The deck is the part of the bridge that wears out first and gets replaced most, so its design is as much about durability as about strength. A cast-in-place concrete deck on girders is typically 200–250 mm thick, spans transversely between girders at 2–4 m, and cantilevers past the outer girder to carry the barrier.

barrierwheel loadgirders

AASHTO allows two design routes. The empirical method (9.7.2) relies on arching action between girders and simply prescribes isotropic reinforcement for decks within its limits; most highway decks qualify. The traditional (strip) method analyses a 1 m strip as a continuous beam for wheel loads and designs it as an RC slab; it is required for overhangs and for decks outside the empirical limits. Overhangs are designed for barrier collision loads as well as wheels, and usually govern the top transverse steel.

Precast full-depth deck panels with UHPC joints, and orthotropic steel decks on long-span and movable bridges, are the alternatives when speed or weight matters.

The empirical method has entry conditions (AASHTO 9.7.2.4): a deck at least 178 mm thick excluding any sacrificial wearing surface, made composite with its girders; an effective span-to-depth ratio between 6 and 18; an effective length of no more than 4.1 m; concrete of at least 28 MPa; and cross-frames or diaphragms throughout. Within them it prescribes four layers of isotropic reinforcement, 0.570 mm²/mm in each direction at the bottom and 0.380 mm²/mm at the top, at no more than 450 mm spacing.

The design of a pretensioned girder is a negotiation between two moments in its life. At transfer, the girder is young, the concrete is weak, and the prestress is at its highest: the bottom must not crush and the top must not crack, so strands are harped (deflected upward at the ends) or debonded near the ends to reduce the moment there. At service, decades later, the losses have taken their share and the full dead and live load is on: the bottom fibre tension is checked under Service III against the allowable, and this check, not strength, usually sets the number of strands.

Then strength: flexural resistance with the strand at its stress at ultimate, shear by the modified compression field theory (sectional model with β and θ), interface shear between girder and deck, and the anchorage zone at the ends. Camber is estimated for transfer and for erection, because a girder that arrives too high or too low costs haunch concrete or grinding.

Section families, AASHTO I-girders, bulb-tees, NU, Florida FIB, Washington WF, Korean PSC I, trade web thickness, bottom-flange strand capacity and stability during handling. Spliced girders with post-tensioning push precast concrete past 60 m.

A long girder also has to survive being lifted, hauled and set. A 45 m bulb-tee is slender sideways, is never perfectly straight, and hangs from lifting loops that let it roll. Mast's analysis (PCI Journal, 1989 and 1993) compares the girder's tendency to roll with its lateral stiffness, and the usual targets are a factor of safety of at least 1.0 against cracking and 1.5 against failure during lifting and hauling. Once set, girders are braced to each other or to the pier before the crane lets go, and stay braced until the diaphragms and deck are in.

A steel I-girder is designed twice: once as a bare steel section carrying the wet deck, and once as a composite section carrying everything after. The first case often governs. During the deck pour the top flange is in compression, unbraced except at cross-frames, and lateral-torsional buckling is the check; on curved or skewed bridges the pour sequence itself must be analysed.

Composite in positive bending, the section is usually compact and reaches its plastic moment. In negative bending over piers the bottom flange is in compression and the deck is cracked, so the section is treated as steel plus rebar, often noncompact, and the web may need longitudinal stiffeners. Shear is carried by the web, with transverse stiffeners allowing tension-field action.

What actually cracks steel bridges is fatigue at details: cross-frame connection plates, cover-plate ends, out-of-plane distortion at web gaps. The design rule is to choose a good detail category first and calculate stress ranges second. Steel tub (box) girders add torsional stiffness for curves and need internal bracing to hold their shape until the deck closes the section.

A narrow girder system can also buckle as a whole even when every girder is well braced to its neighbour: cross-frames stop the girders twisting relative to each other, not the unit rolling together. Yura and co-workers gave the system buckling moment of a twin-girder unit as M_gs = (π²sE/L²)√(I_yI_x), with s the girder spacing. It grows with the spacing and falls with the square of the span, so long, narrow two- or three-girder units, typical of staged construction and widenings, need a system check, plan bracing or another girder.

A balanced-cantilever box is a structure whose stress state depends on when each piece was cast. Cantilever tendons in the top slab hold the arms up; after closure, continuity tendons in the bottom slab carry the sagging moment; and creep then redistributes the moments for years, moving them from the built-as-cantilever pattern toward the built-in-one-piece pattern. Time-dependent analysis, stage by stage, is not optional.

