Wind, Seismic & Environmental Loads

8% of exam

Wind pressures and forces, seismic base shear and vertical distribution of lateral force, snow, rain, and ice loads, impact and moving (vehicular and crane) loads, and their delivery to the lateral system.

5 concepts

Exam areas

D. Wind loads

Wind Velocity Pressure & MWFRS

The ASCE 7-16 velocity pressure qz = 0.00256·Kz·Kzt·Kd·V², the MWFRS design pressure p = q·G·Cp, exposure categories, and the directional procedure for enclosed buildings.

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Wind Loads on Components & Cladding

The ASCE 7-16 C&C design pressure p = qh[(GCp) − (GCpi)], effective wind area, the wall/roof pressure zones, and why local C&C pressures exceed the MWFRS.

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E. Seismic loads

Seismic Base Shear (Equivalent Lateral Force)

The ASCE 7-16 equivalent lateral force base shear V = Cs·W, the seismic response coefficient and its caps, the approximate period, and how SDS, SD1, R and Ie set the demand.

Seismic design on the PE Civil exam almost always starts at the same place: the total lateral force a building must be able to develop at its base when the ground shakes. The Equivalent Lateral Force (ELF) procedure boils the entire dynamic problem down to one static force, the base shear

V = C_s W

, that you then push up the structure. It looks like one multiplication, but the points live in the details — picking the right seismic response coefficient

C_s

, knowing which of its three caps governs, estimating the period correctly, and using the supplied seismic parameters without mixing up

S_{DS}

and

S_{D1}

. This is a NARRATIVE topic: none of these relations appear in the NCEES PE Civil Reference Handbook (Ch 4 Structural carries no ASCE 7 load equations). Teach and cite the governing code, ASCE/SEI 7-16 §12.8 Equivalent Lateral Force Procedure — not a handbook page.

The base shear and the effective seismic weight

The base shear is the seismic response coefficient times the effective seismic weight,

V = C_s W

. The weight

W

is the total dead load plus the prescribed portions of other loads that ride with the structure during an earthquake — ASCE 7-16 §12.7.2 adds storage live load, a partition allowance (at least

10\ \text{psf}

where partitions are present), permanent equipment, and a fraction of flat-roof snow where

p_g

is large. Note what is excluded: ordinary floor live load and roof live load do not count, because they are not reliably present when the ground moves. Getting

W

right is half the problem; a base shear is only as good as the mass it is built on.

V = C_s\,W

The seismic response coefficient

The seismic response coefficient is, in its base form, the design spectral acceleration reduced by the response modification factor and scaled by importance,

C_s = S_{DS}/(R/I_e)

. The numerator

S_{DS}

is the design short-period spectral acceleration (the plateau of the design spectrum). The response modification coefficient

R

rewards ductility — a special moment frame (

R=8

) is allowed far less force than an ordinary cantilever column (

R=1.25

) because it can yield and dissipate energy. The seismic importance factor

I_e

(1.0, 1.25, or 1.5 by Risk Category) raises the demand for buildings that must survive. This base value applies in the constant-acceleration (short-period) region of the spectrum.

C_s = \dfrac{S_{DS}}{R/I_e}

The upper-limit cap at long period

Real buildings are not all short-period. As the fundamental period

T

lengthens, the design spectrum falls off as

S_{D1}/T

, so ASCE 7-16 caps

C_s

by the velocity-region value

C_s = S_{D1}/[T(R/I_e)]

for

T \le T_L

(and by

S_{D1}T_L/[T^2(R/I_e)]

for

T > T_L

, the long-period corner). This upper limit is what governs for most moment-frame and taller buildings — the base equation

S_{DS}/(R/I_e)

is a ceiling that only controls for stiff, short-period structures. If you blindly use

S_{DS}/(R/I_e)

for a flexible building you will badly over-state the force; always compute the period-dependent cap and take the smaller.

C_s \le \dfrac{S_{D1}}{T\,(R/I_e)}\quad (T \le T_L), \qquad C_s \le \dfrac{S_{D1}\,T_L}{T^2\,(R/I_e)}\quad (T > T_L)

The lower-limit floor

There is also a floor:

C_s

may not drop below

0.044\,S_{DS}I_e \ge 0.01

. Where the mapped one-second acceleration is high (

S_1 \ge 0.6g

, the near-fault regime), a second floor

C_s = 0.5\,S_1/(R/I_e)

applies. These minimums keep a baseline lateral capacity in every building regardless of how the period and

R

try to drive the coefficient toward zero. On the exam the lower limit rarely governs for ordinary buildings, but you must check it — a value of

C_s

below the floor is simply wrong, not a smaller (and therefore safer-looking) answer.

