Engineering Question - Max Windload
Category: Science > Physics
Asked by: pamsauto-ga
List Price: $25.00
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.
Re: Engineering Question - Max Windload
Answered By: redhoss-ga on 16 May 2004 07:46 PDT
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
rated this answer:
Very detailed and prcise answer. Researcher did not miss ANY part of the orginal question I asked. Thanks.
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