Wind, Collision, Extreme Events, and Resilience

Engineering story

Tacoma, Sunshine Skyway, and the birth of Extreme Event limits

The 1940 collapse of the Tacoma Narrows bridge in a 42 mph steady wind — visible in the world's most-watched engineering film — killed the assumption that wind is a static load and forced bridge engineers to treat long-span decks as elastic oscillators. Forty years later, the 1980 Sunshine Skyway collapse in Tampa Bay — a phosphate freighter struck a pier column in a squall, dropping a 1,200-ft span and 35 people — created what AASHTO now calls the Extreme Event II limit state and forced every navigable waterway crossing to be sized against a defined vessel-impact load.

Chapter objectives

What you will be able to do

Learning objectives

By the end of this chapter you will be able to:

1Convert a mapped 3-s gust to design wind pressure P_z on superstructure and substructure (§3.8).
2Recognize when vortex shedding, buffeting, or flutter controls a long-span deck and know the aeroelastic screening rules.
3Compute the AASHTO Method II vessel-impact force P_B on a pier from vessel DWT and speed (§3.14).
4Apply the 600-kip static equivalent vehicular collision load on unprotected columns (§3.6.5).
5Combine wind, ice, vessel, and vehicular impact into AASHTO Extreme Event I and II combinations with the proper load factors.
6Assemble a simple resilience metric — return period × downtime × cost — for a bridge under multi-hazard exposure.
7Deliver two worked examples (wind pressure and barge impact) plus a cable-stayed multi-hazard design challenge.

16.1 — Wind on the structure

Design wind pressure from 3-s gust

AASHTO LRFD §3.8

AASHTO now uses the ASCE 7 mapped 3-s gust wind speed V for a defined return period (700 yr for Strength III, 1700 yr for Extreme Event I on major bridges). The design pressure at height z is:

P_z \;=\; 2.56 \times 10^{-6}\, V^2\, K_z\, G\, C_D

(16.1)

$V$: 3-s gust wind speed [mph]
$K_z$: height/exposure coefficient (Table 3.8.1.2.1-1)
$G$: gust factor (1.0 for typical bridges; 0.85 for long span)
$C_D$: drag coefficient (1.3 girder + rail, 2.0 truss)
$P_z$: wind pressure [ksf]

Fig. 16.1Wind on a girder bridge. Pressure P_z acts on the exposed depth d of deck + barrier over the whole span; the resulting lateral force creates overturning at each pier.

Force per unit length on the superstructure:

w_{WS} \;=\; P_z \cdot d

(16.2)

where d is the exposed depth of the girder + barrier + parapet.

Wind on live load (WL)

A 0.10 klf lateral line load acts 6 ft above deck to represent wind on stopped vehicles. Combined with WS at 0.30 × strength value in Strength V, or full value in Service IV for slender bridges.

16.2 — Aeroelastic response

Buffeting, vortex shedding, flutter

AASHTO LRFD §3.8.3

Wind is not just a static pressure — it is a broadband turbulent flow. Three regimes matter for bridges:

Fig. 16.2Wind velocity spectrum — the mean, the turbulence (buffeting) band around f_n, and the aeroelastic band at high frequency (vortex shedding, flutter).

Static / mean drag: covered by Eq. 16.1.
Buffeting: random turbulence excitation at the bridge's natural frequencies — checked by gust factor G and dynamic amplification.
Vortex shedding: lock-in at U = f_n B / St; produces resonant vertical/torsional oscillation of slender decks.
Flutter: negative aerodynamic damping — a self-excited divergent oscillation, cause of Tacoma Narrows.

Fig. 16.3Vortex shedding. Alternating Kármán vortices behind a bluff deck produce an oscillating lift at the Strouhal frequency f_s = St·V/h.

f_s \;=\; \dfrac{\mathrm{St}\, V}{h}, \qquad U_{cr,flutter} \;=\; \eta_c\, f_{n,t}\, B

(16.3)

$\mathrm{St}$: Strouhal number (~0.11 typical deck)
$h, B$: deck depth and width [ft]
$\eta_c$: flutter velocity coefficient (5–12) from wind tunnel
$f_{n,t}$: first torsional natural frequency [Hz]

Fig. 16.4Flutter onset. Total damping (structural + aerodynamic) drops with reduced velocity; where it crosses zero is the critical flutter speed U_cr.

