- #1
Hati
- 10
- 1
Homework Statement
So I have a beam here, I'll post a Photoshop diagram of the problem at the bottom of this section, but its an overhanging beam simply supported at one end, and mid way down another, points A and B. I've changed up the values so I can do my work myself, I don't want someone blurting the answer to me. I need to learn rather than cruise through my class.
The beam is carrying a continuous uniformly distributed load that represents it's own weight of 4kN/m and two vertical loads of 16kN and 10kN
The setup looks like this
I'm to create a shear force and bending moment diagram for this beam.
Homework Equations
So, my relevant equations are very simple, the sum of the moments = 0 because I'm in equilibrium, and so are the forces. I have these equations to work with;
∑M=0
∑F=0
The Attempt at a Solution
Well, to create my shear force diagram I decided to turn the UDL into a point load in the middle, considering I had a load of 4kN/m over 16 meters I ended up with 64kN in the middle of the beam at 8 meters. In hindsight I can see how this might not be right, considering it doesn't take into account support B but I don't know how to take it into account. It isn't at the end of the beam.
Continuing on and hoping for the best I calculated my moments and did the following
∑MA=0
0= 0+(16*4)+(64*8)-(MB*5)+(10*16)
0= 64+512-(MB*5)+160
MB*5=736
∴MB=736/5
=147.2kN
Ok, so I have now the reaction force at support B. I can now use a different calculation to get ahold of A.
if ∑F=0
then A= 64+512-147.2-160
=268.8
and from that I can set up a shear force diagram I'm not so sure is correct but I'll have to go with it.
Homework Statement
so now the bending moment diagram. Time to work out my bending moments.
Homework Equations
I'll take point A, and my equation is this
MA=0
The Attempt at a Solution
so what I have in this beam are a number of forces to work out bending moments from.
I have support A
4 meters down the beam is force a at 16kN
then the translated UDL is force b at 64kN, 8 meters away.
support B exerting a force of 147.2kN upwards
and force c exerting a force of 5kN 10m from A
(Yes, I'm using capitals to represent supports and lowercase to represent force)
so what I did is this
MA=0
a= (16*4)+(64*8)-(147.2*10)-(10*16)
=-1056
b=(64*4)-(147.2*6)-(10*12)
=-747.2
B=-(147.2*2)-(10*8)
=-374.4
c=-(10*6)
=-60
and I get a simple weird bending moment diagram that doesn't fit my situation, you can see it'd be kind of this shape √.
Means I don't really get what's going on unfortunately, I need some help with this. What am I doing wrong?