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Thread: Solving for weight on points supporting concrete block

  1. #1 Solving for weight on points supporting concrete block 
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    Question: How much weight lies on each support if the block weighs 2000 lbs.

    With this scenario, we will have three supports underneath the concrete block.
    This block measures 40 inches by 24 inches by 24 inches in real life. So AB is 40'' and AC is 24'' and BD is 24''. In the drawing, we are looking at the bottom face of the block (24'' by 40'') and the three suppots will be located as follows:
    Support 1 is the circle exactly between A and C. (so its 12'' from A and 12'' from C and its located right on the blocks edge.
    Support 2 is the circle exactly between C and D. Its located 20'' from C and 20'' from D and, just like support 1, its right on the edge of the block.
    Support 3 is located in the corner of the block at point B.


    A-----------------------------------------------------B
    --------------------------------------------------------
    --------------------------------------------------------
    --------------------------------------------------------
    o-------------------------------------------------------
    --------------------------------------------------------
    --------------------------------------------------------
    --------------------------------------------------------
    C---------------------------o-------------------------D

    These are my answers (not exact but close)
    Support 1 holds 723 lbs.
    Support 2 holds 843.145 lbs.
    Support 3 holds 433.809 lbs.

    I am using the same sort of logic I used last time, but I'm not sure if its still applicable, since the problem is very different.


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  3. #2 Re: Solving for weight on points supporting concrete block 
    . DrRocket's Avatar
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    Quote Originally Posted by SteveC
    Question: How much weight lies on each support if the block weighs 2000 lbs.

    With this scenario, we will have three supports underneath the concrete block.
    This block measures 40 inches by 24 inches by 24 inches in real life. So AB is 40'' and AC is 24'' and BD is 24''. In the drawing, we are looking at the bottom face of the block (24'' by 40'') and the three suppots will be located as follows:
    Support 1 is the circle exactly between A and C. (so its 12'' from A and 12'' from C and its located right on the blocks edge.
    Support 2 is the circle exactly between C and D. Its located 20'' from C and 20'' from D and, just like support 1, its right on the edge of the block.
    Support 3 is located in the corner of the block at point B.


    A-----------------------------------------------------B
    --------------------------------------------------------
    --------------------------------------------------------
    --------------------------------------------------------
    o-------------------------------------------------------
    --------------------------------------------------------
    --------------------------------------------------------
    --------------------------------------------------------
    C---------------------------o-------------------------D

    These are my answers (not exact but close)
    Support 1 holds 723 lbs.
    Support 2 holds 843.145 lbs.
    Support 3 holds 433.809 lbs.

    I am using the same sort of logic I used last time, but I'm not sure if its still applicable, since the problem is very different.
    I have not worked the problem out in detail, but it is precisely the same sort of problem as the first one. The only difference is that it involves more spatial dimensions. It is still fundamentally a problem in statics and there are sufficiently few constraints so that it should be statically determinant.'

    You solve it in the same way as the first problem The sum of all vector forces will be zero. The sum of all moments about any point will also be zero. Those two facts, written out as vector equations will give you enough information to solve for all of the forces.

    For a more complete treatment of problems of this nature, consult any book on engineering statics.

    Statically indeterminant problems require application of elasticity in what is usually called "strength of materials". Some books also treat such problems along with statics. But you should not need that additional level of modeling capability for this particular problem.

    It occurs to me that these are pretty common problems in a statics class. Are you taking such a class ? I don't know else you would be doing several problems of this nature.


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  4. #3  
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    I'm thinking they all have to be equal. Support 2 and 3 are equidistant from the longitudinal axis, so they have to be equal to balance the moment (torque) about that axis. Support 1 is on the axis and contributes no moment. Likewise Supports 1 and 3 are equidistant from the transverse axis, and so have to be equal to balance in that direction.

    By the way, I think you mean it is a 40" by 24" rectangle. You shouldn't describe it as "40 inches by 24 inches by 24 inches" unless you mean length, width and height.
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