Full-scale bridge design case files

V(ft/s) = V(knots) × 1.688

Result: 13.5 ft/s

AASHTO's impact-force formula is calibrated with V in knots directly, but ship kinetic energy checks and closure-time screening need ft/s, so the conversion is carried alongside.

Ps = 8.15 · V · √DWT

Result: 13,040 kip

The §3.14 empirical formula gives the equivalent static head-on force for a vessel of given deadweight tonnage striking the pier at speed V (knots); it governs pier stem and footing design directly.

KE = ½ · (DWT·2000) · V(ft/s)² / g

Result: 226,531,697 ft-kip

Comparing kinetic energy to the fender/pier absorbed energy shows whether the structure or a sacrificial fender system needs to absorb the impact — the basis for choosing pier geometry versus dolphins.

M_leaf = W · a

Result: 134,400 kip-ft

This is the overturning moment the counterweight and machinery must balance to hold the leaf in any partially-open position without runaway motion.

M_cw = Wcw · acw

Result: 53,100 kip-ft

The counterweight arm is intentionally short and heavy so the leaf can be balanced within the available pit depth; this moment must be within a few percent of the leaf's own moment.

BR = M_cw / M_leaf

Result: 0.3951 —

A properly balanced leaf sits at BR ≈ 1.00–1.05 (slightly leaf-heavy so the leaf seats firmly closed); values far from unity mean the operating machinery — not the girders — becomes the controlling design element.

AF = N · PA · PG · PC

Result: 0.4875 events/yr (×10⁻³ shown as decimal)

AF combines the number of vessel transits with the probabilities of aberrancy, geometric collision and pier collapse given a hit; a critical bridge like this one targets AF ≤ 0.0001, so the pier protection scheme is sized to that target, not to the raw impact force alone.

For this channel pier, which load case most often governs the foundation depth in the Potomac's soft sediments?

4 points

If your computed balance ratio (M_cw / M_leaf) comes out at 1.35, what does that indicate?

4 points

The computed AF exceeds the 0.0001 target for a critical bridge. What is the correct AASHTO §3.14 response?

4 points

Why is a bascule bridge described as 'two structures — a bridge and a machine'?

4 points

The bascule leaf girders are designated fracture-critical. What follows from that designation?

4 points

Kg ≈ n·(I + A·eg²) [approximated for a typical rolled/plate girder]

Result: 568,121 in⁴

Kg captures how the girder's bending stiffness relative to the deck spreads live load transversely; wider or deeper girders draw more load into a single line.

DF = 0.075 + (S/9.5)^0.6 · (S/L)^0.2 · (Kg / (12·L·ts³))^0.1

Result: 0.6193 lanes/girder

This is the governing §4.6.2.2.2b formula for interior girders with two or more design lanes loaded; because it was recalibrated for the post-widening spacing S, it directly reflects how adding lanes redistributes moment onto each girder line.

M_u = 1.75 · DF · M_LL · (1+IM/100)

Result: 2,667 kip-ft

The Strength I live-load factor (1.75) and the 33% dynamic load allowance (IM) are applied to the per-lane truck moment after it has been distributed to a single girder line by DF.

ADTT_SL = p · ADTT (p ≈ 0.80 for one lane each direction on a wide facility)

Result: 2,560 trucks/day

Fatigue truck frequency is based on the single-lane truck traffic, not total ADTT, since fatigue accumulates per girder from the trucks actually traveling in the lane over it.

N = 365 · n · ADTT_SL

Result: 934,400 cycles/yr

n is the number of stress-range cycles per truck passage (taken as 1.0 for this simply-continuous span length range per Table 6.6.1.2.5-2).

(ΔF)TH = 2.6 ksi (Category E′ per Table 6.6.1.2.5-3)

Result: 2.6 ksi

Category E′ covers the cover-plate-end detail — the worst common fatigue category in AASHTO — reflecting the severe stress concentration at a welded plate termination on a tension flange.

