Concrete and Prestressed Concrete Bridges

Introduction

Concrete bridges range from short reinforced-concrete slabs to long-span prestressed box girders assembled segmentally. Their design is governed not only by ultimate flexural strength, but also by shear, torsion, local wheel effects, fatigue, cracking, deflection, prestress losses, durability and construction sequence. In prestressed and segmental bridges, the structural system changes during erection; consequently, a satisfactory final-state analysis does not guarantee safe construction stages.

This chapter uses Eurocode-style equations for illustration because they form a coherent design framework. The governing national bridge code, traffic model, partial factors, exposure provisions and project specifications must always be applied in practice. Equations from different codes must not be combined without demonstrating compatibility.

Learning Objectives

After studying this chapter, the reader should be able to:

• select appropriate slab, beam, box-girder and segmental bridge systems;
• establish ultimate, serviceability, fatigue and construction-stage combinations;
• design reinforced-concrete sections for flexure, shear and torsion;
• assess slab-strip action, local wheel loading and punching shear;
• determine prestress forces, losses, service stresses and flexural resistance;
• evaluate cracking, deflection, fatigue and durability;
• model staged construction, creep redistribution and segmental joints; and
• prepare robust reinforcement and tendon details.

1. Structural Forms and Behaviour

1.1 Reinforced-concrete slab bridges

Solid slabs are economical for short spans and shallow construction depth. One-way slabs primarily span longitudinally between supports, while skewed, wide or continuously supported slabs exhibit two-way plate action. Equivalent-strip methods are useful for regular layouts, but grillage, plate or shell analysis is preferable where skew, edge beams, concentrated wheel loads or irregular supports produce significant transverse effects.

1.2 Beam-and-slab bridges

Longitudinal girders carry flexure and shear while the deck slab distributes wheel loads transversely. Cross-girders and diaphragms control load distribution, stability and distortion. Composite action between precast girders and an in-situ slab requires interface shear design, surface preparation and adequate connectors.

1.3 Box girders

A closed thin-walled box provides high torsional stiffness and an efficient compression flange. It is therefore suitable for curved bridges, eccentric traffic and longer spans. Design must address longitudinal bending, Saint-Venant torsion, warping, shear lag, web shear, local slab bending and cross-sectional distortion. Diaphragms are normally required at supports and concentrated load-transfer points.

1.4 Segmental bridges

Segmental bridges may use precast match-cast units or cast-in-place balanced cantilevers. Internal or external tendons compress the joints and provide flexural resistance. Temporary conditions—including launching, lifting, cantilever erection, closure and tendon stressing—can govern the design.

2. Design Basis and Structural Analysis

A bridge must be checked for:

• ultimate limit states: flexure, shear, torsion, punching, stability and joint failure;
• serviceability limit states: stress, decompression, cracking, deflection and vibration;
• fatigue from repeated traffic loading;
• accidental and seismic situations where applicable; and
• construction-stage limit states.

A representative persistent ultimate combination is

\[

E_d=\sum \gamma_G G_k+\gamma_{Q,1}Q_{k,1}+\sum\gamma_{Q,i}\psi_{0,i}Q_{k,i},

\]

where \(G_k\) denotes permanent actions, \(Q_k\) variable actions, \(\gamma\) partial factors and \(\psi\) combination factors. This expression is illustrative; the governing bridge code defines the applicable combinations.

Analysis should include self-weight, surfacing, barriers, traffic, braking, wind, thermal gradients, support settlement, shrinkage, creep, prestressing, construction equipment and differential temperature. Moving-load analysis must locate adverse wheel or lane positions. Effective flange widths, cracked stiffness, shear lag and torsional restraint should be represented consistently with the limit state.

3. Reinforced-Concrete Slab Design

3.1 Global flexure

A slab may be designed using plate-analysis moments or code-defined equivalent strips. Longitudinal and transverse reinforcement must correspond to compatible moment fields. Concentrated traffic loads should not be replaced by uniform loads unless the code permits an equivalent-load procedure.

