1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Area Moment of Inertia

  1. Jan 20, 2017 #1
    1. The problem statement, all variables and given/known data
    I'm reading a paper and I'm trying to understand how does the author arrived from equation (1) to the following buckling load equation (2). I know that the author substitutes equation (1) with the dimensions of the geometry but I still could not understand how he comes to last term 6e/t in equation (2).
    2. Relevant equations
    P=Aσmax / [1+ec/r2] (1)

    P=Btσy / [1+6e/t] (2)

    A=cross-sectional area of column
    B,t=geometry of specimen (refer to attached figure)
    c= distance from neutral axis to the outer fiber where σmax occurs
    r, radius of gyration, r2=I/A where I is the moment of inertia computed about the bending axis

    3. The attempt at a solution
    I tried to play around by substituting r2 with I/A. But I don't know how can I expand the results afterwards. Maybe there are some simplifications that I missed.
  2. jcsd
  3. Jan 24, 2017 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The first equation represents loading on a relatively short eccentric/ compression loaded column; the second appears to be that same formula when the max stress reaches yield on a eccentrically loaded rectangular solid column of width B and depth t (found by replacing c with t/2, the distance from section centroid to outer fiber, and by replacing r^2 with I/A, where I is Bt^3/12, and A is Bt). That's the only sense I can make of the 2nd equation.
    Last edited: Jan 24, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted