Beam Deflection Calculator: Simply Supported and Cantilever with AISC Check

How It Works

1. Select Beam Configuration

   Choose simply supported (pinned-pinned) or cantilever (fixed-free) and load type (concentrated point or uniform distributed). Each combination has a different deflection and moment formula.

2. Enter Beam Properties

   Select a standard W-shape from the AISC database or enter custom section properties (moment of inertia I, section modulus S, depth). Enter span in feet and modulus of elasticity E.

3. Enter Loading

   Input point load in pounds or uniform load in pounds per linear foot. The calculator finds maximum moment (PL/4 for SS point, wL-squared/8 for SS uniform) and maximum deflection.

4. Review Stress and Deflection Checks

   Bending stress fb = M/S is compared against AISC ASD allowable (0.66 Fy for compact sections). Deflection is checked against IBC L/360 for live load and L/240 for total load. Both must pass.

Built For

• Structural engineers selecting the lightest W-shape that passes both stress and deflection for a floor beam
• Steel erectors verifying that a specified beam handles the actual field loading conditions
• Building contractors checking header sizes over window and door openings in steel-framed structures
• Maintenance engineers evaluating whether an existing beam can support a new piece of equipment
• Fabricators confirming beam adequacy for mezzanine and platform designs
• Architecture students learning the relationship between moment of inertia, span, and deflection

Features & Capabilities

4 Load Cases

Simply supported point load, simply supported uniform load, cantilever point load, cantilever uniform load. Covers the most common structural scenarios.

AISC W-Shape Database

Select from standard wide-flange shapes with pre-loaded I, S, d, and weight values. No need to look up section properties manually.

Stress Check (ASD)

Compares bending stress fb = M/S against allowable stress Fb = 0.66 Fy for compact sections per AISC ASD. Shows utilization ratio.

Deflection Check (IBC)

Compares calculated deflection against L/360 (live load) and L/240 (total load) limits. Flags violations with clear pass/fail verdict.

Self-Weight Inclusion

Automatically adds beam self-weight to the dead load calculation after you select a trial section. Iterates if self-weight changes the governing section.

PDF Export

Export beam analysis as a branded PDF for engineering submittals or construction documents.

Assumptions

• Beam behaves as a linear elastic member with constant modulus of elasticity E = 29,000 ksi for structural steel
• Simply supported condition assumes pinned supports with zero moment at each end (no rotational restraint)
• Cantilever condition assumes perfectly rigid fixed support with zero rotation and translation at the fixed end
• Allowable bending stress Fb = 0.66 Fy for compact sections per AISC ASD 9th Edition (Fy = 36 ksi or 50 ksi)
• Deflection limits of L/360 for live load and L/240 for total load per IBC Table 1604.3 for floor members
• Beam self-weight treated as a uniform dead load added to applied loading after trial section is selected
• Section properties (I, S, d) taken from AISC Steel Construction Manual W-shape tables

Limitations

• Does not check lateral-torsional buckling — unbraced beams with long unbraced lengths may require reduced allowable stress
• Does not evaluate web crippling or web yielding at concentrated load points and reactions
• Does not design connections — beam end connections require separate analysis for moment, shear, and bearing
• Only covers 4 basic load cases — combined loading, partial uniform loads, and multiple point loads require superposition or more advanced analysis
• Does not address composite beam design (steel beam with concrete deck acting together)
• Shear capacity check not included — typically not governing for W-shapes but critical for short, deep beams and coped sections
• ASD method only — LRFD design per AISC 360 uses different load factors and resistance factors

References

• AISC Steel Construction Manual, 15th Edition — W-Shape Properties and ASD Design Tables
• AISC 360 — Specification for Structural Steel Buildings (design requirements for beams)
• IBC Table 1604.3 — Deflection Limits for Structural Members (L/360, L/240, L/180)
• ASCE 7 — Minimum Design Loads and Associated Criteria for Buildings (load combinations)
• Blodgett's Design of Welded Structures — Beam Design Examples and Deflection Formulas
• Roark's Formulas for Stress and Strain — Beam Deflection and Moment Equations for Various Load Cases

Frequently Asked Questions