A two span continuous beam with loadings as shown in Figure, with supports A and C as fixed and support B as roller. Assume Young's modulus of material and moment of inertia of sections as constant throughout. The slope defection equations formulated for the span AB are : (Notations : M indicates moment and θ indicates the slope at the respective points)

1
\({M_{AB}}={{1\over 3}EI\ {\theta_B}+EI\ {\theta_A}}-{160\over3};\ {M_{BA}}={{2EI\over 3}\ {\theta_B}+EI\ {\theta_A}}+{80\over3}\)
2
\({M_{AB}}={{1\over 3}EI\ {\theta_B}}-{80\over3};\ {M_{BA}}={{2EI\over 3}\ {\theta_B}}+{160\over3}\)
3
\({M_{AB}}={{1\over 3}EI\ {\theta_A}}+{80\over3};\ {M_{BA}}={{2EI\over 3}\ {\theta_B}}+{160\over3}\)
4
\({M_{AB}}={{2\over 3}EI\ {\theta_B}}-{80\over3};\ {M_{BA}}={{1\over 3}EI\ {\theta_B}}+{160\over3}\)

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