Slope-Deflection Method - Examples & Applications

Example

A prismatic beam ABAB of length 6 m6\text{ m} is fixed at A and connected to a rigid joint at B. A central point load P=30 kNP=30\text{ kN} acts on the span. There is no support settlement. Write the member end-moment expressions in terms of the unknown joint rotation θB\theta_B.

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Example

A two-span continuous beam ABCABC has AB=6 mAB=6\text{ m} and BC=4 mBC=4\text{ m}. A is fixed, B is an interior joint, and C is a simple end support. Span AB carries a 30 kN central point load; span BC is unloaded. Constant EIEI. Determine the final end moments.

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Example

A fixed-fixed prismatic beam undergoes a relative support settlement that creates a chord rotation ψ\psi. There is no member load. State how the settlement enters the end moments.

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Example

A single-story portal frame is loaded laterally and is free to sway. What additional unknown and equilibrium relation are required compared with a non-sway beam problem?

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Key Takeaways
  • Slope-deflection treats joint rotations and translations as the primary unknowns.
  • Fixed-end moments represent member loading with the ends locked.
  • Joint equilibrium determines compatible end moments after the displacement unknowns are introduced.
  • Settlement and sidesway enter through chord rotation and must not be ignored when present.