# Finding support reactions for shear and moment diagrams

1. Apr 24, 2014

### mwjrain

Draw the shear and moment diagrams for the beam in the figure. Clearly show all values, including the maximum shear and maximum moment and their positions on the diagrams. Assume the supports at A and C are rollers and D is a pin support. note there is a hinge at point B.

I am having trouble finding the support reactions.
My attempt is:
(Assuming positive Y direction is up)
Moment about b = 10(60)+10A-2(10)5=0
A=-50 kN

Forces in y direction = C+D-50-2(10)-5-18=0
C+D=93

Moment about D= C(12)+60(32)-(50)32-(20)(27)-5(16)-18(6)=0
C=34

D=93-34=59

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2. Apr 25, 2014

### PhanthomJay

Your work is generally very good, however, your error is in the calculation of the moment due to the applied couple at A. You are incorrectly multiplying that couple by a moment arm. The moment of a couple about any point is the couple itself.

3. Apr 25, 2014

### mwjrain

So it would be
Moment about b = 60 +10A-2(10)5=0
A=4 kN

Moment about D = C(12)+60-50(32)-20(27)-5(16)-18(6)=0
C=189kN

Forces in y direction=C+D+4-(2)10-5-18=0
D=-150kN

4. Apr 25, 2014

### PhanthomJay

yes
You still used A = -50 instead of A = +4
make necessary corrections. It is a good idea to look at the FBD of the beam between B and D to check results.

Welcome to PF!

Note: My lightweight monitor made it easy to turn it upside down.

5. Apr 25, 2014

### mwjrain

Sorry about the image being upside down! I didn't realize that. And thank you for the warm welcome.

So
Moment about D= C12-18(6)-5(16)-2(10)27+4(32)+60=0
C=45

Forces in y =D+4+45-20-18-5=0
D=-6

Note (the new pictures going to be sideways. I can't figure out how to fix it on my iPad.) sorry!

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6. Apr 26, 2014

### PhanthomJay

You should show the negative 6 support reaction at D as a downward force of magnitude 6. Otherwise your reactions, shear, and moment diagrams are literally perfect, correctly curved, etc. , this is excellent work.

7. Apr 26, 2014

### mwjrain

Thank you for all the help! Preparing for finals.

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