Mechanical Behaviour and Dimensional Stability

Introduction and Context

Concrete is commonly described as a strong, stiff and durable construction material, yet its mechanical response is neither perfectly elastic nor time-independent. It is a heterogeneous composite consisting of cement paste, aggregates, interfacial transition zones, pores, cracks and—in many modern concretes—supplementary cementitious materials, fibres or chemical admixtures. Its behaviour therefore depends not only on constituent materials but also on loading rate, stress history, moisture, temperature, age, curing, specimen geometry and restraint.

Mechanical behaviour concerns the response of concrete to applied loads, including strength, stiffness, deformation, cracking, fracture and fatigue. Dimensional stability concerns changes in volume or shape that occur without, or in addition to, external loading. Drying shrinkage, autogenous shrinkage, thermal deformation, creep and swelling can produce cracking or loss of prestress even when the applied load is moderate. In restrained members, the principal engineering problem is often not free deformation but the tensile stress generated when deformation is prevented.

This chapter examines these mechanisms and their implications for structural design, assessment, durability and construction quality.

Learning Objectives

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

1. Explain the microstructural basis of compressive, tensile and flexural behaviour of concrete.

2. Distinguish elastic, inelastic, viscoelastic and fracture responses.

3. Interpret stress–strain curves and select appropriate constitutive models.

4. Explain creep, shrinkage and thermal deformation and estimate their effects.

5. Assess the causes and likelihood of restrained cracking.

6. Apply fracture-mechanics and fatigue concepts to concrete members.

7. Recommend practical measures for controlling deformation and cracking.

8. Critically evaluate testing, modelling and monitoring approaches.

1. Concrete as a Heterogeneous, Rate- and Environment-Dependent Material

The hardened cement paste contains capillary pores, gel pores, hydration products and unhydrated particles. Coarse aggregate is usually stiffer and stronger than the paste, while the interfacial transition zone is often more porous and crack-prone. Under load, stresses are distributed non-uniformly. Microcracks may develop at aggregate–paste interfaces before the nominal strength is reached. Consequently, concrete does not behave as a homogeneous, linear-elastic solid over its full stress range.

Important variables include:

• water–binder ratio and degree of hydration;
• aggregate mineralogy, grading, maximum size and stiffness;
• curing temperature, humidity and duration;
• age and loading rate;
• moisture state and temperature history;
• specimen size, geometry and boundary conditions; and
• fibres, reinforcement, admixtures and supplementary cementitious materials.

The terms strength and stiffness must be distinguished. Strength is the stress associated with a specified failure or limit state. Stiffness describes resistance to deformation and is represented, for example, by a modulus of elasticity. A concrete may have high compressive strength but relatively low tensile strain capacity and significant long-term deformation.

2. Compressive Behaviour

2.1 Compression test and strength

The compressive strength of a specimen is conventionally calculated as

\[

f_c = \frac{P}{A}

\]

where \(f_c\) is nominal compressive strength, \(P\) is the maximum applied load, and \(A\) is the loaded cross-sectional area. The expression assumes uniform nominal stress and is applicable to a specified specimen shape, size, curing condition, loading rate and testing standard. It does not imply that the internal stress field is uniform.

Cylinder and cube strengths are not interchangeable. Differences arise from specimen geometry, friction at loading platens, end restraint, aggregate size and testing procedures. Results must therefore be reported with specimen type, age, curing condition and test standard.

2.2 Stress–strain response

At low stress, the stress–strain curve is approximately linear, although local microcracking already occurs. With increasing compression, cracks grow around aggregates and link through the paste. The curve becomes nonlinear, reaches a peak stress, and then descends as damage localises. The descending branch is strongly influenced by specimen size, confinement, aggregate type and testing stability.

The peak strain in normal-strength concrete is commonly of the order of 0.002–0.003, but it is not a universal constant. High-strength concrete may exhibit a steeper ascending branch, a higher peak stress and a more brittle post-peak response. Confinement changes the response substantially: lateral restraint delays crack growth, increases apparent strength and provides a more ductile descending branch.

