Steel and Composite Bridges

Introduction

Steel bridges combine high strength-to-weight ratio, prefabrication, rapid erection and adaptability to long spans. Their design is nevertheless governed by more than nominal material strength. Thin plates can buckle before yielding; repeated traffic loading can initiate fatigue cracks; welded details may possess fracture-sensitive defects; and incomplete systems can be unstable during erection. Steel–concrete composite construction adds further issues, including staged loading, effective slab width, longitudinal shear transfer, deck cracking and time-dependent concrete behaviour.

The engineer must therefore treat strength, stability, fatigue, fracture, constructability, durability and inspection as an integrated design problem. Numerical values in this chapter are illustrative. Final design must follow the governing bridge code, such as AASHTO LRFD, Eurocodes or the applicable national standard, including its resistance factors, partial factors and detailing rules.

Learning Objectives

After studying this chapter, readers should be able to:

• select suitable plate-girder, truss, box-girder and composite bridge forms;
• evaluate bending, shear, local buckling and lateral-torsional buckling;
• design truss members and steel connections for yielding, buckling and fracture;
• analyse thin-walled box girders under torsion;
• calculate composite-section properties using the correct modular-ratio transformation;
• determine longitudinal shear flow and preliminary shear-connector spacing;
• assess fatigue damage and fracture-sensitive details;
• establish bracing and erection-stability requirements; and
• develop corrosion-protection and life-cycle inspection strategies.

1. Structural Forms and Design Basis

1.1 Plate-girder bridges

A plate girder is assembled from flange plates and a relatively slender web. Flanges principally resist bending, while the web transfers shear and maintains flange separation. Intermediate and bearing stiffeners may control web buckling and transmit concentrated forces. Plate girders are particularly effective for short-to-medium and many medium-long spans where rolled sections are inadequate.

1.2 Truss bridges

A truss carries global bending through axial forces in its chords and shear through diagonal and vertical members. Trusses usually obtain structural efficiency from substantial structural depth; they should not generally be described as shallower than comparable solid girders. Their disadvantages include numerous fatigue-sensitive connections, maintenance-intensive surfaces and possible member redundancy concerns.

1.3 Box-girder bridges

Closed steel boxes have high torsional rigidity and are advantageous for curved, skewed and wide-deck bridges. Single-cell and multicell arrangements are used. Design must address plate buckling, shear lag, distortional deformation, warping, diaphragm forces and the stability of open U-shaped sections before deck completion.

1.4 Steel–concrete composite bridges

In positive-moment regions, a concrete deck connected to steel girders commonly resists compression while the steel girder carries most tension. In continuous bridges, negative-moment regions may place the slab in tension and the steel lower flange in compression. Reinforcement, cracking, local buckling and construction sequence then become critical.

1.5 Limit states

A complete design normally investigates:

• ultimate strength: yielding, buckling, rupture and connection failure;
• serviceability: deflection, vibration, deck cracking and permanent deformation;
• fatigue and fracture;
• accidental actions, where required;
• erection and temporary states; and
• durability throughout the intended service life.

Load combinations, dynamic allowances, resistance factors and material properties must be obtained from the governing code.

2. Analysis and Construction Staging

Bridge analysis should represent geometry, stiffness, boundary conditions and load introduction realistically. Global models may use line girders, grillages, space frames, shells or finite elements. Local shell models are appropriate around diaphragms, cross-girders, openings and concentrated loads.

Composite stiffness exists only after the concrete has developed adequate strength and shear connection. A typical staged analysis includes:

1. bare-steel self-weight and wet-concrete loading;

2. activation of composite action;

3. superimposed dead loads;

4. shrinkage, creep and temperature effects; and

5. traffic and other transient actions.

Camber and locked-in stresses depend on the erection method. Bearings, cross-frames and diaphragms should not be idealised as perfectly rigid unless justified. Geometric imperfections and second-order effects are needed where stability is sensitive to deformation.

3. Steel Plate-Girder Design

3.1 Preliminary proportioning

The required girder depth is selected by balancing steel weight, clearance, web slenderness, fabrication, transport and deflection. A deeper girder generally reduces flange force but increases web area and may complicate transport. Flange transitions should be gradual and checked for fatigue.