For a singly reinforced rectangular section with concrete strength not exceeding the limit for the adopted rectangular stress block,

\[

C=0.8bf_{cd}x,

\qquad x=\frac{A_s f_{yd}}{0.8bf_{cd}},

\]

and

\[

M_{Rd}=A_s f_{yd}(d-0.4x).

\]

Here, \(b\) is strip width, \(d\) effective depth, \(x\) neutral-axis depth, \(A_s\) tensile reinforcement, and \(f_{cd}\) and \(f_{yd}\) are design concrete and steel strengths. The stress-block coefficients and ductility limits are code dependent.

3.2 Worked design: one-metre slab strip

A simply supported 6.0 m slab is 250 mm thick. For a one-metre strip, characteristic permanent loading is 8.25 kN/m and the code-derived equivalent traffic loading is 30 kN/m. Take \(d=210\) mm, C35 concrete, \(f_{cd}=23.33\) MPa and \(f_{yd}=435\) MPa.

Using the illustrative ULS combination,

\[

w_{Ed}=1.35(8.25)+1.5(30)=56.14\text{ kN/m}.

\]

For simple support,

\[

M_{Ed}=\frac{w_{Ed}L^2}{8}=252.6\text{ kN m/m}.

\]

Solving

\[

252.6\times10^6=0.8(1000)(23.33)x(210-0.4x)

\]

gives \(x=75.2\) mm and

\[

A_s=\frac{0.8(1000)(23.33)(75.2)}{435}=3225\text{ mm}^2/\text{m}.

\]

Provide 20 mm bars at 95 mm centres, giving 3307 mm²/m. The bar arrangement must also satisfy cover, spacing, fatigue and crack-control requirements.

At a section one effective depth from the support,

\[

V_{Ed}=56.14(3.0-0.21)=156.6\text{ kN/m}.

\]

For members without designed shear reinforcement, an EC2-style resistance is

\[

V_{Rd,c}=\left[C_{Rd,c}k(100\rho_l f_{ck})^{1/3}+k_1\sigma_{cp}\right]b_wd,

\]

not less than

\[

(v_{min}+k_1\sigma_{cp})b_wd,

\]

where \(k=1+\sqrt{200/d}\leq2\), with \(d\) in millimetres, and \(\rho_l=A_{sl}/(b_wd)\) within the code limit. Here \(\sigma_{cp}=0\), \(C_{Rd,c}=0.12\), \(k=1.976\) and \(\rho_l=0.01536\). Thus,

\[

v_{Rd,c}=0.12(1.976)[100(0.01536)(35)]^{1/3}=0.895\text{ MPa},

\]

and \(V_{Rd,c}=188\) kN/m. Since 156.6 kN/m is less than 188 kN/m, the strip passes this one-way shear check. Local wheel effects must still be checked separately.

3.3 Local wheel loads and punching

Wheel contact areas create local transverse and longitudinal bending. The effective loaded area may spread through surfacing and structural depth only as permitted by the governing code. Critical wheel groups, edge proximity and simultaneous global moments must be considered.

For an internal rectangular loaded area \(c_1\times c_2\), a control perimeter at distance \(2d\) has, for rounded corners,

\[

u_1=2(c_1+c_2)+4\pi d.

\]

The nominal punching stress is

\[

v_{Ed}=\frac{\beta V_{Ed}}{u_1d},

\]

where \(\beta\) accounts for eccentric shear where required.

For a 400 mm by 600 mm loaded area, \(d=320\) mm, \(V_{Ed}=500\) kN and \(\beta=1.0\):

\[

u_1=2(0.4+0.6)+4\pi(0.32)=6.021\text{ m},

\]

\[

v_{Ed}=\frac{500\times10^3}{6.021(0.32)}=0.260\text{ MPa}.

\]

With C40 concrete and \(\rho_l=0.006\), the same code model gives \(v_{Rd,c}=0.620\) MPa, so the illustrated internal perimeter passes. The loaded-area perimeter must also be checked against the maximum punching resistance. Edge perimeters, openings, wheel overlap and dynamic load factors can materially reduce resistance.

