×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Snow Load Resultant Vectors

Snow Load Resultant Vectors

Snow Load Resultant Vectors

(OP)
When calculating bending moments in roof joists under snow load should you resolve the snow load into a vector perpendicular to the surface and use the true length of the joist. In the formula wl^2/8 if you compare the results of doing it each way using the true length of the joist - even with the reduced load - results in an increase equal to 1/cos or a 25 percent increase in bending moment for a 9:12 roof.  That's because the cos term used in calculating the true length gets squared.

I know a lot of people don't do this including me on occasion but I am wondering if we are underestimating the stresses.

Thanks,
DPA

RE: Snow Load Resultant Vectors

dpa:

Remember, the snow load is on the projected horizontal surface of the roof.  Therefore, you must recalculate the snow load intensity on the actual length:

Let's define the horizontal span as L, the angle between the horizontal and the rafter as theta, and the snow load on the horizontal area as w.  Then:

- The actual rafter length is L/(cos theta)

- w' = snow load intensity on rafter = w (cos theta)

- The resultant of w' perpendicular to rafter = w'(cos theta)*(cos theta) = w'(cos theta)^2

Substituting into the equation for maximum bending moment:

     M = (w'( cos theta)^2)* ((L/(cos theta))^2)/8

     This results in M = (w*L^2)/8 after  combining and cancelling terms.

Regards

RE: Snow Load Resultant Vectors

jec67 is correct -
In all cases, we take the HORIZONTAL span (not the sloped span distance) and simply use wL^2/8 for the moment; where w is based on the PSF of snow on the projected horizontal area.

On the slope - the 1' x 1' area becomes 1' x 1/cos(theta)' which is larger - so if you go to all the unnecessary touble to do things on the slope - you START with a smaller PSF snow magnitude and end up with the same answer.

RE: Snow Load Resultant Vectors

(OP)
jec67,

 Thanks for the quick response but it seems to me that you have an extra cos theta in the term for snow load intensity perpendiculat to the rafter.  It seems like W*cos(theta) is already the intensity perpendicular to the rafter.  If this is correct you would still be left with a cosine in your calculation.

DPA

RE: Snow Load Resultant Vectors

dpa:

w(cos theta) would be the load in the vertical direction as related to the length of the rafter.  One must then resolve this intensity into the components perpendicular to, and parallel to, the longitudinal axis of the rafter.  Therefore, you will wind up with w(cos theta)^2.

RE: Snow Load Resultant Vectors

jec67

Your original statement of "the resultant of w'perpendicular to the rafter" = w'... is a typo I think??. It should be w(cos theta)^2 not the w'. Nice Job anyway.

RE: Snow Load Resultant Vectors

cap4000

Good catch.  It goes to show, no matter how many times one looks at his or her own work, the simplest problems are not caught.

The equations should read:

- w' = snow load intensity on rafter = w (cos theta)

- The resultant of w' perpendicular to rafter = w(cos theta)*(cos theta) = w(cos theta)^2

Substituting into the equation for maximum bending moment:

     M = (w( cos theta)^2)* ((L/(cos theta))^2)/8

I am sorry for any confusion my earlier post may have created.


RE: Snow Load Resultant Vectors

i design roof joist as stated ealier simply by looking at the projected snow load and the horizontal length.

what is important when looking at the problem that way is to remember to increase the dead load by 1/cos.

RE: Snow Load Resultant Vectors

I must be having a dumb day today.....

If snow loads are supposed to act on the horizontal projection of the sloping surface, then wouldn't "w" act on "L"?  To convert it to the equivalent vertical load intensity along the length of the rafter (equal to L/(cos theta)) then wouldn't w' = w/(cos theta) and not w*(cos theta)???

RE: Snow Load Resultant Vectors

KarlT

The intensity along the length of the rafter is w(cos thaeta).  Think of it this way:  The total load is the horizontal length times the snow intensity on the horizontal plane, or w*L.  To find the intensity along the rafter length, divide the total load by the rafter length.  The rafter length is L/(cos theta).

Substituting:

(w*L)/(L/(cos theta)= w*(cos theta)

RE: Snow Load Resultant Vectors

Well, you know if we could just convince those architects to stay with that old marxist, socialist design from the Bauhaus days, with flat roofs, we wouldn't have to worry about all this complexity.

RE: Snow Load Resultant Vectors

Using the horizontal projected snow load and increasing the DL by diving it by (cos theta) is most common method.

You can "DECREASE" the snow load to along its actual length by multiplying the load by (cos theta).  Then breaking it down further into the appropriate "x" and "y" resultants.  

Either way, the moments and shears are the same.  The horizontal projection method is quicker.  

For additional info, refer to the 2nd ed of "Design of Wood Structures" by Donald Breyer, pages 21 thru 24.
 

RE: Snow Load Resultant Vectors

Just too add just a little more complexity to all off this.
Be very careful of the "deflection" of the rafter based on its true inclined length, and the "axial" load force component acting on the rafter(running down towards the wall end) due to the roof pitch.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources