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What does cross section area mean when dealing with stress/strain?

  1. Apr 4, 2014 #1
    What does "cross section area" mean when dealing with stress/strain?

    1. The problem statement, all variables and given/known data

    For clarification, here is an example problem:

    A circular steel wire 2 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire?

    Relevant equations

    FL = YA(ΔL)


    Apparently, the cross section area for this object is simply pi*r^2 (as for any circle). Can someone tell me exactly what the cross section area is supposed to refer to? I thought it was the area of the plane of the object perpendicular to the applied force, but apparently I'm wrong or not understanding something properly.
     
    Last edited: Apr 4, 2014
  2. jcsd
  3. Apr 4, 2014 #2
    Why do you feel that you are wrong or not understanding something properly?

    Chet
     
  4. Apr 4, 2014 #3
    I don't know what the definition of "cross section area" is. At least not well enough to apply it to the context of elasticity physics problems.
     
  5. Apr 4, 2014 #4

    SteamKing

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    When you put the wire in tension, the tensile stress is calculated using the circular cross-section of the wire.
    The tensile stress σ = F/A, where F is the tensile load (Newtons) and A is the cross section area (m^2), and the stress σ has units of pascals (N/m^2)

    For a circular wire, A = πR[itex]^{2}[/itex] or πD[itex]^{2}[/itex]/4, where R (radius) or D (diameter) of the wire are measured in meters.

    The elongation of an object undergoing a tensile load is

    δ = FL/AE

    where

    F = tensile load (Newtons)
    L = unloaded length of the object (meters)
    A = cross sectional area of the object (m^2)
    E = modulus of elasticity of the material (Pa)

    The cross section just refers to the shape of the loaded object which results from its intersection with a plane oriented normal to the applied load.
     
  6. Apr 4, 2014 #5
    For a long cylindrical body (not necessary a circular cylinder), the cross sectional area is obtained by cutting the cylinder with a knife perpendicular to its axis and looking in at the exposed area. The area that is exposed is the cross sectional area of the cylinder.

    Chet
     
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