continuous glue-lam header, from
original house wall, across added room, across carport bay, and all the
way across door wall of garage. Plywood sheathing on that end of garage.
Gone through 2 hurricanes so far- no twist, no sag, and overhead door
still operates with one hand.

Not that different from adding a 1x10 along the top back edge of cheap
pine shelving unit, to keep it from racking.


I was responding to Benick's post which is misleading. Headers are
also not usually built extending from corner to corner of a building
as you mention. They're cut to span the opening plus the length to
cover the supporting studs on either side. Of course you can modify
any construction to take shear loads, but just having a header doesn't
magically enable the wall-with-opening to resist moments. Your glulam
thing is not typical and not a basis for anything else other than your
house. You've had success with it, but it's not the way things are
usually built. I also don't know how your glulam was designed and the
details of the connection. It is still standing, so that definitely
means something, but I can't comment beyond that.

The shelving analogy has some merit, but it fails on the issue of the
magnitude of the forces. Wind design load can easily be +/- 15 PSF
simultaneously working on the walls and both sides of the roof. The
resultant force would be far greater than pretty much any typical
header connection would be able to withstand. This is why I said it
was misleading to imply that the typical header construction is
capable of satisfying the shear requirements. It can be done, but not
without knowing exactly what you are doing and the exact loads
involved.

Most shelving also has diagonal bracing and doesn't rely on resisting
a 6' moment arm (height of the shelving) with a 7"+ moment arm (the
1x10, fasteners 1" in from edges).

R
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Default Shed project: Shearwall design

On Jun 28, 8:25*am, wrote:
In a free-standing garage, where one wall is almost entirely absent to make
a door opening, what parts of the structure prevent the door wall from
racking?

I am second-guessing myself about my shed plan. *One wall, a gable end wall,
is non-load-bearing but is a shear wall. *Its plan has an 8x8 door opening
in a 12' wide by 9' high wall. *I don't have the background to determine
whether such a wall will have sufficient shear strength. *I'm using
conventional 2x4 framing 16" OC with APA-rated 7/16 OSB sheathing, no
interior sheathing is planned.

The obvious things would be to reduce the door opening, to use heavier
sheathing, and/or sheathe it inside and out. *But first I would like to hear
any advice this august group has to offer, and with my thanks.

--
Due to Usenet spam, emailed replies must pass an intelligence test: if
you want me to read your reply, be sure to include this line of text in
your email, but remove this line before sending, otherwise my filters
will delete your email with all due prejudice. *Thanks!


In a free-standing garage, where one wall is almost entirely absent to make

a door opening, what parts of the structure prevent the door wall from
racking?

the bad new is........(the correct / truthful answer) "not much"

but the good news is

a small (I assume yours in small since you're talking about a 8x8
door)
single story free standing garage requires very little lateral
(shear) capacity unless you're in major wind country


I have a 1930 single story garage with a 16' x 7' door, the garage
is about 22 x 20 (with the garage door & a man door on the 20' face).
So my garage has close to zero lateral capacity on the open face. The
other three walls have stucco over 1x6 horizontal sheathing over 2x4
suds at 16" o/c. It also has 2x4 diagonal blocks in each of the
"solid" walls with a stud bay of the corners.

Not exactly an engineered lateral system but good enough to have
survived the following earthquakes:
87 Whitter (~10 miles), 89 Newport (~10 miles), Landers / Big Bear 92
(~50 miles) and the recent Chino (~15 miles) .


For the Chino quake was working on sawhorses on the driveway in front
of the garage when I felt the ground wave arrive.......I stepped away
from the open garage & watched it sway north/south (the weak
direction) as the rest of the motion arrived.

Bottom line...my ancient garage has very little lateral capacity but
it doesn't need much for e/q's.

The code in CA used to allow "rotation" in the design of three sided
structures but they got kinda conservative (overly imo) & I think they
don't allow it.
Rotation depended on having a relatively rigid diaphragm tying the
walls all together, so that the sides & back worked together to make
up for the "zero lateral" of the front wall.