The section itself is checked for longitudinal bending and shear, for transverse bending of the top slab as a frame, for torsion and distortion when loads are eccentric, and for the thermal gradient that can put more tension in the bottom slab than the traffic does. Diaphragms at piers transfer reactions and anchor tendons; deviators in externally post-tensioned boxes turn the tendons.

Precast segmental boxes use match-cast epoxy joints with shear keys; because there is no reinforcement across the joint, no tension is allowed there under service load, and the joint's durability depends on the tendon grout.

A stay is a bundle of individually sheathed, greased, galvanised strands inside a high-density polyethylene pipe, anchored with wedges in a socket at each end; a main cable is thousands of parallel wires. Both are designed for tension, but their real problems are fatigue and vibration.

Stay fatigue comes from live-load stress ranges at the anchorage; codes limit the stay to about 45–50% of ultimate under service load and require fatigue testing of the anchorage system. Vibration comes from wind, from rain running down the sheath in a rivulet that changes the aerodynamic shape (rain–wind vibration), and from parametric excitation by deck motion; the answers are helical fillets on the pipe, dampers at the deck anchorage, and cross-ties. Every stay is designed to be replaced under traffic.

A stay's own weight makes it sag, so its effective stiffness is lower than a straight bar's, the Ernst modulus, and the catenary geometry decides unstressed length, which matters for fabrication and for the construction sequence.

A bridge that is strong enough can still be uncomfortable or ugly. AASHTO's optional live-load deflection limits are span/800 for vehicles and span/1000 where there are pedestrians; many owners make them mandatory. Deflection is computed with the full width acting together and all lanes loaded.

Camber is the upward curve built into a girder so that it arrives flat under dead load. For prestressed girders it grows with time as creep acts on the prestress; for steel girders it is cut into the web. Getting it wrong shows immediately in the ride and in the deck thickness.

Footbridges have their own problem: people walk at 1.6–2.4 Hz and bridges with a vertical frequency in that range, or a lateral frequency near 1 Hz, can be driven into resonance, London's Millennium Bridge (2000) closed two days after opening for that reason. Design either keeps the frequencies out of the band or adds tuned mass dampers.

The guidance in numbers: the AASHTO Guide Specifications for the Design of Pedestrian Bridges (2009) ask for a fundamental vertical frequency above 3.0 Hz and a lateral one above 1.3 Hz, or a dynamic check. EN 1990 Annex A2 calls for a comfort check when the vertical frequency is below 5 Hz or the lateral and torsional ones below 2.5 Hz, and recommends maximum deck accelerations of 0.7 m/s² vertically and 0.2 m/s² horizontally in normal use, 0.4 m/s² horizontally in a crowd; the Sétra guide (2006) refines this into comfort classes. The Millennium Bridge reopened in 2002 after viscous and tuned mass dampers were fitted.

The two moments of section 6.2 are easier to remember with numbers in them. Take an interior AASHTO Type IV girder, 1,372 mm deep (A = 0.509 m², I = 0.1085 m⁴, centroid 0.628 m above the soffit, so S_b = 0.1728 m³ and S_t = 0.1460 m³), simply supported over 30 m at 2.4 m spacing under a 200 mm structural deck. The girder concrete reaches f′_ci = 40 MPa at transfer and f′_c = 55 MPa in service; the deck is 30 MPa. The strands are 15.2 mm low-relaxation (140 mm², f_pu = 1,860 MPa), jacked to 0.75 f_pu = 1,395 MPa. Compression is positive throughout.

Moments at midspan. Self-weight, 12.5 kN/m: 1,406 kN·m. Wet deck, haunch and forms, 14.0 kN/m carried by the bare girder: 1,575 kN·m. Barriers and other superimposed dead load, 5.0 kN/m on the composite section: 563 kN·m. One lane of HL-93 (the design truck with its 33% dynamic allowance, plus the 9.3 kN/m lane load) gives 3,781 kN·m, and the AASHTO distribution factor for this girder works out at 0.67 lanes, so M_LL+IM = 2,530 kN·m. With the deck transformed into girder concrete (n = 0.74), the composite section modulus at the soffit is S_bc = 0.265 m³.

