Beam Capacity Worked Example — W-shape AISC 360 LRFD

Q: Does the beam capacity calculator check deflection automatically?

Yes. The calculator reports both strength and serviceability (deflection at L/360, L/240, or user-defined limit). The example above shows why deflection often governs.

Q: What code standards does the calculator support?

AISC 360-22 LRFD, AS 4100-2020, EN 1993-1-1 (with UK NA defaults), and CSA S16:24.

Q: How do I get more than 50 free calculations per day?

Register for a free account to get 50 calculations per day. Check the pricing page for higher limits.

Q: How does the Cb factor affect beam capacity?

The Cb factor accounts for non-uniform moment diagrams. For a uniformly loaded simple span, Cb = 1.14 increases nominal capacity by 14% vs Cb = 1.0. Using correct Cb is most impactful near Lp — it can make the difference between inelastic LTB and full plastic moment, saving 5-15% on beam weight.

---- | ----------------- | ----------- | ------------- | ----------- | | 4.0 | Lb < Lp = 5.75 | 277.1 | 249.4 | 0.69 | | 6.0 | Lp < Lb < Lr | 273.6 | 246.2 | 0.70 | | 9.0 | Lp < Lb < Lr | 231.3 | 208.2 | 0.83 | | 13.5 | Lb = Lr = 13.5 | 168.0 | 151.2 | 1.14 | | 20.0 | Lb > Lr (elastic) | 88.3 | 79.5 | 2.16 (FAIL) |

Adding a brace at midspan (reducing Lb from 25 ft to 12.5 ft) would increase capacity by approximately 185%, demonstrating the critical impact of bracing on lateral-torsional buckling resistance. For this span and loading, however, the W18x35 requires a heavier section (as shown in Step 6), even with intermediate bracing.

Step 9: Non-Uniform Moment (Cb Factor)

The example above used Cb = 1.0 (conservative). For a uniformly loaded simple span, the actual Cb = 1.14 produces:

Mn = 1.14 ÃÂÃÂ 273.6 = 311.9 kipÃÂÃÂ·ft (capped at Mp = 277.1) ÃÂÃÂbMn = 0.90 ÃÂÃÂ 277.1 = 249.4 kipÃÂÃÂ·ft Mu / ÃÂÃÂbMn = 171.9 / 249.4 = 0.69 ÃÂ¢ÃÂÃÂ 69% utilization

For other moment diagrams:

A beam with concentrated loads at third-points: Cb ÃÂ¢ÃÂÃÂ 1.01
A beam with equal end moments (uniform M): Cb = 1.0
A beam with one end moment (triangular): Cb ÃÂ¢ÃÂÃÂ 1.67

Using the correct Cb is particularly important near the Lp/Lr boundary where a small increase in capacity can change the economics of the design.

Step 10: Shear Deflection (Shear Deformability)

For short, deep beams (span/depth < 10), shear deflection becomes significant and must be added to the bending deflection. The shear deflection for a uniformly loaded simple span is:

ÃÂÃÂ_v = (w ÃÂÃÂ LÃÂÃÂ²) / (8 ÃÂÃÂ G ÃÂÃÂ A_w)

For the W18x35 at 25 ft: G = 11,200 ksi, A_w = d ÃÂÃÂ t_w = 5.31 inÃÂÃÂ² ÃÂÃÂ_v = (1.5/12) ÃÂÃÂ (300)ÃÂÃÂ² / (8 ÃÂÃÂ 11,200 ÃÂÃÂ 5.31) = 0.024 inches

Total deflection ÃÂÃÂ_total = ÃÂÃÂ_bending + ÃÂÃÂ_v = 0.89 + 0.02 = 0.91 inches

Shear deflection adds only ~2% for this case but can reach 10-15% for beams with span/depth ratios below 8 (deep transfer girders, crane runway beams). Per AISC Design Guide 11, shear deflection is negligible for span/depth > 10.

Step 11: ASCE 7 Load Combination Reference

The beam is checked using the ASCE 7-22 basic load combinations. For this floor beam with dead and live loads only, the governing combinations are:

1.4D — controls when live loads are less than approximately half the dead load
1.2D + 1.6L — controls for typical floor loads with live load exceeding dead load
0.9D — used only when wind or seismic loads produce uplift or reversal

For beams supporting roofs, additional combinations including wind (1.0D + 1.0W, 1.2D + 1.0L + 0.5W), snow (1.2D + 1.0L + 1.0S), and seismic (1.2D + 1.0E + 0.5L) per ASCE 7-22 must be checked. The Steel Calculator beam capacity tool includes all applicable load combinations automatically when the load type is specified.

Step 12: Compactness Check

Verify that the W18x35 is compact per AISC Table B4.1b:

Flange: bf/2tf = 6.00/(2ÃÂÃÂ0.425) = 7.06. ÃÂÃÂ»p = 0.38ÃÂ¢ÃÂÃÂ(E/Fy) = 9.15. 7.06 < 9.15 ÃÂ¢ÃÂÃÂ Compact
Web: h/tw = 53.5. ÃÂÃÂ»p = 3.76ÃÂ¢ÃÂÃÂ(E/Fy) = 90.6. 53.5 < 90.6 ÃÂ¢ÃÂÃÂ Compact

Since the section is compact with Lb < Lr, the beam reaches the full plastic moment modified for LTB. No local buckling reduction applies.

Try the Calculator

Use the Beam Capacity Calculator to check your own beam section, span, and loading with AISC, AS 4100, EN 1993, or CSA S16.

Frequently Asked Questions

Does the beam capacity calculator check deflection automatically? Yes. The calculator reports both strength (bending + shear) and serviceability (deflection at L/360, L/240, or user-defined limit). The example above shows why deflection often governs: the W18x35 had 70% flexural capacity but failed deflection at L/462 vs L/360.

What code standards does the calculator support? AISC 360-22 LRFD, AS 4100-2020, EN 1993-1-1 (with UK NA defaults), and CSA S16:24. The example above uses AISC 360 F2 for flexure and G2 for shear.

How do I get more than 50 free calculations per day? Register for a free account. Registered users get 50 calculations/day. For higher limits, check the pricing page.

How does the Cb factor affect beam capacity? The Cb factor (lateral-torsional buckling modification factor) accounts for non-uniform moment diagrams. For a uniformly loaded simple span, Cb = 1.14, which increases nominal capacity by 14% compared to the conservative Cb = 1.0 assumption. Using the correct Cb is most impactful when Lb is near Lp — it can make the difference between an inelastic LTB check and a full plastic moment, saving 5-15% on beam weight.