The elastic bending stress is

σ = M y/I = M/W,

where M is bending moment, I is the second moment of area, y is the distance from the neutral axis and W = I/y is the elastic section modulus. This equation predicts stress but is not itself a complete resistance check. Compactness, lateral restraint, residual stress and local buckling determine whether yield, plastic or reduced resistance may be used.

3.2 Web shear and shear buckling

The average web shear stress may be estimated as

τ = V/(d_w t_w),

where V is shear, d_w is clear web depth and t_w is web thickness. More accurately, shear stress follows VQ/(It), especially near flange–web junctions.

For an isotropic rectangular web panel simply supported along its boundaries, the elastic shear-buckling stress is

τ_cr = k_τ[π²E/{12(1 − ν²)}](t_w/d_w)²,

where E is Young’s modulus, ν is Poisson’s ratio and k_τ is the shear-buckling coefficient. For a panel aspect ratio a/d_w,

• k_τ = 5.34 + 4/(a/d_w)² for a/d_w ≥ 1;
• k_τ = 4 + 5.34/(a/d_w)² for a/d_w < 1.

These expressions assume ideal plates with appropriate simple supports. Actual design resistance includes imperfections, residual stress, yielding, stiffener behaviour and, where permitted, post-buckling tension-field action. Tension-field resistance depends on anchorage by flanges and stiffeners and must not be assumed without satisfying the code’s boundary requirements.

3.3 Bending, local buckling and lateral-torsional buckling

Compression flanges can buckle locally between the web and free edge or buckle laterally with twist of the whole girder. Lateral-torsional resistance depends on unbraced length, moment gradient, torsional and warping stiffness, load height and restraint conditions. A short formula calibrated for a doubly symmetric, simply supported beam must not be applied indiscriminately to monosymmetric or continuously restrained girders.

Design proceeds by:

1. classifying flange and web slenderness;

2. determining gross, effective or reduced section properties;

3. evaluating cross-sectional bending resistance;

4. evaluating lateral-torsional buckling resistance for each unbraced segment;

5. checking combined bending and shear using the prescribed interaction rule; and

6. checking fatigue, deflection and construction stages.

3.4 Stiffeners and concentrated loads

Bearing stiffeners transfer reactions and may act as columns comprising stiffener plates plus an effective web strip. Intermediate transverse stiffeners reduce web-panel dimensions. Longitudinal stiffeners can increase buckling resistance in very deep webs. Checks include stiffener yielding, local buckling, effective-length buckling, weld transfer and web crippling or patch loading.

Worked Example 1: Plate-girder stresses and web buckling

A welded symmetric girder has a 1,800 mm × 16 mm web and two 500 mm × 30 mm flanges. Steel properties are E = 200,000 MPa, ν = 0.30 and f_y = 355 MPa. The transverse-stiffener spacing is 2,700 mm. Applied actions are M = 9.5 MN·m and V = 2.8 MN.

The overall depth is 1,860 mm. About the horizontal centroidal axis,

I_web = 16(1,800)³/12 = 7.776 × 10⁹ mm⁴.

The distance from the section centroid to each flange centroid is 915 mm. Thus,

I = 7.776 × 10⁹ + 2[500(30)³/12 + (500 × 30)(915)²]

= 32.895 × 10⁹ mm⁴.

The elastic section modulus is

W = I/930 = 35.371 × 10⁶ mm³.

Therefore,

σ = 9.5 × 10⁹/(35.371 × 10⁶) = 268.6 MPa.

This is below f_y, but lateral-torsional and local-buckling checks remain necessary.

The average web shear stress is

τ = 2.8 × 10⁶/(1,800 × 16) = 97.2 MPa.

Here a/d_w = 2,700/1,800 = 1.5, giving

k_τ = 5.34 + 4/(1.5)² = 7.118.

Hence,

τ_cr = 7.118[π²(200,000)/{12(1 − 0.3²)}](16/1,800)²

= 101.7 MPa.

