Question: A cantilever beam ABC is fixed at A and free at C carries UDL of 12 kN/m over its entire span and a point load of 24 kN at B. AB=2m (2 $I$ and BC=3m (I). Determine the slope at c & deflection at C

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Question: A cantilever beam ABC is fixed at A and free at C carries UDL of 12 kN/m over its entire span and a point load of 24 kN at B. AB=2m (2 $I$ and BC=3m (I). Determine the slope at c & deflection at C

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**1. Slope at (C) = $Q_C$**

$ Q_C= Area\ between\ c,A\\ Area[1+2+3+4]\\ =\left[\frac{1}{2}\times2\times\frac{24}{EI} \right]+\left[ 2\times\frac{27}{EI}\right] +\left[\frac{1}{3}\times\frac{48}{EI}\times2 \right]+\left[ \frac{1}{3}\times\frac{54}{EI}\times3\right]\\ = \frac{36+54+32+54}{EI}\\ \boxed{Q_C=\frac{176}{EI}rad}$

**2. Deflection at c=$y_c$**

$ y_C=Area[1+2+3+4]\times C.G\\ =\left[ \frac{36\times4.33}{EI}\right]+\left[ \frac{54\times4}{EI}\right]+\left[ \frac{32\times4.5}{EI}\right]+\left[ \frac{54\times2.25}{EI}\right]\\ = \frac{155.88+216+144+121.5}{EI}\\ \boxed{y_C=\frac{637.38}{EI}m}\underline{Ans.} $

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