Load Combinations Generator

Generate ASCE 7-16 load combinations for steel design with governing combination highlighting. Educational use only.

This page documents the scope, inputs, outputs, and computational approach of the Load Combinations Generator on steelcalculator.app. The interactive calculator is designed to run in your browser for speed, but this documentation is written so the page remains useful (and indexable) even if JavaScript is not executed.

What this tool is for

• Fast screening and iteration while you are exploring a design space.
• Creating a repeatable calculation workflow that a reviewer can audit.
• Learning the terminology and typical "shape" of a load combination check for structural design.

What this tool is not for

• It is not a complete design package and does not replace governing standard, project specification, or an engineer's judgment.
• It is not a substitute for system-level checks (global stability, constructability, fatigue/seismic detailing, etc.).
• It does not guarantee compliance with any specific standard, because compliance depends on configuration, edition, and jurisdictional requirements.

Key concepts this page covers

• ASCE 7-16 LRFD load combinations
• ASCE 7-16 ASD load combinations
• load case definitions (D, L, Lr, S, R, W, E)
• governing combination selection
• CSV export

Inputs and naming conventions (high-level)

The calculator accepts seven load types as defined by ASCE 7-16:

Dead load (D) Permanent loads that act on the structure throughout its service life. Includes self-weight of structural and nonstructural elements, and permanent equipment loads.

Live load (L) Variable loads due to occupancy, use, and movable equipment. Includes floor live loads, roof live loads, and other transient loads.

Roof live load (Lr) Live load on roofs due to maintenance, equipment, or snow accumulation (when snow is considered separately under Lr). Not to be confused with snow load S.

Snow load (S) Load due to snow accumulation. May be combined with other environmental loads (rain, ice) depending on local climate and code provisions.

Rain load (R) Load due to rain accumulation on roofs. Often combined with snow for regions where rain-on-snow is a design consideration.

Wind load (W) Load due to wind pressure on the structure. Directionality and pressure coefficients must be determined per ASCE 7 wind provisions.

Earthquake load (E) Load due to seismic ground motion. Determined using ASCE 7 seismic analysis methods (equivalent lateral force, modal response spectrum, etc.).

ASCE 7-16 LRFD combinations

LRFD (Load and Resistance Factor Design) uses strength-level loads with load factors greater than 1.0 for most load types. ASCE 7-16 Section 2.3.2 specifies seven combinations:

1. 1.4D
2. 1.2D + 1.6L + 0.5(Lr or S or R)
3. 1.2D + 1.6(Lr or S or R) + (0.5L or 0.5W)
4. 1.2D + 1.0W + 0.5L + 0.5(Lr or S or R)
5. 1.2D + 1.0E + 0.5L + 0.2S
6. 0.9D + 1.0W
7. 0.9D + 1.0E

The calculator computes the factored load for each combination and highlights the governing (maximum) value for tension/compression checks.

ASCE 7-16 ASD combinations

ASD (Allowable Strength Design) uses service-level loads with load factors of 1.0 for most load types. ASCE 7-16 Section 2.4.1 specifies eight combinations:

1. D
2. D + L
3. D + (Lr or S or R)
4. 0.6D + 0.6W
5. 0.6D + 0.7E
6. D + 0.75L + 0.75(Lr or S or R)
7. D + 0.75(Lr or S or R) + 0.75W
8. D + 0.75W + 0.75L + 0.75(Lr or S or R)

The calculator computes the combined load for each case and highlights the governing value.

Governing combination selection

For each design check (beam bending, column compression, connection shear, etc.), evaluate the critical combination by comparing factored loads or design effects (moment, shear, axial force). The governing combination is the one that produces the largest demand on the member or connection.

In LRFD, compare factored loads directly to factored resistances (φRn). In ASD, compare combined service loads to allowable resistances (Rn/Ω). The governing combination may differ for strength versus serviceability checks.

CSV export

The calculator provides CSV export functionality to document load combinations for project records or further analysis. The CSV file includes load types, combination formulas, and computed values for all LRFD and ASD cases.

How the Load Combinations Generator Works

The calculator takes individual load values (dead, live, roof live, snow, rain, wind, earthquake) and systematically applies the ASCE 7-16 load factors for both LRFD and ASD methods. For each of the 7 LRFD combinations and 8 ASD combinations, the tool multiplies each load type by its prescribed factor, sums the result, and outputs the total factored demand. The governing combination -- the one producing the largest demand for the design check in question -- is highlighted.

The tool handles the "or" conditions in ASCE 7 combinations (e.g., "0.5(Lr or S or R)" in Combination 3) by evaluating each sub-option and selecting the maximum. For wind and seismic loads that can act in either direction, both positive and negative values are evaluated to capture both additive and counteracting (uplift/overturning) effects.

