Cantilever beam (statically indeterminate)

[durka]

hello everyone,
i have a small problem in calculating a particular loading case of a cantilever beam which is shown on the attached image.

i have found many loading cases of cantilever beams which i am able to solve, however for this one i couldn't find anything unfortunately.

the bending moment equation which i have written is:
M(x)= -Mw+Rwx-R[x-0.4] which i hope is correct



determined needs to be:
a) The maximum deflection at the loading point (695N at 0.4)
b)The maximum values of the reactions at the supports.

for any hints and advices i will be grateful

best regards
durka

 

[hotvette]

The answer is superposition. You know (or can derive) the equation(s) for a cantilever beam (w/o the 2nd support) with a point load. Consider this case to be the sum of two independent loadings, the 2nd of which is at the end of the beam in the upward direction (instead of the support), with a physical constraint that the net displacement of the end of the beam is zero.

 

[durka]

hello hotvette,
thanks for your quick answer.

i have solved a part of the question, but i can not continue because i don't have the equilibrium equations.

i came to the point:
EI DELTA=Mw0.08-Rw0.0106+Rp0.0106-Rp0.032

i don't get any further because the equilibrium equations that i have used don't make any sense so i canot solve it.

i know that i must replace either Rp or Rw and Mw from the equilibrium equations

 

[Studiot]

You cannot solve this from the equilibrium equations alone.

If you follow Hotvette's suggestion an use superposition, you should be able to calculate the cantilever deflection from the load acting without the roller support and equate it to the deflection from the roller support reaction acting without the load.