16.3 — Vessel collision (CV)

AASHTO Method II impact force

AASHTO LRFD §3.14

Every pier within reach of a navigable waterway must resist an equivalent static vessel-impact force P_B. AASHTO's Method II calibrates P_B from vessel dead-weight tonnage (DWT) and impact velocity:

Fig. 16.5Vessel collision on a pier. A drifting or navigating barge/ship applies P_B laterally at the water surface; fenders/dolphins absorb some of the energy before contact.

P_B \;=\; 4{,}112\, V\, \sqrt{\mathrm{DWT}} \times 10^{-5} \;\;[\text{kip, barge/ship, U.S. units}]

(16.4)

$V$: impact velocity [ft/s]
$\mathrm{DWT}$: vessel dead-weight tonnage [tonne]

For barges specifically (§3.14.11):

P_B \;=\; \begin{cases} 4{,}112\, a_B & a_B < 0.34 \\ 1{,}349 + 110\, a_B & a_B \ge 0.34 \end{cases}, \qquad a_B = \dfrac{V\sqrt{K E_H}}{5{,}672}

(16.5)

Method II checkpoint

AASHTO's calibration uses waterway geometry, vessel-frequency data, and pier resistance to target an annual failure probability AF ≤ 0.0001 for a critical bridge, 0.001 for a regular bridge. Load factor γ_CV = 1.0 in Extreme Event II.

16.4 — Vehicular collision (CT)

600-kip static equivalent

AASHTO LRFD §3.6.5

Any pier column within 30 ft of the edge of a roadway (or 50 ft of a railway centerline) must be designed for a 600-kip equivalent static force applied 5 ft above ground unless it is shielded by a Test-Level-5 barrier or has been analysed by refined impact methods.

Fig. 16.5bVehicle collision load — 600 kip applied 5 ft above ground on an unshielded column, per AASHTO §3.6.5.

16.5 — Ice loads

Ice crushing at the water line

AASHTO LRFD §3.9

Where an ice-covered waterway is present, horizontal ice pressure:

F_c \;=\; C_a\, p\, t\, w

(16.6)

$p$: effective ice crushing strength (8–32 ksf)
$t$: ice thickness [ft]
$w$: width of pier exposed to ice [ft]
$C_a$: pier nose shape coefficient

16.6 — Extreme-event combinations

Which loads act together

AASHTO LRFD §3.4.1

Extreme events are treated one-at-a-time with reduced live-load partners:

Extreme Event I: γ_p DC + γ_EQ LL + 1.0 EQ. Earthquake governs.
Extreme Event II: γ_p DC + 0.5 LL + 1.0 CV (or CT, IC, IM, WA). Vessel, vehicle, ice, or scour governs.
Strength III: γ_p DC + 1.0 WS (structure). No LL.
Strength V: γ_p DC + 1.35 LL + 0.4 WS + 1.0 WL. Live load with concurrent wind.
Service IV: γ_p DC + 1.0 WS (cracking/deflection check).

16.7 — Resilience framing

Return periods × downtime × cost

Modern extreme-event design closes with a resilience assessment: annual probability of loss × consequences × recovery time. A fault tree combines the mutually exclusive hazards to bound the expected annual downtime and repair cost:

Fig. 16.7Fault tree for bridge closure. Each hazard contributes an annualized probability; total downtime target ≤ 5 days/yr for a lifeline route.

\lambda_{closure} \;=\; \sum_i P(H_i)\, P(\text{closure}\mid H_i), \qquad \text{EAL} = \sum_i \lambda_i\, C_i

(16.7)

16.8 — Worked example 1

Design wind pressure on a girder bridge

AASHTO LRFD §3.8

Problem statement

A steel plate-girder bridge on the Gulf Coast has 130-ft simple spans with 5-ft-deep girders + a 3-ft F-shape barrier (d = 8 ft exposed). Compute the design wind pressure and per-span wind force at the Extreme Event I event.

