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Last Post 12/16/2010 7:40 PM by  Tim Johnson
Geometry Problems
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Medulus
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08/20/2010 12:40 PM
    We all use basic geometry in our profession.  For instance we know that the area of a gable roof slope is the base times the height or that a triangle is the base times the height divided by two.  Here are a couple that are less common.  What formula would you use and how would you determine the square footage of the following?
     
    You visit a farm after a windstorm.  The domed metal silo is damaged.  How would you calculate the square footage of metal needed to replace the exterior metal?  How would you calculate the dome?  (I've had claims with this scenario.)  BTW, calling a contractor and asking for a quote is NOT the correct answer.
     
    You are asked, after a hurricane, to handle a claim involving a domed sports stadium.  You find that the rubber membrane of the domed roof is compromised and the roof membrane will need replacement.  How do you calculate the square footage of the dome?  (I've also had a claim like this, except that it could be repaired rather than fully replaced.)
    Steve Ebner CPCU AIC AMIM

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    ChuckDeaton
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    08/20/2010 2:17 PM
    On a domed sports stadium, if the roof membrane were being totally replaced, on a job that big i would want to see original documents, the documents from when it was roofed last and the original plans. Working with the architect, we would agree on an engineer whose responsibility would be to determine the number of squares involved and based on agreed specifications we would put the job out for competitive bids and let a contract.

    On a grain bin, I would determine the brand name, it was a Butler, then I would call Butler and have them send me a set of plans and see if they would provide the repair materials.
    "Prattling on and on about being an ass with experience doesn't make someone experienced. It just makes you an ass." Rod Buvens, Pilot grunt
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    Sabre
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    08/20/2010 3:10 PM
    You would need to calculate the surface area of the sphere then divide by 2.
    4 times pi r squared / 2  
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    Ray Hall
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    08/20/2010 3:47 PM
    These are good questions to get you thinking. I was an energy adjuster for London during hurricane Andrew in 1992. We did not know how much a 3 leg jack up rig with 300 foot legs cost to replace on an ACV basis. We just started with the basics of the original cost, increase cost, wear and tear, obsolesce, improvements, past day rate, future day rate, GOM  and world wide needs -past and future. We worked with our engineers and got an agreed amount. We all had lots of insurance and oil patch experience.
     
    You would not hire a person to work private aircraft losses claims unless they had a pilots license. Many of these long tail seafood claims from the BP spill will have  consultants and CPA,s involved, not many roof thumpers will be involved
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    ChuckDeaton
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    08/20/2010 8:20 PM
    Since this thread references sports stadiums and the only domed sport stadium that I am aware of damaged by a catastrophe is the New Orleans Super Dome, damaged in Hurricane Katrina. I would like to know, exactly, how would an adjuster would go about collecting the physical measurements needed to calculate the surface of the decking. Would the decking measurement be the same as the interior ceiling measurement? The measurements would be used to write an estimate so they need to be reasonably accurate.

    Could one person complete the measurements and what equipment would be utilized? Could one of the satellite companies provide a measurement?
    "Prattling on and on about being an ass with experience doesn't make someone experienced. It just makes you an ass." Rod Buvens, Pilot grunt
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    Ray Hall
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    08/21/2010 12:13 AM
    Chuck, did you have your tounge in your cheek. I do not think the superdome roof repair cost was determined by an adjuster getting a data base price out of any adjuster estimating program software. I really think someone is on your computer....please change your password.
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    rickhans
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    08/21/2010 1:15 AM
    When you talk about a dome, does it have a straight surface like an upside down ice cream cone?  If so, and if I remember my geometry, the surface area is the circumference of the base times the length of the slope to the tip divided by 2.   If you are referring to a spherical shape dome, I don't think there is one specific formula without knowing the actual design, especially if the vertical plane has a varying radius.
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    WILLIS
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    08/21/2010 1:22 AM
    Which one of you brave souls plans to climb up on the Dome to secure the necessary measurements to use the formula.  Might consider finding the Architect and look at their building plans  assuming you can read blueprints.  I have climbed up on Farm Silos to take the measurements following hail. Nice View.  Water Towers are interesting. If you ever have a loss check the pillar supports for a cabinet opening. It will give you all the data you need to calculate the dome and all the parts of the tank.  Losses this large is why engineers attended Georgia Tech. 
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    ChuckDeaton
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    08/21/2010 10:21 AM
    The Super Dome belongs to the State of Louisiana and any claim is covered under the State's self insurance program. Claims are handled by contract adjusters. FARA won a bid to take over claims handling for the state and will eventually be responsible for claims on the Super Dome. At least that is what I hear.
    "Prattling on and on about being an ass with experience doesn't make someone experienced. It just makes you an ass." Rod Buvens, Pilot grunt
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    joe60
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    08/21/2010 11:38 AM
    I am willing to bet that  the measurements would be obtained by GPS, including the heigth of the structure, to determine whether the roof is a semi-sphere or a larger or smaller portion of the entire sphere. Sorry Chuck. I did not see your sattellite comment, at first. Not very good attention to detail, on my part.
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    Medulus
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    08/21/2010 1:25 PM
    Bravo, sabre. You have the dome at the top of the silo figured out. Part of the answer. The domed sports stadium is more of a challenge, as I will point out a little later in this post.

    The great thing about being an adjuster in 2010 is that, even if you forget how to calculate something, the formula can be found with a couple clicks of the mouse. The value of pi can be found to any decimal place you want by a couple mouse clicks, as well.

    A few additional comments -- As adjusters we are probably going to get quotes on projects like these, but we should still be able to calculate whether they are based on accurate measurements. I would calculate the area of these, and did, just to be able to double check the accuracy of estimates I obtain from the contractors who will replace them. Sabre gave us the correct formula for a dome. But what formula would you use to determine the amount of siding on the silo?

