L shaped cantilevered beam problem... 1

[MaximeMalou]

Hello everyone,

I am looking for a little help with a problem I have illustrated.

http://files.engineering.com/getfil...-91f5-192fa6c8c37b&file=deflection_sketch.png

I need to figure out the deflection of this L shaped arm when a 12 kg point source is applied at its end. The beam is a hollow shaft outside diameter=0.03m and inside diameter=0.025m.

I started by assuming that the red section is cantilevered to the yellow part. Then, using the deflection formula
fmax=Wl^3/3EI, I found the deflection at the end.

However I am not sure how to proceed from here... How do I figure how the yellow part will react due to the bending moment caused by the point load?

All help is much appreciated!

 

[desertfox]

Hi MaximeMalou

Have a look at my solution however this is only for the vertical deflection, a similar calculation needs to be done to find the horizontal deflection.

desertfox

 

[weab]

For vertical deflections, I'd add 2 components. Find vertical deflection of the red section, as you have done.

Also, calculate the rotation at the top of the vertical section due to an applied moment equal to your load times the cantilever. From that, calculate the deflection due to this rotation. Then add the two deflections. Sorry I don't have the formulas handy.

 

[BAretired]

The moment is W*L at the bend. The rotation at the top of the yellow part is WLh/EI where h is the height of the vertical leg.

So the vertical deflection at the point of load should be WL^3/3EI + WL^2h/EI
or WL^2(L/3 + h)/EI.

BA

 

[MaximeMalou]

Thanks for taking time to answer my question guys! Much appreciated!

 

[desertfox]

Your welcome MaximeMalou

desertfox