For a frame that is prone to sidesway, the slope deflection equation needs to assume the vertical members are displacing with magnitude of delta. From this consideration, the analysis of frame can be conducted as usual:
1. Segmentization of members
2. Selection of slope deflection equations
3. Determination of FEM
4. Elimination of delta terms for horizontal members
5. Elimination of theta terms based on boundary condition
After all the parameters are determined, we construct equilibrium equations containing all unknowns. When sidesway is assumed, it is advisable to construct one more simultaneous equation by taking equilibrium in global horizontal direction. We can calculate the unknowns by solving these simultaneous equations.
The following introduces the solution of sidesway frame using slope-deflection equation. Watch the video above for full details.
Frame overview
Internal moment convention
Slope-deflection equations based on boundary conditions
Application of slope deflection equation
Calculation of fixed end moment
Sidesway consideration
Member boundary conditions
Construction of simultaneous equation and solution of unknowns using matrices
Solution for unknown internal moments
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