Beam Design Guide — Engineering Reference

AISC 360 Chapter F beam design step-by-step: compact sections, Lp/Lr unbraced length, LTB, Cb factor, shear design, and deflection serviceability checks.

Overview

Steel beam design per AISC 360 Chapter F requires checking flexural yielding, lateral-torsional buckling (LTB), flange local buckling (FLB), and web local buckling (WLB). The designer selects a W-shape or built-up section, classifies it as compact, noncompact, or slender per Table B4.1b, then calculates the available flexural strength considering unbraced length and moment gradient.

Shear design per Chapter G and deflection serviceability checks complete the beam design workflow. For composite beams with concrete slabs, Chapter I governs the shear stud and effective width requirements.

Flexural strength and LTB

The nominal moment capacity depends on unbraced length Lb relative to two transition points:

• Lb <= Lp: Full plastic moment Mp = Fy _ Zx applies (compact sections). Lp = 1.76 _ ry * sqrt(E / Fy).
• Lp < Lb <= Lr: Inelastic LTB zone. Capacity transitions linearly from Mp down to 0.7 _ Fy _ Sx at Lr.
• Lb > Lr: Elastic LTB. Capacity given by the critical buckling stress Fcr using the exact expression from AISC Eq. F2-4 involving Cb, J, Sx, ho, and rts.

The moment gradient factor Cb accounts for non-uniform bending moment distributions. For uniform moment Cb = 1.0; for typical gravity loading on simply supported beams Cb ranges from 1.14 to 1.67 per Eq. F1-1.

Worked example — W18x50 simply supported beam

Given: W18x50, A992 (Fy = 50 ksi), span L = 30 ft, uniform load w_u = 2.5 kip/ft (factored), lateral bracing at midspan only (L_b = 15 ft). Properties: Z_x = 101 in^3, S_x = 88.9 in^3, r_y = 1.65 in., r_ts = 1.98 in., J = 1.24 in^4, h_o = 17.4 in.

1. Check compactness: b_f/(2t_f) = 7.50/(2 x 0.57) = 6.58 < 9.15 (compact). h/t_w = 16.86/0.355 = 47.5 < 90.6 (compact). Section is compact.
2. Plastic moment: M_p = F_y x Z_x = 50 x 101 = 5050 kip-in = 420.8 kip-ft.
3. L_p: L_p = 1.76 x r_y x sqrt(E/F_y) = 1.76 x 1.65 x sqrt(29000/50) = 1.76 x 1.65 x 24.08 = 69.9 in. = 5.83 ft.
4. L_r (from AISC Eq. F2-6): L_r ≈ 16.6 ft (calculated from r_ts, J, S_x, h_o, c).
5. Check LTB: L_b = 15 ft. Since L_p (5.83) < L_b (15.0) < L_r (16.6), inelastic LTB governs.
6. C_b factor: For uniform load with midspan brace, C_b ≈ 1.30 (quarter-point moment method).
7. Nominal moment: M_n = C_b x [M_p - (M_p - 0.7 x F_y x S_x) x (L_b - L_p)/(L_r - L_p)] = 1.30 x [5050 - (5050 - 0.7 x 50 x 88.9) x (15.0 - 5.83)/(16.6 - 5.83)] = 1.30 x [5050 - 1939 x 0.852] = 1.30 x 3398 = 4418 kip-in. But M_n cannot exceed M_p = 5050, so M_n = 4418 kip-in = 368.2 kip-ft.
8. Design strength: phi x M_n = 0.90 x 368.2 = 331.3 kip-ft.
9. Required moment: M_u = w_u x L^2 / 8 = 2.5 x 30^2 / 8 = 281.3 kip-ft. Since 281.3 < 331.3, OK.

Shear design

Web shear capacity per AISC 360 Chapter G: phi_v x V_n = 1.00 x 0.6 x F_y x A_w x C_v1, where A_w = d x t_w. For most rolled W-shapes with h/t_w <= 2.24 x sqrt(E/F_y) = 53.9 (A992), the web shear coefficient C_v1 = 1.0 and no transverse stiffeners are needed.

Continuing the example: V_u = w_u x L / 2 = 2.5 x 30 / 2 = 37.5 kip. phi x V_n = 1.00 x 0.6 x 50 x (18.0 x 0.355) x 1.0 = 191.7 kip >> 37.5 kip. Shear is OK by inspection.

Code comparison — beam flexural design

Deflection limits

Beam deflection is a serviceability check using unfactored service loads, not factored LRFD loads:

For the worked example above: service live load w_L = 1.2 kip/ft (assumed), delta = 5 x w_L x L^4 / (384 x E x I_x) = 5 x 0.1 x 360^4 / (384 x 29000 x 800) = 0.95 in. Limit = L/360 = 360/360 = 1.0 in. Since 0.95 < 1.0, deflection OK.

Beam selection tips

• Start with the Z_x required: Z_x,req = M_u / (phi x F_y). This gives the minimum plastic modulus assuming full lateral bracing (C_b = 1.0, compact section). Then verify LTB and adjust upward if needed.
• Use the AISC beam selection tables (Table 3-2) which list beams by Z_x. The table also shows L_p and phi x M_p for quick comparison.
• Deeper beams are more efficient — a W21x44 (Z_x = 95.4) weighs less than a W14x61 (Z_x = 102) for similar capacity, because the deeper section has a larger moment arm.
• Check strong-axis coping — if the beam is coped at the support, the reduced section must be checked for flexural yielding, lateral-torsional buckling of the coped tee, and block shear.

Common mistakes to avoid

• Using Z_x when the section is noncompact — noncompact flanges or webs require reduced capacity per AISC F3 or F4. Some lighter W shapes (e.g., W12x14, W6x8.5) have noncompact flanges for F_y = 50 ksi.
• Ignoring the C_b factor — conservatively using C_b = 1.0 for all cases can oversize beams by 15-40%. For a simply supported beam with uniform load, C_b = 1.14. For a beam with end moments only, C_b can reach 2.27 for single curvature, significantly increasing the LTB capacity.
• Checking deflection with factored loads — deflection limits apply to unfactored service loads. Using LRFD factored loads overstates deflections by 40-60% and leads to unnecessarily heavy beams.
• Not verifying web crippling and web yielding — at concentrated load points (columns, hangers, point loads), the beam web must be checked for local yielding (J10.2), crippling (J10.3), and sidesway buckling (J10.4). These checks often require bearing stiffeners.
• Assuming full lateral bracing when deck is not attached — metal deck provides lateral bracing to the top flange only when properly attached with puddle welds or screws. During construction (before deck placement), the unbraced length equals the beam span or the distance between temporary bracing.

Run this calculation

• Beam Calculator
• Section Properties Database

Related references

• Beam Sizes
• Beam Formulas
• How to Verify Calculations
• Lateral-Torsional Buckling
• Deflection Limits
• Composite Beam Design
• steel beam capacity calculator
• Beam Web Design
• Steel Crane Girder

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.