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

[dechuba]

Homework Statement

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.

The vertical reactions of B and C are:-

Homework Equations

Nothing really

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

thus

$$\sum$$ 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

 

[PhanthomJay]

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.

 

[pongo38]

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.