Rafter Span Table Question

[idecharlotte]

Has anyone noticed the rafter span tables in the IRC and AFPA seem off? I use the horizontal projection and all the factors from the NDS. Although bending seems close, deflection seems way off. For instance, the IRC shows 22'3" for 20/10 loading of 2x10@16" SPF#2 @ L/240. I calculate a deflection of L/168 at that span using 1.4 million psi modulus of elasticity. What am I missing?

http://www.idecharlotte.com

 

[msquared48]

Is the table only listing the live load deflection?

Mike McCann
MMC Engineering

 

[idecharlotte]

I believe the tables are only listing live load deflection but regardless, total load deflection shouldn't be more than L/180. I'm getting L/168

http://www.idecharlotte.com

 

[msquared48]

Check the table again to see if the "span" is the horizontal or the slope length. The effective load applied will depend on that.

Mike McCann
MMC Engineering

 

[idecharlotte]

Roof slope doesn't matter. If you have the IRC you can see the tables for yourself. The span is the horizontal projected span as is the loading. No reduction has been made for the slopes. No slopes are indicated in the tables. So one can assume a flat roof condition and there is no need to account for roof slopes with regards to verifying the span lengths in the tables.

http://www.idecharlotte.com

 

[JAE]

I got the following:

Span = 22'-3"
L/240 = 1.11"

Uniform LL = 20 psf x 1.33 ft = 26.6 plf

E = 1,400,000 psi
Ix for a 2x10 = (1.5 x 9.25^3)/12 = 98.93 in^4

Deflection under LL only:

(5 x 26.6/12 x (22.25 x 12)^4) / (384 x 1,400,000 x 98.8)

= 1.06 inches vs. 1.11 inch limit

Seems pretty close to me. I'm not getting your L/168 = 1.59".

 

[msquared48]

idecharlotte:

Sorry, but I beg to disagree here. See attached calculations. I will have to post twide for both pages.

Mike McCann
MMC Engineering

 

[msquared48]

And the econd page:

Mike McCann
MMC Engineering

 

[JAE]

Mike,

On your equation w(perp) = 1.6/L2.....shouldn't that be 1.43/L2.

The bending moment along L2 should be calculated using the perpendicular force component. The parallel component runs down the longitudinal axis of the beam and thus adds no bending moment to the beam along L2.

This results in the same bending moment for each way of looking at it.

Just asking.

 

[JAE]

Also, your deflection using wu and L1 is the vertical deflection at midspan.

The deflection using w(perp) - which should also be 0.080 k/ft - is the deflection perpendicular to the beam and needs to be converted to a vertical deflection to compare with the other deflection. I don't think the deflections are equivalent but the shears and moments are.

 

[msquared48]

I agree with the moment and shear. My bad on the moment... duh.

However, I do not think that one should compare vertical deflections here, but deflections normal to the main axis of the rafter. I think that will give the true result, particularly if you are dealing with tile roofs where every abnormality is very observable. After all, if the rafter is laid flat, this is the deflection that it actually sees. I get a 25% difference in deflections with this method. It may be more conservative, but I think the roof performance will be much better.

Mike McCann
MMC Engineering

 

[idecharlotte]

I guess I see where the difference lies. I assumed there was a deflection limitation on total load in addition to live load. Assuming a flat roof, my calculations are as follows:
w(LL+DL)= (20+10)psf x 1.33 = 39.9psf
E= 1400000psi
I= 98.8in4
@ 22.25' defl = 1.6" or L/168

Reading through the IRC I don't see a total load deflection criteria. I personally wouldn't design this way, but at least i see where the Code is getting its Tables.
Thanks.

http://www.idecharlotte.com

 

[msquared48]

In the Timber construction manual for roofs, the live load deflection is l/240 and the total load l/180, whereas for floors it is l/360 for live and l/240 for total.

FYI, where ever I have gyp on the ceiling at a roof, I use the same deflection criteria as for the floor.

Mike McCann
MMC Engineering