Given

3-s gust wind speed (700-yr)V = 115 mph (Gulf Coast)
Height of deck (z)40 ft above grade (Exposure C)
K_z1.09 (Table 3.8.1.2.1-1, Exposure C, z = 40 ft)
G, C_DG = 1.0; C_D = 1.3 (girder + rail)
Exposed depth d8 ft

Required

Compute P_z, w_WS, span wind force, and the pier overturning moment (deck 20 ft above pier base).

Step 1 — Design pressure (Eq. 16.1).

Formula

P_z = 2.56\times10^{-6} V^2 K_z G C_D

Substitute

P_z = 2.56\times10^{-6}(115)^2(1.09)(1.0)(1.3)

Result

P_z = 0.048\;\text{ksf} = 48\;\text{psf}

Step 2 — Line load on the superstructure.

Formula

w_{WS} = P_z d

Substitute

w_{WS} = 0.048 \times 8

Result

w_{WS} = 0.384\;\text{klf}

Step 3 — Span wind force delivered to piers.

Formula

W_{span} = w_{WS} L

Substitute

W_{span} = 0.384 \times 130

Result

W_{span} = 49.9\;\text{kip / span (split between two piers)}

Step 4 — Pier overturning moment. Deck 20 ft above pier base, plus the pier's own 20-ft column exposed to wind on it (add 0.30 klf approx.):

Formula

M_{OT} = W_{deck} h_{deck} + w_{pier} h_{pier}^2/2

Substitute

M_{OT} = 25 \times 20 + 0.30 \times 20^2 / 2

Result

M_{OT} = 500 + 60 = 560\;\text{kip-ft (per pier)}

Step 5 — Combine (Strength III). Apply γ = 1.0 (already 700-yr map) plus γ_p = 1.25 on DC. Check pier P–M capacity — for the multi-column bent designed in Ch. 9, 560 kip-ft is well within the biaxial envelope.

Fig. 16.8Figure 16.8. Wind on a 130-ft simple span, d = 8 ft exposed deck + barrier.

Final section detailing (from computed A_s)

Wind demand on plate-girder bridge (Strength III / Extreme I)

Location	A_s required	Bars provided	Spacing / detail
3-s gust V	Gulf Coast map, 700-yr	115 mph	verify with NOAA WX-DB
Pressure P_z	Eq. 16.1	48 psf on superstructure	recompute at z = 60 ft for tall piers
w_WS	P_z × d	0.384 klf	add 0.30 klf on pier column
Wind on LL (WL)	0.10 klf @ 6 ft above deck	included in Strength V	not in Strength III
Aeroelastic check	not required for L < 200 ft	skipped — girder bridge	required for L > 400 ft

For coastal or long-span bridges, upgrade to the 1,700-yr map and add a wind-tunnel-based aeroelastic screening per §3.8.3.

16.9 — Worked example 2

Vessel impact on a river pier

AASHTO LRFD §3.14

Problem statement

A river pier is exposed to a 3,000-ton fully loaded jumbo hopper barge with typical transit speed 6 ft/s (4 knots). Compute the AASHTO Method II barge impact force P_B and check the pier.

Given

DWT3,000 tonne
V6 ft/s (transit)
Vessel mass factor K1.05 (hopper barge)
Bow energy E_H (deformation limit)from AASHTO Fig. 3.14.11-1 ≈ 4,600 kip-ft at V = 6 fps
Pier4-ft-Ø drilled shaft, 40 ft above waterline

Required

Compute a_B, P_B, and the pier base moment; check whether a sacrificial fender is needed.

Step 1 — Barge damage depth parameter a_B (Eq. 16.5).

Formula

a_B = V\sqrt{K E_H}/5{,}672

Substitute

a_B = 6 \sqrt{1.05 \times 4600}/5672

Result

a_B = 6 \times 69.5 / 5672 = 0.074

Step 2 — Since a_B < 0.34, use linear branch.