Strand count from Service III. The loads put 2,981/0.1728 + (563 + 0.8 × 2,530)/0.265 = 17.3 + 9.8 = 27.0 MPa of tension into the bottom fibre. The limit for moderate exposure is 0.50√f′_c = 3.7 MPa, so the prestress must supply at least 23.3 MPa. Losses by the AASHTO approximate method (elastic shortening about 109 MPa, long-term about 165 MPa) leave f_pe ≈ 1,120 MPa, or 157 kN per strand. With the strand centroid 100 mm above the soffit (e = 0.528 m), each kilonewton of prestress gives 1/A + e/S_b = 5.02 kPa at the soffit. Thirty strands give 4,704 kN and 23.6 MPa, leaving a net tension of 3.4 MPa, which passes; twenty-eight would leave 5.0 MPa and fail. The strand count is settled.

Transfer. Just after release the strands are at about 1,275 MPa (P_i = 5,355 kN) and the concrete is only 40 MPa. At midspan the self-weight moment helps: the top is at +0.8 MPa and the bottom at 18.7 MPa, against a compression limit of 0.65 f′_ci = 26 MPa. At the girder end there is almost no self-weight moment, and with all strands straight the top would be at −8.8 MPa, more than six times the 1.4 MPa allowed without bonded reinforcement, while the bottom would reach 26.9 MPa. Harping 8 strands up to 1.15 m above the soffit at the ends raises the end strand centroid to 0.38 m (e = 0.248 m) and turns these into +1.4 and 18.2 MPa. Debonding alone would not do it here: dropping 8 strands at the end still leaves −6.5 MPa at the top, which is why debonding is normally paired with a few top strands.

Strength. M_u = 1.25 (1,406 + 1,575 + 563) + 1.75 × 2,530 = 8,860 kN·m. The neutral axis lies 148 mm down, inside the deck, the strand reaches f_ps = 1,808 MPa, and φM_n = A_psf_ps(d_p − a/2) = 4,200 mm² × 1,808 MPa × (1,472 − 62) mm ≈ 10,700 kN·m, a margin of 21%. Strength was never in doubt: Service III set the strands and transfer set the end detail. A full design adds the hold-down points, the end of the transfer length (60 strand diameters, about 0.9 m) rather than the bare end, the haunch and deck shrinkage, but the order of the checks stays the same.

A deck that merely rests on its girders and a deck tied to them are two different structures. Loose, slab and girder bend separately about their own axes and slip along the interface. Tied, they bend as one section with a single neutral axis high in the girder: in the example of 6.7 the deck raises the section modulus at the soffit from 0.173 to 0.265 m³, and on a steel girder the gain is larger still, because the slab does the work of a heavy top flange. The tie has to carry the horizontal shear at the interface, which is simply the rate at which the force in the slab changes along the span. AASHTO designs bridge girders for full composite action; the partial shear connection common in buildings is not used.

How much deck counts. AASHTO 4.6.2.6 takes the full tributary width for most girders: half the distance to each neighbouring girder, or the overhang at an edge girder. EN 1994-2 instead adds L_e/8 each side, L_e being the distance between points of zero moment, so the width shrinks over interior supports where shear lag concentrates the stress near the webs.

Studs on steel girders. Headed studs are welded to the top flange with a stud gun. AASHTO 6.10.10.4.3 gives the nominal resistance of one stud as Q_n = 0.5 A_sc√(f′_cE_c) ≤ A_scF_u, with φ_sc = 0.85. For a 22 mm stud (A_sc = 380 mm², F_u = 415 MPa) in a 35 MPa deck (E_c ≈ 28,000 MPa) the concrete term is 187 kN and the steel cap 158 kN, so φQ_n = 134 kN. Between the point of maximum positive moment and the support the studs must develop the smaller of the slab's crushing force, 0.85 f′_cb_st_s, and the steel section's yield force. For a girder with 30,000 mm² of 345 MPa steel under a 2.7 m by 220 mm slab, the steel governs at 10,350 kN against 17,700 kN for the slab, and 78 studs are needed in each shear span, for example 26 rows of three.

Fatigue sets the pitch. Under repeated wheel loads a stud is far weaker than its static strength suggests. For infinite life AASHTO allows Z_r = 38d² newtons per stud (d in mm), about 18 kN for the 22 mm stud, a seventh of its factored static resistance. The pitch then follows from p ≤ nZ_rI/(V_srQ), with n the studs per row, V_sr the fatigue shear range and Q the first moment of the transformed slab about the neutral axis. In practice fatigue fixes the spacing and strength only confirms the total. Detailing rules keep the stud working: height at least four diameters, pitch at least six, transverse spacing at least four, and 50 mm each of penetration into the deck and cover over the head.

