Fixed-Fixed Beam Calculator

Reactions · fixing moments MA/MB · deflection · M-diagram

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Load Type

mm
kN/m
Design value (factored)
mm
mm
I = b·h³/12
mm
I = π·d⁴/64
mm
mm
mm⁴

Results

Reaction RA
—
Reaction RB
—
Fixing moment MA
—
Fixing moment MB
—
Max span moment Mspan
—
Governing moment |M|max
—
Moment of inertia I
—
EI stiffness
—
Max deflection fmax
—
Symmetric load — MA = MB, RA = RB.
Deflection > L/300 — check serviceability limit state.
Distance a must be less than beam length L.

Bending Moment Diagram

Formulas — Fixed-Fixed Beam

UDL — w [kN/m]

  • RA = RB = wL/2
  • MA = MB = −wL²/12
  • Mspan = +wL²/24
  • fmax = wL⁴/(384EI)

Central point load — P

  • RA = RB = P/2
  • MA = MB = −PL/8
  • Mspan = +PL/8
  • fmax = PL³/(192EI)

Eccentric load — P at a

  • RA = Pb²(3a+b)/L³
  • RB = Pa²(3b+a)/L³
  • MA = −Pab²/L²
  • MB = −Pa²b/L²
  • f at P = Pa³b³/(3EIL³)

Sign convention

  • Positive moment = sagging (tension in bottom fibre)
  • Negative moment = hogging (tension in top fibre)
  • Fixing moments at walls are hogging (negative)
  • Span moment is sagging (positive)