C_{s,\min} = 0.044\,S_{DS}\,I_e \ge 0.01, \qquad C_{s,\min} = \dfrac{0.5\,S_1}{R/I_e}\ \ (\text{if } S_1 \ge 0.6g)

The approximate fundamental period

The cap depends on the period, and the exam expects the approximate period from building height,

T_a = C_t h_n^{\,x}

, with

h_n

the height above base in feet. The coefficients depend on the framing: steel moment frames use

C_t = 0.028,\ x = 0.8

; concrete moment frames

C_t = 0.016,\ x = 0.9

; eccentrically braced and buckling-restrained frames

C_t = 0.03,\ x = 0.75

; all other systems

C_t = 0.02,\ x = 0.75

. If a rational (modal) analysis gives a computed period

T

, ASCE 7-16 lets you use it only up to

C_u T_a

— you may not take credit for an arbitrarily long, low-force period. Absent an analysis, use

T_a

directly.

T_a = C_t\,h_n^{\,x} \qquad (h_n\ \text{in ft})

The design spectral accelerations

The parameters

S_{DS}

and

S_{D1}

are themselves derived: from the mapped

S_S

and

S_1

, apply site coefficients

F_a

and

F_v

for the site class to get

S_{MS} = F_a S_S

and

S_{M1} = F_v S_1

(the maximum-considered-earthquake values), then take two-thirds:

S_{DS} = \tfrac{2}{3}S_{MS}

and

S_{D1} = \tfrac{2}{3}S_{M1}

. The two-thirds factor converts the MCE (a rare, large event) to the design basis. The exam usually supplies

S_{DS}

and

S_{D1}

directly — but if it hands you

S_S

S_1

, and a site class, this is the chain you walk down first.

S_{DS} = \tfrac{2}{3}F_a S_S, \qquad S_{D1} = \tfrac{2}{3}F_v S_1

Exam strategy

Work it as a short checklist. First get the period

T_a = C_t h_n^x

with the right framing coefficients. Then compute three candidate

C_s

values: the base

S_{DS}/(R/I_e)

, the cap

S_{D1}/[T(R/I_e)]

(use the

T>T_L

form only if told

T_L

is exceeded), and the floor

0.044 S_{DS} I_e

. Take the base value but no greater than the cap and no less than the floor. Multiply by

W

— and confirm

W

excludes ordinary live load. The single most common error is forgetting the long-period cap and reporting the (too large) base value for a flexible building; the second is mixing

S_{DS}

(no

T

) with

S_{D1}

(divided by

T

). Always cite ASCE 7-16 §12.8, never a handbook section.

Key equations

Seismic base shear

V = C_s\,W

$V$ = total design base shear (kip), $C_s$ = seismic response coefficient (dimensionless), $W$ = effective seismic weight (kip) per ASCE 7-16 §12.7.2.

Seismic response coefficient (base form)

C_s = \dfrac{S_{DS}}{R/I_e}

Short-period (constant-acceleration) value. $S_{DS}$ = design short-period spectral accel (g), $R$ = response modification factor, $I_e$ = importance factor.

Upper limit, T ≤ TL

C_{s,\max} = \dfrac{S_{D1}}{T\,(R/I_e)}

Velocity-region cap; governs for most moderate-to-long-period buildings. $S_{D1}$ = design 1-second spectral accel (g), $T$ = fundamental period (s).

Upper limit, T > TL

C_{s,\max} = \dfrac{S_{D1}\,T_L}{T^2\,(R/I_e)}

Long-period (displacement-region) cap beyond the corner period $T_L$ (s, mapped).

Lower limit (general)

C_{s,\min} = 0.044\,S_{DS}\,I_e \ge 0.01

Floor on $C_s$ for all buildings; the result may not fall below this regardless of $T$ or $R$ .

Lower limit (high seismicity)

C_{s,\min} = \dfrac{0.5\,S_1}{R/I_e}

Additional floor where $S_1 \ge 0.6g$ (near-fault). $S_1$ = mapped 1-s MCE accel (g).

Approximate fundamental period

T_a = C_t\,h_n^{\,x}

$h_n$ = structural height (ft). Steel MF $C_t{=}0.028,x{=}0.8$ ; concrete MF $0.016,0.9$ ; EBF/BRBF $0.03,0.75$ ; other $0.02,0.75$ .