The demand is close to the ideal elastic buckling stress. This does not establish adequate design resistance; imperfections, yielding and code resistance factors must be included. The result signals that web-buckling design and stiffener adequacy are controlling issues.

4. Truss Design

4.1 Global action and member forces

Ideal pin-jointed analysis gives axial member forces, but real trusses also develop secondary bending from joint rigidity, eccentricity, member self-weight and floor-beam framing. Gusset plates and connection centrelines should be arranged to minimise eccentricity.

Tension members are checked for gross-section yielding, net-section fracture, block shear and fatigue. Compression members are checked for flexural, torsional or flexural–torsional buckling, local buckling and connection eccentricity.

The Euler elastic buckling stress is

f_e = π²E/(KL/r)²,

where K is the effective-length factor, L is member length and r is the relevant radius of gyration. Euler stress is an elastic reference value, not the design resistance of an imperfect structural member. Code column curves reduce resistance for residual stresses and initial crookedness.

Worked Example 2: Compression diagonal

A truss diagonal carries 3.20 MN compression. Its area is 15,000 mm², effective length KL = 8,000 mm and radius of gyration r = 145 mm. Take E = 200,000 MPa and f_y = 355 MPa.

KL/r = 8,000/145 = 55.17,

f_e = π²(200,000)/(55.17)² = 648.5 MPa.

The nondimensional slenderness is

λ̄ = √(f_y/f_e) = √(355/648.5) = 0.740.

For illustration, using a common code-type buckling curve with imperfection factor α = 0.34,

Φ = 0.5[1 + α(λ̄ − 0.2) + λ̄²] = 0.865,

χ = 1/[Φ + √(Φ² − λ̄²)] = 0.761.

The nominal reduced resistance is

N_b = χAf_y = 0.761(15,000)(355) = 4.05 MN.

It exceeds 3.20 MN before application of the governing resistance factor. The curve and factor must match the applicable code and cross-section type. Connection eccentricity and local buckling also require verification.

5. Bolted and Welded Connections

Connections should be designed from the force path rather than solely from nominal member forces. Relevant limit states include bolt shear, bearing, slip, tear-out, net-section rupture, block shear, weld rupture, base-metal failure, prying and gusset buckling.

High-strength bolts may be designed as bearing-type or slip-resistant connections. Slip resistance is especially important where movement would damage alignment or fatigue performance. Faying-surface preparation, bolt pretension and installation inspection are essential.

For a simplified single-shear bolt model, a nominal shear value sometimes used for preliminary calculation is

R_n = 0.6F_ub A_b,

where F_ub is bolt ultimate strength and A_b is the applicable shank or threaded area. The governing code may prescribe different coefficients and must also be used for bearing, spacing, edge distance and resistance factors.

Worked Example 3: Preliminary bolt-group capacity

Eight M24 property-class 8.8 bolts have tensile-stress area A_b = 353 mm² and F_ub = 800 MPa. Assuming one shear plane through the threaded area and resistance factor φ = 0.75,

φR_n per bolt = 0.75(0.6)(800)(353) = 127.1 kN.

The group shear resistance is

8(127.1) = 1.017 MN.

It exceeds a 0.90 MN concentric shear demand. This conclusion remains conditional on bearing, tear-out, block shear, slip requirements and nonuniform force distribution.

Fillet-weld strength is based on the effective throat, while complete-joint-penetration welds may develop the connected material when properly qualified. Weld terminations should be placed away from high stress ranges where practicable. Quality assurance includes approved procedures, qualified personnel and appropriate nondestructive examination.

6. Box Girders and Torsion

For a thin-walled, single-cell closed section under Saint-Venant torsion, Bredt’s relation gives shear flow

q = T/(2A_m),

where T is torque and A_m is the area enclosed by the wall median line. Local shear stress is

τ = q/t.

For multicell boxes, compatibility of twist and equilibrium determine the individual cell flows. Curvature, support eccentricity and asymmetric loading also cause distortion and warping, requiring diaphragms or cross-frames.