A four sided "box" but open on the top is pretty
strong ..............but take away one of those sides and now its not
so strong.
Add a structural "diaphragm" to tie all three sides together and now
you've got a strong system again.
If you want to play around with the concepts....build a 1/4 model (use
door skin as sheathing) and a brad nailer attach it.
Build it four sided but with the idea of removing one wall, try to
rack it when it has four walls
remove one wall, rack it gently......at the "flat diapghram" (ie the
top of the box), try to rack it again.

If you build it, "nail" the wall sill plates to a 3/4" plywood base
to serve as a foundation.

As Rico mentions....moment resistant systems involving the garage
header are possible but not easy or simple.

Simpson's prefab shearwall may be the best know but they are by far
NOT the best.

I've tested 100's of shearwall configurations as well has the Simpson
& other pre-fab shearwalls.

Check out ShearMax pre-fab panel www.shearmax.com

concepted, designed & developed by a father / son team; very
inventive but most of all stubborn & persistent....a way better
product than the SImpson


OP-

if you cannot add a flat structural diaphragm to the system to tie the
side walls & the back walls together or if "rotation" is no
allowed.......you can probably use a 4' site built panel to take the
load. But unless you have a local prescriptive code you can use or
your local building dept has a free standing garage "canned design"
like a patio cover, you might be stuck getting it engineered.

If you do get it engineered...ask the engineer how he plans to handle
the concentrated panel hold down loads generated by the a pre-fab
panel. A simple slab is not enoough....most likely require some sort
of grade beam at the open face.

btw, I believe ShearMax has approved panel / header moment resistant
connection details that will avoid the need for grade beams.

As crappy as OSB seems, code affords it the same values as plywood
(plus my testing experience has show no significant difference).
Forget aemeijers suggestion of adhesive, imo not worth the cost,
effort, hassle. And bumping up to 2x6 for a garage is waste of
timber.
Addtionally 7/16 OSB is more than enough for a garage.

cheers
Bob
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Default Shed project: Shearwall design

In a free-standing garage, where one wall is almost entirely absent to
make a door opening, what parts of the structure prevent the door wall
from racking?
I am second-guessing myself about my shed plan. One wall, a gable end
wall, is non-load-bearing but is a shear wall. Its plan has an 8x8
door opening in a 12' wide by 9' high wall. I don't have the
background to determine whether such a wall will have sufficient shear
strength. I'm using conventional 2x4 framing 16" OC with APA-rated
7/16 OSB sheathing, no interior sheathing is planned.
The obvious things would be to reduce the door opening, to use heavier
sheathing, and/or sheathe it inside and out. But first I would like
to hear any advice this august group has to offer, and with my thanks.


An 8' door in a 12' wall doesn't leave much to resist shear forces from
winds or earthquakes. It would be best to increase the shed to 16' wide, or
reduce the door to 6' wide so you can have at least 32" on each side (more
would be better).

I'm no engineer, but another option might be to shift the door to one side
so you can increase the width of a shear wall section.

Otherwise, the only solution I can think of would be a welded steel "moment
frame" that basically makes the entire 12' wall a stiff frame than can't
rack. But that could be an expensive option and would probably need
engineer approval with the building department.

Regardless, you'll need to tie the shear walls securely to the foundation
with special anchor ties (Simpson SSTB) and hold downs (Simpson PHD).

Anthony
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Bob,

bumping up to 2x6 for a garage is waste of timber.


Unless you plan to use the garage as a workshop, in which case 2x6
construction allows you to install more insulation. I used 2x6 framing with
R19 insulation in our garage and have never regretted it.

Anthony
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On Jun 29, 7:54*am, HerHusband wrote:
Bob,

bumping up to 2x6 for a garage is waste of timber.


Unless you plan to use the garage as a workshop, in which case 2x6
construction allows you to install more insulation. I used 2x6 framing with
R19 insulation in our garage and have never regretted it.

Anthony


True...but did OP say where the garage is located?
Insulation makes sense for conditioned space.

In most of SoCal insulating a garage is waste of time & money. In
the desert (high or low) or the mountains...... insulation is worth
it.

cheers
Bob




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On Jun 29, 8:50*pm, fftt wrote:
On Jun 29, 7:54*am, HerHusband wrote:

Bob,


bumping up to 2x6 for a garage is waste of timber.


