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Strength in numbers?

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  • Strength in numbers?

    I remember learning/reading that if you take a bundle of toothpicks it's actually stronger than a single wooden piece of the same size. Is this true? Does this hold true for steel? Does it actually increase the load bearing capacity (tensile)? I don't quite see this, so perhaps someone can explain.


  • #2
    (I assume by '... same size..' you mean same total X-sectional area in both cases.) I read a discussion of this concept in a Lincoln Welding book not long ago. That scenario compared a stranded cable vs. a solid cable of same total x-sctnl area. The stranded is stronger as I recall, due to the elastic stretching. I can't recite the exact argument, but it related to the strands offering assistance to each other before the stretching in any one strand reached the breaking point. (that book's explanation was more enlightening than mine..)
    Don't know if you get any of the same CCTV programming in Canada that we have here in U.S., but periodically the 'History Channel' presents a documentary on the construction of the Golden Gate Bridge in SF. That film also addresses the advantages of a stranded cable.

    [This message has been edited by lynnl (edited 06-14-2002).]
    Lynn (Huntsville, AL)


    • #3
      The actual strength (load seen at failure) and stiffness (load needed to deflect a given amount) is based solely on the cross-sectional area of the material.
      But, no material will live up to its theoretical strength because of imperfections in the molecular structure. A bundle of steel wire is stronger (more load at failure) because of a couple of factors:
      - When the wire is drawn, the imperfections are shifted, and aligned more closely along the axis of the wire. Wire strength is improved on the long axis, but is given up on the radial axis (which you aren't going to pull on anyway).
      - When there are multiple load paths (a bundle of wires) it takes more energy to initiate a crack in all the wires, if only one has failed, so failure of a single strand will not propagate across the whole bundle. A solid bar of steel will fail rapidly after a crack has started. Of course, if the x-sectional area is reduced too much (broken strands carry almost none of the load) all of the wires in the bundle will exceed their allowable load and break.
      For toothpicks, there is no drawing process to shift internal defects, so there won't be much increase in tension strength. In bending, the outside of the "beam" is under the most tension, and will fail when its allowable elongation is reached. A solid block of wood will break when bent, where a bundle of toothpicks will slide across each other (imagine bending a deck of cards) and carry more load in bending.

      I'm sure someone else can probably say that in less words and a lot clearer

      [This message has been edited by CompositeEngr (edited 06-14-2002).]


      • #4
        Sounds good to me. I seen a show on some super bridges and they said the same thing. They do take extreme care to ensure the wire is coated properly and spun into a cable as designed, they then ultrasound and xray the cables before and after failure testing in an engineering lab.