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Truss Reactions

Truss Reactions

Truss Reactions

(OP)
I am trying to work through the ASCE 7-98 formula to determine the uplift reaction
on one end of a particular truss. This is a one story residence in Florida with a
cement tile roof.

Taking a truss plan from the truss company the following are given.

ANSI / ASCE 7=98
130 mph
Exposure B
Building Cat. II
Importance Factor 1.0
Enclosure  partially Enclosed
Mean Roof Height > 15'

Live Load 30
Dead Load 25
Pitch 7/12 , Ridge in center
Overhang 20"
Spacing 24" OC
Building is 16' by 21'

Looking at truss 11A which has a span of 16' the reactions are shown as
(1037 and -447) (1037 and -445) for the two bearing points.

My calculations for wind normal to ridge are as follows:

-----------------
Vertical Pressure
-----------------
Qh    = 0.0025 Kz  Kzt  Kd   V^2   I

25.14 = 0.0025 0.7 1.0 0.85 130^2 1.0

Kz  table 6-5 Exp B Case 1 Roof Ht < 40'
Kzt no topo issues use 1.0
Kd  Table 6-6 houses 0.85
V   Wind speed 130 mph Figure 6-1b
I   Importance Factor Table 6-1  houses 1.0


-----------------
Effective Area
-----------------
 4'x8' of plywood 32 sq ft
 
-----------------
Distance 'a'
-----------------
  smaller of 0.1 (16'width) = 1.6'
  or 0.04 (16' least hor dist) = 0.64'
  but not less than 3'
  therefor a = 3'
  
-----------------------------------------------
External Pressure Coefficient Figure 6-5b pg 46
-----------------------------------------------
  Zone 1 = (-0.84) for 32 sq ft
  Zone 2 = (-2.2) with overhang
  

----------------------
Design Pressures (psf)
----------------------
  p = Qh  [ (GCp)-(GCpi)]
  GCpi = (0.55) partially Enclosed
  
  Zone 1
  -34.94 = 25.14 [(-0.84)-(0.55)]
  Zone 2
  -69.14 = 25.14 [(-2.2)-(0.55)]
  
-----------------
Tributary Area
-----------------
  area = [length + (2 x overhang)] (spacing)
  area = [16' + (2 x (20" / 12))] (24 / 12)
  area = 38.7 sq ft
  
-----------------------------------------------
There are 4 'Zone 2' areas at 3' each at 2' wide
-----------------------------------------------
  Zone 2 area = 4 x 2 x 3 = 24 sq ft
  Zone 1 area = Trib Area - Zone 2 area
  Zone 1 Area = 38.7 - 24 = 14.7 sq ft
  
------------------
Pressure on truss
------------------
Note, because I am only considering the windward side of the truss
the areas are halved.
  P1 = (Zone 1 area) (Zone 1 Design Pressure)  
  P1 = (14.7 / 2) (-34.94) = -256.80
  P2 = (Zone 2 area) (Zone 2 Design Pressure)  
  P2 = (24 / 2) (-69.14) = -829.68
  
  Pressure at bearing point
    P1 + P2 = -1086.48
  Dead load applied
    (Trib Area) (DL)
    (38.7) (25) = (967.5 / 2) = 483.7 DL
    Truss Pressure + DL = Total reaction
    -1086.49 + 483.7 = 602.74 Lb.
    
Where did I go wrong?
I'm not an engineer so talk slowly. :)

RE: Truss Reactions

There's a couple of things it might be.  

Some truss engineers use MWFRS pressures for trusses.  Some use components and cladding.  Did you check which were used in your case?

The effective wind areaneed not be less than the span times one-third the span length for members.  See the definition of Effective Wind Area on page 24.  This is good only for member design as the definition states.  For connections you have to use the area tributary to the connector itself.  The output you are reading may be for either one of these.  So the effective area should be the greater of the actual tributary area for the member or (span^2)/3.  For connections it should be the actual tributary area.  

Note also that the governing load case for uplift is usually 0.6D+W on page 5.  That means you can use no more than 60% of the dead load to resist uplift.  Note also that many times truss engineers will account for no more than the lesser of 0.6D or 10psf for dead load resisting uplift.  

Technically, at 7:12 pitch you're at arctan(7/12)=theta=30.3 degrees.  Since that is greater than 30 degrees that puts you on page 47.

RE: Truss Reactions

(OP)
Thank you very much for taking the time to reply. Your information is very helpful.


>>> Some truss engineers use MWFRS pressures for trusses.
Ah, I did see that listed on the truss document but reading a guide book for ASCE 7-98
the author said because the trusses receive wind load directly from the cladding that
they trusses are considered cladding too. I suppose there is some debate there.

> So the effective area should be the
> greater of the actual tributary area for the member or (span^2)/3.  For
> connections it should be the actual tributary area.

