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Simple beam

Simple beam

Simple beam

(OP)
Hello,

Could you help me with one problem.

I've simple beam (see attachment please).



I've assumed that displacement v1 = 1 (therefore end of the beam is anchored - also in attachement).

In handbook I found that Force matrix for that case is equal to:

0
12EI/L^3
6EI/L^2
0
-12EI/L^3
6EI/L^2

And I have question for above matrix. Could you tell me why M2 = M1 ?

Thank you very much,

Lukasz

RE: Simple beam

Is this a homework assignment?

RE: Simple beam

(OP)
Marty007,

No, it is not a homework.

Regards,
Ketler

RE: Simple beam

if i understand your sketch (and i'm not sure i do, you're applying P = 1 and M1 at the tip of the cantilever. in that case M2 .NE. M1 (clearly). I'm not sure what you mean by "V1 = 1, therefore end is anchored" ... are you applying an enforced deflection ?

i don't understand your original "force matrix", can you clarify the terms ?

another day in paradise, or is paradise one day closer ?

RE: Simple beam

I believe the 'force matrix' is in fact the element stiffness matrix for a beam in finite element formulations. The term AE/L is missing probably because there's no direct load on the element. I'm not sure about the sketch either so I'd advise the OP goes back to the basic formulation of the beam element to understand the theory.

RE: Simple beam

If you are considering the case of a uniform beam with a fixed shear displacement of one end with respect to the other, and you are enforcing no rotation at either end of the beam, then the two end moments are equal.

Simple!

http://julianh72.blogspot.com

RE: Simple beam

sorry, but how can that be ? sure the end can be guided, but there's a couple between the shear reaction and the load causing the enforced displacement ... M2 = P1*L-M1 ... no? (i think the guided end moment relieves the moment due to the shear load)

if you apply only a moment at the free end, then of course M2 = M1.

another day in paradise, or is paradise one day closer ?

RE: Simple beam

For a guided (no-end-rotation)shear-only end deflection, the beam takes up an S-curve (with the two ends remaining parallel), and the fixed end moments are equal at both ends of the beam.

http://julianh72.blogspot.com

RE: Simple beam

Don't forget the sign convention for moments / rotations in FEA is anti-clockwise positive at every mode. The end moments are equal, but the moment in the beam is a linear gradient from M tension-on-top at one end to M tension-on-bottom at the other end, and zero moment at mid-span.

http://julianh72.blogspot.com

RE: Simple beam

ok, it's a symmetric problem ... 2 1/2 span cantilevers

another day in paradise, or is paradise one day closer ?

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