Gravity Loads & Load Paths

9% of exam

Dead, live, and construction loads; tributary areas and vertical and lateral load paths; live-load reduction; earth pressure and surcharge; and ASCE 7 strength and allowable-stress load combinations.

5 concepts

Exam areas

A. Dead loads

Dead Loads & Material Unit Weights

Computing dead load from material unit weights and assembly self-weight, adding superimposed dead load, and distinguishing dead from live load.

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B. Live loads

Live Loads by Occupancy

Uniform and concentrated live loads by occupancy from ASCE 7-16 Table 4.3-1, the dual uniform/concentrated check, and partition and roof live loads.

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J. Tributary areas and load paths

Tributary Areas, Load Paths & Live-Load Reduction

Tributary width and area to a member, the vertical gravity load path slab to foundation, and the ASCE 7-16 §4.7 live-load reduction with KLL and AT.

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Vertical & Lateral Load Paths

Tracing gravity load slab to foundation and lateral load diaphragm to shear wall/frame to foundation, the continuous load path, and the role of collectors.

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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 second almost always controls unless dead load overwhelmingly dominates. When roof live, snow, or rain is the lead variable action,

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

applies. Wind enters at full strength as

1.2D + 1.0W + L + 0.5(L_r\text{ or }S\text{ or }R)

, and the uplift/overturning check is combination (5),

0.9D + 1.0W

. Per the §2.3.1 exception, the companion live load

L

may be taken as

0.5L

in the roof-led (3) and wind (4) combinations (and in the §2.3.6 seismic combination), except where

L_0 > 100\ \text{psf}

or in public-assembly areas.

\begin{aligned} &1.\ 1.4D \\ &2.\ 1.2D + 1.6L + 0.5(L_r\ \text{or}\ S\ \text{or}\ R) \\ &3.\ 1.2D + 1.6(L_r\ \text{or}\ S\ \text{or}\ R) + (L\ \text{or}\ 0.5W) \\ &4.\ 1.2D + 1.0W + L + 0.5(L_r\ \text{or}\ S\ \text{or}\ R) \\ &5.\ 0.9D + 1.0W \end{aligned}

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

recovers the service-level effect from a strength-level map).

W_{\text{ASCE 7-16}}\ \text{is strength-level} \Rightarrow \gamma_W = 1.0\ (\text{LRFD}),\quad 0.6\ (\text{ASD})

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)

;

D+0.75L+0.75(L_r\text{ or }S\text{ or }R)

;

D+0.6W

;

D+0.75L+0.75(0.6W)+0.75(L_r\text{ or }S\text{ or }R)

; and the uplift check

0.6D+0.6W

. The

0.75

factor on companion variable loads recognizes that two transient maxima are unlikely to coincide. Note the

0.6D

in the uplift combination — using a full

1.0D

there unconservatively resists overturning.

\begin{aligned} &D \\ &D + L \\ &D + (L_r\ \text{or}\ S\ \text{or}\ R) \\ &D + 0.75L + 0.75(L_r\ \text{or}\ S\ \text{or}\ R) \\ &D + 0.6W \\ &D + 0.75L + 0.75(0.6W) + 0.75(L_r\ \text{or}\ S\ \text{or}\ R) \\ &0.6D + 0.6W \end{aligned}

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

0.6D+0.6W

) for net uplift, overturning, and connection tension. Seismic combinations substitute

E = E_h + E_v

(or

E_h - E_v

) and add the redundancy and overstrength factors in §2.3.6/§12.4 — a separate layer most gravity problems skip. Evaluate the relevant set, take the worst, and design to it.

U_{\text{design}} = \max\big(U_1,\,U_2,\,\dots,\,U_n\big)\ \text{over all applicable combinations}

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

and take the larger; the second usually wins. Whenever wind appears, use

1.0W

(LRFD) or

0.6W

(ASD) — not

1.6W

— and always run the uplift combination (

0.9D+1.0W

0.6D+0.6W

) for net tension, because a member fine in compression can fail in uplift. Reduce the companion

L

0.5L

only where allowed (

L_0 \le 100\ \text{psf}

, not public assembly). State the governing combination explicitly in your answer.

Key equations

LRFD basic gravity combination

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

ASCE 7-16 Eq. 2.3-2; governs most floor members. $D$ =dead, $L$ =live, $L_r$ =roof live, $S$ =snow, $R$ =rain (all service-level nominal loads).

LRFD dead-only combination

U = 1.4D

ASCE 7-16 Eq. 2.3-1; controls only when dead load dominates (roughly $D > 8L$ ).

LRFD roof-load-led combination

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

ASCE 7-16 Eq. 2.3-3; lead action is roof live, snow, or rain. Companion $L$ may reduce to $0.5L$ where permitted.

LRFD wind combination

U = 1.2D + 1.0W + L + 0.5(L_r\ \text{or}\ S\ \text{or}\ R)

ASCE 7-16 Eq. 2.3-4. Wind factor is $1.0$ because 7-16 $W$ is strength-level. $L$ may reduce to $0.5L$ where $L_0\le100$ psf and not assembly.

LRFD uplift/overturning combination

U = 0.9D + 1.0W

ASCE 7-16 §2.3.1 combination (5); minimum dead resisting maximum wind — governs net uplift and anchor/connection tension.

ASD service combination with live

\textstyle\sum = D + L

ASCE 7-16 Eq. 2.4-2; basic gravity service combination compared to $R_n/\Omega$ .

