Design Codes, Loads and Structural Reliability

Introduction and Context

Bridge design is governed by the interaction of structural mechanics, transport demands, environmental actions, construction methods, durability, uncertainty and public safety. Unlike many building structures, bridges are exposed to moving and repeated traffic, vehicle collision, hydraulic effects, temperature gradients, scour, seismic excitation and changing operational demands. Their failure consequences may include loss of life, major economic disruption and interruption of essential transport routes.

Design codes convert these uncertainties into practical rules for analysis, detailing, load combinations, resistance, serviceability and inspection. A code does not replace engineering judgement. It establishes a minimum, consistently defensible basis for design, while the engineer remains responsible for selecting appropriate models, identifying hazards and demonstrating that the structure is fit for its intended purpose.

This chapter presents the principles needed to apply limit-state design, influence lines, dynamic allowances, fatigue provisions and reliability concepts to bridge actions. The terminology and equations are expressed generally. Numerical values for traffic loads, factors and combinations must be taken from the governing national or project standard, such as Eurocodes, AASHTO LRFD, national bridge specifications or a project-specific owner’s requirements. Values from different code systems must not be mixed without explicit justification.

Learning Objectives

On completing this chapter, the reader should be able to:

1. Distinguish permanent, variable, environmental, accidental and seismic actions.

2. Explain the basis of limit-state design and code-based load combinations.

3. Construct and interpret influence lines for moving bridge loads.

4. Apply dynamic amplification and fatigue concepts appropriately.

5. Explain reliability, partial factors, target reliability and model uncertainty.

6. Identify governing actions and combinations for bridge components.

7. Evaluate practical and regulatory issues in a defensible design process.

1. Design Codes as Engineering Frameworks

A modern bridge code normally addresses four connected questions:

• What actions can occur during construction, service and accidental events?
• How should those actions be represented analytically?
• What resistance and deformation limits must the structure satisfy?
• What level of reliability and durability is required?

Codes typically contain provisions for materials, structural analysis, load models, combinations, detailing, durability, inspection and maintenance. They also define terminology, design situations and factors. The governing code should be identified at the beginning of a project, together with its national annexes, amendments, owner requirements and design life.

A sound design basis records at least:

• bridge function, geometry, carriageway arrangement and design life;
• road, rail, pedestrian or mixed traffic classification;
• site wind, temperature, seismic, hydraulic and geotechnical data;
• construction stages and temporary conditions;
• consequence class and importance of the route;
• applicable code hierarchy and departures from standard provisions;
• assumptions requiring confirmation by the client or approving authority.

The use of a code value outside its stated scope is not automatically conservative. For example, a load model calibrated for a major highway may not represent a low-volume rural bridge, and a normal traffic model may be inappropriate for abnormal indivisible loads.

2. Actions on Bridges

An action is an influence capable of producing stress, deformation or movement in a structure. The following classification is useful.

2.1 Permanent actions

Permanent actions, commonly denoted by G, include self-weight of girders, slabs, bearings, barriers, surfacing, utilities and permanently attached equipment. Soil pressures and permanent prestressing effects may also be included according to the code’s definitions.

Self-weight is calculated from geometry and unit weight:

\[

G_k = \gamma_m V

\]

where G_k is the characteristic permanent action, \(\gamma_m\) is the unit weight of the material and V is its volume. The result is a force, normally in newtons or kilonewtons. Where dimensions or material densities are uncertain, the designer should consider code-permitted upper and lower values rather than assuming that self-weight is always favourable.

Superimposed dead loads can change during the bridge life. A wearing course may be resurfaced, utilities may be added and barriers may be replaced. These possibilities should be reflected in the design basis.

2.2 Traffic actions

Traffic actions include concentrated wheel or axle loads, lane loads, braking and acceleration forces, centrifugal forces on curved alignments, pedestrian loading and, where relevant, abnormal vehicles. Traffic models are statistical idealisations and are not literal descriptions of every vehicle.

A traffic load model must be positioned to produce the most adverse effect. This requires consideration of loaded lanes, transverse placement, axle spacing and influence-line ordinates. The critical arrangement for bending may differ from that for shear, reaction, bearing movement or transverse load effects.

Longitudinal braking or traction force is transferred through the deck, bearings and substructure. It may govern bearing design, pier forces, expansion-joint movement and foundation response. Centrifugal action is relevant on curved bridges and acts approximately horizontally, with its code-defined magnitude and point of application.

