Problem:

Using the deflection results for Figure A below, use superposition to determine the deflection equations for the three regions of the beam shown in Figure B$.$

$R_1=\frac{wa}{2l}(2l-a),R_2=\frac{w{a}^2}{2l},V_{AB}=\frac{w}{2l}[2l(a-x)-a^2],V_{BC}=-\frac{w{a}^2}{2l}$

$M_{AB}=\frac{wx}{2l}(2al-a^2-lx),M_{BC}=\frac{w{a}^2}{2l}(l-x)$

$y_{AB}=\frac{wx}{24\text{E}\text{I}\text{l}}[2a{x}^2(2l-a)-x^3-a^2(2l-a{)}^2],y_{BC}=y_{AB}+\frac{w}{24EI}(x-a{)}^4$

Figure BProblem:

Using the deflection results for Figure A below, use superposition to determine the deflection equations for the three regions of the beam shown in Figure B$.$

$R_1=\frac{wa}{2l}(2l-a),R_2=\frac{w{a}^2}{2l},V_{AB}=\frac{w}{2l}[2l(a-x)-a^2],V_{BC}=-\frac{w{a}^2}{2l}$

$M_{AB}=\frac{wx}{2l}(2al-a^2-lx),M_{BC}=\frac{w{a}^2}{2l}(l-x)$

$y_{AB}=\frac{wx}{24\text{E}\text{I}\text{l}}[2a{x}^2(2l-a)-x^3-a^2(2l-a{)}^2],y_{BC}=y_{AB}+\frac{w}{24EI}(x-a{)}^4$

Figure B