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

In summary, the question involves a weightless beam supported by a pin at B and a roller bearing at C, with a UDL of 4 kN/m and a clockwise couple of 11.2 kNm at A. The vertical reactions at B and C can be determined using the sum of clockwise moments equal to the sum of anticlockwise moments. The UDL can be replaced by a downward concentrated load of 24 kN at the center of the beam, and the moment equation can be redone using B as the point of reference. Checking the answer by taking moments about any other point should result in a balanced equation.
  • #1
dechuba
1
0

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.

Problem 1.jpg


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

[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
 
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  • #2
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.
 
  • #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.
 

1. What is a pin support in a weightless beam?

A pin support is a type of support used in structural engineering where a beam is allowed to rotate freely at the support point. This means that the pin support can only provide vertical reactions, but not horizontal reactions.

2. What does UDL stand for?

UDL stands for Uniformly Distributed Load. It is a type of load that is evenly distributed along the length of a beam, causing a constant magnitude of force per unit length.

3. How do you calculate the vertical reaction at a pin support?

The vertical reaction at a pin support can be calculated by taking the sum of all the vertical forces acting on the beam and setting it equal to zero. This will give you the magnitude of the vertical reaction at the pin support.

4. Can the vertical reaction at a pin support change with a UDL applied?

Yes, the vertical reaction at a pin support can change with a UDL applied. This is because the UDL adds an additional force to the beam, which can affect the overall balance of forces and result in a different vertical reaction at the pin support.

5. How does the magnitude of the UDL affect the vertical reaction at a pin support?

The magnitude of the UDL directly affects the vertical reaction at a pin support. As the magnitude of the UDL increases, the overall force acting on the beam will also increase, resulting in a higher vertical reaction at the pin support.

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