2.3 Wind actions

Wind acts on superstructure surfaces, vehicles, signs, barriers and, during construction, partially completed components. A simplified pressure relationship is:

\[

q = \frac{1}{2}\rho V^2

\]

where q is velocity pressure, \(\rho\) is air density and V is wind speed. The actual design force requires aerodynamic coefficients, exposure, height, turbulence, dynamic response and code-defined combination factors. The equation assumes a flow-based pressure idealisation; it is not by itself a complete bridge wind model.

Wind may govern lateral stability, bearing forces, construction stages, cable vibration or aeroelastic behaviour. Long flexible bridges require specialist wind-tunnel or computational studies where code simplifications are insufficient.

2.4 Thermal actions

Uniform temperature change produces free expansion or contraction. For a restrained member, the one-dimensional elastic thermal stress is approximately:

\[

\sigma_T = E\alpha \Delta T

\]

where \(\sigma_T\) is thermal stress, E is Young’s modulus, \(\alpha\) is the coefficient of thermal expansion and \(\Delta T\) is the temperature change. This expression applies to idealised complete axial restraint and elastic behaviour. In real bridges, bearings, joints, cracking, creep, slip and partial restraint alter the response.

Codes generally distinguish uniform temperature change from temperature gradients through the depth or width of the deck. Gradients can produce curvature, secondary moments and local stresses. Thermal actions are especially important for continuous decks, integral bridges, restrained bearings and expansion-joint design.

2.5 Hydraulic and geotechnical actions

Hydraulic actions include water pressure, current drag, buoyancy, waves, floating debris, ice where relevant and scour. Hydrostatic pressure at depth h is:

\[

p = \rho_w g h

\]

where p is pressure, \(\rho_w\) is water density, g is gravitational acceleration and h is depth below the free surface. This relationship assumes still water and neglects dynamic effects.

Scour is often a governing hazard for bridge foundations. It reduces the effective embedment and may expose piles or spread foundations to unsupported lengths. Design must consider contraction scour, local scour, long-term degradation and flood events, using hydraulic and geotechnical investigation rather than a simple arbitrary allowance.

2.6 Seismic actions

Seismic design is based on ground-motion hazard, site response, structural mass, ductility, energy dissipation, irregularity and foundation behaviour. A simplified base-shear expression is:

\[

V_b = C_s W

\]

where \(V_b\) is design base shear, \(C_s\) is a code-defined seismic response coefficient and W is the seismic weight. The coefficient incorporates factors such as spectral acceleration, period, ductility and importance. The equation is a code model, not a universal law, and may be inadequate for long, irregular or highly flexible bridges requiring multimodal response-spectrum or time-history analysis.

Seismic detailing must address ductile mechanisms, bearing displacement, unseating, seat width, shear keys, liquefaction and foundation demand. Force-only checks are insufficient where displacement compatibility governs.

2.7 Collision and accidental actions

Accidental actions include vehicle impact on piers or barriers, vessel collision, derailment, fire, explosion and construction accidents. The design philosophy may involve prevention, protection, controlled energy absorption, redundancy and consequence reduction. Not every accidental event is designed for as a full factored load; codes often specify risk-based or scenario-specific provisions.

The designer should identify vulnerable components, establish credible impact energies or forces, consider alternative load paths and verify that local damage does not cause disproportionate collapse. Inspection and protection systems are part of the risk-control strategy.

3. Limit-State Design

Limit-state design verifies that specified unacceptable conditions are not reached during relevant design situations. Two broad categories are used.

3.1 Ultimate limit states

Ultimate limit states concern collapse, loss of equilibrium, rupture, excessive instability, overturning, sliding, fatigue fracture where classified as ultimate, and failure of foundations or connections. A generic resistance condition is:

\[

E_d \leq R_d

\]

where \(E_d\) is the design effect of actions and \(R_d\) is the design resistance.

A common partial-factor representation is:

\[

E_d = E\left(\gamma_F F_k\right), \qquad R_d = \frac{R_k}{\gamma_M}

\]

where F_k is a characteristic action, \(\gamma_F\) is an action factor, R_k is characteristic resistance and \(\gamma_M\) is a material or resistance factor. The exact treatment varies by code, particularly for geotechnical design and favourable actions.

3.2 Serviceability limit states

Serviceability limit states control deflection, vibration, cracking, stress, bearing movement, joint operation, ride quality, drainage and appearance. They protect functionality and durability rather than directly preventing collapse. Serviceability combinations usually use reduced or characteristic values of variable actions and may include frequent or quasi-permanent values.

