Fixed-Fixed Beam with Point Load

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 with Point Load

Fixed-Fixed Beam with Point Load

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}