A useful idealisation for design is a parabolic or equivalent rectangular stress block, but such idealisations should not be confused with the actual material curve. For nonlinear analysis, the complete stress–strain relationship, unloading rules and fracture-energy parameters may be required.

2.3 Factors affecting compressive strength

Strength generally increases with reduced water–binder ratio and improved curing, but the relationship is affected by aggregate strength, hydration kinetics, entrained air and admixture compatibility. At low water–binder ratios, self-desiccation and autogenous shrinkage may become significant. Elevated early curing temperatures can increase early strength but may produce non-uniform hydration and adversely affect later-age properties. Recycled aggregate and lightweight aggregate may reduce stiffness or strength but can improve sustainability or internal curing, depending on their characteristics.

3. Tensile and Flexural Behaviour

Concrete is weak in direct tension because cracks propagate through the paste, transition zone and aggregate interfaces. Direct tensile testing is experimentally difficult because slight eccentricity can produce bending and premature failure. Splitting-cylinder and flexural tests are therefore frequently used, but they measure different properties.

For a diametral splitting test, the nominal tensile stress at failure is often calculated as

\[

f_{ct,sp}=\frac{2P}{\pi LD}

\]

where \(P\) is the applied load at failure, \(L\) is specimen length and \(D\) is specimen diameter. This equation assumes the standard cylindrical geometry, diametral loading and the conventional elastic stress interpretation. The actual fracture process is not uniform tension throughout the specimen.

For a simple prismatic beam tested in third-point or centre-point loading, the nominal modulus of rupture may be calculated from the appropriate flexural formula in the relevant standard. Because the stress distribution and failure location depend on loading arrangement, the result should not be treated as identical to direct tensile strength.

Concrete tensile behaviour has three important stages:

1. Uncracked stage: stress and strain are approximately proportional, with local flaws developing.

2. Cracking stage: a dominant crack forms when tensile stress reaches the cracking strength.

3. Post-cracking stage: plain concrete loses load-carrying capacity rapidly, whereas fibre-reinforced concrete may transfer stress across cracks through fibre bridging.

Reinforcement does not prevent all cracking; it distributes cracks and limits their widths. Fibres can improve post-cracking toughness, impact resistance and energy absorption, but performance depends on fibre type, dosage, orientation, bond and concrete quality.

4. Elasticity, Inelasticity and Constitutive Modelling

The instantaneous modulus of elasticity is the slope of the initial or specified portion of the stress–strain curve. A secant modulus is defined by the slope joining the origin to a selected point, while a tangent modulus is the local slope at a particular stress. These values are not interchangeable.

For a uniaxial elastic idealisation,

\[

\sigma=E\varepsilon

\]

where \(\sigma\) is stress, \(E\) is Young’s modulus and \(\varepsilon\) is strain. This relation assumes small strain, linear elasticity, reversible deformation and a defined loading direction. Concrete satisfies these assumptions only approximately and over a limited stress range.

Under multiaxial stress, Poisson’s ratio relates lateral and longitudinal elastic strains. However, cracking, aggregate interlock and damage make Poisson’s ratio stress-dependent. Advanced analysis may use damaged-plasticity, smeared-crack, discrete-crack, microplane or nonlinear fracture models. Model selection should reflect the purpose of analysis: a design check may require a calibrated stress block, while a research simulation of crack propagation may require fracture energy, softening laws and mesh-objective regularisation.

A key issue in finite-element modelling is strain localisation. If a softening law is expressed only in terms of strain, predicted energy dissipation may depend on mesh size. Crack-band approaches, cohesive-zone models or discrete cracks introduce a characteristic length or fracture energy to obtain more objective results.

5. Fracture Mechanics of Concrete

Concrete is quasi-brittle. It contains a fracture process zone ahead of a visible crack, where microcracking, aggregate bridging, friction and crack deflection occur. Linear elastic fracture mechanics is useful when the process zone is small relative to the member, but quasi-brittle fracture often requires nonlinear fracture mechanics.