A bridge can satisfy ultimate strength and still be unacceptable because of excessive vibration, joint leakage, cracking, bearing displacement or poor riding quality. Consequently, serviceability is not an optional refinement.

3.3 Design situations and combinations

Design situations may include persistent service, transient construction, accidental, seismic and fatigue situations. A general combination concept is:

\[

E_d = E\left[\gamma_G G_k + \gamma_Q Q_{k,1} + \sum_i \gamma_{Q,i}\psi_{0,i}Q_{k,i}\right]

\]

for an ultimate combination with one leading variable action and accompanying variable actions reduced by combination factors \(\psi_{0,i}\). Symbols and factors differ among standards. The leading action is the variable action most responsible for the effect being checked.

The combination must be formed for the response quantity under consideration. A traffic action leading for midspan moment may not lead for an uplift reaction or transverse pier force. Favourable and unfavourable effects should be separated where the code requires it.

4. Influence Lines and Moving Loads

An influence line shows the value of a response quantity—reaction, shear, moment or axial force—at a specified section as a unit load moves across a structure. It differs from a bending-moment diagram, which shows response variation along the structure for a fixed load arrangement.

For a statically determinate simply supported beam of span L, the influence line for the left reaction at a load position x is:

\[

I_{R_A}(x)=\frac{L-x}{L}

\]

The influence line for bending moment at a section a from the left support is:

\[

I_M(x)=

\begin{cases}

\dfrac{x(L-a)}{L}, & 0\leq x\leq a\\

\dfrac{a(L-x)}{L}, & a\leq x\leq L

\end{cases}

\]

The ordinate has units of length for a unit force, so multiplying it by a force gives moment. For a point load P, the response is P times the influence-line ordinate at the load position. For a distributed load w, the response is w times the signed area under the relevant portion of the influence line.

For moving axle loads, place the vehicle so that the algebraic sum of axle loads multiplied by corresponding ordinates is maximised or minimised. Absolute maximum moment may require the critical axle near the section and is not always obtained by placing the vehicle symmetrically.

For statically indeterminate bridges, influence lines may be curved and must be obtained using elastic analysis, matrix methods, finite elements or a verified structural-analysis program. The principle remains valid within the assumed linear structural model.

5. Dynamic Allowance and Bridge Response

A moving vehicle produces effects different from those of an equivalent static load because of vehicle suspension, road unevenness, bridge vibration, speed, damping and interaction between vehicle and structure. Codes account for this using dynamic allowance, impact factors or dynamic load factors.

A simplified design effect may be written:

\[

E_{dyn} = (1+\phi)E_{stat}

\]

where \(E_{stat}\) is the specified static traffic effect and \(\phi\) is the code-defined dynamic allowance. This is a design approximation, not a universal amplification law. The value may depend on span, bridge type, surface condition and load model.

Dynamic allowance should not be applied indiscriminately to actions such as uniform temperature, static earth pressure or every component of a wind action. Its scope must be read in the governing standard. For long-span bridges, resonance, vortex shedding, flutter, pedestrian-induced vibration and vehicle–bridge interaction may require dynamic analysis rather than a single impact factor.

6. Fatigue and Repeated Traffic

Fatigue is progressive damage caused by repeated stress or strain cycles. A bridge may experience millions of relatively small cycles, so fatigue can govern details even when static strength is adequate. Critical locations include welded attachments, flange and web connections, bolted joints, reinforcement details, orthotropic decks and regions affected by stress concentrations.

The basic stress range is:

\[

\Delta\sigma = \sigma_{max}-\sigma_{min}

\]

where \(\Delta\sigma\) is the stress range. Fatigue resistance is usually represented by an S–N curve relating stress range to allowable number of cycles. For variable-amplitude loading, a commonly used cumulative damage rule is Miner’s rule:

\[

D=\sum_i\frac{n_i}{N_i}\leq 1.0

\]

where n_i is the number of applied cycles in stress range category i and N_i is the corresponding cycles to failure from the applicable fatigue curve. This rule assumes linear cumulative damage and is an approximation; it does not fully capture sequence effects, overload retardation, corrosion or weld defects.

Fatigue design requires a realistic traffic spectrum, stress-concentration assessment, correct detail category, fabrication quality, inspection regime and consideration of residual stresses. Nominal stress, hot-spot stress and effective notch stress are different methods and must not be interchanged casually. Welded details often have fatigue resistance governed by geometry and fabrication rather than parent-metal yield strength.

