Calculating Bending Moments Along a Beam

[ryanmcarthy]

Homework Statement

Calculate bending monents at 1m intervals along the beam

Homework Equations

The Attempt at a Solution

I'm not sure where to start really? I think this is nearly there?

Ma = 0
M1 = -5 x 1
M2 = (-5 x 2) + 26.7
M3 = (-5 x 3) + 26.7 - 10
M4 = (-5 x 4) + 26.7 - 10
M5 = (-5 x 5) + 26.7 - 10
M6 = (-5 x 6) + 26.7 - 10
M7 = (-5 x 7) + 26.7 - 10
M8 = (-5 x 8) + 26.7 - 10 + 53.3
M9 = (-5 x 9) + 26.7 - 10 + 53.3
M10 = (-5 x 10) + 26.7 - 10 + 53.3 - 20

 

[SteamKing]

This is the same beam and loading you were given and asked to generate the shear diagram. To find the bending moments along the beam, calculate the area under the shear diagram up to a given point located along the length of the beam.

 

[ryanmcarthy]

I don't know what you mean?

I thought you calculated it like what I have done above?

 

[ryanmcarthy]

Actually, I can see my attempt is totally wrong :(

 

[ryanmcarthy]

Is this more like it?

Ma = 0
M1 = (-5 x 1)
M2 = (-5 x 2) + 26.7
M3 = (-5 x 3) + (26.7 x 2) -10
M4 = (-5 x 4) + (26.7 x 3) - (10 x 2)
M5 = (-5 x 5) + (26.7 x 4) - (10 x 3)
M6 = (-5 x 6) + (26.7 x 5) - (10 x 4)
M7 = (-5 x 7) + (26.7 x 6) - (10 x 5)
M8 = (-5 x 8) + (26.7 x 7) - (10 x 6) + 53.3
M9 = (-5 x 9) + (26.7 x 8) - (10 x 7) + (53.3 x 2)
M10 = 0

 

[SteamKing]

Well, there must have been another ryanmcarthy who posted a question in this same homework forum entitled "Shear Force Diagram Help". This other fellow had a beam with the same support and applied loads as your problem has. He was trying to figure out the shear force diagram for his beam. You could take his shear diagram, calculate the area under it at each location specified in the current problem, and obtain your bending moments.

 

[ryanmcarthy]

Yes, that is me. That isn't what I didn't understand...

I don't understand what you mean by "You could take his shear diagram, calculate the area under it at each location specified in the current problem, and obtain your bending moments"

 

[SteamKing]

I said that because that is the relationship between the shear force diagram and the bending moment diagram.

 

[ryanmcarthy]

I've drawn the shear force diagram, so would it be possible please for someone to show me how to calculate the points to draw a bending moment diagram? Not to draw the diagram for me, but show how you calculate the points?
Ma = 0
.
.
.
m10 = 0

I know the rules state you need to try, but I have and do not understand how to go about doing them?

This is my shear force drawing:

v
Thanks a lot

 

[SteamKing]

Do you know what the relationship is between the shear force and bending moment on a beam? That would go a long way to helping you make your bending moment calculations.

(Hint: try this link -
http://people.virginia.edu/~pjm8f/engr162/beam/shear_force_and_bending_moment.htm

 

[ryanmcarthy]

Brilliant, thank you! So I get these now:

M0=0
M1= -(5*1*1/1)= -2.5kNm
M2= -(5*2*2/2)= -10kNm
M3= (26.7*1)-(5*3*3/2)= 4.2kNm
M4= (26.7*2)-(5*4*4/2)-(10*1)= 3.4kNm
M5= (26.7*3)-(5*5*5/2)-(10*2)= -2.4kNm
M6= (26.7*4)-(5*6*6/2)-(10*3)= -13.2kNm
M7= (26.7*5)-(5*7*7/2)-(10*4)= -29kNm
M8= (26.7*6)-(5*8*8/2)-(10*5)= -49.8kNm
M9= (26.7*7)+(53.3*1)-(5*9*9/2)-(10*6)= -22.3kNm
M10=0