Years = A / (N · Δf³), A = 1.2×10¹⁰ ksi³ for Category E′

Result: 53.89 years

This finite-life check governs whenever the effective stress range exceeds (ΔF)TH; if Δf were below threshold the detail would have effectively infinite life instead, which is the key judgement call in the rubric below.

After widening added two more lanes, the interior girder DF increased. What is the direct engineering consequence?

4 points

Your computed effective stress range Δf is compared to (ΔF)TH = 2.6 ksi. If Δf is below (ΔF)TH, what does the finite-life calculation above actually tell you?

4 points

Why is the original cover-plate termination a Category E′ detail rather than something more forgiving like Category B?

4 points

What is the key philosophical difference between the original 1960s ASD design and today's LRFR evaluation of this same girder?

4 points

During staged deck replacement, why must each construction stage be analyzed as its own composite section rather than reusing the final-condition analysis?

4 points

VDZ = 2.5·V0·(V/VB)·ln(Z/Z0) [simplified as V·Kz below]

Result: 117.84 mph

The basic 3-second gust speed is adjusted upward for the exposure category and height above the water surface, since the deck of a 1,600-ft suspension span sits well above typical terrain-exposure assumptions.

PD = 0.00256 · Kz · G · Cd · V²

Result: 42.3 psf

This is the ASCE-derived base pressure equation adopted by §3.8: pressure scales with the square of wind speed, so the difference between a 100-mph and 130-mph design event is not linear — it is nearly a 70% increase in force.

w = PD · D

Result: 465.33 lb/ft

Multiplying the pressure by the exposed structural depth gives the distributed lateral load the towers, cables and wind-tongue bracing must ultimately resist.

W = w · L

Result: 744.53 kip

Summed over the full 1,600-ft main span, this is the total lateral demand the cable system and tower saddles must carry into the anchorages — illustrating why cable and tower sizing on a long suspension span is often wind-controlled, not traffic-controlled.

L/D

Result: 145.45 —

Tacoma Narrows had L/D ≈ 350 with a shallow plate-girder deck; modern practice treats L/D above roughly 200 combined with a solid (non-truss) deck as a flag for detailed aeroelastic study, since deck torsional stiffness scales poorly with span growth.

B/D

Result: 3.09 —

A low B/D (narrow, deep-relative deck) is more prone to torsional flutter; a stiffening truss deck like the 1952 span's open-grid truss cross-section behaves very differently from a shallow plate-girder box of the same width.

FSI = (L/D) / (B/D) = L/B

Result: 47.06 —

This ratio of span to deck width is a coarse, first-pass screening number used to decide whether a section-model wind-tunnel study is warranted before committing to a final deck cross-section — it is not a substitute for the actual aeroelastic analysis, only a trigger for ordering one.

On this 1,600-ft suspension main span, which load type most often governs cable and tower sizing?

4 points

Your computed L/D ratio is well above 200 and the deck uses an open-truss stiffening system rather than a shallow solid girder. What should this combination trigger?

4 points

The 1952 and 1973 spans sit side by side under identical wind exposure. What does comparing them primarily teach?

4 points

Why is dehumidification identified as the highest-value single maintenance intervention for the main cables?

4 points

Why does replacing an open steel-grid deck with an orthotropic or lightweight-concrete deck matter specifically on the suspension unit?

4 points

An = Agross · (1 − section loss %)

Result: 16.28 in²

The rating is always computed on the section that exists today, not the drawing section — corrosion and pack rust between built-up plates reduce the effective area the rivets must transfer.

Pn = φy · Fy · An

Result: 510.38 kip

Yielding of the gross-to-net transition and rivet bearing/shear are both checked; this step gives the yielding-based capacity used as the baseline for the load rating factor.

N = 365 · n · ADTT_SL

Result: 346,750 cycles/yr

Riveted built-up members are checked as Category C or D details, which are more fatigue-resistant per cycle than modern welded cover plates, but the truss has already accumulated decades of cycles at this rate.

N_total = N · years in service

Result: 29,473,750 cycles

This is a coarse estimate assuming roughly constant traffic over the service life; real assessments would weight earlier decades' lower traffic more carefully, but it establishes the order of magnitude of cumulative damage.