7. Structural Reliability

Structural reliability is the probability that a structure performs its intended function over a specified reference period. Let the limit-state function be:

\[

Z=R-E

\]

Failure occurs when Z < 0. R represents resistance and E represents load effect, including relevant uncertainties. If R and E are statistically characterised, the failure probability is:

\[

P_f=P(Z<0)

\]

For normally distributed, statistically independent R and E, the reliability index is:

\[

\beta=\frac{\mu_R-\mu_E}{\sqrt{\sigma_R^2+\sigma_E^2}}

\]

where \(\mu\) denotes mean and \(\sigma\) denotes standard deviation. This expression is restricted to the stated normality and independence assumptions. In general reliability analysis, nonlinear limit states and non-normal variables require transformations or methods such as FORM, SORM, simulation or response-surface approaches.

Reliability has several dimensions:

• aleatory uncertainty: natural variability in loads, material strength and traffic;
• epistemic uncertainty: lack of knowledge, model error and incomplete inspection;
• temporal uncertainty: changing traffic, deterioration and climate;
• spatial uncertainty: variation along a member or across a site.

Partial safety factors are calibrated so that routine design checks achieve an implicit reliability level while remaining practical. Calibration may use probabilistic models, target reliability indices, consequence classes and economic optimisation. A higher-consequence bridge may justify stronger robustness, redundancy, inspection or seismic requirements, although the code’s prescribed factors must still be followed.

Reliability-based assessment is especially valuable for existing bridges. Inspection data can update resistance models, deterioration rates and load distributions. Bayesian updating, for example, can reduce uncertainty when measurements provide credible information. However, apparent statistical precision must not exceed the quality of the inspection and monitoring data.

8. Integrated Design Procedure

A professional workflow is as follows:

1. Establish the code hierarchy, design life, consequence class and bridge function.

2. Define geometry, materials, construction stages, bearings, joints and foundation conditions.

3. Compile site hazards: traffic, wind, temperature, flood, scour, seismicity, collision and accidental events.

4. Select code load models and record all assumptions.

5. Build a structural model appropriate to the response being checked.

6. Use influence lines or moving-load analysis to locate critical traffic arrangements.

7. Apply dynamic, fatigue and combination rules only within their stated scope.

8. Check ultimate, serviceability, fatigue, robustness, durability and constructability requirements.

9. Perform sensitivity studies for uncertain parameters and identify governing assumptions.

10. Independently review calculations, software inputs, results and drawings.

Software output is not evidence of correctness by itself. Equilibrium checks, simplified hand calculations, mesh sensitivity, reaction checks and comparison with expected influence-line behaviour are essential quality controls.

9. Illustrative Worked Example: Moving Load on a Simply Supported Beam

Consider an idealised simply supported bridge girder with span L = 20 m. A single axle load P = 200 kN travels across the span. Determine the maximum bending moment at a section located a = 8 m from the left support, ignoring dynamic allowance.

The influence-line ordinate for moment at the section is:

\[

I_{M,max}=\frac{a(L-a)}{L}

=\frac{8(20-8)}{20}=4.8\text{ m}

\]

The maximum static moment caused by the point load occurs when the axle is at the section:

\[

M_{max}=P I_{M,max}=200(4.8)=960\text{ kN·m}

\]

If the governing code specifies a dynamic allowance \(\phi=0.15\) for this particular traffic action, the amplified effect would be:

\[

M_{dyn}=1.15(960)=1104\text{ kN·m}

\]

This result is valid only under the stated idealisations: linear elastic response, a statically determinate beam, a single point load, no load distribution effects and a code allowance applicable to the action. A real bridge design would distribute wheel loads among girders, include the complete traffic model, self-weight, combinations, shear, torsion, fatigue and serviceability.

10. Applied Case: Reliability Review of an Existing Highway Bridge

Background

This illustrative case concerns a 35-year-old two-lane reinforced-concrete bridge. Original drawings indicate a design traffic model that is less severe than the current legal vehicle population. Inspections identify carbonation, cracking near the midspan soffit and corrosion at several reinforcement locations.

Problem

A conventional reassessment using nominal original dimensions suggests adequate flexural strength, but the margin is small. The owner must decide whether to impose a load restriction, strengthen the bridge or increase inspection and monitoring.

Analysis

The engineering team first verifies the structural system, concrete properties, reinforcement and actual wearing-course thickness. A moving-load model is developed using current traffic survey data. Influence lines identify the critical vehicle positions, while dynamic allowance is applied according to the current assessment standard. Core tests and reinforcement surveys update material and geometry information.