The energy release rate is commonly expressed conceptually as

\[

G=-\frac{\partial U}{\partial A}

\]

where \(U\) is the potential energy available to the structure and \(A\) is crack area. Crack growth occurs when the available energy reaches the material resistance, subject to the selected fracture criterion. The equation assumes a consistent definition of potential energy and crack area; in concrete, the resistance is not a single constant because the fracture process zone evolves with crack extension.

Mode I refers primarily to opening, Mode II to in-plane sliding and Mode III to tearing. Structural concrete commonly experiences mixed-mode fracture. Fracture energy, often defined as energy dissipated per unit crack area, is more informative than tensile strength alone for analysing post-peak behaviour and size effects.

Size effect is important: larger geometrically similar members often exhibit lower nominal failure stress because a larger crack-like flaw and a greater proportion of localised fracture energy influence failure. Ignoring size effect can lead to unconservative extrapolation from laboratory specimens to massive structural members.

6. Fatigue and Repeated Loading

Fatigue is progressive damage caused by repeated or cyclic loading. It is relevant to bridges, pavements, offshore structures, crane supports, railway structures and machine foundations. Damage may occur in concrete, reinforcement, interfaces or the surrounding ground.

Fatigue performance depends on maximum and minimum stress, stress range, load sequence, frequency, moisture, temperature, sustained stress and existing cracks. A useful descriptor is the stress ratio

\[

R=\frac{\sigma_{min}}{\sigma_{max}}

\]

where \(\sigma_{min}\) and \(\sigma_{max}\) are the minimum and maximum stresses in a cycle. The ratio must be defined consistently, particularly when compression and tension occur in the same cycle.

S–N relationships associate stress range with cycles to failure, but they are empirical and valid only within the test conditions from which they were derived. Miner’s linear cumulative damage rule is sometimes written as

\[

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

\]

where \(n_i\) is the number of applied cycles at stress level \(i\), and \(N_i\) is the cycles to failure at that level. Failure is conventionally predicted when \(D\) approaches unity. This rule ignores sequence effects, stiffness degradation, crack closure and environmental changes; it should therefore be used cautiously and with appropriate standards or calibrated models.

Fatigue assessment should include inspection of existing cracks, realistic load spectra, reinforcement fatigue, dynamic amplification and serviceability limits. For reinforced concrete, bond deterioration and bar stress concentration may control performance before global collapse.

7. Creep

Creep is the time-dependent increase in strain under sustained stress. Total strain may be represented conceptually as

\[

\varepsilon_{total}=\varepsilon_{elastic}+\varepsilon_{creep}+\varepsilon_{shrinkage}+\varepsilon_{thermal}+\varepsilon_{other}

\]

provided that the components are defined consistently and the interaction between them is acknowledged. This is a strain decomposition, not a universal constitutive law.

Basic creep occurs under sustained load without moisture exchange, whereas drying creep occurs with simultaneous drying. Creep is influenced by age at loading, relative humidity, member size, stress level, concrete maturity, aggregate stiffness and curing. Higher-strength concrete often creeps less, but low permeability can increase self-desiccation and autogenous effects.

A simplified coefficient approach writes creep strain as

\[

\varepsilon_{cr}=\varphi\frac{\sigma}{E_{c,load}}

\]

where \(\varphi\) is the creep coefficient, \(\sigma\) is sustained stress and \(E_{c,load}\) is the elastic modulus used for the loading age. This relation assumes approximately linear creep, generally appropriate only when sustained stress is below a specified fraction of strength and the concrete is not undergoing severe nonlinear damage. Design codes provide models for estimating \(\varphi\), but model uncertainty may be substantial for unusual concretes or environments.

Creep can reduce stress caused by imposed deformation, redistribute load between concrete and reinforcement, increase deflection, alter prestress and relieve thermal stress. It is beneficial when it relaxes restraint stress, but harmful when it produces excessive long-term deflection or loss of prestressing force.