Worked Example 4: Box-girder torsion

A single-cell box encloses a median-line area of 4.0 × 2.5 = 10.0 m² and carries T = 18 MN·m. With a uniform 20 mm wall thickness,

q = 18/(2 × 10) = 0.90 MN/m = 900 N/mm,

τ = 900/20 = 45 MPa.

This is the Saint-Venant torsional shear only. Bending shear, distortion, plate buckling and diaphragm forces must be superimposed. During erection, an open U-girder has much lower torsional stiffness than the completed closed composite system and normally requires temporary bracing.

7. Steel–Concrete Composite Design

7.1 Modular-ratio transformation

Under linear-elastic behaviour and full interaction, steel and concrete at the same level have equal strain. Let

n = E_s/E_c.

When concrete is transformed to an equivalent steel section, its area and second moment are divided by n:

A_c,transformed = A_c/n,

I_c,transformed = I_c/n.

This follows because E_s(A_c/n) = E_cA_c. Multiplying concrete properties by n would be incorrect for transformation to steel. Conversely, transforming steel to concrete requires multiplication of steel properties by n.

The effective slab width must be determined from the applicable code to represent shear lag. Separate modular ratios may be required for short-term and long-term loading.

Worked Example 5: Correct transformed composite section

A steel girder has A_s = 30,000 mm² and I_s = 20.0 × 10⁹ mm⁴ about its own centroid. A 2,500 mm effective-width slab is 250 mm thick. The slab centroid is 1,000 mm above the steel centroid. Take E_s = 200 GPa and E_c = 32 GPa.

n = 200/32 = 6.25.

The concrete area transformed to steel is

A′_c = (2,500 × 250)/6.25 = 100,000 mm².

The transformed neutral axis above the steel centroid is

ȳ = 100,000(1,000)/(30,000 + 100,000) = 769.23 mm.

The slab’s transformed centroidal inertia is

I′_c = [2,500(250)³/12]/6.25 = 0.5208 × 10⁹ mm⁴.

Therefore,

I_tr = 20.0 × 10⁹ + 30,000(769.23)²

+ 0.5208 × 10⁹ + 100,000(1,000 − 769.23)²

= 43.598 × 10⁹ mm⁴.

For a positive composite moment of 7.0 MN·m, assume the bottom steel fibre is 900 mm below the steel centroid. Its tensile stress is

σ_s = 7.0 × 10⁹(769.23 + 900)/(43.598 × 10⁹)

= 268.0 MPa.

The slab top is 1,125 mm above the steel centroid, or 355.77 mm above the transformed neutral axis. The steel-reference transformed stress there is

σ_ref = 7.0 × 10⁹(355.77)/(43.598 × 10⁹) = 57.1 MPa.

The actual concrete stress is

σ_c = σ_ref/n = 57.1/6.25 = 9.14 MPa compression.

These stresses apply to the stated elastic, uncracked, fully composite stage. Bare-steel stresses from loads applied before composite action must be added separately.

7.2 Shear connectors

Headed studs transfer longitudinal shear and resist separation between slab and girder. Connector resistance may be controlled by stud failure, concrete crushing or splitting. Fatigue often controls spacing even when static strength is adequate.

The elastic longitudinal shear flow at an interface is

q_L = VQ/I_tr,

where V is vertical shear and Q is the first moment of the transformed area above or below the interface about the transformed neutral axis.

Using the preceding section under V = 2.0 MN,

Q = 100,000(1,000 − 769.23) = 23.077 × 10⁶ mm³,

q_L = 2.0 × 10⁶(23.077 × 10⁶)/(43.598 × 10⁹)

= 1,059 N/mm.

If two studs per transverse row each provide 100 kN design resistance, the strength-based maximum spacing is

s = 2(100,000)/1,059 = 189 mm.

A preliminary spacing of 175 mm satisfies this simplified strength calculation. Minimum and maximum spacing, fatigue, deck reinforcement, stud group effects and constructability must also be checked.

