TheStructuralCalc

Beam Bending Moment, Shear and Deflection Calculator

Reactions, shear and bending moment diagrams and elastic deflection for a single-span beam, across thirteen standard load cases — simply supported, cantilever, fixed at both ends and propped cantilever.

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Units

Every field below also takes its own unit typed inline — e.g. "12ft" or "12'" — regardless of this setting.

Load case

Geometry

Loads

Section (optional)

Deflection is reported only when E and I are known — directly, or from a material and shape.

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Mmax = 56.25 kN·m · Vmax = 37.50 kN · L/δ = 569

SIMPLY SUPPORTED, UNIFORM LOADSHEARMOMENTL = 6 m
Maximum moment
56.25 kN·m
Maximum shear
37.50 kN
Max deflection
10.55 mm
Left reaction
37.50 kN

Calculation

  1. 1Support reactions
    R_1 = R_2 = \frac{wL}{2}
    R = \frac{12.500 \times 6.000}{2} = 37.500
    R_137.50 kN
  2. 2Maximum bending moment within the span
    M_{max} = \frac{wL^2}{8}
    M_{max} = \frac{12.500 \times 6.000^2}{8} = 56.250
    M_{max}56.25 kN·m
  3. 3Maximum elastic deflection
    \delta_{max} = \frac{5wL^4}{384EI}
    \delta_{max} = 10.55 \quad (L/\delta = 569)
    \delta_{max}10.55 mm

    Span-to-deflection ratio L/569. Compare against the serviceability limit for the finishes being supported.

Assumptions

  • Prismatic member, linear-elastic material, small deflections.
  • Loads are static and applied in the plane of bending.
  • Supports are idealised as frictionless pin and roller, or as fully rigid where an end is fixed.

What this calculator does not check

  • Single span only — no continuous beams, overhangs or moving loads.
  • Does not check the section: no flexural, shear, lateral-torsional buckling or local buckling capacity.
  • Deflection is the elastic value for the gross section; it makes no allowance for creep, shrinkage or cracking.
  • Self-weight is not added automatically. Include it in the applied load.
  • The fixed and propped cases assume the support genuinely develops the end moment. A connection that rotates redistributes moment towards midspan and is not modelled.

Results are for preliminary sizing and educational use. They are not a design and must be reviewed, verified and sealed by a licensed or registered engineer before being used in construction.

beam-bending-moment v1.1.0 · n/a · input 2182f25932349dda