Use this engineering calculation for a transparent preliminary estimate or independent arithmetic check when geometry, materials, loads, operating conditions, and units are defined consistently.

Gross Moment Meters4 (m⁴)

Required number input.

Cracked Moment Meters4 (m⁴)

Required number input.

Cracking Moment Newton Meters (N·m)

Required number input.

Applied Moment Newton Meters (N·m)

Required number input.

Branson interpolation for reinforced-concrete effective second moment: Ig before cracking, then (Mcr/Ma)^3Ig+[1−(Mcr/Ma)^3]Icr. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Effective Moment Meters4 (m⁴)

The resulting effective moment meters4 returned as a number.

• Simple beam equations assume stated supports, loads, linear elasticity, small deflection, and an appropriate section property. Shear deformation, local buckling, lateral-torsional buckling, cracking, creep, connections, dynamics, and code combinations may govern.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check assumptions against drawings, measurements, current material data, and the applicable design code. Apply required load combinations and safety factors, then obtain qualified review and testing for consequential designs.

• Moment Inertia Circle

  Centroidal second moment of area of a solid circular section about any in-plane diameter: πd⁴/64.

• Moment Inertia Rectangle

  Centroidal second moment of area for a solid rectangle about the axis parallel to its width: bh³/12.

• Bending Stress

  Extreme-fiber bending stress magnitude in an elastic beam section from bending moment, neutral-axis distance and second moment.