7.3 Negative moment and deck behaviour

In continuous bridges, the deck over internal supports is commonly in tension. Analysis may use cracked-section properties, effective reinforcement and tension-stiffening rules prescribed by the code. Shear connectors may remain necessary for force transfer even where concrete tension is neglected. Concrete shrinkage and thermal gradients can produce tensile stress independently of traffic moment.

8. Fatigue and Fracture

Fatigue assessment is based on stress range rather than maximum stress alone. Detail categories represent weld geometry, attachment type and expected crack initiation location. The nominal-stress method is suitable for classified details; hot-spot or fracture-mechanics approaches may be required for unusual geometry.

Miner’s cumulative damage rule is

D = Σ(n_i/N_i),

where n_i is the applied number of cycles in range i and N_i is the cycles to failure at that range according to the applicable S–N curve. Conventionally, D ≤ 1 is required, subject to code-specific rules.

Worked Example 6: Fatigue accumulation

For an illustrative detail, suppose the S–N relation in the relevant range is

N = 2.0 × 10⁶(80/Δσ)³,

with Δσ in MPa. The detail experiences 2.0 million cycles at 60 MPa and 5.0 million cycles at 40 MPa.

At 60 MPa,

N_1 = 2.0 × 10⁶(80/60)³ = 4.741 × 10⁶,

n_1/N_1 = 0.4219.

At 40 MPa,

N_2 = 2.0 × 10⁶(80/40)³ = 16.0 × 10⁶,

n_2/N_2 = 0.3125.

Thus D = 0.7344. The simplified spectrum satisfies D ≤ 1, although remaining life, inspection uncertainty and future traffic growth should be considered.

Fracture assessment considers toughness, temperature, plate thickness, stress level, flaw size and redundancy. Fracture-critical or nonredundant members require enhanced material control, fabrication inspection and in-service examination. Sharp re-entrant corners, abrupt thickness transitions and weld defects should be avoided.

9. Bracing and Erection Stability

Cross-frames, diaphragms and lateral bracing restrain compression flanges, distribute lateral loads and stabilise girders during construction. Their forces arise from wind, curvature, skew, differential deflection, geometric imperfections and stabilisation demands.

The completed bridge may be stable while an erection stage is not. Critical checks include:

• lifting and transport stresses;
• stability of isolated girders;
• open-box or U-girder torsion;
• wet-concrete loading before composite action;
• temporary support settlement;
• partially tightened connections; and
• wind during crane operations.

Temporary works should be designed to explicit load combinations and removal sequences. Bracing members, connections and anchorage must possess adequate stiffness as well as strength; a nominal brace that deforms excessively may not provide effective restraint.

10. Corrosion Protection and Durability

Durability begins with detailing. Water traps, narrow crevices, inaccessible surfaces and leaking deck joints should be eliminated. Drainage should direct contaminated water away from steel and bearings.

Protection options include multilayer paint systems, metallising, galvanising for suitable components, weathering steel in appropriate environments and dehumidification of closed boxes. Weathering steel is unsuitable where persistent wetness, marine chlorides or de-icing salt accumulation prevents formation of a stable patina.

Designers should specify surface preparation, coating compatibility, dry-film thickness, stripe coating at edges and bolts, inspection access and safe future repainting. Closed boxes require ventilation or controlled internal environments and safe-access provisions.

11. Illustrative Case: Continuous Composite Highway Bridge

Background

This fictional case concerns a three-span continuous highway bridge with spans of 45 m, 60 m and 45 m. Four welded steel plate girders support a reinforced-concrete deck. The bridge is located in a de-icing-salt environment.

Problem

Preliminary analysis identified slender webs, high negative moment over the piers, fatigue-sensitive flange transitions and poor stability of individual girders during deck casting. Deck cracking was expected over the internal piers because the bridge is continuous, not simply supported.

Analysis

A staged grillage model applied steel self-weight and wet-concrete load to the noncomposite girders. Composite stiffness was activated only after concrete strength development. Cracked composite properties were used over internal supports. Local shell models evaluated cross-frame connections and web patch loading.

Positive-moment regions were checked using effective slab width and full shear connection. Over the piers, longitudinal reinforcement carried slab tension while the steel lower flange was checked as a compression element. Web panels near supports required bearing stiffeners and shear-buckling verification. Fatigue assessment focused on welded attachments and transverse flange-splice details.

