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Math Help - Application of Parallel Axis Theorem

  1. #1
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    Application of Parallel Axis Theorem

    I am a civil engineer and have been in the field for 10 years so I have forgotten some basic theories of Maths.

    For me, what I remember is // axis theorem is able to make second moment of area of a section with reference with respect to any axis. In the basic bending theory of beam, the longitudinal bending stress is equal to M y / I where M is bending moment, y is the perpendicular distance to the neutral axis and I is the second moment of inertia.
    (Pls see this webpage for details: Bending) - Wikipedia, the free encyclopedia. As y is the distance measuring form the neutral axis, the stress is not zero at both extremities. I was wondering whether I can shift the NA downward to the bottom of a section so that the bending stress is bottom is “zero”





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  2. #2
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    I want to help, I have taken a course on Civil Engineering and I know what you are talking about but I do not understand the question.
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  3. #3
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    Quote Originally Posted by Catjacob View Post
    I am a civil engineer and have been in the field for 10 years so I have forgotten some basic theories of Maths.

    For me, what I remember is // axis theorem is able to make second moment of area of a section with reference with respect to any axis. In the basic bending theory of beam, the longitudinal bending stress is equal to M y / I where M is bending moment, y is the perpendicular distance to the neutral axis and I is the second moment of inertia.
    (Pls see this webpage for details: Bending) - Wikipedia, the free encyclopedia. As y is the distance measuring form the neutral axis, the stress is not zero at both extremities. I was wondering whether I can shift the NA downward to the bottom of a section so that the bending stress is bottom is “zero”





    Umm, I see this only now.
    Maybe my initial browsings on the "New Posts" hid it before I got to it.

    I am also a civil engineer who has been on the field mostly, in constructions, and none in structural design, but I still understand the principles.
    Besides, one doesn't have to have studied Civil Engineering in order to understand what you mean.

    You know that the NA (neutral axis) passes through the centroid of the cross section of the beam. So if you want to put the NA at the bottom of the beam, then you have to put the centroid at the bottom of the beam. Which is impossible.

    Very close to the bottom is possible if the beam is composite, the heavy components being at the bottom of the composite beam.
    Or if the beam, homogenous or composite, is shaped such that the bottom is ridiculously larger and/or heavier than the top. Like an inverted T, for example.
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  4. #4
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    Thanks for your reply.

    The full storey is that I have a bridge deck which is subjected to differential temperature strain from temperature (e.g at the top of the bridge deck, T=t1; at d=200mm, T=t2; at d=350, T=t3....). I can work out the bending moment from the temp. load and want to convert the bending moment back a linear temp distribution across the bridge deck which is the only method the analysis program can deal with.

    The simplest input is T=0 at bottom and it goes up lineraly to an equivalent temp at the bridge deck
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  5. #5
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    Quote Originally Posted by Catjacob View Post
    Thanks for your reply.

    The full storey is that I have a bridge deck which is subjected to differential temperature strain from temperature (e.g at the top of the bridge deck, T=t1; at d=200mm, T=t2; at d=350, T=t3....). I can work out the bending moment from the temp. load and want to convert the bending moment back a linear temp distribution across the bridge deck which is the only method the analysis program can deal with.

    The simplest input is T=0 at bottom and it goes up lineraly to an equivalent temp at the bridge deck
    That's not the full story, because I cannot visualize your structure.
    d=200mm, 350mm, ....
    Those are about 8inches, 14in, ...
    The floor deck is that thick?
    Reinforced concrete? Thick steel plate? Asphalt concrete?
    That thick?
    Oh, the bridge carries "abnormal" traffic? Military ordnance? Missiles? Rocketships? Super-Heavy Equipment?

    Anyway, whatever, so the deck is thicker than 350mm.
    And, my understanding now, so far, is that your want to design the deck to accomodate also the temperature-induced stresses by the heat/cold at the top of the deck. And you found field tests that the temperature's actual "distribution" is not linear. And you want to "distribute" the varying temperature-stresses, or the flexural stresses due to the temperature distribution, linearly because your computers were programmed only unto that linear distribution.

    If I am still on track, why not go ahead and assume the stress at the bottom of the deck be zero and increasing linearly towards the top? We always assume such ways in design---uniformly distributed loads for wheel/concentrated loads; concentrated loads for uniform loads---for the maximum stress possible.

    Still I don't get it why you initially wanted to lower the NA of the deck.

    If my understanding is wrong, was wrong, it's because the story is not complete nor clear to me as yet.

    Sorry, but I always need drawings/plans and field findings/observations in solving field problems. I do not like guessworks or punchings-in-the-air.
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