Steel Beam Calculator

Structural Mechanics & AISC 15th Edition Beam Theory

Simply supported steel beam design balances flexural bending stress, shear, and serviceability deflection:

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• Maximum Bending Moment & Shear Formulas (Simple Span)**:

M_max = (w L^2) / (8) (ft-lbs) V_max = (w L) / (2) (lbs)

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• Required Section Modulus (S_x) Formula**:

S_x,req = M_max × 12F_b = M_max × 1233,000 psi (in^3)

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• Deflection Serviceability**:

Δ_allow = (L × 12) / (360) inches

I_x,req = (5 w L^3 × 1728 × 360) / (384 × 29,000,000 × 12) (in^4)

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• AISC Standard W-Beam Benchmark Capacities**:

• W8×18: S_x = 15.2 in^3 | I_x = 61.9 in^4 | 18 lbs/ft

• W8×24: S_x = 20.9 in^3 | I_x = 82.7 in^4 | 24 lbs/ft

• W10×22: S_x = 23.2 in^3 | I_x = 118.0 in^4 | 22 lbs/ft

• W10×30: S_x = 32.4 in^3 | I_x = 170.0 in^4 | 30 lbs/ft

• W12×26: S_x = 33.4 in^3 | I_x = 204.0 in^4 | 26 lbs/ft

• W16×40: S_x = 64.7 in^3 | I_x = 518.0 in^4 | 40 lbs/ft

How to Use This Calculator

Enter your Clear Span Length (e.g. 18 in ft), Tributary Load Width (e.g. 14 in ft), Floor / Roof Design Load (PSF) — choose from Residential Floor: 50 PSF (40 Live + 10 Dead Load), Heavy Residential / Tile Floor: 60 PSF (40 Live + 20 Dead), Roof with Snow Load: 40 PSF (30 Snow + 10 Dead), Allowable Deflection Criteria — choose from L/240 (Roof / Minimum Code Limit), L/360 (Standard Residential Floor - No Plaster Cracking), L/480 (Stiff Floor / Tile Substrate / High Precision), and Structural Project Benchmark — choose from Custom Beam Span & Load, 18 ft Basement Main Girder (14 ft Trib, 50 PSF) → W10×22 (or W10×30) Beam, 16 ft Double Garage Header (10 ft Trib, 40 PSF) → W8×18 Beam. Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Required Section Modulus Sx (in3): Sx = (M * 12) / Fb (A992 steel Fy = 50 ksi, Fb = 33 ksi = 33,000 psi)

Required Moment of Inertia Ix (in4): delta = 5 w L^4 / (384 E I) <= L / deflRatio

Ix = (5 wPLF L^3 1728 deflRatio) / (384 * 29

Worked Example

A structural engineer designing an 18-ft girder span supporting 14 ft of residential floor (700 PLF) calculates the required moment of inertia as 95.0 in^4, specifying a W10×22 or W10×30 steel beam with 4-inch steel column bearing plates.

Understanding Your Result

Evaluate your result in the context of your specific use case and relevant industry standards or reference values. A single calculated result is a starting point — test two to three scenarios to understand how sensitive the outcome is to your key input assumptions. For high-stakes decisions, verify your result against a secondary source or subject-matter expert before acting.