Approach and solution

Flange sizes were varied gradually to reduce weight without abrupt fatigue-sensitive changes. Intermediate web stiffeners were placed where shear resistance required them. Cross-frames were installed before girder release from cranes and retained through deck casting. A balanced concrete placement sequence limited differential girder deflection.

Stud spacing was governed by both longitudinal shear and fatigue. Pier-region reinforcement was increased and crack widths were checked. Deck joints were eliminated over the piers, drainage was redirected away from girder ends, and a zinc-rich multilayer coating system was specified with enhanced edge treatment.

Outcome

The revised design satisfied staged stability, strength, serviceability and fatigue requirements. The erection model also established maximum wind limits and concrete-placement sequences. Inspection walkways and reference locations for future crack monitoring were incorporated.

Learning points

Continuity explains negative-moment deck cracking over piers. Composite properties cannot be used for wet-concrete loads unless temporary measures create composite action. Erection bracing must be designed, not improvised. Durability and inspectability are most economically achieved during initial detailing.

12. Governance, Technology and Professional Practice

Bridge engineers have an ethical duty to document assumptions, independent checks, design changes and unresolved risks. Fabrication deviations must be assessed rather than accepted informally. Inspection findings should be communicated promptly to the asset owner.

Building-information models can coordinate geometry, diaphragms, reinforcement and erection sequences. Structural-health monitoring can track strain, vibration, temperature and crack growth. Machine-learning systems may assist anomaly detection, but their results require validated data, uncertainty assessment and engineering review. Responsibility for safety remains with competent professionals.

Contemporary developments include high-performance steels, accelerated bridge construction, robotic welding and inspection, digital twins, low-carbon deck systems and improved fatigue-retrofit techniques. Their adoption should be based on verified performance and life-cycle value rather than novelty.

Chapter Summary

Steel bridge design integrates global analysis with local plate behaviour, member stability, connection mechanics, fatigue, fracture and corrosion control. Plate girders require checks of flange resistance, web shear buckling, stiffeners and lateral-torsional stability. Trusses achieve efficiency through structural depth and axial action but require careful buckling and connection assessment. Closed boxes efficiently resist torsion through circulating shear flow, while erection-stage open sections can be highly flexible.

For concrete transformed to steel, the correct transformed properties are A_c/n and I_c/n, where n = E_s/E_c. Composite analysis must distinguish bare-steel and composite stages and provide adequate longitudinal shear transfer. Fatigue depends on stress-range history and detail category, while fracture control requires toughness, redundancy and inspection. Safe erection, drainage, coating access and life-cycle governance are fundamental design responsibilities.

Key Terms

Plate girder: Fabricated beam composed principally of flange plates and a web plate.

Shear buckling: Instability of a web or plate subjected primarily to in-plane shear.

Tension-field action: Post-buckling diagonal tensile resistance developed in a properly anchored web panel.

Lateral-torsional buckling: Coupled lateral displacement and twist of a beam under bending.

Effective width: Portion of a plate or slab treated as effective in resisting longitudinal stress.

Truss: Framework carrying loads mainly through axial forces in interconnected members.

Net section: Remaining cross-sectional area after deductions for holes or discontinuities.

Block shear: Combined tension and shear rupture around a connection block.

Gusset plate: Plate connecting multiple truss or bracing members.

Shear flow: Force per unit length transmitted through a thin wall or interface.

Bredt’s relation: Thin-walled closed-section relationship q = T/(2A_m).

Modular ratio: Ratio n = E_s/E_c used in transformed-section analysis.

Composite action: Structural interaction of steel and concrete through interface shear transfer.

Shear connector: Device transferring longitudinal shear and resisting separation at a composite interface.

Fatigue detail category: Classification defining an S–N relationship for a structural detail.

Miner’s rule: Linear cumulative-fatigue-damage model D = Σ(n_i/N_i).

Fracture toughness: Material resistance to unstable propagation of an existing crack.

Erection stability: Stability of the incomplete structural system during construction.

