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Thread: Deflection of a rectangular hollow section

  1. #1
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    Deflection of a rectangular hollow section

    Hi,
    Building a vertical boat lift.
    I have chosen alumimuim alloy as my material for this project, weight and corrosion resistance are the factors in chosing this alloy. ( I suspect 6061, but I do not know that exact alloy until I buy the sections).

    I will upload a drawing, but in a nut shell it's a hollow rectancular beam support at the outside edge with a load applied in 2 places on the beam. There will be 2 beams to hold a 3000 lbs boat, add 1000 lbs for fuel and gear. So the total load applied to both beams is 4000 lbs.

    I would like to know the deflection of the beam at the loads, and what s the safe deflection for this al. alloy.
    Would also enjoy seeing the steps used to get the answer so I can try different sized sections

    Thanks for any help.

    Mark
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  2. #2
    Technical Fellow Kelly_Bramble's Avatar
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    See...

    Structural Beam Bending Equations / Calculation Supported on Both Ends Loaded Two equal Loads

    You are going to need to know what the beam section modulus's are..

  3. #3
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    Yep, got to that page. It's the beam section modulu's that I don't quite understand yet.

  4. #4
    Technical Fellow Kelly_Bramble's Avatar
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    Quote Originally Posted by MarkS View Post
    Yep, got to that page. It's the beam section modulus that I don't quite understand yet.
    Well, you need to know what the structural shapes look like on your boat support/lift. If you open up the calculator link on the structural beam deflection webpage given there is a variable termed Moment of Inertia (MI). The MI is the section property you need as well as the Modulus of Elasticity.

    The MI is geometry dependent. Lets just say that you use a steel channel C10 x 25.

    See the following chart..

    Structural Steel Channel Section Properties Moment of Inertia, Steel Beam Size, Cross Section Area



    For C10 x 25 the MI, Ixx =91.2 in^4 if the channel is loaded from the top of the illustration. If the loading is from the left or right side of the illustration then Iyy = 3.36 in^4. Notice that the MI is perpendicular to the loading.

    You will also need to determine the steel channel Modulus of Elasticity, which for structural steel ASTM A36 would be 30 x 10^6 psi or there about.

    In design, first select the material and shapes you would LIKE to use, run the numbers and interate until you meet your FOS, cost and design requirements.

    After all of this get a ME or equivalent to check your design and calculations..

    Be aware that all element of the design need a look-see (bolts, welds, cables, hydraulics actuators, etc...)

  5. #5
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    Hi, Thanks for your replies.
    For the rectangular section, of 2" x 5" I get a moment of inertia of 35.46
    For Alum. alloy I get a 10.2 lbs/sq in x 10^6 modulus of elasticity.

    On the structural beams calculator, there are a few questions.
    W is understood,
    l is understood
    a is distance from imposed load to support point
    v is assumed to be 1/2 of l
    x is not understood

    Distance to neutral axis /plane is no understood

    if you can help with this, then I can input the parameters into the calculator a check my work.

    Thanks very much
    Last edited by MarkS; 08-13-2014 at 08:47 AM.

  6. #6
    Technical Fellow Kelly_Bramble's Avatar
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    Quote Originally Posted by MarkS View Post
    x is not understood

    Distance to neutral axis /plane is no understood

    if you can help with this, then I can input the parameters into the calculator a check my work.

    Thanks very much
    Go back to the equations webpage...

    X is used to calculate the stress between the nearest load and the support point. I would just set this equal to "a".

    Distance to neutral axis - get hold of a pen or pencil. Holding it in front you bend it to form a smiley face shape - don't break it! The bottom surface of the pen/pencil has put in tension and the top has been put in compression. Somewhere in between there is a location where there is not any tension or compression - this is the neutral axis.

    Usually, for a symmetrical section it is equal to 1/2 the height.

  7. #7
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    Hi Kelly,

    Thanks, this confirms my assumptions.
    I will go back to the calculator and add these new values
    Last edited by MarkS; 08-13-2014 at 10:15 AM.

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    Hi,

    Please see attached image.
    Am I getting this correct ?

    Seems like a lo of defection.

    Thanks
    Mark
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    Last edited by MarkS; 08-13-2014 at 10:48 AM.

  9. #9
    Technical Fellow Kelly_Bramble's Avatar
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    Quote Originally Posted by MarkS View Post
    Hi,

    Please see attached image.
    Am I getting this correct ?

    Seems like a lo of defection.

    Thanks
    Mark

    Yes, it is and tensile yield for 6061-T6 aluminum is 40 ksi and your at 36 ksi stress.

    You need more beef... I suggest not less than 2 FOS (max loading stress of 20 ksi) or better.. Increase the MI of the structural shape or stronger material.

  10. #10
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    I increased the wall thickness to 1/4".
    This yields a 20,212.766 stress.
    Still almost 1" of deflection.
    Giving that the loading my tend to e somewhat dynamic,(high rough waves might tend to lift some weight off the boat if not raised high enough), and the frequent loading and unloading of the beam I would still feel that th1/4" wall is not strong enough.
    Will check what other sections I can get.
    Thanks

  11. #11
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    How's 12,500 stress, with .59673 " deflection between loads ?

  12. #12
    Technical Fellow Kelly_Bramble's Avatar
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    Quote Originally Posted by MarkS View Post
    and the frequent loading and unloading of the beam I would still feel that th1/4" wall is not strong enough.
    It's a lot easier to "over engineer" this then to engineer it "just right". There always unseen loading and stress imparted due to assembly imperfections or material anomalies.

    Also, consider that the boat may weight much more than the empty weight. Beer, fishing poles, rednecks and such on the boat while lifted.

  13. #13
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    I am going to go with the 2 x 6. 1/4" section.
    Thanks for your help, and guidance.
    It's been a fun learning process.

    Thanks again.
    Mark

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