# Solution to Problem 692 | Beam Deflection by Method of Superposition

**Problem 692**

Find the value of EIδ midway between the supports for the beam shown in Fig. P-692. (Hint: Combine Case No. 11 and one half of Case No. 8.)

**Solution 692**

The midspan deflection from Case No. 8 and Case No. 11 are respectively,

$\delta = \dfrac{5w_oL^4}{384EI}$ | |

$\delta = \dfrac{ML^2}{16EI}$ |

The given beam is transformed into a simple beam with end moment at the right support due to the load at the overhang as shown in the figure below.

EIδ = ½ of EIδ due to uniform load over the entire span - EIδ due to end moment

$EI \, \delta_{midspan} = \dfrac{1}{2}\left[ \dfrac{5(120)(12^4}{384} \right] - \dfrac{2160(12^2)}{16}$

$EI \, \delta_{midspan} = 16\,200 - 19\,440$

$EI \, \delta_{midspan} = -3\,240$

$EI \, \delta_{midspan} = 3\,240 \, \text{ lb}\cdot\text{ft}^3 \, \text{ upward}$ *answer*

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