8. Shrinkage and Swelling

Shrinkage is a reduction in volume without external load. Major mechanisms include:

• Plastic shrinkage: water loss from fresh concrete before setting, often under hot, dry or windy conditions.
• Drying shrinkage: moisture loss from hardened concrete and associated capillary and gel-pore effects.
• Autogenous shrinkage: internal volume reduction caused by hydration and self-desiccation, especially at low water–binder ratios.
• Carbonation shrinkage: dimensional change associated with carbonation reactions near exposed surfaces.

Drying shrinkage is governed by relative humidity, member size, curing, paste content, aggregate restraint and environmental exposure. Aggregate generally restrains paste shrinkage; stiff, well-graded aggregate can reduce overall shrinkage. Excessive paste volume tends to increase it.

Swelling may occur when dry concrete reabsorbs moisture, although recovery is often incomplete. Chemical expansion can result from expansive agents, delayed ettringite formation or alkali–silica reaction. Such processes must be distinguished from ordinary reversible moisture movement.

Shrinkage is commonly measured as a change in length relative to a reference length. Results depend strongly on specimen dimensions, curing regime, sealing and measurement age. Laboratory free-shrinkage values should not be transferred directly to a restrained structural member without considering restraint and environmental history.

9. Thermal Deformation and Thermal Cracking

For an unconstrained, homogeneous material over a moderate temperature range, thermal strain may be approximated by

\[

\varepsilon_T=\alpha\Delta T

\]

where \(\alpha\) is the coefficient of thermal expansion and \(\Delta T\) is the temperature change. This assumes constant \(\alpha\), negligible temperature gradient and free deformation. Concrete is not perfectly homogeneous: aggregate mineralogy, moisture and temperature influence \(\alpha\).

Thermal cracking may be caused by heat of hydration in massive pours, rapid cooling of exposed surfaces, daily temperature cycles or differential temperature through a member. A temperature gradient can produce curvature even when the average temperature remains unchanged. Young concrete is particularly vulnerable because its tensile strength and modulus develop simultaneously while hydration generates heat.

Thermal control strategies include low-heat binders, supplementary cementitious materials, reduced cement content, pre-cooling materials, post-cooling pipes, insulated formwork, staged placement, controlled formwork removal and monitoring of internal and surface temperatures. The appropriate strategy depends on the predicted thermal field, restraint and required construction schedule.

10. Restrained Cracking

A free element may shorten through shrinkage or cooling. If restraint prevents this movement, tensile stress develops. In a simplified fully restrained elastic case,

\[

\sigma_r=E\varepsilon_i

\]

where \(\sigma_r\) is restraint stress, \(E\) is the relevant modulus and \(\varepsilon_i\) is imposed strain. For concrete, a more realistic expression must include creep, relaxation, cracking, reinforcement, partial restraint and time-dependent stiffness. Thus the elastic expression is an upper-bound idealisation rather than a general prediction.

The cracking risk depends on the relationship between tensile stress and tensile strength, and on the rate at which stress develops. A useful conceptual criterion is

\[

\sigma_{t,induced} \geq f_{t,available}

\]

where the available tensile strength is age- and temperature-dependent. Cracking is more likely when imposed strain develops rapidly, tensile strength is low, restraint is high and stress relaxation is limited.

Sources of restraint include:

• foundation or substrate friction;
• reinforcement continuity;
• adjoining walls, columns or older concrete;
• changes in member thickness or geometry;
• internal temperature gradients; and
• differential shrinkage between layers.

Crack width and spacing depend on reinforcement ratio, bar diameter and spacing, cover, bond, concrete tensile properties and restraint. Crack control is not equivalent to crack elimination. Well-distributed reinforcement generally produces more numerous, narrower cracks than sparse reinforcement.

