# 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 Equations

### Reactions

$latex R_A = R_B = \frac{P}{2} &s=1$

### Shear Force

$latex V(x) = q (\frac{L}{2}-x) &s=1$

$latex V_A = -V_B = \frac{P}{2} &s=1$

### Bending moment

$latex M(x) = \frac{P}{8} (4x – L) \quad X = (0, \frac{L}{2}) &s=1$

$latex M_{min}(ends) = – \frac{PL}{8} &s=1$

$latex M_{max}(center) = \frac{PL}{8} &s=1$

### Deflection

$latex \delta(x) = \frac{Px^2}{48EI}(3L – 4x) \quad X = (0, \frac{L}{2}) &s=1$

$latex \delta_{max}(center) = \frac{PL^3}{192EI} &s=1$