Steel Beam Design per NSCP 2015 / AISC 360: Flexure, Shear, and Deflection with a Worked Example

By Engr. Ruel H. Cepeda, Structural Engineer

NSCP 2015 Chapter 5 (Structural Steel) is based on AISC 360 (the 2010 edition) and permits either Load and Resistance Factor Design (LRFD) or Allowable Strength Design (ASD). This article covers the LRFD checks for a laterally supported, compact W-shape beam — flexure, compact limits, lateral-torsional buckling, shear, deflection — with ASD equivalents, then sizes a 6 m simply supported floor beam by worked example.

LRFD and ASD: Two Paths, One Code

LRFD compares factored demand (from factored loads, e.g. 1.2D + 1.6L) against factored capacity, φR_n, φ<1. ASD compares service-load demand (unfactored D + L) against allowable capacity, R_n/Ω, Ω>1. Both are valid under NSCP 2015 / AISC 360 and size similar members — but never mix the two in one check. LRFD is the more common basis in current Philippine practice and is used below, with ASD shown for comparison.

Step 1 — Required Flexural and Shear Strength

For a simply supported beam under uniform gravity load, factor the loads: w_u = 1.2w_D + 1.6w_L, then get the required strengths from statics: M_u = w_uL²/8   V_u = w_uL/2, with L the span. Wind, seismic, and other combinations may govern other members, but gravity D + L almost always governs a floor beam.

Step 2 — Nominal Flexural Strength of a Compact, Braced Beam

For a compact section with the compression flange continuously braced, or braced at intervals not exceeding L_p (Step 4), AISC 360 Chapter F gives the nominal flexural strength as the full plastic moment:

M_n = M_p = F_y·Z_x

LRFD: φ_bM_n≥M_u, φ_b=0.90. ASD: M_n/Ω_b≥M_a, Ω_b=1.67. Z_x, the plastic section modulus, exceeds the elastic S_x since it reflects full plastic yield rather than first yield at the extreme fiber.

Step 3 — Compact-Section Limits (Local Buckling)

M_n = M_p only holds while flange and web stay under the compact limit λ_p, AISC 360 Table B4.1b:

E = 200,000 MPa. Rolled W-shapes are compact in the web at nearly all common yield strengths; flange compactness varies by shape and is the check worth confirming. Between λ_p and the noncompact/slender limit λ_r, M_n reduces linearly toward 0.7F_yS_x; beyond λ_r elastic local buckling governs, a further reduction. Uncommon for current hot-rolled catalogs — manufacturer tables usually flag compactness directly.

Step 4 — Lateral-Torsional Buckling and Bracing

Between brace points the compression flange can buckle sideways and twist (LTB) before reaching M_p. AISC 360 Chapter F sets the behavior by unbraced length L_b against limits L_p and L_r:

• L_b ≤ L_p: M_n = M_p, as in Step 2.
• L_p < L_b ≤ L_r: inelastic LTB — M_n reduces linearly toward 0.7F_yS_x, scaled by moment-gradient factor C_b (1.0 for uniform moment, higher for a favorable diagram such as uniform load).
• L_b > L_r: elastic LTB, M_n drops further; L_r needs torsional constants beyond r_y and F_y — read it from a manufacturer/AISC table.

The compact, fully-braced limit: L_p = 1.76·r_y·√(E/F_y). A deck fastened to the top flange gives continuous bracing, keeping L_b well under L_p; discrete braces (joists, purlins, straps) must be spaced within L_p for the same M_p capacity.

Step 5 — Shear Strength

AISC 360 G2.1 gives the nominal shear strength as V_n = 0.6·F_y·A_w·C_v1 (C_v1 is written C_v in AISC 360-10 / NSCP 2015), A_w = d·t_w. For rolled I-shape webs with h/t_w≤2.24√(E/F_y) — true for essentially all standard W-shapes — C_v1=1.0, φ_v=1.00 (LRFD), Ω_v=1.50 (ASD); check φ_vV_n≥V_u, or V_n/Ω_v≥V_a. Beyond that limit φ_v drops to 0.90 and Ω_v rises to 1.67. Shear rarely governs an ordinary rolled beam, but check it — especially coped ends, deep girders, or heavily loaded short spans.

Step 6 — Deflection Serviceability

Maximum midspan deflection under uniform load: Δ = 5wL⁴/(384EI), using unfactored service loads. The limits commonly used in practice, consistent with the general deflection tables of the NSCP / IBC family: L/360 for live load alone (protecting finishes/ceilings) and L/240 for total load, D + L. Tighter limits — L/480 is typical — apply where vibration or plaster finishes are a concern; confirm the governing limit against the project spec. The same check applies under ASD; only flexure/shear switch to Ω_b=1.67 and Ω_v=1.50.