11. Worked Application: Early-Age Thermal Risk in a Wall

Consider an illustrative concrete wall cast against a rigid foundation. Thermal analysis predicts that, after cooling, the wall tends to shorten by a total free strain of 300 microstrain, or \(0.000300\). Assume that the effective modulus at the relevant age is 18 GPa and that the foundation provides an idealised restraint factor of 0.60. Ignoring creep and cracking initially, the estimated restraint stress is

\[

\sigma_r=R E\varepsilon_i

\]

where \(R=0.60\). Therefore,

\[

\sigma_r=0.60(18,000\ \text{MPa})(0.000300)=3.24\ \text{MPa}.

\]

If the available tensile strength at the critical age is 2.4 MPa, the preliminary stress-to-strength ratio is

\[

\frac{3.24}{2.4}=1.35.

\]

The idealised calculation indicates a significant cracking risk. It is not a final design result because creep and stress relaxation may reduce stress, while temperature gradients, local restraint and construction joints may increase it. A professional assessment would use a time-dependent thermal model, verify material properties at the relevant age, examine reinforcement for crack distribution, and specify monitoring and curing controls.

Possible measures include reducing peak temperature, slowing cooling, increasing distributed reinforcement, modifying pour length, improving curing and introducing planned contraction joints where structurally acceptable.

12. Integrated Case Study: Illustrative Warehouse Slab

Background

An industrial warehouse slab developed irregular cracks within two weeks of casting. The slab was large, lightly reinforced and placed during dry, windy weather. A high early-strength concrete with a relatively low water–binder ratio was used to meet the construction programme.

Problem and analysis

Inspection found shallow plastic-shrinkage cracks in exposed areas and deeper transverse cracks near restrained column lines. Records showed rapid surface evaporation, limited curing during the first day and a substantial drop in night-time temperature. The low water–binder ratio also suggested autogenous shrinkage. The slab was restrained by the sub-base, column bases and edge thickening.

The cracking could not be attributed to one mechanism. Early evaporation produced plastic shrinkage before adequate tensile capacity developed. Subsequent drying and autogenous shrinkage imposed additional strain, while thermal contraction increased demand. Differential restraint concentrated cracks near geometric discontinuities.

Approach and solution

The remedial and preventive programme included crack mapping, depth measurement, rebound and core testing where justified, review of batch records, and measurement of slab moisture and temperature. Non-structural cracks were sealed using a compatible repair system after movement assessment. The future construction specification required evaporation-rate control, immediate curing, a curing compound compatible with the final floor system, saw-cut timing, improved joint layout, and a revised concrete mixture with reduced paste shrinkage. Additional distributed reinforcement was considered near restraints.

Outcome and learning points

The revised practice reduced early cracking in subsequent pours. The principal lesson was that dimensional stability is a system problem involving mixture design, weather, geometry, restraint, curing and construction sequence. Post-crack repair is less reliable and usually more expensive than controlling the initiating mechanisms.

13. Testing, Monitoring and Professional Decision-Making

A credible evaluation should combine laboratory testing, field observations and structural analysis. Recommended practices include:

• report age, curing, moisture condition, specimen geometry and loading rate;
• use companion specimens for strength, modulus, shrinkage and creep where possible;
• distinguish free deformation from restrained deformation;
• calibrate thermal models using measured internal and surface temperatures;
• use maturity methods cautiously and verify them for the actual mixture;
• measure crack width, length, depth and activity rather than recording only visual presence; and
• document uncertainty in material properties and restraint assumptions.

Digital sensors, fibre-optic strain gauges, distributed temperature sensing and automated crack imaging can improve monitoring. Machine-learning methods may assist anomaly detection or prediction, but they do not replace sound mechanics, representative data, sensor validation or engineering responsibility. Data governance is important where monitoring information affects safety decisions, contractual claims or public infrastructure records.

14. Challenges, Limitations and Contemporary Developments

The principal limitations in predicting concrete deformation are material variability, incomplete knowledge of restraint, uncertain environmental histories and interaction among mechanisms. Code models are essential for consistency but may be unreliable outside their calibration ranges, particularly for ultra-high-performance concrete, recycled aggregates, massive members, low-carbon binders or unusual curing conditions.

