NDS wood diaphragm Table 4.2--what if inclined roof? 3

[hippo11]

In the NDS 2005 wood diaphragm Tables 4.2A, B, and C, values are given for different nailing patterns, sheathing thickness, grade, etc...but what if my roof is a 30 degree gable? Does anyone know where I can read about how inclines affect unit shear resistance values, etc., for a sloped roof diaphragm?

Thanks.

 

[JAE]

StructuralEIT,

Using your example, I have a 10 kip horizontal force coming in at the node.

The node has only two elements attached to it: the sloping diaphragm and the vertical wall.

Free body diagram

The 10 kip force can only be resisted by the horizontal COMPONENT of the diaphragm. There is nothing else to resist it.

Thus, there is a sloping RESULTANT which is comprised of a horizontal COMPONENT (equal to the 10 kips and is LESS than the sloping Resultant) and a vertical COMPONENT.

So (Horiz 10kips)² + Vertical² = Sloping Resultant²

The vertical component is a downward force resisted by axial force in the vertical wall. Both the vertical wall and the sloping diaphragm have axial compression.

[Σ]F = 0 in both directions.

 

[Lion06]

I may be coming over to the dark side, I just want to think about it a little more.

 

[CJJS]

JAE,
OK. I see what you are saying now. I think both ways are correct as hippo11 notes.

 

[hippo11]

Not to get too philosophical about this...but the whole idea of "horizontal" and "vertical" components is really just man's attempt to simplify and categorize a truly 3-D world of infinite axes into 2 axes, artificially called by someone "X" and "Y" or "horizontal" and "vertical".

You can legitimately resolve any resultant into components on of any set of axes you want, called "P" and "Q", oriented at 22.32345 degrees and 112.32345 degrees (as long as they're perpendicular to each other).

I think as long as you fully design for either

1. your resultant OR

2. ALL your components

that you are being geometrically correct.

 

[CJJS]

JAE,
How does the shear from the windload on the wall get into the roof diaphragm if the wall can only take axial load?

 

[JAE]

Well, the wall can take only axial load via the top node, but yes, the wind is actually delivered to the diaphram via bending and shear.

Here's a layout of the FBD:

 

[CJJS]

Thank you. That helps clear it up. So, the two ways to check the diaphragm are:
1. Calculate the horizontal unit shear (H divided by the projected horizontal length) and compare it to the tabulated allowable.
2. Calculated the unit shear along the lenth of the diaphragm (R divided by actual length of panel) and compare it to the tabulated allowable.

Correct?

 

[JAE]

You take the H from the wall analysis, and it is applied horizontally along the eave.

(my sketch above shows it in the form of a concentrated load in kips, but in reality, the lateral wind comes into the diaphragm along the wall in lbs./ft.)

This is like a horizontal uniform load on a "horizontal" beam...the beam being the diaphragm spanning from end-wall to end-wall.

Then you calculate the "R" value in lbs/ft (= H/cos[Θ]). This is your uniform load on the diaphragm.

Calculate your diaphragm end shear = 0.5 x (R x Length of wall)/(depth of diaphragm along the slope). This is your diaphragm shear to be compared with the IBC tables or equivalent.

 

[hippo11]

how'd you upload an image? useful

 

[JAE]

hippo11 -

key on the "Process TGML" button below the message window and it will show you how to insert an image (Under the "Image" section).

You have to have a website where you can upload pictures and link to them. I use VillagePhotos.com but there are a number of sites out there. Then you just insert the URL of the photo on the site into a message box on Eng-Tips.

 

[Lion06]

I think I agree with JAE now. That means that the studs need to be designed for a significant axial load in addition to the out-of-plane wind load. Weel, it can be significant if the roof has a decent slope to it.
Does this normally happen - adding in that compression?

 

[CFSEng]

Well I haven't fully given in to the 'Dark Side' yet

Wouldn't the FBD shown assume the diaphragm is a support as drawn? I thought the idea of a diaphragm is the support is the shearwall which typically is on a wall perpendicular to the wall drawn. I would think the diaphragm would need to be thought of more as a 3d plate element with horizontal supports along the shearwalls.

Of course this discussion is neglecting any actual uplift or downward forces from the wind directly applied to the diaphragm