4. Flexure, Shear and Torsion in Beams and Boxes

4.1 Flexural design and detailing

Flexural design requires equilibrium, strain compatibility and code stress–strain relationships. Ductility limits neutral-axis depth and ensures that reinforcement yields before concrete crushing. Compression reinforcement may be required where depth is restricted or moment reversal occurs.

Detailing is part of resistance, not an afterthought. Bars must have adequate anchorage beyond theoretical cut-off points. Reinforcement should be continued through regions vulnerable to redistribution, fatigue or accidental damage. Congestion at bearings, diaphragms and tendon anchorages should be resolved using three-dimensional detailing.

4.2 Shear resistance

Shear models differ among codes. In the EC2 variable-angle truss model, a member requiring links is checked using

\[

V_{Rd,s}=\frac{A_{sw}}{s}zf_{ywd}\cot\theta

\]

and

\[

V_{Rd,max}=\frac{\alpha_{cw}b_wz\nu_1f_{cd}}{\cot\theta+\tan\theta}.

\]

The design condition is

\[

V_{Ed}\leq\min(V_{Rd,s},V_{Rd,max}).

\]

Thus, concrete-strut crushing and link resistance are alternative governing limits in this model; resistance is not the lesser of an isolated concrete contribution and a link contribution. Other codes employ calibrated formulations combining concrete and reinforcement terms, and their rules must be followed as a complete system.

Here, \(A_{sw}/s\) is transverse steel per unit length, \(z\) is the internal lever arm, \(\theta\) is the compression-strut angle, \(\nu_1\) reduces cracked-concrete strength and \(\alpha_{cw}\) accounts for compression-state effects. Minimum links, maximum spacing, anchorage and fatigue remain mandatory even where calculated demand is low.

4.3 Torsion and shear–torsion interaction

Closed boxes resist torsion efficiently through a circulating shear flow. Cracked-section torsion is commonly idealised as a thin-walled spatial truss. For an effective enclosed area \(A_k\), the transverse torsional resistance is

\[

T_{Rd,s}=2A_k\frac{A_{sw,t}}{s}f_{ywd}\cot\theta.

\]

Required longitudinal torsional reinforcement satisfies

\[

A_{sl}f_{yd}\geq\frac{T_{Ed}u_k\cot\theta}{2A_k},

\]

where \(u_k\) is the perimeter of the effective shear-flow path. It should be distributed around that perimeter and anchored effectively.

A representative concrete-strut interaction check is

\[

\frac{V_{Ed}}{V_{Rd,max}}+\frac{T_{Ed}}{T_{Rd,max}}\leq1,

\]

with

\[

T_{Rd,max}=\frac{2\nu_1\alpha_{cw}f_{cd}A_kt_{ef}}{\cot\theta+\tan\theta}.

\]

These expressions are applicable to compatible variable-angle truss models; code-specific definitions of \(A_k\), \(t_{ef}\) and interaction must be used.

4.4 Quantitative shear–torsion example

A box-girder web region has \(V_{Ed}=800\) kN, \(T_{Ed}=250\) kN m, \(b_w=0.40\) m, \(z=1.08\) m, \(A_k=0.60\) m² and \(t_{ef}=0.20\) m. Take \(f_{cd}=26.67\) MPa, \(f_{ywd}=435\) MPa, \(\nu_1=0.552\), \(\alpha_{cw}=1.0\), and \(\theta=30^\circ\), so \(\cot\theta=1.732\).

\[

V_{Rd,max}=2.75\text{ MN},\qquad T_{Rd,max}=1.53\text{ MN m}.

\]

The strut interaction is

\[

\frac{0.800}{2.75}+\frac{0.250}{1.53}=0.455<1.0.

