Slope deflections method analysis of beam

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Discussion Overview

The discussion revolves around the slope deflections method for analyzing beams, specifically addressing the conditions under which beams curve upwards versus downwards. Participants are exploring the necessity of considering both scenarios in their analysis and the implications of relative displacements between beam members.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the need to consider both upward and downward curvatures of the beam, suggesting that only the downward curvature is necessary based on visual observations.
  • Another participant raises a question about why only one scenario of relative displacement (member B displaced relative to A) is considered, implying that the reverse scenario (member A displaced relative to B) might also be relevant.
  • A participant seeks clarification on whether it is essential to consider both curvature cases and suggests that superimposing graphs might illustrate the beam's behavior.
  • Several posts express a desire for further explanation or clarification, indicating uncertainty about the concepts being discussed.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the necessity of considering both curvature cases or the approach to relative displacements, indicating that multiple competing views remain in the discussion.

Contextual Notes

Participants express uncertainty regarding the assumptions made in the analysis, particularly about the necessity of considering both upward and downward curvatures and the implications of relative displacements.

fonseh
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Homework Statement


why we need to consider 2 conditions , the beam curve downwards ( as in 11-3) and beam curve upwards ( as in 11-4) ?
What's the difference between 2 cases ?

I notice that in both cases , the author assume clockwise as positive
here are the 3 consecutive pages of notes

Homework Equations

The Attempt at a Solution


I think the second cases where the curve curve upwards is unnecessary because we can see that the curve curve downwards (U shape) in the first photos .
 

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why for the relative linear dispalcement , we just have to consider one scenario only , namely consider the case where the member B is displaced relative to A ? Why we don't have to consider the case where the member A is displaced relative to B ?
 
Is there anything wrong with these cases ?
 
Can someone explain it ?
Or we need to consider 2 cases ( where the curve curve upwards and curve downwards) because it is a must to do so ? The beam will curve like this one if we superimpose 2 graph ? The red part represent the shape of graph , while the black line represent the beam
 

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