Bridge Construction Engineering — Bridge Engineering & Design

18.1 — Engineering story

The West Gate Bridge and the birth of construction engineering

In October 1970, span 10–11 of the West Gate Bridge in Melbourne — a 367-ft steel box-girder span being closed with a lateral camber correction — buckled and dropped 112 m into the Yarra River, killing 35 workers. The forensic finding was unambiguous: the final design was adequate; the erection sequence was not. Bolts had been removed to force alignment; a temporary kentledge weight made the situation critical. In modern practice every non-trivial bridge is designed twice — once for service and once for construction — and every construction sequence is checked against a code-defined set of Construction Load Combinations.

18.2 — Chapter objectives

What you will be able to do

Learning objectives

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

1Choose an appropriate erection scheme (span-by-span, balanced cantilever, incremental launching, cable-stayed cantilever) from site, span, and clearance constraints.
2Apply AASHTO §3.4.2 construction load factors and check Strength I-C and Service I-C combinations.
3Design falsework and formwork for wet-concrete + construction live load per the AASHTO Guide Design Specification for Bridge Temporary Works.
4Compute camber for steel and prestressed girders combining DL deflection, long-term creep/shrinkage, and grade adjustment.
5Check the unbalanced moment on a segmental pier during balanced-cantilever erection.
6Size a two-crane pick for a steel plate-girder lift, including impact and rigging factors.
7Deliver two worked examples (falsework + segmental unbalanced moment) and a full erection design challenge over live traffic.

18.3 — Erection schemes

Choosing how to build the bridge

The erection scheme is chosen jointly by the designer and the contractor based on span length, ground access, clearance below, alignment curvature, and available lifting capacity. Four families cover most modern bridges:

Fig. 18.1Erection-scheme decision tree. Site + span → scheme.

Span-by-span: girders lifted or launched onto a completed pier line; simplest, up to ~150 ft.
Balanced cantilever: cast-in-place or precast segments extended symmetrically from each pier; 150–800 ft, ideal over water/valleys.
Incremental launching: a segmental box is cast in a stationary yard and jacked forward over the piers; needs constant depth and a straight or constant-radius alignment.
Cable-stayed cantilever: tower and stay cables installed first, deck extended from the tower in balanced pairs; typical for main spans > 500 ft.

18.4 — Construction loads

Loads that only exist during erection

AASHTO LRFD §3.4.2

AASHTO defines the following temporary loads:

CLL — construction live load: workers, tools, small vehicles, typically 20 psf on decks and 10 psf on walkways.
CE — construction equipment: cranes, form travelers, launching noses, kentledge — an actual weight, applied at its actual location.
WCT — wind on the partially completed structure — usually a 40 mph service wind but a 90 mph short-term event for cranes.
PS/CR/SH — locked-in stresses from post-tensioning, creep, and shrinkage that shift during erection.

Construction load combinations (§3.4.2)

Strength I-C: 1.25 DC + 1.5 CE + 1.5 CLL + 1.25 WCT
Service I-C: 1.0 (DC + CE + CLL + WCT) — deflection & stability

18.5 — Falsework and formwork

Temporary support for cast-in-place concrete

Fig. 18.2Falsework and formwork elevation. Shoring towers on mudsills carry stringers and joists supporting the deck forms.

Design loads on falsework (Guide Design Spec. §2):

w_{fw} \;=\; \gamma_{wc}\, t \;+\; w_{forms} \;+\; \text{CLL} \;+\; \text{impact from vibration}

(18.1)

$\gamma_{wc}$: wet concrete unit weight [150 pcf]
$t$: deck thickness (add slab + haunch) [ft]
$w_{forms}$: form + joist dead weight [psf, typ. 10–15]
$\text{CLL}$: construction live load [20 psf on decks]

Falsework failure modes

Overloaded mudsill · lateral instability from missing bracing · premature form stripping · differential settlement of adjacent towers. All four have caused fatalities on U.S. bridge projects.

18.6 — Camber

Building the girder up so it deflects down to grade

AASHTO LRFD §6.10.3, §5.9

Fig. 18.3Camber diagram. Fabricated shape (up) + DL deflection (down) + long-term creep/shrinkage → final grade profile.

\Delta_{camber} \;=\; \Delta_{DL,steel} \;+\; \Delta_{deck} \;+\; \Delta_{SDL} \;+\; \Delta_{creep+shrink} \;+\; \Delta_{grade}

(18.2)

$\Delta_{DL,steel}$: girder self-weight deflection
$\Delta_{deck}$: cast-in-place deck on non-composite section
$\Delta_{SDL}$: superimposed dead load (barriers, FWS, utilities)
$\Delta_{creep+shrink}$: long-term time-dependent — PC girders only
$\Delta_{grade}$: planned adjustment to match roadway profile

Rule of thumb

For a simple-span steel plate-girder highway bridge, total camber at midspan is typically L/800 to L/500. For a 100 ft span this is 1.5–2.4 in.

