Deflection of box section - result Discrepancies

[Mech King]

Hello everyone,

I have a beam deflection problem. I haven’t looked at deflections for a while now and I can't understand why my solution is a million miles out fro the results I have seen through testing.

Problem:

I have a beam made from 100x40x3mm mild steel box section which is 2100mm in length. See attached figure for free body diagram of the loading on the beam. Please note the loads P1, P2 and P3 are applied individually and then removed before applying another load, so there is only one load on the beam at anyone time.

The beam is welded to the supports underneath the beam (labeled “support reactions”)

The beam is loaded against its widest face and hence I have used the “second moment of area” value as given from the data sheet in its Y axis.


Relevant formulas:

E=200,000 N/mm2 for steel
I = 361000 mm^4


Solution:

My first load case is the individual force P1 applied to the left hand side of the beam:

P1=22,017N

Cantilever moment load (as per Shigley’s Mech eng Design book):

Ymax = (M*L^2)/2EI
Ymax = [(22017*177.5^2)*177.5^2]/(2*E*I)
Ymax = 0.86 mm

Query of Solution:

I have had this problem tested and the deflection of the beam was 6.77mm. My results are showing a figure which is about 8 times too small?
Could somebody please help me understand where I am going wrong?
I have a similar problem with the remaining two load case scenarios set out in the free body diagram, for loads P2 and P3 also, but I wanted to clear up this scenario here before progressing.
What do you think?

 

[minger]

Well, you don't have a pure moment load. You have an applied shear load, which will then cause a moment.

I assume you're looking at the Appendix, Table A-9.4 Cantilever - moment load. If you notice, it shows the reaction force at the fixed support $$R_1 = 0$$. You will surely have a reaction. I don't see any cases in there which match yours. You may have to do this the ol' fashioned way, through integration. Are you familiar with shear/moment diagrams and analytic methods for calculating these things?

 

[Mech King]

Hi Minger,

Thanks for the reply.

I am familliar with these methods but haven't looked at them since university so I am a little rusty. I will give it a shot this weekend and show you the results. I am guessing you are familliar with therse methods?

Cheers

 

[minger]

I also haven't done exactly that in quite some years. From what I remember though, it's as simple as integrating the shear load 4 times and applying the correct boundary conditions as the constants of integration. I may be mistaken though...