------------------ | ------ | --------- | | Dead load | D | 0.50 klf | | Live load | L | 0.80 klf | | Snow load | S | 0.30 klf | | Wind load (upward) | W | -0.40 klf | | Seismic load (upward) | E | -0.60 klf |

Determine the critical LRFD and ASD factored loads per ASCE 7-16.

LRFD Evaluation

Combination Formula Factored Load (klf)
LRFD-1 1.4(0.50) 0.70
LRFD-2 1.2(0.50) + 1.6(0.80) + 0.5(0.30) 0.60 + 1.28 + 0.15 = 2.03
LRFD-3 1.2(0.50) + 1.6(0.30) + 0.5(0.80) 0.60 + 0.48 + 0.40 = 1.48
LRFD-3b 1.2(0.50) + 1.6(0.30) + 0.5(-0.40) 0.60 + 0.48 - 0.20 = 0.88
LRFD-4 1.2(0.50) + 1.0(-0.40) + 0.80 + 0.5(0.30) 0.60 - 0.40 + 0.80 + 0.15 = 1.15
LRFD-5 1.2(0.50) + 1.0(-0.60) + 0.80 + 0.2(0.30) 0.60 - 0.60 + 0.80 + 0.06 = 0.86
LRFD-6 0.9(0.50) + 1.0(-0.40) 0.45 - 0.40 = 0.05
LRFD-7 0.9(0.50) + 1.0(-0.60) 0.45 - 0.60 = -0.15

LRFD results:

For the W18x46 with a 30 ft span, the maximum factored moment (LRFD-2) is:

Mu = wu × L^2 / 8 = 2.03 × 30^2 / 8 = 228.4 kip-ft

The beam moment capacity (phiMn for W18x46, A992 steel):

phiMn = 0.90 × 340 = 306 kip-ft > 228.4 kip-ft  (OK)

ASD Evaluation

Combination Formula Factored Load (klf)
ASD-1 0.50 0.50
ASD-2 0.50 + 0.80 1.30
ASD-3 0.50 + 0.30 0.80
ASD-4 0.50 + 0.75(0.80) + 0.75(0.30) 0.50 + 0.60 + 0.225 = 1.325
ASD-5a 0.50 + 0.7(-0.40) 0.50 - 0.28 = 0.22
ASD-5b 0.50 + 0.7(-0.60) 0.50 - 0.42 = 0.08
ASD-6a 0.50 + 0.75(0.80) + 0.75(0.7)(-0.40) + 0.75(0.30) 0.50 + 0.60 - 0.21 + 0.225 = 1.115
ASD-6b 0.50 + 0.75(0.80) + 0.75(0.7)(-0.60) + 0.75(0.30) 0.50 + 0.60 - 0.315 + 0.225 = 1.01
ASD-7 0.6(0.50) + 0.7(-0.40) 0.30 - 0.28 = 0.02
ASD-8 0.6(0.50) + 0.7(-0.60) 0.30 - 0.42 = -0.12

ASD results:

Maximum ASD moment:

Ma = wa × L^2 / 8 = 1.325 × 30^2 / 8 = 149.1 kip-ft

The allowable moment (Mn/Omega for W18x46, A992 steel):

Mn/Omega = 340 / 1.67 = 203.6 kip-ft > 149.1 kip-ft  (OK)

Load Combination Comparison: LRFD vs ASD

Feature LRFD (Section 2.3.1) ASD (Section 2.4.1)
Number of combinations 7 8 (plus alternates)
Dead load factor (gravity) 1.2 to 1.4 1.0
Live load factor 1.6 1.0 (or 0.75 in combinations)
Wind load factor 1.0 (strength-level W) 0.7 (converts to ASD-level)
Seismic load factor 1.0 (strength-level E) 0.7 (converts to ASD-level)
Counteracting dead load 0.9D 0.6D
Resistance side phi factors (0.75-0.90) Omega factors (1.67-2.0)
Reliability basis Calibrated to beta ~ 3.0 Empirical, non-uniform reliability
Economy for live-load-dominated More efficient Less efficient
Economy for dead-load-dominated Less efficient More efficient

When LRFD governs: LRFD typically produces more economical designs when live load is a large fraction of the total load (high L/D ratio). Office buildings, parking garages, and warehouse structures with heavy live loads benefit from LRFD.

When ASD governs: ASD may be more economical for dead-load-dominated structures such as concrete buildings, masonry shear walls, and heavy foundations where the L/D ratio is low. Some engineers prefer ASD for simpler connection design.

Notable Changes from ASCE 7-10 to ASCE 7-16

ASCE 7-16 introduced several significant changes affecting load combination calculations:

1. Wind load factor reduction: In ASCE 7-10, wind loads were already converted to strength level, so the load factor was 1.0W in LRFD combinations. ASCE 7-16 maintains this approach. However, for designers transitioning from ASCE 7-05 (where wind loads were ASD-level and the factor was 1.6W), this remains a common source of confusion. ASCE 7-16 wind maps provide strength-level pressures directly.

