Worked out problem on slope deflection method on portal frame.
Download worked out problem on portal frame.
This workbook consists of one hand written problem on a portal frame. This work employs slope deflection method. Bending moment and shear force drawing is also drawn at the end. This workbook is employs SI units.
To download hand written notes click the button below.
Slope deflection equations for a portal frame without sway :
\[{M_{AB}} = {M_{FAB}} + \frac{{2EI}}{L}\left[ {2{\theta _A} + {\theta _B}} \right]\]
\[{M_{BA}} = {M_{FBA}} + \frac{{2EI}}{L}\left[ {2{\theta _B} + {\theta _A}} \right]\]
\[{M_{BC}} = {M_{FBC}} + \frac{{2EI}}{L}\left[ {2{\theta _B} + {\theta _C}} \right]\]
\[{M_{CB}} = {M_{FCB}} + \frac{{2EI}}{L}\left[ {2{\theta _C} + {\theta _B}} \right]\]\[{M_{CD}} = {M_{FCD}} + \frac{{2EI}}{L}\left[ {2{\theta _C} + {\theta _D}} \right]\]
\[{M_{DC}} = {M_{FDC}} + \frac{{2EI}}{L}\left[ {2{\theta _D} + {\theta _C}} \right]\]
Boundary conditions and joint equillibrium equations :
\[{M_{BA}} + {M_{BC}} = 0\]
\[{M_{CB}} + {M_{CD}} = 0\]
\[{\theta _A} and\ {\theta _D} = 0\]
The above mentioned equations are applied to solve for bending moment in the work book. Slope deflecction method is used in continuous beam and frames to analyze bending moment and shear force.
Refrence
1. Hibbeler R. C. (2017). Structural Analysis (9th edition.). Pearson Publishers Pvt Ltd.
2. Ramamrutham S. (2020). Strength of Materials (20thedition.).Dhanpat rai publishing company.
3. Khurmi R. S. (2018). A Textbook Of Strength Of Materials (Revised edition.). S Chand And Company Ltd.
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