Concrete girders. Precast girders have no studs: the stirrups are left projecting into the deck and the girder top is roughened. The interface is checked by shear friction (AASHTO 5.7.4), v_ni = cA_cv + μ(A_vff_y + P_c); for a deck cast on a girder roughened to an amplitude of 6 mm, c = 1.9 MPa and μ = 1.0. A top trowelled smooth in the yard loses most of the cohesion term, so the roughness is checked before the deck is cast.

Time. Superimposed dead load acts on a deck that creeps away from it, so it is resisted with a long-term modular ratio (3n in AASHTO, n_L = n₀(1 + ψ_Lφ_t) in EN 1994-2); using short-term properties for permanent load understates the steel stresses.

Precast girders arrive as simple spans, and a line of simple spans needs a joint at every pier. Joints leak, and the water and de-icing salt that pass through them destroy bearings, pier caps and girder ends. The standard remedy is to make the girders continuous for superimposed load. They are erected simply supported; a cast-in-place continuity diaphragm is placed between the girder ends at each pier, with the deck or just before it; and from then on barriers, surfacing and traffic act on a continuous beam. Girder and deck weight are carried by simple spans, everything after by a continuous one.

Over the pier, deck reinforcement in tension and the girder bottom flanges in compression resist the negative moment. The gain is at midspan: for a uniform load on one of two equal continuous spans the peak positive moment is about 0.096 wL², against 0.125 wL² for a simple span, a reduction of nearly a quarter in what is often the largest single moment component. The bottom flange near the pier, already precompressed by the strands, has to be checked for the extra compression.

The difficulty is time. The girders keep changing after the connection is made: creep under the prestress makes them camber upward, and the deck shrinks relative to the older girder. A continuous beam restrains both, and girder creep usually wins, producing a positive restraint moment at the pier that opens a crack at the bottom of the diaphragm. If the crack opens far enough, a bridge designed as continuous behaves partly as simple spans under live load. The effect, studied in detail in NCHRP Report 519 (2004), is why AASHTO 5.12.3.3 (5.14.1.4 before 2017) requires a positive moment connection at the bottom of the diaphragm: strands extended from the girder ends and bent up into the diaphragm, or bars projecting from the girder ends.

AASHTO offers a simple route and an analytical one. The simple route is to provide a positive moment connection with a resistance of at least 1.2 M_cr and to require, in the contract documents, that the girders be at least 90 days old when continuity is made; by then roughly 60% of their creep and 70% of their shrinkage has taken place. The analytical route is to compute the restraint moments by time-dependent analysis, and to treat the connection as fully effective only if the bottom of the diaphragm stays in compression under superimposed permanent load, settlement, creep, shrinkage, half the live load and the temperature gradient. Where a 90-day wait clashes with the programme, the analysis often costs less than storing girders.

A lighter variant, the link slab, makes only the deck continuous. The girders stay simply supported on their own bearings, and a short length of deck over the pier, debonded from the girder tops, is reinforced to follow the end rotations without wide cracks. It removes the joint without the restraint moments and suits the rehabilitation of old simple-span bridges.

A bridge is skewed when its supports are not square to its axis. The skew angle θ is measured between the support line and the normal to the girders, so a square bridge has θ = 0. Up to about 20° a skewed bridge behaves much like a square one. Beyond that the load seeks the shortest path to the supports, across the obtuse corners: reactions and shears rise there, the acute corners lighten and can lift off, midspan moments fall a little, and the girders twist as their ends rotate about a skewed line.

AASHTO captures the first-order effects with correction factors on the distribution factors. Put the girder of 6.7 on a 45° skew and the moment factor becomes 1 − c₁(tan θ)^1.5 = 0.91, while the shear in the obtuse-corner girder is multiplied by 1 + 0.20(Lt_s³/K_g)^0.3 tan θ = 1.15: nine percent less moment, fifteen percent more shear. At large skews, or outside the formulas' limits, a grillage or finite-element model is the right tool.

Steel girders on a skew add a geometric problem. Under dead load each girder deflects by a different amount at a given cross-frame line, so the girders roll sideways (layover) unless the cross-frames are detailed to fit a chosen deflected state: no-load fit, steel dead load fit or total dead load fit. Current US guidance generally prefers steel or total dead load fit for straight skewed bridges, so that the webs end plumb under the final load, and no-load or steel dead load fit for curved ones, so that erection stays manageable. Cross-frames run along the skew up to 20° and square to the girders beyond it (AASHTO 6.7.4.2). Near an obtuse corner, a cross-frame tying a stiff support to a flexible midspan point attracts large forces and is often omitted or moved.