Formula

P_B = 4{,}112\, a_B

Substitute

P_B = 4{,}112 \times 0.074

Result

P_B = 304\;\text{kip}

Cross-check via Eq. 16.4 (ship form):

Formula

P_B = 4{,}112 V \sqrt{DWT}\times10^{-5}

Substitute

P_B = 4{,}112(6)\sqrt{3000}\times10^{-5}

Result

P_B = 4{,}112(6)(54.8)/100{,}000 = 13.5\;\text{kip — ship form N/A for barge, use Eq. 16.5}

Step 3 — Pier base moment. Force applied 5 ft above WSE, pier fixity 40 ft below WSE (drilled shaft):

Formula

M_B = P_B \times h_{arm}

Substitute

M_B = 304 \times (5 + 40)

Result

M_B = 13{,}700\;\text{kip-ft (Extreme II)}

Step 4 — Combine (Extreme Event II). γ = 1.0 CV + 0.5 LL + 1.0 DC + scour envelope from Ch. 14. Check the 4-ft-Ø drilled shaft P–M capacity — typically requires either a larger shaft or a sacrificial pier-nose fender that dissipates ≥ 30 % of the kinetic energy.

Step 5 — Fender sizing. Kinetic energy of barge:

Formula

KE = \tfrac12 m V^2

Substitute

KE = 0.5 (3000\times2000/32.2)(6)^2

Result

KE = 3.35\times10^6\;\text{ft-lb} = 3{,}350\;\text{kip-ft}

A rubber-cell fender that absorbs 1,000 kip-ft (30 %) reduces P_B by ~15 % — usually enough to bring pier demand back within capacity.

Fig. 16.9Figure 16.9. 3,000-ton hopper barge striking a river pier at 6 fps; impact P_B applied 5 ft above WSE.

Final section detailing (from computed A_s)

Barge-impact design of river pier

Location	A_s required	Bars provided	Spacing / detail
Design vessel	AF ≤ 0.001 (regular)	3,000-ton hopper barge, V = 6 fps	vessel frequency from lock records
P_B (bare pier)	Eq. 16.5 barge form	304 kip @ 5 ft above WSE	Ext. Event II, γ = 1.0
Base moment	pier P–M envelope	13,700 kip-ft	requires 6-ft Ø shaft if no fender
Fender system	absorb ≥ 30 % KE	3-cell rubber fender + timber facing	6 ft from pier face
Fender maintenance	inspect after each impact	5-yr replacement cycle	part of bridge O&M program

Method II is an equivalent-static procedure; for critical bridges (Sunshine Skyway, I-40 Bay), the owner may commission a Method III/IV dynamic vessel-impact analysis with soil-structure interaction.

16.10 — Guided practice

Truck-collision retrofit

A single-column pier next to a freeway has M_n = 5,200 kip-ft and shear V_n = 380 kip. Is a Test-Level-5 concrete barrier required, or does the pier resist 600 kip at 5 ft above ground directly?

Expected result

M_demand = 600 × 5 = 3,000 kip-ft ≪ 5,200 ✓ flexure; V = 600 kip > 380 kip — shear governs and TL-5 barrier is required, or add hoops/spiral to raise V_n above 600 kip.

16.11 — Mini design challenge

Multi-hazard: cable-stayed river crossing

Fig. 16.10Design challenge. Cable-stayed river crossing — check 1,700-yr wind + design vessel + Extreme Event II combination.

Deliver:

Static wind pressure P_z on deck and tower for the 1,700-yr gust; aeroelastic screening (vortex-shedding and flutter velocity).
Design vessel selection (from AASHTO §3.14 AF calibration for a "critical" bridge) and computed P_B.
Extreme Event II combination at the base of the river tower.
Vehicular collision (§3.6.5) at approach columns — barrier vs. direct design.
Resilience fault tree — target ≤ 3 closure-days/yr for a lifeline crossing.
Fender/dolphin plan and a one-page multi-hazard memo.

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16.12 — Chapter summary

What you leave with

Design wind pressure P_z = 2.56×10⁻⁶ V² K_z G C_D (Eq. 16.1) and w_WS = P_z·d for the exposed depth.
Aeroelastic regimes — buffeting, vortex shedding (f_s = St·V/h), flutter (U_cr = η_c f_n,t B).
Vessel-impact force P_B by Method II (Eq. 16.5 for barges, Eq. 16.4 for ships), applied at WSE elevation.
600-kip vehicular-collision force on unshielded columns, 5 ft above ground.
Extreme Event I (earthquake) and II (vessel / vehicle / ice) load combinations with γ = 1.0.
Resilience framing: EAL = Σ P(H) × downtime × cost, and lifeline targets ≤ 3–5 days/yr.