Thanks of that clarification.
Funny, as it turns out the tributary is also 32 sq ft  (16 x 2)

As for area calculations in this matter, is there a time when you use the actual
area of the sloped surface? I was using the span and not the actual surface area.

>>> Since that is greater than 30 degrees that puts you on page 47.
Thanks for pointing me to the correct page.


Here are the revised calculations, still 156 lbs. higher than the truss guy, but I'll
keep looking for the difference.

--------------------------
Vertical Pressure - MWFRS
--------------------------
Qh    = 0.0025 Kz  Kzt  Kd   V^2   I

22.27 = 0.0025 0.62 1.0 0.85 130^2 1.0

Kz  table 6-5 Exp B Case 2 Roof Ht < 20'
Kzt no topo issues use 1.0
Kd  Table 6-6 houses 0.85
V   Wind speed 130 mph Figure 6-1b
I   Importance Factor Table 6-1  houses 1.0


-----------------
Effective Area
-----------------
 4'x8' of plywood 32 sq ft
 
-----------------
Distance 'a'
-----------------
  smaller of 0.1 (16'width) = 1.6'
  or 0.04 (16' least hor dist) = 0.64'
  but not less than 3'
  therefor a = 3'
  
-----------------------------------------------
External Pressure Coefficient Figure 6-5b pg 46
-----------------------------------------------
  Zone 1 = (-0.86) for 32 sq ft
  Zone 2 = (-1.93) with overhang
  

----------------------
Design Pressures (psf)
----------------------
  p = Qh  [ (GCp)-(GCpi)]
  GCpi = (0.55) partially Enclosed
  
  Zone 1
  -31.40 = 22.27 [(-0.86)-(0.55)]
  Zone 2
  -55.23 = 22.27 [(-1.93)-(0.55)]
  
-----------------
Tributary Area
-----------------
  area = [length + (2 x overhang)] (spacing)
  area = [16' + (2 x (20" / 12))] (24 / 12)
  area = 38.7 sq ft
  
-----------------------------------------------
There are 4 'Zone 2' areas at 3' each at 2' wide
-----------------------------------------------
  Zone 2 area = 4 x 2 x 3 = 24 sq ft
  Zone 1 area = Trib Area - Zone 2 area
  Zone 1 Area = 38.7 - 24 = 14.7 sq ft
  
------------------
Pressure on truss
------------------
Note, because I am only considering the windward side of the truss
the areas are halved.
  P1 = (Zone 1 area) (Zone 1 Design Pressure)  
  P1 = (14.7 / 2) (-31.40) = -230.79
  P2 = (Zone 2 area) (Zone 2 Design Pressure)  
  P2 = (24 / 2) (-55.23) = -662.76
  
  Pressure at bearing point
    P1 + P2 = -893.55
  Dead load = (Trib Area) (DL)
    (38.7) (25) = (967.5 / 2) = 483.7 DL
  Dead Load Adjusted = (0.6) (483.7 DL) = 290.22
  
  Total reaction = Truss Pressure + DL.6
    -893.55 + 290.22 = 603.33 Lb.

RE: Truss Reactions

Whether to use components and cladding or MWFRS for trusses is open to debate.  If you search this site you'll find a few different threads discussing this topic.  That may be the difference that you are seeing in your numbers, but then it could be something else also.  If you get really bored, try using the MWFRS numbers and see what you come up with.

Yes you can, and really should, use the actual sloped area for your wind force instead of just the horizontal projection of the area.  For symmetrical trusses though it really won't make a difference.  

When you put the pressures on the truss like this, you'll see that the pressures are directed vertically and away from each other at an angle.  If the truss is symmetric then the horizontal component of those forces (pressure*area) will cancel out.  You are then left with the vertical components acting upward.  

With these vertical components, you are getting a slightly smaller pressure that acts over a slightly larger area, so you end up with the about same result.  If your truss is not symmetric however, you will not get the same result as if you just used the horizontal projection of the area like we are talking about above.  You may end up with unbalanced uplift forces and a net horizontal force that you have to deal with.

RE: Truss Reactions

(OP)

Thanks again..
In the last calculations I did use the MWFRS of 0.62 for Kz and changed the Zone 1 & 2
External Pressure Coefficients which would lower the net uplift but because of my error
using the full dead load in the first calculations the second calculations net was nearly
the same.

I'll look for another truss package so I can compare may calculations to another source.

RE: Truss Reactions

A note about MWFRS & C&C:
Mitek truss designers (and others) have the capability to design trusses with a Hybrid MWFRS+C&C criteria.
That is not the maximum forces & reactions for all conditions, but rather;
The truss component itself is correctly designed with C&C criteria.
The reactions (vert/uplift/horz) are based on MWFRS for the system of trusses and the EOR's use in building design.

Building design with only MWFRS truss calcs, or only C&C calcs, makes for extra EOR expense in time.

RE: Truss Reactions

(OP)
Thanks for the information.
That might explain the deference I see in there calcs & mine.

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