wind loading on 20m tall lattice tower

huangyhg

wind loading on 20m tall lattice tower
i need to evaluate the structural safety of a 20m high steel lattice tower against overturning, built of galvanised steel pipes.  
the tower is of 1.5m equal sided triangular section in plan at the bottom, tapering to about 0.5m equal sided triangular section at the top.
the footing is of concrete, size 2.0m x 2.0m x 0.9m thick and the top is 0.1m above the ground.
the soil bearing capacity is estimated to be 150 kn/m2 and the self weight of the tower is estimated to be 1 ton.
the wind speed in the area is estimated at 40m/s.
my biggest problem is in determining the overturning moment due to wind.
bsems  
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in the us, towers are generally analyzed using software.  there are some out there specifically designed for towers such as eri tower.  a free standing tower like yours can also be modeled in most structural analysis software accurately.  for the latter case you will have to do more hand calcs to apply the wind loads to the tower face.  the standard is tia/eia-222-f structural standards for steel antenna towers and antenna supporting structures.
if you just need to check overturning (you're sure the structure is ok?), then figure the wind loads based on the applicable code and draw your free body diagram.  apply the load in different directions which will make you moment arm to the foundations vary to determine the worst case.  tia uses wind from three different directions.  all of your dimensions are in meters so i imagine you are not in the us and the tia may not be the code to use.
i tried the calculation assuming that the tower was solid, which is very much a worst-case assumption. using a wind pressure of 1/2*rho*v^2, i came up with the following equation for moment as a function of tower height:
     m(x) = 1500x - 50x^2
integrating this from 0 to 20 gives me an overturning moment of 166,000 n-m.
marty
bsems,
the wind speed of 40m/s looks like a basic wind speed to me. if you refer to your code, you will find several factors on top of this depending upon importance and life of the structure. so ultimately you will be working with much higher wind speeds.
i would say that the overturning moment is about 500 kn-m.
bsems:
use the eia/tia code to determine the loads on your tower.  this code is provided in both english and metric.  you only have to calculate the area of one face of the tower and apply the proper cf ratios for the two different directions that you need to check, along with the gust response factors, exposure coefficient and other items.  don't forget to add any appurtenances such as ladders, cables, dishes and antennas.  this all can be set up as a simple manual analysis using a spreadsheet.  a good example of how to proceed is provided in example problem 11 of the wind commentary to the uniform building code published by the structural engineers association of washington (state).  use the eia/tia for you forces, but follow the simple procedure shown in the commentary.
also research the archieves for other comments concerning tower design as this item has been discussed a number of times.
get a copy of asce 7 and use it. it has provisions for latticed towers. i am sure the british code has the same provisions because i used them.
you have to address the solid ratio when computing wind force. this means that you have to have the tower member sizes.
once you determine the wind force on each vertical panel, or total wind force, you can apply it at the center of gravity of the entire tower height and you can secure the over turning moment. do not ignore the additional moment due to the tower base shear depending on its height above the base of the footing.
the use of 3-d software such as staad is a good way to check on the tower   
you can use cp3 chapter v part ii [british], bs8100 [british and more relevant - but may be a little complicated at first] or as3995 [australian] or as1170.2-2002 [australian], or eia rs 222e or f [and similar other international standards] to calculate solidity ratio and subsequent wind forces on the tower.  you need to know panel height, geometry and section sizes.  20m tower is a small structure and can be easily analysed manually.  however there are dedicated software like mstower to calculate this.  you need to apply height factor, gust factor etc to the basic design wind speed before establishing the applicable wind pressure.  usse this pressure to calculate module forces and then the base bending moment.  hope above suggestion will help you.