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Beam Bending Question

  1. Nov 21, 2015 #1
    Bonjouro!
    Firstly, as this is my first post here, I would like to say thank you to everyone who is a part of the site and Hello!
    I've used this forum a number of times, but this is the first time I've posted here as this user!

    If the flexural stiffness of a beam is 25 MNm^2, and the beam is made of steel, what is the breadth and depth of the beam (or at least beam dimensions that would work)

    I did this by saying
    I = bd^3/12

    EI = 25,000,000,000 Nmm^2
    E = 200,000 MPa
    I = 1,500,000mm^4
    Using I = b*d^3 / 12
    Assuming breadth (b) is 50mm, I get depth (d) as 31.072mm, but apparently this is wrong and I cannot figure out why :'(

    My question comes from this thing I found on the internet, which gives me these FEA results, but they don't match up!
    View post on imgur.com

    Please help PhysicsForum guys! You're my only hope!
     
    Last edited: Nov 21, 2015
  2. jcsd
  3. Nov 21, 2015 #2

    SteamKing

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    I think your problem comes down to a mistake in handling the units of EI and E somewhere.

    Let's take the original data:

    EI = 25 MN-m2, where E = 200 GPa = 200 × 109 N/m2

    By dividing EI by E, we get:

    I = EI / E = 25 × 106 N-m2 / (200 × 109 N/m2) = 1.25 × 10-4 m4

    Since there are 103 mm / m, there are 1012 mm4/m4

    So I = 1.25 × 10-4 m4 = 1.25 × 10-4 m4 ⋅ 1012 mm4/m4 = 1.25 × 108 mm4

    taking b = 50 mm and assuming a rectangular cross-section for I:

    I = bh3 / 12 = 50h3 / 12 = 1.25 × 108 mm4

    h3 = 3 × 107 mm3

    h ≈ 310.7 mm
     
  4. Nov 21, 2015 #3
    Brother! You have saved me. iT was the units, that were the issue. Now I know better. Thank you!
     
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