\]

The transverse steel demands are

\[

\left(\frac{A_{sw}}s\right)_V=rac{800\times10^3}{1.08(435\times10^6)(1.732)}=982\text{ mm}^2/\text{m},

\]

\[

\left(\frac{A_{sw,t}}s\right)_T=rac{250\times10^3}{2(0.60)(435\times10^6)(1.732)}=277\text{ mm}^2/\text{m}.

\]

Closed 12 mm links at 125 mm spacing provide 1809 mm²/m from two legs for shear and 905 mm²/m per torsion-resisting leg. A conservative combined utilisation is

\[

982/1809+277/905=0.849<1.0.

\]

This detailing is satisfactory for the illustrated steel-demand check, subject to minimum reinforcement, longitudinal torsion steel, anchorage, fatigue and local web checks.

5. Prestressed-Concrete Section Design

5.1 Prestressing concepts

Prestressing introduces compression and an opposing moment before traffic loading. Pretensioned tendons bond to concrete after release. Post-tensioned tendons are stressed after concrete hardening and may be bonded by grouting or remain external and replaceable.

For a prestress force \(P\) at eccentricity \(e\) below the centroid, stresses in a section under positive sagging moment \(M\), taking compression as positive, are

\[

\sigma_t=\frac PA-\frac{Pey_t}{I}+\frac{My_t}{I},

\]

\[

\sigma_b=\frac PA+\frac{Pey_b}{I}-\frac{My_b}{I}.

\]

These elastic equations apply to an uncracked section with the adopted sign convention. Transfer, construction, frequent and characteristic combinations must be checked separately.

5.2 Prestress losses

Immediate losses include:

• elastic shortening of concrete;
• friction and unintended duct wobble;
• anchorage seating; and
• short-term relaxation during stressing, where relevant.

For a post-tensioned tendon,

\[

P(x)=P_0e^{-(\mu\theta+kx)},

\]

where \(\mu\) is curvature-friction coefficient, \(\theta\) accumulated angular change in radians, \(k\) wobble coefficient and \(x\) tendon length. This expression assumes the code’s friction model and consistent units.

The three standard intrinsic long-term material mechanisms are concrete creep, concrete shrinkage and tendon relaxation. Approximate free-strain expressions such as \(\Delta f_p\approx E_p\varepsilon_{cs}\) are useful for interpretation but generally overestimate or misrepresent loss unless restraint, transformed-section behaviour, loading age and interaction are included. Sequential stressing can also cause delayed elastic-shortening losses in previously stressed tendons; this is a construction-sequence effect, not a fourth independent long-term material mechanism. Reliable design uses code time-step or age-adjusted analysis rather than simply adding unrelated maximum losses.

5.3 Worked prestressed box-section design

A bonded post-tensioned box has \(A=6.0\) m², \(I=8.0\) m⁴, \(y_t=1.2\) m, \(y_b=1.8\) m and tendon eccentricity \(e=0.90\) m. Sixteen thousand square millimetres of strand are stressed to a total jacking force of 22.0 MN. Immediate losses are 2.0 MN. Calculated long-term losses are 1.0 MN from creep, 0.6 MN from shrinkage and 0.4 MN from relaxation, after accounting for interaction. Thus,

\[

P_i=20.0\text{ MN},\qquad P_e=18.0\text{ MN}.

\]

At transfer, the self-weight moment is 12 MN m:

\[

\sigma_t=3.333-2.700+1.800=2.433\text{ MPa compression},

\]

\[

\sigma_b=3.333+4.050-2.700=4.683\text{ MPa compression}.

\]

At the governing service combination, \(M=28\) MN m:

\[

\sigma_t=3.000-2.430+4.200=4.770\text{ MPa compression},

\]

\[

\sigma_b=3.000+3.645-6.300=0.345\text{ MPa compression}.

\]

The section is therefore uncracked under the stated service combination, subject to code stress limits.