The assessment separates uncertainties in resistance, traffic, deterioration and analysis model. Corrosion is represented by reduced reinforcement area and bond-sensitive detailing is reviewed. A fatigue check is made for heavily trafficked reinforcement details using the measured traffic spectrum. Scour and bearing condition are assessed separately because they may create failure modes not represented by the flexural model.

Approach and solution

Three alternatives are compared:

• immediate load restriction;
• cathodic protection and concrete repair followed by reassessment;
• flexural strengthening combined with corrosion mitigation and a revised inspection plan.

The preferred solution is selected using safety, whole-life cost, construction disruption, residual uncertainty and route importance. Strengthening is not accepted solely because it increases nominal capacity; details, anchorage, fatigue effects, fire protection and inspection access are also checked.

Outcome

The case demonstrates that reliability assessment is a decision process, not merely a numerical probability calculation. Inspection information can increase confidence, but deterioration and future traffic must be modelled explicitly. The final intervention should be documented with assumptions, uncertainty, trigger levels for monitoring and a future reassessment date.

Learning points

• Existing-bridge assessment should use observed evidence where credible.
• Governing failure modes may be deterioration, scour, fatigue or bearings rather than simple flexural strength.
• Reliability and risk decisions should include consequences and maintainability.
• Load restrictions and strengthening are engineering controls that must be integrated with inspection and management systems.

11. Limitations, Governance and Contemporary Practice

Codes are periodically calibrated and cannot anticipate every unusual structural form, climate trend or operational change. Climate change may alter flood levels, scour, temperature ranges, wind regimes and traffic demand. Designers should follow current code amendments and owner guidance, and undertake project-specific hazard studies where evidence indicates that historical assumptions are no longer representative.

Ethically, engineers must not manipulate combinations, omit adverse construction stages or select favourable model assumptions merely to obtain acceptance. Design records should make uncertainty visible. Independent checking is particularly important for bridges with unusual geometry, major public consequences, novel materials or complex construction sequences.

Digital twins, structural-health monitoring, unmanned inspection and machine-learning tools can support condition assessment and anomaly detection. Artificial intelligence may help classify defects or identify traffic patterns, but it does not replace code interpretation, validated mechanics or professional responsibility. Training data may be biased, sensor readings may drift and automated classifications require human verification.

Best practice is therefore to combine code compliance with transparent assumptions, independent verification, lifecycle thinking, robust detailing, inspection access and a maintenance strategy established at design stage.

Chapter Summary

Bridge design codes provide a structured framework for identifying actions, combining them, checking resistance and controlling serviceability. Permanent, traffic, wind, thermal, hydraulic, seismic, collision and accidental actions require different physical models and cannot be amplified or combined indiscriminately. Limit-state design compares design effects with design resistance at ultimate and serviceability conditions.

Influence lines are fundamental for locating critical moving-load positions. Dynamic allowances approximate vehicle–bridge interaction within defined limits, while fatigue assessment addresses repeated stress ranges and cumulative damage. Reliability theory expresses safety through a limit-state function, failure probability and, under restricted assumptions, a reliability index. Partial factors are practical code-based representations of uncertainty and target reliability.

Professional bridge engineering requires more than software calculations. It requires a documented code hierarchy, appropriate load models, independent checks, sensitivity analysis, attention to construction and deterioration, and ethical management of uncertainty. Reliability-based thinking is particularly valuable for existing bridges and lifecycle decisions.

Key Terms

Action: Influence capable of causing structural response.

Characteristic value: Representative value of an action or resistance used as a basis for design.

Design effect: Calculated structural response after application of relevant design factors.

Dynamic allowance: Code-defined increase representing dynamic traffic effects.

Fatigue: Progressive damage caused by repeated stress or strain cycles.

Influence line: Variation of a response quantity as a unit load moves across a structure.

Limit state: Condition beyond which specified performance is no longer satisfied.

Load combination: Defined simultaneous set of actions used for a design check.

Partial factor: Factor applied to an action or resistance to account for uncertainty.

Permanent action: Action whose magnitude or application is substantially constant during a design situation.

Reliability index: Standardised measure of separation between resistance and load effect under specified assumptions.

Failure probability: Probability that the limit-state function is less than zero.

Scour: Removal of bed or bank material by flowing water around a bridge foundation.

Serviceability limit state: Condition involving unacceptable use, appearance, movement, vibration or durability.

Ultimate limit state: Condition associated with collapse, instability or loss of load-carrying capacity.

