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 Subject: Engineering Question - Max Windload Category: Science > Physics Asked by: pamsauto-ga List Price: \$25.00 Posted: 15 May 2004 11:50 PDT Expires: 14 Jun 2004 11:50 PDT Question ID: 346834
 ```What is the maximun windspeed a fence that is constructed this way can withstand before the posts will break off? The top height of the fence is 8 feet from the ground, the fence has sheet steel on it that is 7 feet tall and starts at the eight foot height and comes down to 1 foot off the ground. The posts that hold the fence up are 4"x6" Green Treated SPF Pine. The posts are orentatied with the 6 inch side parrallel to the fence's face and are 8 foot on center. The fence has 2x4 girts on it that are nailed to the posts with the 2 inch side touching the post and the time is nailed to the girts. The fence is fully exposed to the wind.Please show your math with this answer or provide a link to the math.```
 ```Hello pamsauto, your question is a fairly simple problem in statics. You did a very good job of providing all necessary info. To convert wind speed to force per square foot: Force (lbs/square foot) = wind speed (miles/hour)^2 x .0027 This force (actually pressure) acts on an area (tributary area) of the amount of fence supported by each post: A = 7 ft (material height) x 8 ft (post spacing) = 56 ft^2 (square feet) The distance from the ground (where the maximum bending stress in the post occurs) to the vertical center of the sheet steel is: D = (7 ft / 2) + 1 ft = 3.5 + 1 = 4.5 ft What we have here is actually a cantilever beam. The post being a beam fastened at one end (the ground) and free at the other. The formula for the bending moment in this case is: M = F x L (or in our case D) The bending moment (overturning torque) is found by: M = F (force of wind) x D = wind speed^2 x .0027 x 56 ft^2 x 4.5 ft Multiplying by 12 (inches per foot) to change the answer into inches^3 we have: = wind speed^2 x 8.16 The strength of a 4x6 post in bending (section modulus) is calculated by: S (section modulus) = b (base) x d (other dimension)^2 / 6 Since a 4x6 is actually 3.5 x 5.5: S = 5.5 x 3.5^2 / 6 = 5.5 x 12.25 / 6 = 11.2 inches^3 NOTE: The way you have chosen to orient the 4x6 is the weak direction for wind loading. If oriented in the other way, S would be: S = 3.5 x 5.5^2 / 6 = 17.6 inches^3 The formula for the bending stress (Fb) is: Fb = M / S or bending moment / section modulus Writing this another way we have: M = Fb x S Substituting the values we have calculated above we get: wind speed^2 x 8.16 = Fb x 11.2 inches^3 Dividing both sides of the equation by 8.16 we have: wind speed^2 = Fb x 1.37 Taking the square root of both sides we have: wind speed (miles per hour) = sqrt (Fb x 1.37) Here is where we must do some estimating. The values published for the bending strength (Fb) for SPF lumber vary quite a bit depending on where the wood is harvested and exactly what species of pine is involved. I think a conservative number might be 800 psi. This is the value given in my "Machinery's Handbook" for White Pine in an outside location. Using this number we have: wind speed = 33 MPH If you were to orient the 4x6 in the other direction, you would increase the wind speed to 42 MPH. If the actual strength of the 4x6 posts is greater that what I used, you will also get an increase. For instance the value given for Southern Yellow Pine is 1100 psi. Using this higher number and orienting the 4x6 in the stronger direction you would get 48 MPH. I suspect that you are surprised at the low MPH numbers we calculated. I know you would like to see a 100 MPH figure instead. One thing in your favor is that these calculations assume that the wind is acting exactly perpendicular to the fence. In actual conditions this is hard to achieve. Also, wind is not a constantly applied force and you can apply factors which will increase the rating (published numbers range from 1.3 to 1.6). Applying the 1.3 number would give us an increase to 1.3 x 42 or 55 MPH. Another factor is where you live related to maximum wind speeds seen in your area. You didn't say how you are planting the 4x6 posts into the ground. There is the possibility that the fence could blow over before the posts break. I hope that this answers your question and helps you in your design choices. I will assume no liability for these calculations and they are offered strictly for academic interest with absolutely no applications to the real world (sounds like the disclaimer at the beginning of "South Park" doesn't it). Redhoss``` Request for Answer Clarification by pamsauto-ga on 16 May 2004 12:53 PDT ```Exactly the answer I was looking for. I had thought of the "Ground Breakout" problem also. For a 25 dollar tip would you be willing to figure this out also? The posts are in the gound 30 inches. They are in a 12 inch diameter hole. The bottom 6 inches of the post are in packed soil. The top 24 inches are poured 3000psi concrete. It has not been vibrated if this matters. The soil condidtions are 8 inches of black soil on top and the rest is a very loose and course gravel. Some holes when drilled would collapse below the black dirt.``` Clarification of Answer by redhoss-ga on 16 May 2004 15:03 PDT ```Thank you for your kind words. It makes a poor old burned out engineer feel good to be appreciated. I have done many footing calculations and I don't like doing them (very tedious by hand). They are very inexact, tend to be very conservative (over designed), and without soil tests pretty useless. I have built a few fences and many carports. Your footing design looks adequate to me and I think it would be a toss up as to whether the footing or 4x6 would fail first. If you are really interested, you might perform a test. I did this accidently one time. A city building department questioned my footing design. I met the city plan checker at the job site. I arrived there first and noticed that a forklift had accidently driven over one of my columns. The column was bent over at the base and the footing hadn't budged. I showed this to the plan checker and he was satisfied.```
 pamsauto-ga rated this answer: ```Very detailed and prcise answer. Researcher did not miss ANY part of the orginal question I asked. Thanks.```