Unless you plan to use the garage as a workshop, in which case 2x6
construction allows you to install more insulation. I used 2x6 framing with
R19 insulation in our garage and have never regretted it.


Anthony


True...but did OP say where the garage is located?
Insulation makes sense for conditioned space.

In most of SoCal insulating a garage is waste of time & money. * In
the desert (high or low) or the mountains...... insulation is worth
it.


The OP is posting from a SLCC.edu account - Salt Lake City Community
College, so it gets hot and it gets cold.

Upon looking at some of the climate data, the shear wall situation is
less critical in SLC than in some hypothetical unknown location where
conservative advice must be given. SLC has only had two tornadoes in
115 years. Like I said above, let the local code and shear
requirements dictate the design - they shouldn't be too onerous.

R
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On Jun 29, 11:29*pm, "benick" wrote:
"benick" wrote in message
"Smitty Two" wrote in message
wrote:


In a free-standing garage, where one wall is almost entirely absent to
make
a door opening, what parts of the structure prevent the door wall from
racking?


The back wall.


You've NEVER seen a garage...LOL...Sorry about laughing but that was
funny...Once all 4 walls are up it will be fine...No extra thick sheathing
required..Use a 2X8 header with half inch sheating in the middle to make 3
1/2 inches for the wall thickness if using 2X4's.......


My garage (newly built) has a 28X9 foot gable wall with 2 10X8 doors , 2X8
headers , , half inch sheathing , walls bolted to the slab with with no
problems..(Licensed Contractor Built) No steele or glulams or other mumbo
jumbo crap..Doors work perfect ..No racking...No problems at all and we get
3-5 feet of snow and 60+ MPH winds...Every garage I've seen is built that
way....I suppose if you live in hurricane alley or earthquake prone
california , maybe ...It is after all just a SHED....


I have to design for 120 MPH winds, but, more to the point, which in
your opinion is preferable - giving someone advice sight/site unseen
and them having a problem, or telling them to err on the side of
caution? Explain your answer. Show all your work. You have three
minutes. Good luck.

R
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"RicodJour" wrote in message
...
On Jun 29, 11:29 pm, "benick" wrote:
"benick" wrote in message
"Smitty Two" wrote in message
wrote:


In a free-standing garage, where one wall is almost entirely absent to
make
a door opening, what parts of the structure prevent the door wall from
racking?


The back wall.


You've NEVER seen a garage...LOL...Sorry about laughing but that was
funny...Once all 4 walls are up it will be fine...No extra thick
sheathing
required..Use a 2X8 header with half inch sheating in the middle to make
3
1/2 inches for the wall thickness if using 2X4's.......


My garage (newly built) has a 28X9 foot gable wall with 2 10X8 doors , 2X8
headers , , half inch sheathing , walls bolted to the slab with with no
problems..(Licensed Contractor Built) No steele or glulams or other mumbo
jumbo crap..Doors work perfect ..No racking...No problems at all and we
get
3-5 feet of snow and 60+ MPH winds...Every garage I've seen is built that
way....I suppose if you live in hurricane alley or earthquake prone
california , maybe ...It is after all just a SHED....


I have to design for 120 MPH winds, but, more to the point, which in
your opinion is preferable - giving someone advice sight/site unseen
and them having a problem, or telling them to err on the side of
caution? Explain your answer. Show all your work. You have three
minutes. Good luck.

R
I thought he was in Salt Lake City...ie..No hurricanes or
earthquakes....Giving general advice and personal experiences site unseen is
what we do on here...I had no idea you had to be an engineer to post on
here.. Don't hurt your arm patting yourself on the back...I don't have to
explain **** to you and take your 3 minutes and stick it up your arse and
explain the feeling..You have 3 minutes ...Good Luck...

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exactly where on this site are there free plans?
provide a link.


wrote in message
...
On Mon, 29 Jun 2009 20:49:55 -0700 (PDT), RicodJour
wrote:

On Jun 29, 11:29 pm, "benick" wrote:
"benick" wrote in message
"Smitty Two" wrote in message
wrote:

In a free-standing garage, where one wall is almost entirely absent
to
make
a door opening, what parts of the structure prevent the door wall
from
racking?