Curved girders carry torsion as well as bending. In a curved steel I-girder the flange forces change direction at each cross-frame, and their radial component bends the flange sideways between cross-frames. The V-load method estimates the lateral flange moment as M_lat ≈ Mℓ²/(10RD), with M the girder moment, ℓ the cross-frame spacing, R the radius and D the web depth. A 2 m deep girder on a 200 m radius carrying 10,000 kN·m, with cross-frames at 6 m, gets 90 kN·m of lateral moment in each flange, 54 MPa in a 500 × 40 mm flange. AASHTO combines the two stresses by the one-third rule, f_bu + f_ℓ/3 ≤ φ_fF_n, and caps f_ℓ at 0.6 F_y. Curved I-girders cannot stand alone during erection and go up in braced pairs or on temporary supports; tub girders, with their closed section, suit tight curves better. In curved concrete boxes the tendons press toward the centre of curvature with a force of P/R per metre, which web reinforcement must hold so that a tendon cannot break out through the side of the web.

Put one loaded lane near the edge of a box girder and the load does three things at once. Part of it bends the box as a beam, shared by both webs. Part of it twists the box, and a closed section resists twisting with a shear flow q that runs around the cell. The rest tries to change the shape of the cross-section, racking the rectangle toward a parallelogram: distortion. The first two are what boxes are good at; the third is what diaphragms are for.

Torsion. For a single closed cell Bredt's formulas apply: q = T/(2A₀) and J = 4A₀²/Σ(s/t), where A₀ is the area enclosed by the wall centrelines and s/t is the length of each wall divided by its thickness. Take a concrete box with webs 6.0 m apart and 2.5 m between slab centrelines, a 250 mm top slab, a 200 mm bottom slab and 400 mm webs. Then A₀ = 15 m², Σ(s/t) = 66.5 and J = 13.5 m⁴. The same walls opened into a U, with J = Σbt³/3, give 0.15 m⁴: closing the cell makes the section about ninety times stiffer in torsion. A torque of 6,000 kN·m produces q = 200 kN/m, a shear stress of 0.5 MPa in a 400 mm web, added to the vertical shear in one web and subtracted in the other. The critical web is designed for both together, with longitudinal steel for the axial component of the torsion. The torque must also reach the ground: a box on single bearings at its intermediate piers needs pairs of bearings, or a monolithic connection, somewhere along its length, and a curved box on single bearings can lift off its inner supports.

Distortion. If nothing holds the corners, the eccentric load deforms the cross-section. The walls bend transversely as a frame, and because the distortion varies along the span the walls also warp, picking up longitudinal distortional warping stresses. Between diaphragms the box behaves like a beam on an elastic foundation, the foundation being the frame stiffness of the cross-section. Concrete boxes have walls thick enough that the frame action usually suffices, and diaphragms are placed only at supports, deviators and anchorages. Thin-walled steel boxes are different: internal cross-frames at intervals along the span keep the shape, and their spacing is one of the main design decisions.

During construction a steel tub is an open U until the deck hardens and closes it, and as the numbers above show, an open section has a small fraction of the torsional stiffness of the closed one. A horizontal truss of top lateral bracing between the top flanges makes it a quasi-closed section for the wet-deck stage; omitting it, or making it too light, is a known cause of excessive twist and instability during the deck pour.

An orthotropic deck is a steel plate stiffened by longitudinal ribs and transverse floor beams, so that its stiffness differs in the two directions (orthogonal-anisotropic, shortened). The same plate does three jobs: it is the top flange of the main girders or box, the deck spanning between floor beams together with its ribs, and the plate spanning between ribs under each wheel. With its surfacing it weighs roughly half as much as a concrete deck of the same width, which is why it is the deck of most long-span suspension and cable-stayed bridges, of movable spans, and of old bridges re-decked to lose weight; the Golden Gate Bridge's concrete deck was replaced by an orthotropic one in the 1980s.

Typical geometry. A deck plate of 14–18 mm; closed trapezoidal ribs about 300 mm wide and 250–350 mm deep, 6–10 mm thick, at about 600 mm centres; floor beams every 3–5 m, with cut-outs through which the ribs run continuously; 40–80 mm of asphalt surfacing. Early decks with 10–12 mm plates were economical in steel and expensive in repairs.