Review Questions

Short Answer Questions

1. Why is an elastic bending-stress check insufficient for a slender plate girder?

2. Distinguish shear buckling from tension-field action.

3. Why do trusses commonly use greater structural depth than solid girders?

4. State the correct concrete properties when transforming a composite section to steel.

5. Identify four factors affecting fatigue performance of a welded bridge detail.

Long Answer Questions

1. Develop a complete limit-state design sequence for a welded plate girder, including stiffeners and lateral restraint.

2. Explain the design of tension and compression members in a steel truss, including connection limit states.

3. Discuss torsion, distortion, warping and erection behaviour in steel box girders.

4. Explain staged analysis of a continuous steel–concrete composite bridge from steel erection to long-term service.

5. Develop an integrated fatigue, fracture and corrosion-management strategy for an existing steel bridge.

Analytical / Application Questions

1. Design the web-panel proportions and transverse stiffeners for a plate girder subjected to specified bending and shear, including a shear-buckling calculation.

2. For a given steel girder and concrete slab, calculate the transformed neutral axis, composite inertia, stresses and required shear-connector spacing.

3. Develop and justify an erection-bracing scheme for three curved steel box girders before deck closure, including critical construction load cases.

Multiple Choice Questions with Answers

Question 1

For the plate girder in Worked Example 1, what is the elastic bending stress under 9.5 MN·m?

A. 97.2 MPa

B. 101.7 MPa

C. 268.6 MPa

D. 355.0 MPa

Correct Answer: C. 268.6 MPa

Question 2

A web panel has a/d = 1.5. Using kτ = 5.34 + 4/(a/d)², what is kτ?

A. 6.12

B. 7.12

C. 8.90

D. 12.01

Correct Answer: B. 7.12

Question 3

Why can a truss use steel efficiently for a long-span bridge?

A. It develops efficiency through structural depth and predominantly axial member forces.

B. It always has less structural depth than a plate girder.

C. Its joints eliminate all fatigue effects.

D. Its compression members cannot buckle.

Correct Answer: A. It develops efficiency through structural depth and predominantly axial member forces.

Question 4

A single-cell box encloses 10 m² and carries 18 MN·m torque. What is its Saint-Venant shear flow?

A. 0.45 MN/m

B. 0.90 MN/m

C. 1.80 MN/m

D. 3.60 MN/m

Correct Answer: B. 0.90 MN/m

Question 5

Eight bolts each have a factored shear resistance of 127.1 kN. What is the group resistance under concentric shear?

A. 0.508 MN

B. 0.900 MN

C. 1.017 MN

D. 1.271 MN

Correct Answer: C. 1.017 MN

Question 6

A concrete slab has area 625,000 mm² and n = Es/Ec = 6.25. When transformed to steel, what is its area?

A. 100,000 mm²

B. 625,000 mm²

C. 3,906,250 mm²

D. 4,531,250 mm²

Correct Answer: A. 100,000 mm²

Question 7

At a concrete fibre, the steel-reference transformed stress is 57.1 MPa and n = 6.25. What is the actual concrete stress magnitude?

A. 6.25 MPa

B. 9.14 MPa

C. 57.1 MPa

D. 356.9 MPa

Correct Answer: B. 9.14 MPa

Question 8

An interface shear flow is 1,059 N/mm. Two studs per row each provide 100 kN design resistance. What is the calculated maximum row spacing based only on strength?

A. 94 mm

B. 175 mm

C. 189 mm

D. 212 mm

Correct Answer: C. 189 mm

Question 9

A fatigue spectrum gives damage fractions of 0.4219 and 0.3125. What is the Miner damage sum?

A. 0.1094

B. 0.7344

C. 1.3125

D. 1.7344

Correct Answer: B. 0.7344

Question 10

Which load should ordinarily be applied to the bare-steel section unless temporary composite action is deliberately provided?

A. Traffic applied after deck curing

B. Parapet load installed after composite action

C. Wet-concrete load during deck casting

D. Future resurfacing load

Correct Answer: C. Wet-concrete load during deck casting