For an illustrative ULS flexural check, take C50 concrete, \(f_{cd}=33.3\) MPa, design tendon stress \(f_{pd}=1426\) MPa, compression-flange width \(b=3000\) mm and tendon depth \(d_p=2100\) mm. Assuming bonded-tendon strain compatibility confirms development of the adopted tendon stress,

\[

x=\frac{16000(1426)}{0.8(3000)(33.3)}=285.5\text{ mm},

\]

\[

z=d_p-0.4x=1985.8\text{ mm},

\]

\[

M_{Rd}=16000(1426)(1985.8)=45.3\text{ MN m}.

\]

For \(M_{Ed}=42.0\) MN m, the illustrated flexural resistance is adequate. A complete design must additionally verify flange geometry, tendon strain, web shear, anchorage zones, fatigue, minimum reinforcement, ductility and accidental tendon-loss scenarios.

5.4 Anchorage and deviation zones

Concentrated anchorage forces generate local bearing stress, bursting tension and spalling tension. Local-zone reinforcement should follow the tested anchorage system, while general-zone stresses require strut-and-tie or refined elastic analysis. Deviators for external tendons transfer large transverse forces and must be checked for local cracking, fatigue and replaceability.

6. Serviceability, Fatigue and Durability

Crack control depends on steel stress, bar diameter, spacing, cover and bond. Prestressed bridges may be required to remain in compression or within a limited tensile stress under specified combinations. Deflection calculations should include cracking, creep, shrinkage, prestress, tendon profile, construction sequence and support settlement. Camber predictions are inherently uncertain and should be accompanied by sensitivity ranges.

Fatigue checks apply to reinforcement, prestressing steel, couplers, anchorages and concrete compression or shear where required. Stress ranges should be obtained from fatigue traffic models rather than the static ULS combination.

Durability design includes adequate cover, low-permeability concrete, crack control, drainage, waterproofing, joint detailing and access for inspection. Post-tensioning ducts must be fully grouted where bonded protection is intended. Grout voids, leaking joints and poorly drained anchorages can cause hidden corrosion and brittle tendon failure.

7. Construction-Stage and Segmental Design

A staged model should activate segments, supports, tendons and loads at their actual ages. It should represent:

1. segment casting or erection;

2. temporary supports and erection equipment;

3. tendon stressing and anchorage seating;

4. creep, shrinkage and modulus development;

5. closure pours and continuity tendons;

6. support changes and bearing locking; and

7. superimposed dead and traffic loads.

Balanced-cantilever construction produces large negative moments over piers before continuity is established. The two cantilevers are rarely perfectly balanced, so temporary wind, erection tolerances and an unbalanced segment must be checked. Creep and shrinkage redistribute moments after closure. Temperature at closure influences locked-in forces. Segmental joints require sufficient compression, shear-key resistance and interface preparation; joints should not be assumed to transmit tension unless specifically designed to do so.

Precast segments also require checks for lifting, storage, transport and temporary support. External tendons introduce secondary moments and their ultimate strength increase may be smaller than for bonded tendons because local strain compatibility is absent.

8. Illustrative Case Study: Balanced-Cantilever Box Girder

Background

An illustrative 120 m main-span highway bridge uses a cast-in-place, single-cell prestressed box erected in balanced cantilever. The pier table is followed by 3 m segments. Web depth reduces towards midspan.

Problem

A final-state analysis satisfied service stresses, but the contractor proposed casting one cantilever segment two days before its opposite segment. The wet segment and traveller imposed an additional 1.0 MN at approximately 60 m from the pier, creating a 60 MN m temporary unbalanced moment. Early-age concrete strength and stiffness were lower than their 28-day values.

Analysis and solution

A time-dependent staged model was developed using actual concrete ages. It included traveller movement, tendon stressing sequence, shrinkage, creep, closure temperature and temporary wind. The initial erection sequence exceeded the specified temporary tensile-stress limit at the top slab near the pier and produced excessive bearing uplift demand.

The revised scheme used a temporary stabilising tie, restricted the maximum segment imbalance to one casting operation, delayed traveller advancement until strength verification, and added temporary top tendons. Survey observations of cantilever elevation were compared with predicted envelopes after every two segments. Closure geometry was corrected through controlled casting levels rather than by unapproved forced alignment.