Fatigue is the design. Every axle that passes is a full stress cycle at the details under the wheel, and a heavy-traffic lane sees tens of millions of them. The crack locations are few and well documented: the rib-to-deck weld, where cracks start at the root or the toe and grow into the deck plate or up the rib wall; the rib-to-floor-beam connection and the edges of the cut-outs, where the ribs rotate under load and pry against the floor-beam web; the field splices of the ribs; and the splices of the deck plate. A root crack growing into the deck plate is the dangerous one: it cannot be seen from below until it is through, and often shows first as failing surfacing.

Details are now chosen by test and confirmed by analysis. Current US guidance regards 16 mm as the practical minimum deck plate under truck wheels, and asks for rib-to-deck welds with deep penetration (some recent Chinese decks are welded from both sides by robots working inside the rib), generous cut-out shapes and bolted rib splices. AASHTO 9.8.3, aligned with the FHWA Manual for Design, Construction, and Maintenance of Orthotropic Steel Deck Bridges (2012), recognises three design levels: Level 1 uses details whose fatigue resistance has been proven by testing, and Levels 2 and 3 add progressively more refined analysis of local stresses, up to a 3D finite-element model of the panel. In Eurocode practice EN 1993-2 Annex C recommends detail geometry and EN 1993-1-9 gives the fatigue categories.

Surfacing matters more than it looks. Bonded asphalt spreads the wheel and stiffens the plate, but its stiffness falls steeply with temperature: in a Gulf summer, with the surface past 60 °C, the plate carries the wheel almost alone. The Netherlands, which found fatigue cracks in heavily trafficked motorway decks in the late 1990s, renovated several of them with a bonded high-strength concrete overlay that greatly reduced the local stress ranges, and thin UHPC overlays now do the same job elsewhere.

In a girder bridge the dead-load moments follow from statics. In a cable-stayed bridge the designer chooses them. The stays are supports whose forces can be set at will, so the engineer picks a target permanent state, usually a deck and tower that carry their dead load with small bending moments, the deck at its design profile and the tower plumb, and then finds the stay forces that produce it. A common start makes the deck moments match those of a continuous beam on rigid supports at the anchorages, then refines the forces to minimise bending in deck and tower.

A first estimate. For a composite deck weighing 300 kN/m with stays in two planes at 12 m spacing, each stay carries about 300 × 12/2 = 1,800 kN vertically. At 30° to the horizontal the stay force is 1,800/sin 30° = 3,600 kN, and its horizontal component, about 3,100 kN, enters the deck as compression. Summed stay by stay toward the tower, these components make the deck near the tower a heavily loaded column whose stability has to be checked. With 15.7 mm strands (150 mm², 279 kN breaking load) and the common service limit of 45% of the guaranteed ultimate strength, one strand is good for 126 kN; if live load and temperature add a quarter to the dead-load force, the stay needs about 36 strands and gets a standard 37-strand anchorage.

Construction stages. The bridge is built as a growing cantilever: erect a segment, install and stress its stay, advance the traveller, repeat. Every stage has its own stresses and geometry, and some, such as the longest cantilever before closure in a storm, govern parts of the deck and tower. Installation forces are found by backward analysis, dismantling the finished bridge stage by stage in the model, and checked by a forward analysis that includes creep and shrinkage for concrete decks, which a backward analysis cannot reproduce exactly. One property simplifies control: in a linear elastic structure the final state depends on the unstressed lengths of the stays and the stress-free shapes of the segments, not on the order in which they were stressed. Fabricating stays to their unstressed lengths, and checking forces by lift-off tests or by the stay's fundamental frequency (T = 4mL²f₁², with m the mass per metre), is the basis of geometry control. Surveys are taken at night or at dawn, when the structure is at a uniform temperature.

Sag and stiffness. The Ernst modulus of section 6.5, E_eq = E/[1 + (γL_h)²E/(12σ³)], shows why the stress level matters. For a stay with a horizontal projection of 200 m and an effective unit weight of 97 kN/m³ (strand, sheath and filler, per unit of steel area), the reduction in stiffness is under 2% at 700 MPa but nearly a fifth at 300 MPa. Construction-stage models must use the stress-dependent value.

Losing a stay. Every stay is designed to be replaceable, and the structure must also survive losing one suddenly. The PTI stay-cable recommendations (DC45.1) require stability with any one stay lost, with a dynamic amplification factor of 2.0 on its force when the event is analysed statically.