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Simple Mechanical Questions

  1. Apr 18, 2012 #1
    1. The problem statement, all variables and given/known data

    A) A circular rod is subjected to a bending moment of 315Nm. What is the minimum diameter of the rod required so that the maximum stress does not exceed 200N/mm2?

    B) If the Modulus of Elasticity for the material from which the rod is made of is 100kN/mm2, what radius will the rod be deformed to when stressed to the maximum allowable?

    2. Relevant equations

    A) [itex]\frac{M}{I}[/itex] = σ

    B) [itex]\frac{M}{σ]}[/itex] = [itex]\frac{ρ]}{E]}[/itex]

    Second moment of Area for a circle of diameter d, about its Neutral Axis is [itex]\frac{∏d}{64}[/itex]

    3. The attempt at a solution

    A) M=314N/m
    σ=200MN/m2
    I=[itex]\frac{∏d]}{64}[/itex]

    [itex]\frac{314}{[itex]\frac{∏d}{64}[/itex]}[/itex]=200×106

    d=0.0752m

    B) M=413Nm
    E=100GN/m2
    σ=200MN/m2

    [itex]\frac{314}{200×106}[/itex]=[itex]\frac{ρ}{100×109}[/itex]

    ρ=157,000m (Ridiculous answer, I know)

    I haven't done mechanics in a while, so I was wondering if someone could double check that I'm on the right track.

    Chuur Chuur
     
  2. jcsd
  3. Apr 18, 2012 #2
    Bending stress is Mc/I not M/I. Check your units.
     
  4. Apr 18, 2012 #3
    But how would that formula work though?

    I wouldn't be able to solve for c, since I'm asked to find the diameter. If I substitute that in, then I'd have [itex]\frac{M\frac{d}{2}}{\frac{∏d}{64}}[/itex]=σ

    where c = [itex]\frac{d}{2}[/itex]
     
  5. Apr 19, 2012 #4
    You are provided with the bending moment and the maximum stress. You can easily determine diameter from that information. The formula you have above is missing an exponent.
     
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