The back wall.

You've NEVER seen a garage...LOL...Sorry about laughing but that was
funny...Once all 4 walls are up it will be fine...No extra thick
sheathing
required..Use a 2X8 header with half inch sheating in the middle to
make 3
1/2 inches for the wall thickness if using 2X4's.......

My garage (newly built) has a 28X9 foot gable wall with 2 10X8 doors ,
2X8
headers , , half inch sheathing , walls bolted to the slab with with no
problems..(Licensed Contractor Built) No steele or glulams or other
mumbo
jumbo crap..Doors work perfect ..No racking...No problems at all and we
get
3-5 feet of snow and 60+ MPH winds...Every garage I've seen is built
that
way....I suppose if you live in hurricane alley or earthquake prone
california , maybe ...It is after all just a SHED....


I have to design for 120 MPH winds, but, more to the point, which in
your opinion is preferable - giving someone advice sight/site unseen
and them having a problem, or telling them to err on the side of
caution? Explain your answer. Show all your work. You have three
minutes. Good luck.

R


You can get a set of stamped engineered plans for 140MPH here for
free.
http://www3.leegov.com/dcd/BuildingS...ShedAppReq.htm





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On Jun 30, 1:19*am, wrote:


You can get a set of stamped engineered plans for 140MPH here for
free.http://www3.leegov.com/dcd/BuildingS...ShedAppReq.htm


Such plans won't be accepted in a state where the engineer isn't
licensed. It's also kind of odd that an engineer would expose
themselves to such liability without remuneration.

R
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On Jun 30, 12:19*am, "benick" wrote:
"RicodJour" wrote in message

...
On Jun 29, 11:29 pm, "benick" wrote:



"benick" wrote in message
"Smitty Two" wrote in message
wrote:


In a free-standing garage, where one wall is almost entirely absent to
make
a door opening, what parts of the structure prevent the door wall from
racking?


The back wall.


You've NEVER seen a garage...LOL...Sorry about laughing but that was
funny...Once all 4 walls are up it will be fine...No extra thick
sheathing
required..Use a 2X8 header with half inch sheating in the middle to make
3
1/2 inches for the wall thickness if using 2X4's.......


My garage (newly built) has a 28X9 foot gable wall with 2 10X8 doors , 2X8
headers , , half inch sheathing , walls bolted to the slab with with no
problems..(Licensed Contractor Built) No steele or glulams or other mumbo
jumbo crap..Doors work perfect ..No racking...No problems at all and we
get
3-5 feet of snow and 60+ MPH winds...Every garage I've seen is built that
way....I suppose if you live in hurricane alley or earthquake prone
california , maybe ...It is after all just a SHED....


I have to design for 120 MPH winds, but, more to the point, which in
your opinion is preferable - giving someone advice sight/site unseen
and them having a problem, or telling them to err on the side of
caution? *Explain your answer. *Show all your work. *You have three
minutes. *Good luck.

I thought he was in Salt Lake City...ie..No hurricanes or
earthquakes....Giving general advice and personal experiences site unseen is
what we do on here...I had no idea you had to be an engineer to post on
here.. Don't hurt your arm patting yourself on the back...I don't have to
explain **** to you and take your 3 minutes and stick it up your arse and
explain the feeling..You have 3 minutes ...Good Luck...


Stop being so emotional. It's unseemly.

I was the one that mentioned Salt Lake City, but that is still an
assumption until the OP says otherwise. I still use an email account
from my college days - many schools provide a lifetime account.

Your experience with your "newly built" garage really doesn't mean
anything in the way of experience - even if it was "contractor
built". Your experience in construction, whatever that may be, does
not seem to extend to structural design, so it is probably best if you
stick to your area of expertise and not argue with people about stuff
outside that area.

You are confused about what shear resistance is and what is entailed
in designing construction to handle those loads. That isn't a problem
unless you give advice based on that confusion. The attic floor could
be designed and built as a diaphragm to transfer the shear loads, but
it is easier and cheaper to deal with the shear load at the wall with
the opening. A couple of options have been given.

R
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