Frames with inclined legs using slope-deflection method

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SUMMARY

The discussion centers on the application of the slope-deflection method in structural analysis, specifically addressing a problem from "Structural Analysis" by Aslam Kassimalli. The key point raised is the inconsistency in assuming the slope at point C is zero while simultaneously treating it as an unknown in the slope-deflection equations. Participants argue that the tangent at point C' should not be considered parallel to member AC, as the rotations at points C and D are influenced by the stiffness of connected members.

PREREQUISITES
  • Understanding of the slope-deflection method in structural analysis
  • Familiarity with structural behavior of frames and members
  • Knowledge of deflected shapes and their tangents in structural mechanics
  • Proficiency in writing and solving slope-deflection equations
NEXT STEPS
  • Study the derivation of slope-deflection equations in detail
  • Explore examples of frames with inclined legs using the slope-deflection method
  • Learn about the impact of member stiffness on frame rotations
  • Review case studies from "Structural Analysis" by Aslam Kassimalli for practical applications
USEFUL FOR

This discussion is beneficial for civil and structural engineers, students studying structural analysis, and professionals involved in designing and analyzing frame structures using the slope-deflection method.

Ashu2912
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Homework Statement


This is a diagram from "Structural Analysis" by Aslam Kassimalli while solving frames using slope-deflection method. In the figure, the tangent to the deflected shape at C` is parallel to the original member AC implying that the slope at C is zero. However, later they have considered θC (the slope at C) as an unknown while writing the slope deflection equations. Why so?

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The Attempt at a Solution

 

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I don't think you can assume that the tangent at C' (the prime symbol ' is not clear enough in the figure) is parallel to AC. The tangent at D' is not visibly parallel to BD, and shouldn't be. In general, I would expect both C and D to rotate somewhat, because the rotation is only partially restrained by the stiffness of the attached members.
 

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