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Vertical reactions of pin supports of a weightless Beam with a UDL applied

  1. Jul 17, 2010 #1
    1. The problem statement, all variables and given/known data

    The question is:

    The weightless beam, ABCD, shown in Figure below is supported by a pin support at B, and a roller bearing at C. There is a 4 kN/m UDL along the whole beam, as shown. There is an 11.2kNm clockwise couple at A.

    Problem 1.jpg

    The vertical reactions of B and C are:-

    2. Relevant equations

    Nothing really

    3. The attempt at a solution

    Now I'm assuming that since If I start from at B= 0 to find the vertical reaction of C

    For the UDL, it would be 4 x (1.8+2+2.2) = 24


    [tex]\sum[/tex] Mb = 0 = 11.2kNm - Vc x 2 - 24 x 3

    However, I keep on getting the incorrect answer with Vc. Usually I've been doing problems where the pin supports are at the ends of a beam.

    Any help and tips would be appreciated for this type of problem
  2. jcsd
  3. Jul 17, 2010 #2


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    Gold Member

    For the purposes of determining the reactions, the UDL of 4 kN/m may be replaced by a downward concentrated load of 24 kN acting at the center of the beam, that is, at 3 m from the left end. Now redo your moment equation about B and watch plus and minus signs.
  4. Jul 18, 2010 #3
    Problems with signs in this type of problem are avoided if, instead of setting the sum of moments =0, you set up your equation as "sum of clockwise moments = sum of anticlockwise moments". That way, all terms are positive. Also you can check your answer by taking moments about any other point than B. They should balance, whatever point is chosen.
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