2. Rain load provisions: ASCE 7-16 enhanced rain load (R) requirements, including updated ponding instability checks. Rain load is now more likely to govern in combinations involving roof loads, particularly for flat or low-slope roofs with significant drainage design loads.

3. Updated wind speed maps: ASCE 7-16 introduced risk category-dependent wind speed maps, replacing the single map approach of ASCE 7-10. This means the base wind velocity used to compute W varies by risk category (I, II, III, IV), directly affecting load combination results.

4. Seismic load amendments: ASCE 7-16 refined the overstrength factor (Omega_0) application and expanded the conditions under which the redundancy factor (rho) may be taken as 1.0. These changes affect how E is computed before entering the load combinations.

5. Tornado loads: ASCE 7-16 Chapter 32 introduced tornado loads as a new environmental load type. For structures in Tornado Risk Category II, III, and IV, tornado loads must be considered in combinations when the tornado design wind speed exceeds the basic wind speed. This is effective for the 2024 IBC adoption cycle.

ASCE 7-22 Load Combination Changes

ASCE 7-22 Section 2.3 (LRFD) and Section 2.4 (ASD) retain the same combination count and format as ASCE 7-16 but introduce key revisions. The dead load factor in LRFD Combination 1 increases from 1.4 to 1.4D remains; however, the companion load factor on Lr in Combination 3 changes from L or 0.5W to the greater of L or 0.5W. ASD Combination 7 (0.6D + 0.7W) adjusts to 0.6D + 0.6W per ASCE 7-22 Supplement 1. For seismic, ASCE 7-22 aligns E with the multi-period response spectrum of Chapter 11 and updates redundancy factor rho applicability. Wind loads now reference ASCE 7-22 Chapter 26 (strength-level wind), which supersedes ASCE 7-16 wind maps. When designing to AISC 360-22, use ASCE 7-22 combinations. For jurisdictions still enforcing IBC 2021/ASCE 7-16, the combinations on this page remain applicable.

Special Load Combinations

Beyond the basic seven LRFD and eight ASD combinations, ASCE 7-16 and AISC 360 require consideration of special loading conditions:

Pattern Live Load

For continuous beams and frames, the live load must be arranged in patterns that produce the maximum moment, shear, or deflection at each critical section. The common patterns include:

AISC 360 requires pattern loading per ASCE 7, which specifies that the full unfactored live load be placed on the spans that produce the most critical effect, with no live load on other spans.

Notional Loads

AISC 360 Chapter C requires notional loads for stability design when the ratio of second-order to first-order drift exceeds 1.7, or when the structure relies on the lateral system for stability:

Ni = 0.002 × Yi

Where Ni is the notional load applied at level i, and Yi is the gravity load at level i from the LRFD combination (or ASD combination multiplied by 1.6). Notional loads account for initial out-of-plumbness and must be applied in the direction that produces the most destabilizing effect.

Overstrength Factor (Omega_0)

For seismic design, ASCE 7-16 Section 12.4.3 requires special seismic load combinations with the overstrength factor:

LRFD:  1.2D + Omega_0 × E + L + 0.2S
ASD:   D + 0.7 × Omega_0 × E + 0.75L + 0.75S

The overstrength factor amplifies the seismic load to ensure that specific structural elements (collector elements, drag struts, elements anchoring nonstructural components) are designed for the maximum force that can be delivered by the yielding lateral system. Typical Omega_0 values range from 2.0 to 3.0 depending on the seismic force-resisting system.

Frequently Asked Questions

What is the difference between LRFD and ASD load combinations? LRFD (Load and Resistance Factor Design) applies load factors greater than 1.0 to the nominal loads and uses resistance factors (phi) less than 1.0 on the nominal strength. ASD (Allowable Stress Design) uses load factors of 1.0 (or reduced values for combined loads) and divides the nominal strength by a safety factor (Omega). Both methods are calibrated to achieve similar reliability. LRFD is generally preferred for new design because it provides a more uniform reliability across different load ratios.

Why does ASCE 7-16 use 1.2D + 1.6L instead of equal factors? The load factors are calibrated based on the statistical variability of each load type. Live load has more uncertainty than dead load (larger coefficient of variation), so it receives a higher factor (1.6 vs. 1.2). This ensures a consistent target reliability index (beta approximately 3.0 for gravity combinations) regardless of the dead-to-live load ratio. Equal factors would over-design for dead-load-dominated members and under-design for live-load-dominated members.

When do the 0.9D + W and 0.9D + E combinations govern? These counteracting combinations govern when uplift, overturning, or sliding is a concern. The 0.9 factor on dead load represents the minimum expected dead load (accounting for construction tolerances and material variability), while the full wind or seismic load acts to destabilise the structure. Typical governing cases include: roof connections under wind uplift, foundations under overturning moment, and anchor bolts in tension.

Related pages

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.