Structural Engineering Calculators
Free structural engineering calculators for beam deflection, second moment of area, and section modulus, for rectangular, circular, and hollow tube sections.
Structural Engineering Calculators - Beam Deflection and Section Properties
Structural design starts with the geometry of a cross-section and ends with checking how a beam actually behaves under load. These calculators cover the core structural engineering workflow: find a section’s second moment of area, find its section modulus, then use both in a beam deflection check against real span, material, and load values, all using classical Euler-Bernoulli beam theory.
Three Structural Engineering Calculators
Beam Deflection Calculator (Simply Supported) - Maximum deflection of a simply supported beam under a central point load (delta = PL³/48EI) or a uniformly distributed load (delta = 5wL⁴/384EI), with an interactive chart of the deflection curve along the full span and an automatic L/360 serviceability check.
Second Moment of Area Calculator - Second moment of area (I) for a rectangle (I = bh³/12), a solid circle (I = πd⁴/64), or a hollow circular tube (I = π(D⁴−d⁴)/64), returned in both mm⁴ and cm⁴ with a labeled cross-section diagram for each shape.
Section Modulus Calculator - Elastic section modulus (Z = I/c) for the same three cross-sections, a rectangle (Z = bh²/6), a solid circle (Z = πd³/32), or a hollow circular tube (Z = π(D⁴−d⁴)/32D), used directly in the bending stress formula sigma = M/Z.
Structural Design Fundamentals
Second Moment of Area vs Section Modulus - Second moment of area (I) measures a section’s resistance to bending deflection. Section modulus (Z = I/c) measures its resistance to bending stress. Both matter for a complete beam design: I feeds the deflection check, Z feeds the strength check.
Simply Supported Beam - A beam resting on a pin support at one end and a roller support at the other, both allowing free rotation with no moment restraint. Maximum deflection under a central point load or a uniformly distributed load always occurs at midspan, by symmetry.
Serviceability vs Strength - A beam can pass a strength check (it will not break) while still failing a serviceability check (it deflects too much for comfort or function). The common L/360 deflection limit is a serviceability requirement, separate from and in addition to a stress-based strength check.
Frequently Asked Questions
Which calculator should I use first when designing a beam?
Start with the Second Moment of Area Calculator to get I for your chosen cross-section, then use the Section Modulus Calculator for the same dimensions to get Z, and finally the Beam Deflection Calculator to check whether the beam deflects within an acceptable limit under your actual span and load.
Do these calculators only work for simply supported beams?
Yes, the Beam Deflection Calculator applies specifically to simply supported beams (pin support at one end, roller at the other). Cantilever and fixed-end beams use different deflection formulas and are not covered by this calculator.
What cross-sections are supported?
The Second Moment of Area and Section Modulus calculators both support a solid rectangle, a solid circle, and a hollow circular tube, the three most common structural cross-section shapes for hand calculations.
What deflection limit does the beam calculator check against?
The Beam Deflection Calculator checks the computed deflection against the common L/360 serviceability limit (span divided by 360). Stricter project-specific limits such as L/240 or L/480 should be checked manually against the reported deflection value.