Deflection and Slope, cantilever beam
Hi guys, I have been a question to solve this week to do with deflections and slopes at the free end of a cantilever beam. I have calculated the deflection and slope for the point load and UDL, but I'm not sure whether to add them together or not?.. as they're both acting on the beam?
A cantilever beam with a length of 7meters, has a 2KN point load at the free end and a UDL of 3KN/m along its length. Calculate the deflection and slope at the free end. *Assume the flexural stiffness [EI]is 800MPa.
This is what I've got so far:
For the point load
dy/dx [COLOR=#545454][FONT=arial]= (FL^2) / 2EI
[/FONT][/COLOR]dy/dx [COLOR=#545454][FONT=arial]= 61.25x10^-6
y = (FL^3) / 3EI
[/FONT][/COLOR][COLOR=#545454][FONT=arial]y = 285.83[/FONT][/COLOR][COLOR=#545454][FONT=arial]μm
[/FONT][/COLOR][COLOR=#545454][FONT=arial]
For the udl:
[/FONT][/COLOR]dy/dx [COLOR=#545454][FONT=arial]= (wL^3) / 6EI
[/FONT][/COLOR]dy/dx [COLOR=#545454][FONT=arial]=214.4x10^-6
y = (wL^4) / 8EI
[/FONT][/COLOR][COLOR=#545454][FONT=arial]y = 1.12m[/FONT][/COLOR][COLOR=#545454][FONT=arial]m
[/FONT][/COLOR][COLOR=#545454][FONT=arial]
[/FONT][/COLOR][COLOR=#545454][FONT=arial]Now what? Do i add them?
Thanks,
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