18.7 — Balanced cantilever

Segmental erection over water and valleys

AASHTO LRFD §5.14.2

Fig. 18.4Balanced cantilever construction. Segments cast in pairs; each pier supports two growing cantilevers with a form traveler on each leading edge.

The controlling temporary demand is the unbalanced moment at the pier when one cantilever is one segment ahead of the other:

M_{unbal} \;=\; \dfrac{w\,(L_R^2 - L_L^2)}{2} \;+\; W_{FT}\cdot a_{FT} \;+\; \text{CLL asymmetry}

(18.3)

$w$: self weight of the box + wet segment [klf]
$L_R, L_L$: right and left cantilever lengths (segment counts) [ft]
$W_{FT}$: form-traveler weight (typ. 50–120 kip) [kip]
$a_{FT}$: form-traveler lever arm from pier CL [ft]

Design rule

M_unbal + wind on the deep-section box must be ≤ pier + temporary blocking capacity. If not, either add stability towers, temporary tie-downs to the pier cap, or restrict the maximum lead of one cantilever.

18.8 — Incremental launching

Casting yard + hydraulic jacks + launching nose

Fig. 18.5Incremental launching. A steel launching nose reduces the leading cantilever moment as the girder crosses each pier.

During launching, every deck cross-section passes through both maximum positive and maximum negative moment at each pier. The girder therefore requires top and bottom PT plus temporary sliding bearings at each pier. Launching nose length is chosen so that the cantilever moment ≈ 40–60 % of the fully supported moment.

18.9 — Girder lifting and rigging

Two-crane picks and pick-point selection

Fig. 18.6Two-crane girder pick. Optimum pick point a ≈ 0.207 L equalizes positive and negative bending in the girder during the lift.

P_{crane,\,required} \;=\; 1.10\,W_{girder} \;+\; W_{rigging} \;+\; W_{spreader}

(18.4)

$1.10$: 10 % dynamic impact factor for a slow lift
$W_{girder}$: girder weight (steel + shear studs + attached diaphragms) [kip]
$W_{rigging}$: slings, shackles, cables [kip]

18.10 — Worked example 1

Falsework tower under a wet slab

Step 1 — Wet concrete load.

Formula

w_{wc} = \gamma\,t = 150\cdot(8/12) = 100\;\text{psf}

Substitute

W_{wc} = 100 \times 40 \times 8

Result

W_{wc} = 32{,}000\;\text{lb} = 32.0\;\text{kip}

Step 2 — Forms + construction LL.

Formula

W_{form+CLL} = (15 + 20)\times 40\times 8

Substitute

= 35\times 320

Result

= 11{,}200\;\text{lb} = 11.2\;\text{kip}

Step 3 — Total unfactored + impact.

Formula

P = (32.0 + 11.2)\times 1.10

Substitute

P = 43.2\times 1.10

Result

P = 47.5\;\text{kip per tower}

Step 4 — Factored (Strength I-C).

Formula

P_u = 1.25\,W_{wc} + 1.50\,W_{form+CLL}

Substitute

P_u = 1.25(32.0) + 1.50(11.2)

Result

P_u = 40.0 + 16.8 = 56.8\;\text{kip}

Step 5 — Tower capacity. A standard 4-leg tubular frame shore rated at 20 kip/leg has P_n = 4 × 20 = 80 kip. Check: 56.8 < 80 ✓.

Step 6 — Mudsill bearing. Two 4 × 12 timber mudsills give A = 2 × (4/12)(4) = 2.67 ft². For q_allow = 3.0 ksf on compacted fill:

Formula

q = P/A = 56.8/2.67

Result

q = 21.3\;\text{ksf} > 3.0\;\text{ksf — NG, enlarge mudsills}

Redesign with 4 × (6 × 8 ft) mats → A = 8 × 6 = 48 ft²; q = 1.2 ksf ✓.

Fig. 18.7Figure 18.7. Single shoring tower supporting a 40 ft × 8 ft tributary of an 8-in. cast-in-place deck.