AASHTO LRFD §3.8 Wind · §3.14 Vessel · §3.6.5 Vehicle Collision · §3.9 Ice

Section 2

Fully Worked Examples

Complete AASHTO LRFD solutions with knowns, assumptions, step calculations, verification, and design commentary. Difficulty rises from basic to consulting-grade.

Worked Example 1

Design vessel-impact force per AASHTO Vessel Collision Guide

Basic

Problem

Compute the equivalent static impact force P_s.

Step-by-Step

P_{s} = 8.15\cdot V\cdot \sqrt{DWT} (kip, DWT in tons, V in ft/s per AASHTO commentary)

P_{s} = 8.15\cdot 13.5\cdot \sqrt{40000} = 110.0\cdot 200

Result

P_{s} = 22{,}000 kip (approx)

Design Verification

P_s of 20,000–30,000 kip is realistic for major shipping channels (e.g., Sunshine Skyway, Chesapeake Bay Bridge). ✓

Discussion

Vessel-impact design follows AASHTO Vessel Collision Guide (Method II or III). Extreme Event II γ_CV = 1.0. Full probabilistic analysis usually required for interstate river crossings.

Worked Example 2

Vehicle collision force on a bridge pier (fixed object)

Intermediate

Problem

Determine collision force F_CT and mitigation option.

Step-by-Step

Setback 12 ft < 30 ft \rightarrow §3.6.5 applies unless protected.

F_{CT} = 600 kip point load at 5 ft above ground (equivalent static)

Design Verification

TL-5 barrier is the standard bridge-pier protection for interstate roadways. Providing it converts the force check into a barrier design check.

Discussion

Never rely on 'unlikely event' arguments. §3.6.5 is a code requirement below 30-ft clear setback; either design for 600 kip or install a rated barrier.

Worked Example 3

Flood loading during Extreme Event II

Intermediate

Problem

Compute pier lateral load from stream + debris.

Step-by-Step

p = C_{D}\cdot V^{2}/1000 (ksf, V in fps per §3.7.3.1)

Result

p = 1.4\cdot 100/1000 = 0.14 ksf

F_{pier} = p\cdot A_{face} = 0.14\cdot 160

Result

F_{pier} = 22.4 kip

Design Verification

Add hydrostatic and buoyancy per §3.7.1 and §3.7.2. For skewed flow use §3.7.3.2 modification.

Discussion

Extreme Event II combines flood + scour + vessel/vehicle simultaneously with reduced γ_LL. See §3.4.1 Table 3.4.1-1 for the full combination.

Section 3

Guided Practice

Complete the missing steps. Use Hints for AASHTO article pointers and setup logic before revealing the full step. Submit at the end to send your work to your instructor.

Guided Problem 1

AASHTO wind pressure (Method I)

Bridge exposure C, elevation $z = 40\ \text{ft}$ , 3-s gust design wind $V = 115\ \text{mph}$ , $K_z = 0.98$ , $G = 1.0$ , $C_d = 1.3$ .

Step 1

Design pressure $P_z = 2.56\times10^{-6}V^{2}K_zGC_d$ (ksf).

Answer

Step 2

Convert to psf.

Answer

Step 3

Distributed girder wind (klf) for exposed depth $D = 6\ \text{ft}$ .

Answer

Step 4

Total force on 120-ft span (kip).

Answer

Guided Problem 2

Vehicle collision on pier (§3.6.5)

Unprotected pier < 30 ft from edge of travel way and < 50 ft from centerline of railway. Static equivalent CT load.

Step 1

AASHTO CT static equivalent design force (kip).

Answer

Step 2

Height of application above ground (ft).

Answer

Step 3

Load combo $\gamma_{CT}$ at Extreme Event II.

Answer

Step 4

Alternative: TL-5 barrier at 3 ft protects pier — CT then reduced to (kip).

Answer

Guided Problem 3

Fire — heat flux vs. spall onset

Tanker fire under prestressed concrete girder. Cover = 2 in, exposure 60 min at 1832°F (ASTM E119), governed by spall risk at $\ge 750\ ^{\circ}\text{F}$ reinforcement temperature.

Step 1

Approximate temperature at 2-in cover after 60 min per ACI/PCI charts (°F).

Answer

Step 2

Compressive strength retention at 850°F (fraction of $f'_c$ ).

