Structural analysis influence lines in beams

[Romulus3]

Homework Statement

http://antishift.org/image.php?id=16122&size=medium

Homework Equations

Static Equilibrium equations: since most of the supports are rollers, only y-forces are considered as well as moment equations. I'm pretty sure E and F are hinges so there are no moments around E and F.

The Attempt at a Solution

I'm having trouble with solving the FBD equations. First I drew an FBD of segment AE and placed a unit load on the beam at a distance x away from A. Then I solved for the vertical reactions at A and E. But once i do this, I don't know how the reaction a C is affected. can anyone please help me with this? If I know how to do part (a), I am confident I can do the rest. thanks!

 

[radou]

Are you familiar with the kinematic procedure to find influence lines? I always found it pretty much easier than the standard (i.e. static) procedure.

Basically, if you want to find the influence line for some statical quantity, then you have to remove its "realization" (i.e. the bond which allows this quantity (force, torque...) to act) and turn your determinate system into a mechanism with one degree of freedom. You add a generalized unit force at the place where you released the bond (internal or external) and create the displacement sketch of the system, which presents the influence line for the mentioned statical quantity.

 

[Romulus3]

Hey radou,

is this the Müller Breslau Principle? I remember skimming over that in my textbook, and your description seems similar. However, the problem states I should solve using statics.

 

[radou]

Hey radou,

is this the Müller Breslau Principle? I remember skimming over that in my textbook, and your description seems similar. However, the problem states I should solve using statics.

Well, you can start with a sketch of the influence line of the vertical reaction at C with the Müller Breslau Principle (since it's almost trivial to find it), perhaps it will help you to reason about "influences" in the static procedure. I'm a bit foggy with that procedure, so I can't be of any great help right now. Should revise it, though.