Outcome

The revised sequence met temporary stress and stability criteria, while the final tendon quantity remained unchanged. Monitoring detected a systematic camber deviation caused by a higher-than-assumed early creep response; subsequent casting levels were adjusted within approved tolerances.

Learning points

• Construction stages can govern even when the completed bridge is adequate.
• Concrete age and tendon sequence must be represented explicitly.
• Temporary works form part of the structural safety system.
• Monitoring is most useful when linked to predefined intervention thresholds.

9. Professional Practice and Contemporary Developments

Good practice includes independent design checking, documented assumptions, code-consistent software verification and reconciliation of design models with erection methods. Designers must not conceal adverse results by selectively changing stiffness or load distribution assumptions. Inspection access, tendon replacement and whole-life carbon should be considered alongside initial cost.

Current developments include ultra-high-performance concrete, lightweight decks, replaceable external tendons, fibre-reinforced reinforcement, digital fabrication and structural-health monitoring. Machine-learning tools can help detect anomalous strain or deflection patterns, but they do not establish structural safety independently. Data quality, explainability, cybersecurity and engineer review remain essential.

Chapter Summary

Concrete bridge design integrates structural form, load distribution, ultimate resistance, serviceability, durability and construction sequence. Slabs require global plate or strip design together with local wheel and punching checks. Reinforced-concrete shear design must follow a complete code model: in a variable-angle truss model, link resistance is limited by concrete-strut crushing rather than being treated as the lesser of independent concrete and link contributions. Box girders require quantitative shear–torsion interaction and closed reinforcement paths.

Prestressed design involves transfer and service stresses, immediate losses, the three intrinsic long-term loss mechanisms—creep, shrinkage and relaxation—and strain-compatible ultimate resistance. Segmental bridges demand age-dependent staged analysis because temporary conditions, joint compression, tendon sequence and creep redistribution may govern. Reliable detailing, inspection access, construction control and independent verification are fundamental to safe bridge engineering.

Key Terms

Anchorage zone: Region in which concentrated prestressing force spreads into the concrete section.

Balanced cantilever: Segmental erection method in which segments are added approximately symmetrically about a pier.

Bursting reinforcement: Reinforcement resisting transverse tensile forces behind a prestress anchorage.

Construction-stage analysis: Analysis representing the changing structural system, loads and material ages during erection.

Creep: Time-dependent concrete strain under sustained stress.

Decompression: Limit state at which precompression at a specified fibre reduces to zero.

Effective prestress: Prestressing force remaining after applicable immediate and long-term losses.

External tendon: Tendon located outside the concrete section but within or around the structural envelope.

Friction loss: Prestress reduction caused by tendon curvature and duct wobble during stressing.

Punching shear: Localised two-way shear failure around a concentrated load or support.

Relaxation: Reduction in tendon stress with time under approximately constant strain.

Segmental bridge: Bridge assembled or cast as successive structural segments.

Shear lag: Non-uniform longitudinal stress distribution across a wide flange.

Shrinkage: Time-dependent volume reduction of concrete largely independent of applied stress.

Strut-and-tie model: Equilibrium model representing discontinuity regions using compression struts, tension ties and nodes.

Tendon eccentricity: Distance between the tendon force line and section centroid.

Torsional shear flow: Circulating shear force per unit length in a thin-walled closed section.

Variable-angle truss model: Shear-design model using concrete compression struts and transverse steel ties with a selectable code-limited strut angle.

Review Questions

Short Answer Questions

1. Why must local wheel effects be checked separately from global slab-strip bending?

2. Distinguish immediate prestress losses from long-term material losses.

3. State the two resistance limits used in a variable-angle shear truss model.

4. Why are closed links necessary for torsion?

5. What is the purpose of a bridge closure-stage analysis?

Long Answer Questions

1. Explain the analysis and design procedure for a reinforced-concrete slab bridge, including plate action, flexure, one-way shear, punching and detailing.