Final section detailing (from computed A_s)

Falsework tower + mudsill

Location	A_s required	Bars provided	Spacing / detail
Vertical load / tower	56.8 kip factored	80 kip rated shore	70 % util.
Bracing	2 % vert. load lateral	X-bracing every 6 ft	screw jacks top + bottom
Mudsill area	q ≤ 3.0 ksf	48 ft² timber mat	q = 1.2 ksf
Screw-jack extension	≤ 12 in.	8 in. + 4 in. reserve	grade adjustment
Inspection	before every pour	PE-stamped checklist	AASHTO Guide Spec §3

All falsework carrying more than 15 % of the deck load must have a PE-stamped shop drawing and be inspected before, during, and after concrete placement.

18.11 — Worked example 2

Balanced-cantilever unbalanced moment

Given: segment length s = 15 ft; w = 15 klf; L_L = 3s = 45 ft cast, L_R = 4s = 60 ft cast + FT at 60 ft.

Step 1 — Self-weight unbalance.

Formula

M_{unbal,DL} = \dfrac{w(L_R^2 - L_L^2)}{2}

Substitute

= \dfrac{15(60^2 - 45^2)}{2} = \dfrac{15(3600 - 2025)}{2}

Result

= \dfrac{15\times 1575}{2} = 11{,}810\;\text{kip-ft}

Step 2 — Form traveler.

Formula

M_{FT} = W_{FT}\cdot a_{FT} = 100\times 60

Result

M_{FT} = 6{,}000\;\text{kip-ft}

Step 3 — CLL asymmetry. 20 psf × 40 ft wide × 15 ft last seg = 12 kip at 52.5 ft:

Formula

M_{CLL} = 12\times 52.5

Result

M_{CLL} = 630\;\text{kip-ft}

Step 4 — Wind (WCT). 15 psf on 12 ft depth × 60 ft × 30 ft arm to pier base:

Formula

M_{wind} = (0.015)(12)(60)(30)/2

Result

M_{wind} \approx 160\;\text{kip-ft (small)}

Step 5 — Combine (Strength I-C).

Formula

M_u = 1.25\,M_{unbal,DL} + 1.5\,M_{FT} + 1.5\,M_{CLL} + 1.25\,M_{wind}

Substitute

= 1.25(11810) + 1.5(6000) + 1.5(630) + 1.25(160)

Result

M_u = 14{,}762 + 9{,}000 + 945 + 200 = 24{,}907\;\text{kip-ft}

Step 6 — Pier check. Assume 12 ft × 6 ft solid pier at pier table with φM_n = 22,000 kip-ft. 24,907 > 22,000 NG.

Engineering decision. Two options:

Add temporary tie-down bars from pier cap to segment 3 on the trailing side — reduces unbalance by ~30 %, new M_u ≈ 17,500 kip-ft ✓.
Restrict maximum lead to ½ segment: L_R = 3.5s = 52.5 ft → M_unbal = 5,600 kip-ft; but doubles cycle time.

Selection: tie-downs — cheaper and preserves the schedule.

Fig. 18.8Figure 18.8. Segmental box, 15 ft segments, w = 15 klf, form traveler = 100 kip at 15 ft leading edge.

Final section detailing (from computed A_s)

Segmental pier during balanced-cantilever erection

Location	A_s required	Bars provided	Spacing / detail
M_unbal (self)	≤ φM_n pier + tie-downs	11,810 → 6,900 kip-ft w/ ties	3 pairs 1¼-in Ø high-strength bars
M_FT	leading side only	100 kip × 60 ft = 6,000 kip-ft	removed before next segment
Tie-down location	back-cantilever side	segment 3 top slab	3 ft from pier cap
Monitoring	geodetic + strain	prisms + vibrating-wire gages	read before each cast
Wind cutoff	V_10 min ≤ 45 mph	posted on control shack	pause casting when exceeded

Every segmental bridge should have a documented erection manual signed by a licensed PE. The temporary tie-downs count as post-tensioning and are checked with §5.9 stress limits.

18.12 — Guided practice

Pick-point selection for a plate girder

A 180 ft × 6.5 ft steel plate girder weighs 65 klb. Two identical cranes lift it symmetrically at distance a from each end. Show that a ≈ 0.207 L minimizes the maximum moment magnitude (|M⁺| = |M⁻|) and compute the two crane loads including a 10 % impact factor.

Expected result

a = 0.207 × 180 = 37.3 ft. w = 65 / 180 = 0.361 klf. Each crane picks P = (65 × 1.10)/2 = 35.8 kip. |M|_max = wa²/2 = 0.361 × 37.3² / 2 ≈ 251 kip-ft — same magnitude positive at midspan and negative at each pick point.

18.13 — Mini design challenge

Erecting a 220 ft plate girder over live traffic

Fig. 18.9Design challenge. Nighttime pick of a 220 ft × 90 klb plate girder over an urban interstate. Available closure window: 6 h.

