Structural analysis influence lines in beams

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Discussion Overview

The discussion revolves around the analysis of influence lines in beams, particularly in the context of a homework problem involving static equilibrium equations and the application of the Müller Breslau Principle. Participants explore different methods for determining influence lines, including kinematic and static approaches.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant describes their approach to solving the free body diagram (FBD) equations for a beam segment and expresses confusion regarding the effects on reactions at different supports.
  • Another participant suggests a kinematic procedure for finding influence lines, stating it is easier than the static method and describes the process of turning a determinate system into a mechanism.
  • Some participants question whether the method described aligns with the Müller Breslau Principle, noting that the original problem requires a static solution.
  • There is a suggestion to sketch the influence line for a specific vertical reaction to aid in understanding the static procedure, although one participant admits to being unclear about the static method.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate method for solving the problem, with some advocating for the kinematic approach while others emphasize the need to adhere to static methods as specified in the homework. The discussion remains unresolved regarding the best approach to take.

Contextual Notes

Participants acknowledge limitations in their understanding of the static procedure and the Müller Breslau Principle, indicating potential gaps in knowledge that may affect their ability to solve the problem.

Romulus3
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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!
 
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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 statistical 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 statistical quantity.
 
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. :frown:
 
Romulus3 said:
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. :frown:

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. :rolleyes:
 

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