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Slope and Deflection of a Simply Supported Beam

  1. Dec 12, 2012 #1
    The title is fairly misleading but is within the subject.

    I have drawn up a beam of my own as part of my classwork because what bothers me is how you would find Young's Modulus [E] and the second moment of inertia without being given them.

    Every question I have looked at has given me the two values combined hence, EI.

    The beam I have drawn is 10m long. From the LHE going right, 2m in is a 90kN point load, 3.5m in from LHE is a 8kN point load, from 2m in from LHE across by 3m is a UDL 12kN/m, and 7.5m in from LHE is a final point load of 10kN.

    RL = 103,1kN and RR = 40.9kN

    In order for me to find ymax at the mid-point of the beam I require an EI value which because it's a beam I made myself, I do not have.

    What I have available that I think was relevant:

    a sheet that shows me data for different types of beams, with D x B, Ixx and Zxx values.
    The bending equation: E/R=sigma/y=M/I
    Ixx=bd^3/12

    I had a go at this over 6 weeks ago and I got my E and I values, however I've lost the notes that have the calculations on them.

    The values I got were, E = 200x10^9N/m and I = 2.9....x10^-3cm^4


    All I am asking here for is the route / method taken to find the E and I - not EI, but the two individual values for the beam described above.

    I would use symbols to draw the beam here but it would look a mess, but then again:



    RL = 103.1kN |_2m_| 90kN_1.5m_| 8kN_3m_| 12kN/m[UDL] _2.5m_| 10kN_2.5m_| RR = 40.9kN

    |____|[][][]|[][][]______|______| (Looks similar to this)


    So if you know how to do all this just imagine your given this beam mainly to find the slope and deflection - which I know how to do.

    Unfortunately you need an EI value, to find that you need both E and I.

    If you know the method please share it here because my mind is blank haha.
     
  2. jcsd
  3. Dec 12, 2012 #2

    AlephZero

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    This is posted is in the wrong section, but anyway....

    I depends on the geometry of the beam's cross section. Ixx=bd^3/12 is correct for a solid rectangular section.

    E depends on the material. Basically you have to measure it, but the values for many materials have already been measured and tabulated. 200x10^9N/m^2 (note, m^2 not m) is a reasonable value for steel.

    Google will find you tables of formulas for I for different shaped beams, and values of E for different materials.
     
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