Deliver:

Erection scheme comparison (two-crane pick vs. self-launching gantry) with cost/time trade-off.
Selected pick plan — crane sizes, boom radius/angle chart, pick-point locations, ground bearing.
MPT (maintenance of traffic) diagram — lane closures, detour, MASH TL-3 barrier layout, portable message signs.
Temporary support system — bent, timber cribbing, or falsework — to hold the girder if crane hydraulics fail mid-pick.
Wind and lightning cutoff criteria; documented halt-and-secure procedure.
Construction-load check on the receiving piers and bearings; approach girder impact factor.
PE-stamped erection manual, tabletop simulation, and daily go/no-go checklist.

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18.14 — Chapter summary

What you leave with

Erection scheme choice — span, clearance, alignment, and lifting capacity are the four inputs.
AASHTO §3.4.2 construction combinations: Strength I-C = 1.25 DC + 1.5 CE + 1.5 CLL + 1.25 WCT.
Falsework loads: w_fw = γ_wc·t + w_forms + CLL, factored and checked against tower rating and mudsill bearing.
Camber Δ = Δ_DL,steel + Δ_deck + Δ_SDL + Δ_creep+shrink + Δ_grade; total L/500 to L/800 for typical spans.
Balanced-cantilever unbalanced moment M_unbal = w(L_R² − L_L²)/2 + W_FT·a_FT, controlled with tie-downs or lead limits.
Incremental launching needs top + bottom PT and a launching nose sized so cantilever moment ≈ 40–60 % of the fully-supported value.
Two-crane pick: crane load = 1.10 W_girder / 2, pick point a ≈ 0.207 L for equal positive/negative moment.
Every non-trivial erection plan is documented in a PE-stamped erection manual with hold-points, monitoring, and wind cutoffs.

AASHTO LRFD §3.4.2 Construction Combinations · §5.14.2 Segmental · §6.10.3 Constructibility · Guide Spec Bridge Temporary Works

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

Falsework live load per AASHTO Guide Specifications for Bridge Temporary Works

Basic

Problem

Compute the design live load per square foot on the falsework deck.

Step-by-Step

w_{DL} = 0.155\cdot (8/12) = 0.1033 ksf

Result

103 psf

20 psf minimum + 75 psf equipment allowance

Result

95 psf

Design Verification

≈200 psf is the classic falsework rule-of-thumb for 8-in decks. ✓

Discussion

Never design falsework to service-load ratios only. AASHTO Guide Spec requires γ = 1.3 on total DL+CLL for shoring capacity — collapses at Cypress, Willow Island, and Skagit all traced to underestimated construction loads.

Worked Example 2

Segmental cantilever tip deflection during erection

Intermediate

Problem

Determine Δ_tip from the new segment self-weight only.

Step-by-Step

\Delta = P\cdot L^{3}/(3\cdot EI) = 220\cdot 2160^{3} / (3\cdot 4.1\times10⁹)

Result

\Delta \approx 1.80 in downward

Typical constructed camber for 180-ft cantilever tip \approx 3–5 in \ \text{— new deflection consumes ~40% of remaining camber.}

Design Verification

Field survey should record ≤±20% of predicted Δ. Larger deviations mean the geometry-control model needs re-tuning before the next segment.

Discussion

Balanced-cantilever schemes fail when geometry drifts: mismatched tip elevations at closure. Track cumulative Δ segment-by-segment, not just at closure.

Worked Example 3

Post-tensioning force loss at anchorage set

Advanced

Problem

Compute the tendon force immediately after seating at the live end.

Step-by-Step

\Delta f_{f} = f_{pj}\cdot (1 - e^{-(K\cdot \alpha + \mu \cdot L)}) = 202.5\cdot (1 - e^{-(0.20\cdot 0.15 + 0.0002\cdot 220)}) = 202.5\cdot (1 - e^{-0.074})

Result

\Delta f_{f} = 14.5 ksi

x = \sqrt{E_{p}\cdot \Delta _{a} / (\Delta f_{f} / L)} = \sqrt{28500\cdot 0.375 / (14.5/220)}

Result

x \approx 402 in \approx 33.5 ft

Design Verification

PTI/AASHTO limits f_po ≤ 0.70·f_pu = 189 ksi at anchorage AFTER seating. Here 198 ksi > 189 → jacking stress or set must be revised.

Discussion

Anchor set losses are frequently underestimated in the field. Verify Δ_a on-site with a dial indicator; a 1/16-in error on a 200-ft tendon can push you outside code limits.