Fixed-Fixed Beam with Point Load is a beam type that has fixed supports on both ends and transverse point load located in the middle.

Fixed-Fixed Beam Equations

Reactions

$R_A = R_B = \frac{P}{2}$

Shear Force

$V(x) = q (\frac{L}{2}-x)$
$V_A = -V_B = \frac{P}{2}$

Bending moment

$M(x) = \frac{P}{8} (4x - L) \quad X = (0, \frac{L}{2})$
$M_{min}(ends) = - \frac{PL}{8}$
$M_{max}(center) = \frac{PL}{8}$

Deflection

$\delta(x) = \frac{Px^2}{48EI}(3L - 4x) \quad X = (0, \frac{L}{2})$
$\delta_{max}(center) = \frac{PL^3}{192EI}$