The calculator also identifies the minimum load case -- the combination that produces the smallest (or most negative) demand -- which is critical for uplift, overturning, and net tension checks on foundations and connections. For members that can experience load reversal (roof beams under wind uplift, columns in moment frames), both the maximum and minimum governing combinations must be checked.

Key Equations

LRFD Combination 2 (typically governs for gravity):

U = 1.2*D + 1.6*L + 0.5*max(Lr, S, R)

LRFD Combination 4 (wind + gravity):

U = 1.2*D + 1.0*W + 0.5*L + 0.5*max(Lr, S, R)

LRFD Combination 6 (minimum gravity, counteracting wind -- critical for uplift):

U = 0.9*D + 1.0*W

LRFD Combination 7 (minimum gravity, counteracting seismic):

U = 0.9*D + 1.0*E

ASD Combination 8 (three-load concurrent):

U = D + 0.75*W + 0.75*L + 0.75*max(Lr, S, R)

Load factor rationale:

• 1.6 on live load: accounts for high variability and statistical uncertainty in live load magnitude
• 1.2 on dead load: accounts for minor variation in material weight and construction tolerance
• 0.9 on dead load (uplift cases): lower-bound dead load to avoid overestimating the stabilizing effect of self-weight
• 1.0 on wind and seismic: these are already at strength level (mapped to specific return periods) in ASCE 7-16

IBC exception for garages (ASCE 7-16 footnote): When L ≤ 100 psf and L is from a single occupancy, the 0.5L companion factor in Combinations 3-5 may be reduced to 0.5L0AT_reduction if live load reduction is applicable.

Design Code Requirements

Key differences: ASCE 7-16 uses a wind load factor of 1.0 because the mapped wind speeds already represent strength-level events. Eurocode EN 1990 uses a wind load factor of 1.5 because EN wind speeds are at a lower return period. Australian AS/NZS 1170 uses ultimate-level wind speeds (similar to ASCE 7) with factor 1.0. Canadian NBCC uses 1.4 on wind because NBCC wind pressures are specified at a 50-year return period (not strength-level). These differences mean load factors from different codes must never be mixed.

Step-by-Step Example

Problem: Determine the governing LRFD load combination for a roof beam in Chicago, IL with the following service loads: D = 25 psf, Lr = 20 psf, S = 25 psf, W = +/-30 psf (net), E = 0 (low seismic).

Step 1 -- Evaluate all LRFD combinations:

Step 2 -- Identify governing combinations: Maximum gravity: Combination 3b at 85.0 psf (1.2D + 1.6S + 0.5W). This governs beam strength. Maximum uplift: Combination 6 at -7.5 psf net upward. This governs connection and anchorage design.

Step 3 -- Convert to line load for a 10-ft tributary width: wu = 85.0 _ 10 / 1000 = 0.85 kip/ft (factored). wu_uplift = 7.5 _ 10 / 1000 = 0.075 kip/ft (net uplift).

Result: Design beam for 0.85 kip/ft factored gravity (Comb. 3b). Design roof-to-beam connections for 0.075 kip/ft net uplift (Comb. 6). The snow load combined with wind produces the highest gravity demand, not the dead + live combination -- which is why all combinations must be checked.

Common Design Mistakes

• Checking only Combination 2 (1.2D + 1.6L) for all members: Combination 2 governs for interior floor beams with no environmental loads. For roof members, exterior columns, and foundations, wind or snow combinations (3, 4, 6) frequently govern. Engineers who only check Combination 2 miss the controlling case.
• Forgetting to check uplift combinations (0.9D + 1.0W): Net uplift on roof beams, edge columns, and foundations is caused by wind suction exceeding the stabilizing dead load. This is the most commonly missed combination and has caused connection failures where bolts or welds were not designed for tension reversal.
• Mixing load factors between LRFD and ASD: Using a 1.6 factor on live load (LRFD) with ASD allowable stresses, or using service loads with LRFD resistance values, produces incorrect results. The entire design must be performed consistently in one method.
• Applying the 0.75 three-load factor to LRFD instead of ASD: The 0.75 concurrent load factor (D + 0.75L + 0.75S + 0.75W) is an ASD-specific provision in ASCE 7 Section 2.4. LRFD combinations use specific factors for each load type without a blanket reduction.
• Not identifying which combination governs for each member: Different members in the same structure can be governed by different combinations. A roof beam may be governed by snow + wind (Comb. 3), while an interior column is governed by gravity only (Comb. 2). The governing combination must be identified per member, not for the whole building.
• Using 1.0W with pre-ASCE 7-10 wind speeds: ASCE 7-10 and later use strength-level (ultimate) wind speeds with a load factor of 1.0. Older editions (ASCE 7-05 and earlier) used nominal wind speeds that require a 1.6 factor on W. Using 1.0W with old wind speed maps underestimates wind load by 37%.

