Gravity Loads & Load Paths

K. Load combinations

ASCE 7 Load Combinations (LRFD & ASD)

The ASCE 7-16 strength (LRFD) and allowable-stress (ASD) load combinations, how to find the one that governs a member, and the 1.0W wind factor.

Almost every PE Civil Structural design problem begins by turning a list of nominal loads — dead, live, roof live, snow, wind, seismic, rain, earth — into the single factored demand a member must resist. That step is the load combination, and it is where points quietly leak away: examinees pick the wrong design philosophy (LRFD vs ASD), apply the wrong factor to wind, or stop at the first combination instead of checking which one actually governs. This is a NARRATIVE topic. The combinations are not in the NCEES PE Civil Reference Handbook — they live in ASCE 7-16, Minimum Design Loads and Associated Criteria for Buildings and Other Structures, Chapter 2 (§2.3 strength design, §2.4 allowable stress design). Cite ASCE 7-16, not a handbook page, for every factor here, and use the edition NCEES supplies — 7-16, never 7-22.

Two design philosophies, two factor sets

ASCE 7 lets you design by either of two methods, and the load factors differ completely between them — you must commit to one and never mix. Strength design, called Load and Resistance Factor Design (LRFD) for steel and concrete, amplifies the loads (factors greater than 1.0 on the dominant actions) and compares the factored demand

U

to a reduced capacity

\phi R_n

. Allowable Stress Design (ASD) keeps the loads at or below their nominal (service) values and compares the demand to an allowable capacity

R_n/\Omega

. The combinations themselves come from §2.3 (LRFD) and §2.4 (ASD); the resistance side (

\phi

\Omega

) comes from the material code (AISC 360-16, ACI 318-14, NDS 2018, TMS 402-16).

\text{LRFD: } U \le \phi R_n \qquad\qquad \text{ASD: } \textstyle\sum \text{loads} \le \frac{R_n}{\Omega}

The LRFD (strength) combinations

ASCE 7-16 §2.3.1 gives five basic (non-seismic) strength combinations, numbered (1) through (5); the seismic combinations were relocated to §2.3.6 in 7-16 (do not expect 'seven' here — that count is a holdover from 7-05/7-10). The two that govern most gravity members are

1.4D

and

1.2D + 1.6L + 0.5(L_r\text{ or }S\text{ or }R)

The 1.0W factor — a 7-10/7-16 change you must know

Older ASCE 7 editions (through 7-05) used a

1.6W

load factor on wind because the wind maps returned roughly 50-year (service-level) speeds. ASCE 7-10 and 7-16 re-mapped the basic wind speed to strength-level (ultimate) values tied to a risk-category-dependent return period (300 to 3,000 years, 700-year for the standard Risk Category II), so the wind load

W

already carries the strength margin and the LRFD factor dropped to

1.0

. Carrying a

1.6

over from memory or an old text is a classic, costly error. The matching ASD factor is

0.6W

(because

1.0/1.6 \approx 0.6

The ASD (allowable-stress) combinations

ASCE 7-16 §2.4.1 gives the service-level combinations used with allowable stresses (and conventionally with timber and masonry design, and with steel when ASD is chosen). The basic set keeps load factors at or below 1.0:

D

;

D+L

;

D+(L_r\text{ or }S\text{ or }R)

Finding the combination that governs

A member must be designed for the maximum demand across every applicable combination — you cannot guess which one wins. For a pure-gravity interior beam,

1.2D+1.6L

almost always beats

1.4D

unless

D > 8L

(the crossover). When wind or seismic is present, two checks matter: the maximum (additive) case for strength, and the minimum-gravity-with-lateral case (

0.9D+1.0W

Exam strategy

First decide the philosophy: if the problem says LRFD,

\phi

, or factored, use §2.3; if it says ASD, allowable,

\Omega

, or service, use §2.4 — and never carry a factored load into an ASD allowable check or vice versa. For gravity-only members, compute both

1.4D

and

1.2D+1.6L+0.5L_r

Key equations

LRFD basic gravity combination

U = 1.2D + 1.6L + 0.5(L_r\ \text{or}\ S\ \text{or}\ R)

Worked examples

Governing LRFD demand on a floor beam

Problem. An office floor beam carries (as line loads to the beam) dead $D$ , live $L$ , and roof-live $L_r$ that produce uniform pressures of $D=80\ \text{psf}$

Common pitfalls

•Mixing LRFD and ASD in one check: never compare a factored demand ( $1.2D+1.6L$ ) to an allowable capacity ( $R_n/\Omega$ ), or a service demand to $\phi R_n$

References

ASCE/SEI 7-16, Minimum Design Loads and Associated Criteria for Buildings and Other Structures — §2.3 (Strength Design / LRFD) and §2.4 (Allowable Stress Design)
ASCE/SEI 7-16 — Commentary C2 (basis of the strength-level wind map and the 1.0W / 0.6W factors)
AISC 360-16 / Steel Construction Manual, 15th ed. — application of LRFD ($\phi$) and ASD ($\Omega$) with the ASCE 7 combinations

A. Dead loads

Dead Loads & Material Unit Weights

B. Live loads

Live Loads by Occupancy

J. Tributary areas and load paths

Tributary Areas, Load Paths & Live-Load Reduction

Vertical & Lateral Load Paths