Propped cantilever deflection

[Enhineyero]

I notice that the calculated elastic deflection at tip of propped cantilever beam is dependent on backspan. Deflection increases as backspan length go up.
deflection at tip of pure cantilever: PL^3/3EI
Deflection at tip of propped cantilever: P(Lc)^2/3EI x (Lb+Lc)


For example I have a 10kN point load on a 2m long pure cantilever 200UB25 beam, deflection = 6mm. On a propped cantilever with a back span of say 8m, deflection = 28mm. Thats more than 4x increase and it doesnt feel right.

Any thoughts on this.

 

[rb1957]

can the OP draw what he's asking about ? I've tried to follow the thread but we're using words in a confusing (to me) way.

A propped cantilever to me is built-in (fixed) at one end and simply supported at the other (or it can have an overhang.
You can add the complexity of finite stiffness' if you like.

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

 

[Tomfh]

Rb1957,

It was this arrangement, with the back span varying in length.

 

[BridgeSmith]

Well, whatever you call it, it shouldn't be a mystery or a surprise that a longer backspan results in more deflection of the cantilever - the longer the backspan, the less stiff the beam is. The less stiff the beam is, the more rotation of the beam at the supports under the same loading.

For the record, I'm with steveh49 on avoiding the term "propped cantilever" altogether. The configuration shown by HTURKAK and the latest post by Tomfh, I would call a simple beam with a cantilever. I would call the beam configuration in the diagram posted by steveh49 a fixed-pinned beam.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[rb1957]

does the triangle mean anything more than a pinned support ? (and the circle a roller support)

so this is a simply supported beam with an overhang ?
the overhang could be considered a (fixed end) cantilever, with the two supports creating the fixed end moment as a couple.

so the maximum deflection occurs on the simple span or the overhang depending on the relevant lengths ?

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

 

[BridgeSmith]

the overhang could be considered a (fixed end) cantilever, with the two supports creating the fixed end moment as a couple.

With a back span, the cantilever is not fixed at the support. The beam can rotate over the support. If you calibrate the load on the simple span relative to the load on the cantilever correctly, you can achieve zero rotation at the roller support, which would have give the same resulting deflection of the cantilever as a fixed support.

Of course, there is no such thing as a fully fixed support in the real world, anyway, but some are stiff enough to be modeled as such, so the model closely approximates the real behavior.

Rod Smith, P.E., The artist formerly known as HotRod10