Frequently Asked Questions

Which ASCE 7-16 LRFD combination governs for a floor beam with D = 20 psf and L = 50 psf? With only dead and live load and no environmental loads, compare LRFD Combination 1 (1.4D = 28 psf) against Combination 2 (1.2D + 1.6L = 1.2×20 + 1.6×50 = 24 + 80 = 104 psf). Combination 2 governs at 104 psf — 3.7 times the service dead load alone. The load factor on live load is 1.6 because live load has greater variability than dead load. For the equivalent ASD check, Combination 2 (D + L = 70 psf) governs, and the member is designed for Rn/Ω ≥ 70 psf rather than φRn ≥ 104 psf.

Why does LRFD Combination 6 (0.9D + 1.0W) use 0.9D instead of 1.2D? Combination 6 is the uplift or overturning case where wind load acts opposite to dead load. Using 0.9D — a reduced dead load — is intentionally conservative: it accounts for the possibility that actual dead load may be 10% less than nominal due to material tolerances or weight estimates. If 1.2D were used, the self-weight would appear to resist the wind more strongly than it actually does, which is unconservative for net uplift checks. The 0.9 factor is therefore a lower-bound on dead load applied only when dead load is stabilizing, not when it is additive with the design load.

What is the governing LRFD combination for a roof beam with D = 15 psf, S = 30 psf, and W = ±25 psf? Evaluate Combination 3 (1.2D + 1.6S + 0.5W): 1.2×15 + 1.6×30 + 0.5×25 = 18 + 48 + 12.5 = 78.5 psf. Compare Combination 4 (1.2D + 1.0W + 0.5S): 1.2×15 + 1.0×25 + 0.5×30 = 18 + 25 + 15 = 58 psf. Combination 3 governs for the gravity-plus-snow case at 78.5 psf. For net uplift, check Combination 6 (0.9D + 1.0W): 0.9×15 − 25 = 13.5 − 25 = −11.5 psf net uplift — this governs the connection and anchorage design with a net upward demand of 11.5 psf.

What is the combined LRFD factored load for a column with D = 100 kips, L = 80 kips, and E = 60 kips? Check LRFD Combination 5 (1.2D + 1.0E + 0.5L): 1.2×100 + 1.0×60 + 0.5×80 = 120 + 60 + 40 = 220 kips. Check Combination 2 (1.2D + 1.6L): 1.2×100 + 1.6×80 = 120 + 128 = 248 kips. Combination 2 governs for gravity-only at 248 kips; Combination 5 governs when seismic is present if the seismic component is larger. Also check Combination 7 (0.9D + 1.0E): 0.9×100 − 60 = 30 kips net tension — this minimum axial case governs column splice and anchor bolt design when seismic creates net uplift.

How does the 0.75 live load reduction factor work in ASD Combination 8? ASD Combination 8 is D + 0.75W + 0.75L + 0.75(Lr or S or R). The 0.75 factors reflect statistical improbability of simultaneous maximum wind, live, and roof environmental loads. If D = 20 psf, L = 50 psf, W = 30 psf, and S = 20 psf (with no Lr or R): combination = 20 + 0.75×30 + 0.75×50 + 0.75×20 = 20 + 22.5 + 37.5 + 15 = 95 psf. Compare to Combination 2 (D + L = 70 psf) and Combination 3 (D + S = 40 psf): Combination 8 governs at 95 psf for this loading scenario.

When does load combination 1.4D control over combinations with live load? LRFD Combination 1 (1.4D) only governs when dead load is very large relative to live load — typically for heavy equipment foundations, mass concrete structures, or members that support predominantly self-weight. The crossover occurs when 1.4D > 1.2D + 1.6L, which simplifies to 0.2D > 1.6L, or D > 8L. For a typical floor beam with D = 50 psf and L = 50 psf, Combination 1 gives 70 psf versus Combination 2 gives 140 psf — Combination 2 dominates by 2:1. Combination 1 rarely governs in building design except for extremely heavy dead loads with minimal live load.

Related pages

• Snow load calculator
• Wind load calculator
• Seismic load calculator
• Beam capacity calculator
• Load combinations — ASCE 7 LRFD & ASD reference
• Snow load calculation — ASCE 7 design procedure
• Live load reference — IBC and ASCE 7 occupancy table
• Wind load calculation — ASCE 7 MWFRS and C&C
• Seismic design categories — ASCE 7 SDC reference
• How to verify calculator results
• Disclaimer (educational use only)
• Load Combinations CSA S16
• Load combinations AS 4100
• Load combinations ASCE 7-16
• Wood timber design calculator

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

The site operator provides the content "as is" and "as available" without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.