Maximizing Bending Moment in Simply Supported Beams: An Experimental Approach

[SteamKing]

You have to be careful in reading the beam diagram. The UDL is 5 kN/m, not 5 N/m.

 

[Big Jock]

oxon88 and SteamKing are the values in the table correct in post 30. I am using these as reference while I' am working them out??...

 

[SteamKing]

They seem to be OK.

 

[Big Jock]

That's what I have found so far. Having a little trouble getting the 30kN load deflection figures and wanted to double check that these were the values I was looking for...

 

[SteamKing]

If you can't resolve your problem, post a sample calculation, like you did for the UDL.

 

[Big Jock]

30000x7x2/6x200x10^9x150x10^-6(10^2x2^2-7^20) Think my problem is what the values of a and b are I have been alternating between 3 and 7 and plugging these into the formulas mentioned but not having much joy whichever way I do it...

 

[SteamKing]

30000x7x2/6x200x10^9x150x10^-6(10^2x2^2-7^20) Think my problem is what the values of a and b are I have been alternating between 3 and 7 and plugging these into the formulas mentioned but not having much joy whichever way I do it...

Your calculation isn't coming out correct because you are not using the right equation.

It looks like you are trying to determine deflection for x = 2 m

Use Eq. 7, first part from the attachment, since 0 < 2 < 7:

y = [(P*b*x)/(E*I*L)]*(L^2 - x^2 - b^2)

Part of the confusion is the table uses 'l' for L, and it can be overlooked easily. You forgot to divide by L and in the parenthesis part, you multiplied L^2 by x^2 when you should have subtracted.

 

[Big Jock]

Thanks very much your spot on and all my numbers all look like the others listed and so des my graph. Many thanks again for your patience.

 

[Big Jock]

SteamKing which formula would you use to find the I value to half the maximum deflection in the beam? Which I guess is the sum which at 5m is 49.20mm...

 

[SteamKing]

Look at the formulas you used to calculate deflection. Where is the I used in all of the formulas? What relative value of I would cause the deflection of the beam to be half of its original value?

 

[Big Jock]

Steamking should I be used for the sum of deflections, 5kNm-1 udl load, 20kN or 30kN point loads to determine. What I value for the beam would be required to halve the maximum
deflection of the beam ?

 

[SteamKing]

Isn't the total deflection the sum of the individual deflections caused by the UDL and the two point loads?

What would happen if you took the formulas for the deflections caused by each of these loads and added them up?

Don't you get [Bunch of Stuff] / EI + [Bunch of Stuff] / EI + [Bunch of Stuff] / EI ?

How does the value of I influence the value of the deflection of the beam?

 

[bonsai]

Oxon88, how did you do with these questions? Were the answers you provided correct? Seem to be struggling with this and could use some guidamnce...