1. Not finding help here? Sign up for a free 30min 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!

Cantilivered beam deflection

  1. Oct 1, 2014 #1
    1. The problem statement, all variables and given/known data

    Okay this is the problem I have:

    I have a Steel Channel beam which has an cross sectional height of 300mm. It is 150mm in depth. Its wall thickness is 20mm.

    This beam is 6meters long as has a 10kN/m UDL applied. It is fixed at one side and unsupported at the tip.

    I have worked out the Neutral Axis about the xx at 44.8214mm and the Moment of Inertia as 32.93x109mm4

    I now need to determine maximum tensile bending stress and its exact location in the beam cross section.

    2. Relevant equations

    I know maximum bending stress is equal to (max stress = my/I)


    3. The attempt at a solution

    Now I know I, and I have YCenter at 150mm and xCenter at 44.8214mm now I don't know how to get Mmax and it's exact distance.

    I think Mmax is (L2x10kn/m)/2 but I could be incorrect?

    I have attached a picture of my working if that helps
     

    Attached Files:

  2. jcsd
  3. Oct 1, 2014 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    This is why you should get in the habit of constructing shear force and bending moment diagrams for these types of beam problems (not just cantilevers, however).
     
  4. Oct 1, 2014 #3
    Okay I've got the reaction at the end (left hand side of beam to be) 60kN, and moment to be 180kn.

    Where can I go from here?
     
  5. Oct 1, 2014 #4

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    I don't understand. Haven't you learned how to construct the shear force and bending moment diagram for a beam, given its loading? This procedure should have been taught and learned before you started tackling stress calculations.
     
  6. Oct 2, 2014 #5
    Sorry I didn't convey my understanding properly.

    I have found the maximum moment to be 180kn (60kn (UDL as point load) * length of cantilever)

    Now I am just worried if my Moment of Inertia is correct or not. I have done it a few times and have different answers all the time.

    I also know the y value in the equation given by (just 300mm (size of cross section) - 44.8214mm (where N.A is located) )

    I obviously know maximum bending stress in a beam will occur at the fixed end, but as for where it appears in the cross section, will it occur at the top section since it is positive so (300mm-44.8124mm) =257.1786mm?
     
    Last edited: Oct 2, 2014
  7. Oct 2, 2014 #6

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    The correct units for the bending moment are kN-m.

    Why is that? This seems to be a rather simple cross section. The MOI can be calculated in at least a couple of different ways. Each method of calculation should agree with the other. I can't check you calculations because the image you attached is too small for me to read your handwriting.

    It's not clear from your description if the beam is oriented with the 300 mm dimension in the vertical direction or the 150 mm dimension. In any event, only one of the neutral axis locations will give you the correct value of the bending stress in the beam, and it is not necessarily the one you have chosen.

    For example, if the beam measures 300 mm deep in the vertical direction, then the y distance to the outer fiber must be based on this depth, and not the distance to the N.A. measured along the 150 mm dimension, which we could call the breadth of the beam, to distinguish it from the depth..
     
  8. Oct 2, 2014 #7

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You might want to re-check your MOI calculation. The MOI of the channel cannot be greater than the MOI for a rectangular section which is 300 mm deep by 150 mm wide. Your MOI seems high, by at least two orders of magnitude. It's a simple calculation; you can type it into a reply message rather than posting an image.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Cantilivered beam deflection
  1. Beam Deflection (Replies: 3)

  2. Beam Deflection (Replies: 3)

  3. Deflection of a beam (Replies: 4)

  4. Beam Deflection (Replies: 0)

Loading...