2. Derive the elastic fibre-stress expressions for an eccentrically prestressed section and discuss transfer and service checks.

3. Compare the structural behaviour and design requirements of beam-and-slab, box-girder and segmental bridges.

4. Explain shear–torsion interaction in a concrete box girder, including reinforcement and concrete-strut checks.

5. Discuss prestress losses and explain why an interactive time-step calculation is preferable to simple addition of nominal percentages.

Analytical / Application Questions

1. Develop a staged-analysis plan for a three-span balanced-cantilever bridge, identifying each activation, load event and required limit-state check.

2. A deck slab is subjected to overlapping wheel contact areas near an edge. Explain how you would determine critical flexural and punching actions and how the edge modifies the control perimeter.

3. For a prestressed box girder with service tension at the bottom fibre, evaluate the relative merits of increasing tendon force, increasing eccentricity, changing section properties and introducing bonded reinforcement.

Multiple Choice Questions with Answers

Question 1

In the EC2-style variable-angle truss model, the design shear resistance of a member requiring links is governed by which expression?

A. The lesser of the isolated concrete contribution and link contribution

B. The greater of link resistance and concrete-strut resistance

C. The lesser of link resistance and concrete-strut crushing resistance

D. The sum of link resistance and concrete-strut crushing resistance

Correct Answer: C. The lesser of link resistance and concrete-strut crushing resistance

Question 2

Which set contains the three intrinsic long-term material mechanisms of prestress loss?

A. Creep, shrinkage and tendon relaxation

B. Friction, anchorage seating and creep

C. Elastic shortening, friction and shrinkage

D. Wobble, bearing deformation and relaxation

Correct Answer: A. Creep, shrinkage and tendon relaxation

Question 3

Why are closed box girders particularly effective under eccentric traffic loading?

A. They eliminate longitudinal bending

B. They possess high torsional stiffness

C. They require no diaphragms

D. They prevent shear lag completely

Correct Answer: B. They possess high torsional stiffness

Question 4

For the illustrated 6 m slab strip, what ULS design moment was obtained?

A. 126.3 kN m/m

B. 168.4 kN m/m

C. 252.6 kN m/m

D. 336.8 kN m/m

Correct Answer: C. 252.6 kN m/m

Question 5

What is the principal purpose of longitudinal torsion reinforcement?

A. To complete the spatial truss and resist longitudinal tensile forces

B. To increase the elastic modulus of concrete

C. To eliminate anchorage-zone bursting

D. To prevent all service deflection

Correct Answer: A. To complete the spatial truss and resist longitudinal tensile forces

Question 6

In the prestressed box example, what was the effective prestress after all stated losses?

A. 16 MN

B. 18 MN

C. 20 MN

D. 22 MN

Correct Answer: B. 18 MN

Question 7

Which effect is most likely to be missed by analysing only the completed configuration of a segmental bridge?

A. Concrete density

B. Temporary unbalanced cantilever moment

C. Characteristic traffic axle spacing

D. Twenty-eight-day cylinder strength

Correct Answer: B. Temporary unbalanced cantilever moment

Question 8

For the shear–torsion example, the concrete-strut interaction ratio was approximately:

A. 0.455

B. 0.849

C. 1.000

D. 1.530

Correct Answer: A. 0.455

Question 9

Which action is essential when checking punching around a wheel load near a slab edge?

A. Use the full internal control perimeter without modification

B. Ignore global slab moments

C. Account for the reduced edge control perimeter and load eccentricity

D. Replace the wheel load by bridge self-weight

Correct Answer: C. Account for the reduced edge control perimeter and load eccentricity

Question 10

Why may external tendons show a smaller ultimate stress increase than bonded tendons?

A. External tendons have zero initial prestress

B. External tendons cannot carry tension

C. Local section strain compatibility does not directly determine their strain

D. External tendons are always made from mild steel

Correct Answer: C. Local section strain compatibility does not directly determine their strain