What is the formula for bending moment of a beam subjected to UDL and a point load?

  1. 1. The problem statement, all variables and given/known data
    1.What is the formula to calculate the bending moment of a beam subjected to UDL?
    2.What is the formula to calculate the bending moment of a beam subjected to point load?

    2. Relevant equations

    Bending moment (UDL) = WL^2/8 (Kg-mm or Kg-m)

    Bending moment (point load) = Force x Distance ( This is actually for a horizontal beam with load acting is a point load) (Kg-mm or Kg-m)

    What is the formula for bending moment of a vertical beam subjected to a point load and a UDL on the top of it (load applied axially)?

    3. The attempt at a solution

    I come through several formulas, like (W * X)(X/2) when a UDL is acting over the cantilever beam. I am bit confused how do they arrive with these formulas and where should I use what?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. rock.freak667

    rock.freak667 6,231
    Homework Helper

    Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    Well a UDL is like a "rectangularly" distributed load, so the load effectively acts at the center of the beam i.e. at a distance of L/2. Since the entire length is L, the load is WL (since UDL = W N/m)

    so BM = Force*distance = (WL)(L/2)
     
  4. SteamKing

    SteamKing 9,968
    Staff Emeritus
    Science Advisor
    Homework Helper

    Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    You also need to know something about how the ends of the beam are supported. Are they fixed, free, or simply supported?
     
  5. Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    For a horizontal simply supported beam of length L subject to udl w, the maximum bending moment is at the centre and equal to
    wL^2/8 distributed along the span parabolically.
    For a horizontal simply supported beam of length L, and subject to a point load P at mid-span, the maximum bending moment is PL/4. If the point load is applied at aL (0<a<L) from one end, the maximum bending moment is Pa(1-a)/L just under the load.
    The bending moment at any other point on the span can be found by simple statics.

    "What is the formula for bending moment of a vertical beam subjected to a point load and a UDL on the top of it (load applied axially)?"
    That would be a centrally loaded column, if I understand correctly.
     
  6. Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    SteamKing: The ends are fixed, there is no movement in any direction.
     
  7. Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    Thanks everyone for your effects in helping me.
    Yes exactly it is a centrally loaded column which is subjected to load on top of it, so whats the BM for UDL and point load?
     
  8. Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    rock.freak667 will have to interpret the application of his formula.
    wL^2/8 is the maximum BM at the centre of a udl of w kg/m for a simply supported beam.

    In fact, all these questions about formulas can be resolved by standard tables available in books or the web, such as:
    http://structsource.com/analysis/types/beam.htm

    You will find the required formulas for the fixed supports subject to udl in your case at the above link. Bending moments at different lengths along the span has to be obtained by superimposing the simply supported moment (parabolic) with the end moments by statics.

    For the vertical "beam", are both loads (point and udl) applied vertically and axially?

    A centrally loaded column not subject to lateral loads does not incur first order bending moments. Second and higher order bending moments could be caused by lateral buckling or deflections (P-delta effects).
     
  9. Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    mathmate:In the above link you gave if I use the formula for the FIXED-FIXED BEAM WITH UNIFORM LOAD (my case), my BM at the center would be for x=L/2 is WL^2/24. Hoping this would help, let me check and get back to you. Thanks mathmate.

    And my column is only loaded vertically downward over the top. Sorry I might have confused in the above posts.
     
  10. Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    Maximum positive bending moment at the centre of wL^2/24 is correct for a fixed-fixed beam.

    If you are doing the design of a beam, do not forget that the negative support moments of wL^2/12 are higher than that at the centre.

    Draw the bending moment diagram would make it clear.
     
  11. Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    I assume the above case is only for the horizontal beams, what about the BM for column with UDL and point load?
     
  12. Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    As per my previous response:

    "A centrally loaded column not subject to lateral loads does not incur first order bending moments. Second and higher order bending moments could be caused by lateral buckling or deflections (P-delta effects)."

    Is the column monolithic with other structures? If so, there would have to be bending moments at the junctions and would not be considered as purely centrally loaded.

    This bending moment (at the junction of beam/column) has to be calculated with an indeterminate structural analysis taking into account of the loads on the beam, size (stiffness) of the beams and columns, and load on the column, the possible deflections due to lateral (wind, earthquake, etc.) or asymmetrical loading, etc.
     
  13. Re: What is the formula for bending moment of a beam subjected to UDL and a point loa

    Thanks. I got it.
     
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