Design spectral accelerations

S_{DS} = \tfrac{2}{3}F_a S_S, \quad S_{D1} = \tfrac{2}{3}F_v S_1

From mapped $S_S$ , $S_1$ and site coefficients $F_a$ , $F_v$ ; the $\tfrac{2}{3}$ scales MCE to design basis.

Computed-period upper bound

T \le C_u\,T_a

A rationally computed period may be used for the cap only up to $C_u T_a$ ( $C_u$ from ASCE 7-16 Table 12.8-1, ~1.4–1.7).

Worked examples

Base shear for a steel moment-frame building

Problem. A 9-story special steel moment frame has $h_n = 120\ \text{ft}$ and an effective seismic weight $W = 12{,}000\ \text{kip}$ . The site gives $S_{DS} = 1.0g$ , $S_{D1} = 0.6g$ , and $S_1 = 0.4g$ . Assume $T \le T_L$ (the mapped long-period transition $T_L$ exceeds the building period). Use $R = 8$ , $I_e = 1.0$ . Find the design base shear by the ELF procedure.

Solution. Period (steel MF,

C_t = 0.028

x = 0.8

T_a = 0.028\,(120)^{0.8} = 0.028(46.08) = 1.29\ \text{s}

. Base

C_s = \dfrac{S_{DS}}{R/I_e} = \dfrac{1.0}{8/1.0} = 0.125

. Upper-limit cap (

T \le T_L

C_{s,\max} = \dfrac{S_{D1}}{T(R/I_e)} = \dfrac{0.6}{1.29\,(8)} = \dfrac{0.6}{10.32} = 0.0582

. Lower limit:

0.044\,S_{DS}I_e = 0.044(1.0)(1.0) = 0.044

. (And

S_1 = 0.4 < 0.6

, so the near-fault floor does not apply.) Governing: the cap

0.0582

is below the base

0.125

and above the floor

0.044

, so

C_s = 0.0582

V = C_s W = 0.0582\,(12{,}000) = 698\ \text{kip}

. **Answer:

V \approx 698\ \text{kip}

(using

C_s = 0.0582

).** Sanity check: a 9-story frame is flexible, so the long-period cap should govern over the short-period base value — it does, cutting the coefficient from

0.125

0.0582

. Reporting

0.125\times12{,}000 = 1{,}500\ \text{kip}

would be the classic over-statement from ignoring the cap.

C_s = \min\!\left(0.125,\ \frac{0.6}{1.29(8)}\right) = 0.0582, \quad V = 0.0582(12{,}000) = 698\ \text{kip}

Stiff short-period building — base value governs

Problem. A 2-story bearing-wall building ('other' system, $R = 4$ ) has $h_n = 24\ \text{ft}$ , $W = 3{,}200\ \text{kip}$ , $S_{DS} = 0.9g$ , $S_{D1} = 0.35g$ , $I_e = 1.25$ (Risk Category III). Find $C_s$ and $V$ .

Solution. Period ('other',

C_t = 0.02

x = 0.75

T_a = 0.02\,(24)^{0.75} = 0.02(10.84) = 0.217\ \text{s}

. Base

C_s = \dfrac{S_{DS}}{R/I_e} = \dfrac{0.9}{4/1.25} = \dfrac{0.9}{3.2} = 0.281

. Cap:

C_{s,\max} = \dfrac{S_{D1}}{T(R/I_e)} = \dfrac{0.35}{0.217(3.2)} = \dfrac{0.35}{0.694} = 0.504

. Floor:

0.044\,S_{DS}I_e = 0.044(0.9)(1.25) = 0.0495

. Governing: the base

0.281

is below the cap

0.504

and above the floor, so

C_s = 0.281

V = C_s W = (0.9/3.2)(3{,}200) = 0.28125(3{,}200) = 900\ \text{kip}

. **Answer:

V \approx 900\ \text{kip}

(with the exact

C_s = 0.28125

; rounding

C_s

0.281

gives

899

).** Sanity check: for a stiff, short-period building the cap does NOT govern — exactly the opposite of the tall-frame case — so here the short-period base equation controls, which is the correct behavior. Note

I_e = 1.25

raised both the base coefficient and the floor.