    The dome I measured and inspected was actually the sports stadium/concert venue belonging to the city of Hampton, Virginia, after Hurricane Isabel. Walking on it was actually fun, and much easier than one might imagine. The problem with using Sabre's formula to calculate the area of the stadium dome is how to get the value of "r" (the radius of the circle). The seating gets in the way of accurately measuring the radius from the floor. The only real measurements you can get that are pertinent are the measurement across the top of the dome and perhaps the circumference. So how do you figure it out?


    Steve Ebner CPCU AIC AMIM

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    Medulus
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    08/21/2010 3:49 PM
    BTW, rickhans raised an issue that is also relevant for measuring a dome. Assuming a spherical type dome, we also need to consider whether this dome is really half a sphere or something less than half a sphere. The most we can say is that it is a portion of a sphere.  How would we determine what portion that is?
    Steve Ebner CPCU AIC AMIM

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    jdacree
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    08/21/2010 6:30 PM
    for the value "r" if you know a chord and and a chord height the solution is

    c2+4h/8h=r This only works for a circle. machinery handbook has the same type of calculation for a sphere.

    once you have the "r" then you can measue from the top of the dome to the eaves to determine the percentage of the spere.
    Jim Acree Stupidity is the art of not trying to learn Ignorance is the lack of opportunity to learn I am ignorant
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    Medulus
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    08/22/2010 6:51 PM
    Jdacree, I'll ask you to please explain what a chord is.
     
    BTW, the answer to calculating the amount of material needed to reskin the exterior of the stack of the silo is 2piR (circumference of a circle) times the height.  Most of the time it wraps around and overlaps, so there would be a 10% waste factor or so, even though the pieces are most likely preformed in various lengths.    The dome is then calculated using the formula for a sphere, as shared earlier in this thread, and dividing it in half.
     
    We may have the answer to the dome problem, too, as soon as we find out what a chord is.  I'm not being coy, here.  I really don't know.
    Steve Ebner CPCU AIC AMIM

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    jdacree
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    08/22/2010 6:58 PM
    A chord is the distance across the bottom of the spherical segment. Think of an ice cream cone. The chord is where the top of the cone meets the ice cream.
    Jim Acree Stupidity is the art of not trying to learn Ignorance is the lack of opportunity to learn I am ignorant
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    jdacree
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    08/22/2010 7:02 PM
    The chord height is the distance from the chord to the top of the spherical segment. Once you have firgured the "r" value you can use the chord height to figure the percentage of the sphere. Example if the chord height is 10 feet and the R value is 100 feet, the percentage of the sperical segement is 10%. Knowing this then the area of the segement is 10% o the area of the spere.
    Jim Acree Stupidity is the art of not trying to learn Ignorance is the lack of opportunity to learn I am ignorant
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    Medulus
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    08/22/2010 7:04 PM
    Isn't the distance across the bottom of the spherical segment the diameter, which is twice the radius? Or do you mean the curved distance across the bottom?  Wouldn't that be virtually the same as the distance across the top of the spherical section?  It seems to me that the top is easier to measure than the bottom, which might be 40 or 50 feet off the floor.
    Steve Ebner CPCU AIC AMIM

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    Medulus
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    08/22/2010 7:20 PM
    I am getting your calculation for the percentage of a sphere. And I thank you for sharing that, but I'm still not clear about the chord measurement, or how you would obtain it for that matter.

    I have a couple suggestions though for getting the radius measurement, assuming there are stadium seats, etc in the way of measuring the radius across the floor below. One is to use a laser to measure it by having someone hold up something to bounce the laser off on one side of the inside of the dome, hopefully standing at the same height as the laser operator standing on the exact opposite side of the dome. This would give you the diameter, which would then be divided by 2 for the radius.
    The second is to measure around the rim of the dome and use the reverse formula used for determining the circumference. If 2piR is used to determine the circumference then R=C/2pi. In order to get a relatively accurate measurement of the rim, one would need a measuring wheel and considerable nerve, especially if the dome goes to the edge of the building.

    Trust me, though, it really was fun walking around on the dome in Hampton, with a view of the bay in the distance.
    Steve Ebner CPCU AIC AMIM

    "With great power comes great responsibility." (Stanley Martin Lieber, Amazing Fantasy # 15 August 1962)
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    jdacree
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    08/22/2010 7:20 PM
    Diameter is the distance across at the midpoint of a circle. Think of a 1" bar cut down the middle. the chord is 1" (the diameter) and the height is .5" (the radius). In those cases where you have less than half of the radius above the top of the building, envision a ball sitting on top of a glass, then you have to get a chord measurement. Assuming that the building is round the measurement from the insided wall to the opposite inside wall (the top of the glass) would give the chord. A measurement from the top of the wall to the top of the roof (the amonunt of the ball sitting inside the cup) is the chord height. Those 2 measurements will give you the R value. Then by using the calculation you can figure the % of the area of the sphere. If you do not have the engineering drawings to determine the surface area of a spherical segement this calculation will get you very close, dependent on the accuracy of your measurements.
    Jim Acree Stupidity is the art of not trying to learn Ignorance is the lack of opportunity to learn I am ignorant
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    Medulus
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    08/22/2010 7:26 PM
    Looked it up with a google source. If I'm understanding this right (and who knows because I seem to be having a conversation with myself right now) a chord is the distance between any two points on the base of the dome, meaning that the diameter would be a chord, but not the only measurement of a chord. Am I getting it now?
    Steve Ebner CPCU AIC AMIM

    "With great power comes great responsibility." (Stanley Martin Lieber, Amazing Fantasy # 15 August 1962)
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