Steel Beam (LRFD)

How it calculates

The Steel Beam (LRFD, AISC 360-22) calculator runs a strength and deflection check per the current AISC Specification on hot-rolled steel beams with any number of spans and loads.

Section classification (AISC 360-22 B4)

Flanges and webs are classified as compact, noncompact, or slender by comparing width-to-thickness ratios to lambda_p and lambda_r limits. The classification decides whether the full plastic moment is available or a local buckling reduction applies.

Flexural capacity - AISC 360-22 Chapter F

Positive and negative bending are checked independently. For compact sections: utilization = Mu / (phi × Mp) ≤ 1.0, with phi = 0.9. Flange local buckling reductions apply to noncompact and slender flanges. Web local buckling is checked for HSS. Lateral-torsional buckling is evaluated using the unbraced length Lb, limiting lengths Lp and Lr, and the Cb moment gradient factor. The governing flexural capacity is the minimum from all applicable limit states.

Shear capacity - AISC 360-22 Chapter G

Web shear capacity uses: utilization = Vu / (phi × 0.6 Fy Aw Cv) ≤ 1.0. For W, M and S shapes bent about the strong axis with h/tw below 2.24√(E/Fy), phi = 1.0 and Cv1 = 1.0. Other I-shapes and channels bent about the strong axis use phi = 0.9 and Cv1 from web slenderness. HSS, tees, angles and weak-axis bending use phi = 0.9 and Cv2.

Load combination analysis

The LRFD strength combinations in the project's list (1.4D; 1.2D + 1.6L + 0.5Lr; 1.2D + 1.6S + f1L; 0.9D + 1.0W; etc.) are evaluated with FEA. The calculator identifies the governing combination for moment and for shear separately. Unfactored load cases are also run for deflection calculations.

Deflection checks

Three deflection limits are tracked independently, each checked span by span:

• Instantaneous deflection - from live, roof live, snow and 0.42W cases, compared to the lesser of L/n and an absolute limit (defaults L/360 and 2 in)
• Long-term deflection - checked against its own limit (default L/240) and reported when it is more critical than the instantaneous check
• Simplified DL+(LL or SL) deflection - default combination D + L + Lr, limit L/240 by default

utilization = delta / delta_allow ≤ 1.0 for each criterion. The critical (worst-case) result across all spans is shown in the summary.

Inputs summary

Geometry: section designation, yield strength Fy (ksi), plan length, span lengths, support types, incline pitch, tributary spacing. Loads: dead, live, roof live, snow, wind as uniform, partial, point, or moment loads at any position. Design criteria: separate deflection limits for each of the three serviceability checks.

Outputs summary

Summary outputs include critical moment demand and capacity, governing load combination for moment and shear, shear demand and capacity, and deflection ratios for all three criteria. Inclined beams also report maximum factored vertical and horizontal reactions. Reactions are structured for automatic load linking to connected column and footing calculations.