Answer

Step 3

Prestress steel strength retention at 850°F (fraction of $f_{pu}$ ).

Answer

Step 4

Recommend action (1 = replace girder, 0 = keep).

Answer

Guided Problem 4

Blast — pier stand-off distance

Truck bomb 1000 lb TNT equivalent. Column diameter 4 ft. Compute scaled distance and peak reflected pressure at stand-off $R = 30\ \text{ft}$ .

Step 1

Scaled distance $Z = R/W^{1/3}$ (ft/lb^0.3333333333333333).

Answer

Step 2

Peak reflected pressure (psi) at $Z = 3.0$ (Kingery-Bulmash tables).

Answer

Step 3

Total impulse (psi·ms) approx $250\,W^{1/3}/R$ .

Answer

Step 4

Design load classification per DOD guidance for $Z = 3$ : Category?

Answer

Section 4

Independent Practice

Every problem randomizes its inputs. Work each step, submit for immediate feedback, request new values to practice again.

Practice 1

Wind pressure (Method I)

V (mph)

V = 140 mph

K_z

Kz = 1.05 -

C_d

Cd = 1.9000000000000001 -

Step 12.56e-6·V²·K_z·1·C_d (ksf).

Answer (ksf)

Randomized inputs, symbolic grading (±2%).

Practice 2

Girder wind distributed load

P_z (ksf)

Pz = 0.066 ksf

Exposed depth

D = 6.5 ft

Step 1P_z·D.

Answer (klf)

Randomized inputs, symbolic grading (±2%).

Practice 3

Blast scaled distance

Stand-off (ft)

R = 65 ft

W (lb TNT)

W = 4500 lb

Step 1R/W^(1/3).

Answer (ft/lb^(1/3))

Randomized inputs, symbolic grading (±2%).

Practice 4

Truck fire heat flux (rough)

Time (min)

t = 95 min

Step 1Temp ≈ 400 + 300·log10(8t+1) (°F, ASTM E119 approx).

Answer (°F)

Randomized inputs, symbolic grading (±2%).

Practice 5

Vessel collision load (barge)

DWT (ton)

DWT = 1500 ton

V (ft/s)

V = 9 ft/s

Step 1≈ 4.112·√DWT·V.

Answer (kip)

Randomized inputs, symbolic grading (±2%).

Practice 6

Seismic vs wind governing

Wind base shear

Vw = 30 kip

Seismic base shear

Vs = 450 kip

Step 1max of the two.

Answer (kip)

Randomized inputs, symbolic grading (±2%).

Practice 7

Vehicle collision on pier — moment

CT force

CT = 550 kip

Height above base

h = 11 ft

Step 1CT·h.

Answer (k-ft)

Randomized inputs, symbolic grading (±2%).

Practice 8

Barrier design impact (TL-4)

F (kip)

F = 72 kip

Length (ft)

L = 7 ft

Step 1M ≈ F·L (approx moment demand).

Answer (k-ft)

Randomized inputs, symbolic grading (±2%).

Practice 9

Column progressive-collapse alternate path

Column tributary load

Ptrib = 1350 kip

Remaining columns

n = 2 -

Step 1Redistribute to remaining columns.

Answer (kip)

Randomized inputs, symbolic grading (±2%).

Practice 10

Overturning stability of pier

Dead weight

Wd = 450 kip

Arm (ft)

a = 5 ft

Lateral wind

Fw = 75 kip

Height

h = 21 ft

Step 1Restoring = W·a.

Answer (k-ft)

Step 2Overturning = F·h.

Answer (k-ft)

Step 3FS = Mres/Movr.

Answer (-)

Randomized inputs, symbolic grading (±2%).

Practice 11

Ice load (§3.9)

Ice thickness (ft)

t = 0.5 ft

Pier width (ft)

w = 5.5 ft

Ice pressure (ksf)

p = 22 ksf

Step 1F = p·t·w.

Answer (kip)

Randomized inputs, symbolic grading (±2%).

Practice 12

Resilience — closure days from initial cost premium

Cost premium (%)

prem = 13 %

Baseline closure (days)

days0 = 290 days

Step 1Reduce closure ≈ 5·premium (days).

Answer (days)

Randomized inputs, symbolic grading (±2%).