Worked Example — 6 m Simply Supported Floor Beam

Given: Span L = 6.0 m; dead load (incl. self-weight allowance) w_D = 12.0 kN/m; live load w_L = 8.0 kN/m (office); top flange continuously braced by a floor deck. Trial section: W310×39, A992-class steel, F_y = 345 MPa, E = 200,000 MPa.

Assumed section properties for this example (representative of a current manufacturer/AISC-CISC metric table; confirm before final design):

1. Factored and service loads

w_u=1.2(12.0)+1.6(8.0)=14.4+12.8=27.2 kN/m.
M_u=27.2×6.0²/8=27.2×36/8=122.4 kN·m.
V_u=27.2×6.0/2=81.6 kN.

2–3. Compactness and bracing check

√(E/F_y)=√(200000/345)=√579.7=24.08.
Flange: λ_p=0.38×24.08=9.15; actual b_f/2t_f=8.51<9.15 — compact.
Web: λ_p=3.76×24.08=90.5; actual h/t_w=47.2<90.5 — compact.
L_p=1.76×38.3×24.08=1623 mm≈1.62 m. The deck-braced top flange gives an effective L_b well under L_p, so M_n=M_p applies with no LTB reduction.

4. Flexural capacity

M_p=F_y·Z_x=345×610×10³=210,450,000 N·mm=210.45 kN·m.
φ_bM_n=0.90×210.45=189.4 kN·m.
Check: M_u/φ_bM_n=122.4/189.4=0.65<1.0 — OK (65% utilized).

5. Shear capacity

2.24√(E/F_y)=2.24×24.08=53.9; actual h/t_w=47.2<53.9 → C_v1=1.0, φ_v=1.00.
A_w=d·t_w=310×5.8=1798 mm².
V_n=0.6×345×1798×1.0=372,186 N=372.2 kN.
φ_vV_n=1.00×372.2=372.2 kN.
Check: V_u/φ_vV_n=81.6/372.2=0.22<1.0 — OK (22% utilized).

6. Deflection

Live load only: Δ_LL=5×8.0×6000⁴/(384×200000×84.8×10&sup6;) [w in N/mm, L in mm]=5×8×1.296×10¹&sup5;/(6.510×10¹&sup5;)=7.96 mm.
Limit: L/360=6000/360=16.67 mm. 7.96<16.67 — OK (48% utilized).
Total load (D+L): Δ_total=Δ_LL×(20.0/8.0)=7.96×2.5=19.9 mm.
Limit: L/240=6000/240=25.0 mm. 19.9<25.0 — OK (80% utilized).

7. ASD cross-check

M_a=(12.0+8.0)×6.0²/8=20.0×4.5=90.0 kN·m; M_p/Ω_b=210.45/1.67=126.0 kN·m>90.0 — OK (71% utilized).
V_a=20.0×6.0/2=60.0 kN; V_n/Ω_v=372.2/1.50=248.1 kN>60.0 — OK (24% utilized). Deflection is checked once, at service load, for both methods.

W310×39 satisfies all three checks, with deflection — not strength — the closest call, a common outcome for floor beams at ordinary office loads. Cross-check any trial section with the free simple beam calculator and beam deflection calculator, or the sister site's beam calculator on RHCES.

Assumptions & Limitations

• Applies to compact, doubly symmetric hot-rolled W-shapes braced at L_b≤L_p; not noncompact/slender sections, built-up girders, or long unbraced lengths beyond Step 4's concept-level treatment.
• Single-span, simply supported, uniform gravity load only; axial load, torsion, and biaxial bending (AISC 360 Chapter H) are not addressed.
• Worked-example properties are assumed values for a nominal W310×39; confirm exact listed properties before final design.
• F_y=345 MPa (A992-class) is assumed; other grades, including Fy≈248 MPa (A36-class) still common locally, change every capacity and require a re-run.
• L/360 (live) / L/240 (total) are common defaults; some specs require tighter limits (e.g., L/480) — confirm the project spec.
• Composite action and connection design (bolts/welds, bearing, web crippling) are outside this article's scope.

Frequently Asked Questions

When can I use M_n = M_p = F_yZ_x without a full LTB check?

When the section is compact (Step 3) and L_b≤L_p=1.76r_y√(E/F_y). Continuous deck bracing or braces spaced within L_p both qualify; beyond L_p, use the C_b-based LTB provisions instead.

Why did the example pass flexure and shear with margin but deflection with less room?

Floor beams for ordinary loads are often deflection-governed: the stiffness for L/360 and L/240 typically exceeds what flexure and shear alone demand.

Should a Philippine project use LRFD or ASD?

NSCP 2015 permits either, applied consistently. LRFD is more common in current practice; ASD remains valid for quick hand checks. Never mix the two — a factored load is never compared against allowable capacity.

Checking flexure, shear, and deflection together — not strength alone — keeps a "passing" beam from becoming a bouncy or sagging floor on site. Try the simple beam calculator and beam deflection calculator, or browse all free web tools; offline spreadsheets are on the download page.