Traffic load model: Code idealisation of vehicle actions for structural analysis.

Thermal gradient: Temperature variation through a structural cross-section producing curvature or secondary effects.

Robustness: Ability to limit disproportionate consequences from local damage or unforeseen events.

Miner’s rule: Approximate cumulative fatigue-damage rule based on cycle fractions.

Model uncertainty: Difference between the real structural system and its analytical representation.

Review Questions

Short Answer Questions

1. Distinguish an ultimate limit state from a serviceability limit state.

2. What information does an influence line provide?

3. Define dynamic allowance and state why it should not be applied universally.

4. What is meant by model uncertainty in reliability analysis?

5. Name four actions that may be important in bridge design besides self-weight and traffic.

Long Answer Questions

1. Explain how a bridge design basis should establish the applicable code hierarchy, design life, hazards and design situations.

2. Describe the classification and treatment of permanent, traffic, wind, thermal, hydraulic, seismic and accidental actions.

3. Explain the principles of partial-factor limit-state design and the role of leading and accompanying variable actions.

4. Discuss fatigue assessment of a steel or reinforced-concrete bridge, including stress range, S–N curves and cumulative damage.

5. Explain how reliability-based assessment can improve decisions for an ageing bridge.

Analytical / Application Questions

1. A 24 m simply supported girder has a critical section 9 m from the left support. Derive the maximum influence-line ordinate for a point load at that section and explain where the load should be placed.

2. A bridge has an estimated static traffic effect of 1,250 kN·m. If the applicable code explicitly permits a dynamic allowance of 20% for that action, calculate the amplified effect and state two reasons why the result is not a complete design check.

3. An existing bridge shows reinforcement corrosion, increased traffic and possible pier scour. Develop a reliability-informed assessment plan identifying data requirements, critical failure modes, analysis methods and possible management actions.

Multiple Choice Questions with Answers

Question 1

Which expression represents the limit-state condition used in a basic resistance check?

A. E_d ≥ R_d

B. E_d ≤ R_d

C. E_d = 0

D. R_d = 0

Correct Answer: B. E_d ≤ R_d

Question 2

For a simply supported beam, the maximum influence-line ordinate for moment at a section is obtained when a point load is placed at:

A. The left support

B. The right support

C. The section being investigated

D. The quarter-span point in every case

Correct Answer: C. The section being investigated

Question 3

What does a dynamic allowance primarily represent in ordinary bridge traffic design?

A. Increase due to vehicle–bridge dynamic effects

B. Increase in concrete unit weight

C. Reduction in thermal movement

D. Reduction in fatigue cycles

Correct Answer: A. Increase due to vehicle–bridge dynamic effects

Question 4

In the limit-state function Z = R − E, failure occurs when:

A. Z > 1

B. Z = R + E

C. Z < 0

D. E = 0 only

Correct Answer: C. Z < 0

Question 5

Miner’s rule evaluates fatigue damage using:

A. The sum of applied cycles divided by span

B. The sum of n_i/N_i

C. The product of stress and temperature

D. The ratio of resistance to dead load only

Correct Answer: B. The sum of n_i/N_i

Question 6

The hydrostatic pressure at depth h in still water is represented by:

A. p = ρ_w g h

B. p = EαΔT

C. p = 1/2 ρV²

D. p = R/E

Correct Answer: A. p = ρ_w g h

Question 7

Which action is most directly associated with loss of foundation embedment during flooding?

A. Fatigue

B. Scour

C. Thermal gradient

D. Centrifugal force

Correct Answer: B. Scour

Question 8

For normally distributed, independent resistance and load effect, the reliability index is:

A. (μ_R + μ_E)/(σ_R − σ_E)

B. (μ_R − μ_E)/√(σ_R² + σ_E²)

C. σ_R/μ_R

D. μ_E/μ_R

Correct Answer: B. (μ_R − μ_E)/√(σ_R² + σ_E²)

Question 9

A static traffic effect is 800 kN·m and an applicable dynamic allowance is 15%. The amplified effect is:

A. 680 kN·m

B. 800 kN·m

C. 815 kN·m

D. 920 kN·m

Correct Answer: D. 920 kN·m

Question 10

Which statement best describes a bridge design code?

A. A replacement for engineering judgement in every situation

B. A framework establishing minimum consistent requirements and models

C. A guarantee that failure is impossible

D. A document applicable without regard to jurisdiction or project requirements

Correct Answer: B. A framework establishing minimum consistent requirements and models