C_s = \min\!\left(\tfrac{0.9}{3.2},\ \tfrac{0.35}{0.217(3.2)}\right) = 0.28125, \quad V = 0.28125(3{,}200) = 900\ \text{kip}

Long-period frame — the lower-limit floor governs

Problem. A tall, flexible special steel moment frame in a low-to-moderate seismic region has $h_n = 200\ \text{ft}$ and $W = 18{,}000\ \text{kip}$ . The site gives $S_{DS} = 0.5g$ , $S_{D1} = 0.18g$ , and $S_1 = 0.12g$ ( $T \le T_L$ ). Use $R = 8$ , $I_e = 1.0$ . Show that the minimum $C_s$ floor governs, and find $V$ .

Solution. Period (steel MF,

C_t = 0.028

x = 0.8

T_a = 0.028\,(200)^{0.8} = 0.028(69.31) = 1.94\ \text{s}

. Base

C_s = \dfrac{S_{DS}}{R/I_e} = \dfrac{0.5}{8/1.0} = 0.0625

. Upper-limit cap (

T \le T_L

C_{s,\max} = \dfrac{S_{D1}}{T(R/I_e)} = \dfrac{0.18}{1.94\,(8)} = \dfrac{0.18}{15.52} = 0.0116

. Lower limit (general):

C_{s,\min} = 0.044\,S_{DS}I_e = 0.044(0.5)(1.0) = 0.0220 \ge 0.01

. (Near-fault floor does not apply:

S_1 = 0.12 < 0.6

.) Governing: the period cap

0.0116

falls BELOW the floor

0.0220

, so the floor controls —

C_s = 0.0220

(not the smaller cap value).

V = C_s W = 0.0220\,(18{,}000) = 396\ \text{kip}

. **Answer:

V \approx 396\ \text{kip}

(using the floor

C_s = 0.0220

).** Sanity check: for a very long-period building in low seismicity the velocity cap drives

C_s

down past the minimum, so the floor — not the cap or the base value — sets the demand. Had you simply taken the cap

0.0116

, you would have reported a non-compliant

V = 209\ \text{kip}

, about half the required value.

C_s = \max\!\left(0.044 S_{DS} I_e,\ \min(0.0625,\ 0.0116)\right) = 0.0220, \quad V = 0.0220(18{,}000) = 396\ \text{kip}

Common pitfalls

•Citing the NCEES PE Civil Handbook (§4 Structural) for the base-shear method — it contains NO ASCE 7 seismic equations. The governing source is ASCE/SEI 7-16 §12.8; cite it and the edition.
•Reporting the base value $S_{DS}/(R/I_e)$ for a flexible building and skipping the long-period cap $S_{D1}/[T(R/I_e)]$ . For most moment frames the cap governs and gives a much smaller (correct) $C_s$ .
•Confusing $S_{DS}$ and $S_{D1}$ : $S_{DS}$ (short-period) appears alone; $S_{D1}$ (one-second) is always divided by the period $T$ . Swapping them changes the answer by a factor of $T$ .
•Forgetting the lower-limit floor $0.044 S_{DS} I_e$ (and the $S_1 \ge 0.6g$ near-fault floor). A $C_s$ below the floor is not a smaller safe answer — it is simply non-compliant.
•Using the wrong $C_t$ , $x$ for the framing type, or putting $h_n$ in the wrong units. $T_a = C_t h_n^x$ takes $h_n$ in FEET; mismatching the framing coefficients (e.g., steel MF vs. 'other') shifts the period and the governing cap.
•Citing the wrong code edition — ASCE 7-22 or the 2015 NEHRP — when NCEES supplies ASCE 7-16. The $C_s$ caps and period coefficients are edition-specific.
•Including ordinary floor or roof live load in the effective seismic weight $W$ . ASCE 7-16 §12.7.2 includes dead load, storage/partition allowances, permanent equipment, and heavy snow — but not transient live load.

References

ASCE/SEI 7-16, Minimum Design Loads and Associated Criteria for Buildings and Other Structures — §12.8 Equivalent Lateral Force Procedure
ASCE/SEI 7-16 — §11.4 Seismic Ground Motion Values (SDS, SD1, Fa, Fv) and §12.7.2 Effective Seismic Weight
ASCE/SEI 7-16 — Tables 12.2-1 (R, Cd, Ω0) and 12.8-1, 12.8-2 (Cu, Ct, x)

Seismic Force Distribution & Story Drift

Vertical distribution Fx = Cvx·V with the period-dependent k-exponent, story shears, amplified story drift against the allowable, and accidental/torsional eccentricity.

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G. Snow, rain, and ice

Snow, Rain & Ice Loads

The ASCE 7-16 flat-roof snow pf = 0.7·Ce·Ct·Is·pg, sloped-roof and drift/unbalanced snow, rain ponding load, and atmospheric ice on the exposure factors.

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