ASD combined live + roof

\textstyle\sum = D + 0.75L + 0.75(L_r\ \text{or}\ S\ \text{or}\ R)

ASCE 7-16 Eq. 2.4-4; the $0.75$ accounts for non-coincident transient maxima.

ASD wind combination

\textstyle\sum = D + 0.6W

ASCE 7-16 Eq. 2.4-5; $0.6W$ converts the strength-level map back to a service-level wind effect.

ASD combined live + wind + roof

\textstyle\sum = D + 0.75L + 0.75(0.6W) + 0.75(L_r\ \text{or}\ S\ \text{or}\ R)

ASCE 7-16 Eq. 2.4-6; companion-factored gravity plus reduced wind.

ASD uplift combination

\textstyle\sum = 0.6D + 0.6W

ASCE 7-16 §2.4.1 combination 7; $0.6D$ (not $1.0D$ ) resists overturning and uplift conservatively. The seismic ASD uplift case is not in §2.4.1 in 7-16: it is §2.4.5 combination 10, $0.6D - 0.7E_v + 0.7E_h$ .

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 $D=80\ \text{psf}$ , $L=50\ \text{psf}$ , and $L_r=20\ \text{psf}$ over the tributary area. Working in pressures, determine the governing factored uniform load $w_u$ by LRFD.

Solution. Apply the §2.3 combinations in pressure terms. Eq. 2.3-1:

1.4D = 1.4(80) = 112\ \text{psf}

. Eq. 2.3-2 (live leads):

1.2D + 1.6L + 0.5L_r = 1.2(80) + 1.6(50) + 0.5(20) = 96 + 80 + 10 = 186\ \text{psf}

. Eq. 2.3-3 (roof-live leads, companion

0.5L

allowed):

1.2(80) + 1.6(20) + 0.5(50) = 96 + 32 + 25 = 153\ \text{psf}

. Governing:

w_u = \max(112,\,186,\,153) = 186\ \text{psf}

, from Eq. 2.3-2. Sanity check: with

L > L_r

and a moderate

D/L

ratio, the live-led combination should dominate, and it does. Final answer:

\mathbf{w_u = 186\ \text{psf}}

(combination

1.2D+1.6L+0.5L_r

w_u = 1.2(80) + 1.6(50) + 0.5(20) = 186\ \text{psf}

Column axial: LRFD vs ASD, gravity and wind

Problem. A column carries axial dead $D=120\ \text{k}$ , live $L=90\ \text{k}$ (office, $L_0\le100\ \text{psf}$ ), and wind axial $W=\pm60\ \text{k}$ . Find the governing factored axial demand by (a) LRFD and (b) ASD.

Solution. (a) LRFD, §2.3 (companion

L

reduces to

0.5L

where wind leads): Eq. 2.3-2:

1.2(120) + 1.6(90) = 144 + 144 = 288\ \text{k}

. Eq. 2.3-4 (wind,

1.0W

1.2(120) + 1.0(60) + 0.5(90) = 144 + 60 + 45 = 249\ \text{k}

. LRFD governing compression

= \max(288,\,249) = 288\ \text{k}

. (b) ASD, §2.4: Eq. 2.4-2:

D + L = 120 + 90 = 210\ \text{k}

. Eq. 2.4-5:

D + 0.6W = 120 + 0.6(60) = 120 + 36 = 156\ \text{k}

. Eq. 2.4-6:

D + 0.75L + 0.75(0.6W) = 120 + 67.5 + 27 = 214.5\ \text{k}

. ASD governing

= \max(210,\,156,\,214.5) = 214.5\ \text{k}

. Sanity check: the LRFD demand (

288\ \text{k}

) is roughly

1.35\times

the ASD demand (

214.5\ \text{k}

) — exactly the kind of ratio expected because LRFD amplifies loads while ASD does not. Final:

\mathbf{P_u = 288\ \text{k}}

(LRFD,

1.2D+1.6L

);

\mathbf{P_a = 215\ \text{k}}

(ASD, Eq. 2.4-6).

P_u = 1.2(120)+1.6(90) = 288\ \text{k};\quad P_a = 120 + 0.75(90) + 0.75(0.6\cdot60) = 214.5\ \text{k}

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 $\phi R_n$ . Pick one philosophy per check.
•Using a $1.6W$ wind factor. In ASCE 7-16 the wind map is strength-level, so the LRFD factor is $1.0W$ and the ASD factor is $0.6W$ . Carrying $1.6W$ from an old edition overdesigns and is a wrong-edition error.
•Citing a handbook page for these combinations. They are in ASCE 7-16 §2.3 / §2.4, not the NCEES PE Civil Reference Handbook — and the supplied edition is 7-16, not 7-22.
•Skipping the uplift combination. A member sized for $1.2D+1.6L$ compression can still fail under $0.9D+1.0W$ (LRFD) or $0.6D+0.6W$ (ASD) net tension — always run the minimum-gravity case for wind.
•Using $1.0D$ (not $0.6D$ ) in the ASD overturning/uplift check. The reduced dead factor is what makes the check conservative; full dead unconservatively holds the structure down.
•Reducing the companion $L$ to $0.5L$ where it is not allowed — $L_0 > 100\ \text{psf}$ or public-assembly occupancies keep the full $L$ in the wind and roof-led combinations.
•Stopping at the first combination. The governing demand is the maximum over all applicable combinations; $1.4D$ versus $1.2D+1.6L$ flips only near $D\approx8L$ .

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