(ΔF)TH = 10 ksi (Category C, riveted connection, per Table 6.6.1.2.5-3)

Result: 10 ksi

Riveted connections are typically classified Category C or D, both substantially more fatigue-tolerant than the E/E′ welded cover-plate details found on the same-era welded girders elsewhere in the network.

Years = [A/(N·Δf³)] − years already in service, A = 4.4×10¹⁰ ksi³ (Category C)

Result: 1,062 years

Subtracting years already in service from the total finite-life estimate gives the remaining service life at the detail if the measured stress range and traffic hold roughly constant going forward — a negative result signals the detail should already be in the infinite-life regime or under close monitoring.

RF = (Pn − γDC·DC) / (γLL·LL·(1+IM)) [simplified: RF ∝ Pn]

Result: 1.51 —

A simplified proxy rating factor (normalized against an assumed factored demand of 250 kip) shows whether the measured section loss has already eroded the member below RF = 1.0 for legal loads — the trigger for load posting or member replacement.

Why are riveted built-up members from the 1930s–40s often more fatigue-tolerant per cycle than welded cover-plate details from the 1960s–70s?

4 points

What is the technical basis for designating a truss tension member as fracture-critical?

4 points

Why does pack rust between built-up plates matter enough to be a primary inspection finding rather than a cosmetic note?

4 points

If your computed 'remaining years of finite fatigue life' comes out negative, what is the correct engineering interpretation?

4 points

Why is a lightweight or exodermic deck replacement described as 'buying' live-load capacity on this truss?

4 points

Fr1 = V1 / √(g·y1)

Result: 0.1978 —

The Froude number characterizes the balance between inertial and gravity forces in the approach flow, which directly controls how vigorously the flow can scour around an obstruction like a pier.

K2 = (cosθ + (L/a)·sinθ)^0.65

Result: 1.21 —

Even a small skew between the flow direction and the pier's long axis dramatically increases the effective obstruction width the flow sees, which is why K2 grows quickly with both angle and pier elongation.

K3 = 1.1 (small dunes, typical tidal/estuarine bed)

Result: 1.1 —

K3 accounts for the bedform regime; the tidal, sediment-laden C&D Canal environment is represented here by a small-dune bed condition, a common assumption absent site-specific bed survey data.

ys = 2.0·K1·K2·K3·a^0.65·y1^0.35·Fr1^0.43

Result: 15.62 ft

This is the standard HEC-18 clear-water/live-bed local pier scour equation; note it caps in practice at ys/a ≈ 2.4 for Fr1 ≤ 0.8, so the raw formula result should always be checked against that envelope for reasonableness.

Elev_scour = ys (measured from existing bed)

Result: 15.62 ft below mudline

This depth defines the new effective ground surface the foundation must be checked against for both bearing and lateral capacity — everything above this elevation is assumed to contribute no resistance during the design flood/tidal event.

Residual = TotalEmbedment − ys

Result: 22.38 ft

A positive residual embedment with adequate margin (engineers typically want several diameters/widths of pile or shaft still engaged below scour) confirms the foundation retains adequate bearing and lateral capacity in the scoured condition; a small or negative value means the foundation must be deepened or protected.

Exposure = ys − footingTop

Result: 9.62 ft

If this value is positive, the scour hole reaches below the top of the footing itself, meaning the footing is directly exposed to flow and must be checked for undermining, not just the piles/shafts beneath it — a materially more severe condition than pure pile-embedment loss.

The Chesapeake City replacement bridge set its piers back from the navigation channel entirely. How does this relate to the scour calculation above?

4 points

Your K2 factor grows quickly as the angle of attack θ increases, especially for an elongated pier (large L/a). What is the practical design implication?

4 points

Why is scour analysis at a tidal canal crossing like the C&D Canal treated differently from a typical riverine crossing?

4 points

If your 'footing exposure' step comes out positive (scour reaches below the top of footing), what is the correct engineering response?

4 points

The case's takeaway states 'the tie is the whole bridge.' How does that relate to the foundation scour check you just performed?

4 points