Contemporary developments include low-carbon cement systems, shrinkage-reducing admixtures, internal curing using saturated lightweight aggregate, fibre-reinforced and strain-hardening cementitious composites, embedded sensing, digital twins and probabilistic service-life assessment. These technologies offer benefits but introduce new uncertainties. For example, supplementary cementitious materials may reduce heat generation yet alter strength development, autogenous shrinkage and carbonation resistance. Sustainability decisions must therefore consider whole-life performance rather than cement reduction alone.

Best practice is to integrate mixture design, structural detailing, construction planning and monitoring from the project outset. Crack control should be treated as a performance objective supported by quantified risk assessment, not as an afterthought.

Chapter Summary

Concrete exhibits nonlinear, heterogeneous and time-dependent behaviour. Compressive strength is governed by the cementitious matrix, aggregate, interfaces, curing and testing conditions, while tensile and flexural performance is controlled by crack initiation and propagation. Elastic equations are useful idealisations but must be applied within their assumptions.

Fracture mechanics explains the role of fracture process zones, energy dissipation and size effects. Fatigue assessment requires attention to stress range, stress ratio, load sequence and environmental conditions. Creep increases long-term deformation and can relax restraint stresses, whereas shrinkage and thermal deformation generate cracking when movement is restrained. Early-age thermal effects, drying shrinkage and autogenous shrinkage often interact.

Reliable crack control requires understanding restraint, estimating time-dependent tensile stress, providing suitable reinforcement and joints, controlling temperature and moisture, and monitoring construction. Numerical models and AI-enabled sensing are valuable only when supported by validated material data and engineering judgement.

Key Terms

Concrete strength: Stress associated with a specified failure or limit condition.

Modulus of elasticity: Ratio or slope relating stress to elastic strain under defined conditions.

Tensile strength: Resistance to direct tensile stress before fracture.

Flexural strength: Nominal tensile strength inferred from a flexural beam test.

Microcracking: Formation of small cracks before or around macroscopic failure.

Fracture process zone: Region ahead of a crack containing distributed nonlinear damage.

Fracture energy: Energy dissipated per unit area of advancing crack.

Quasi-brittle material: Material showing limited inelastic deformation and a finite fracture process zone.

Fatigue: Progressive damage caused by repeated or cyclic loading.

Stress ratio: Minimum cyclic stress divided by maximum cyclic stress.

Creep: Time-dependent strain under sustained stress.

Basic creep: Creep measured without significant moisture exchange.

Drying creep: Creep occurring while concrete is drying.

Drying shrinkage: Volume reduction caused principally by moisture loss.

Autogenous shrinkage: Internal contraction associated with hydration and self-desiccation.

Thermal strain: Deformation caused by temperature change.

Restraint: Prevention or limitation of free deformation.

Crack width: Opening measured across a crack at a specified location and time.

Stress relaxation: Reduction in stress under sustained strain or imposed deformation.

Strain localisation: Concentration of deformation in a narrow region, often a crack band.

Review Questions

Short Answer Questions

1. Why are compressive strength and elastic modulus not interchangeable properties?

2. Distinguish drying shrinkage from autogenous shrinkage.

3. What is the significance of the fracture process zone in concrete?

4. State two factors that influence creep.

5. Why does restraint increase the risk of cracking?

Long Answer Questions

1. Explain the complete compressive stress–strain response of concrete and discuss the effects of confinement.

2. Compare direct tensile, splitting tensile and flexural tests, including their limitations.

3. Discuss the mechanisms of creep and their consequences for reinforced and prestressed concrete.

4. Explain fracture energy, size effect and the implications for nonlinear finite-element analysis.

5. Describe a comprehensive strategy for controlling thermal and shrinkage cracking in a massive concrete pour.

Analytical / Application Questions

1. A restrained member experiences an imposed strain of 0.00025. If the effective modulus is 20 GPa and the restraint factor is 0.45, estimate the elastic restraint stress and explain why the result may overestimate actual stress.

2. Develop a field investigation plan for a slab that exhibits cracks one day after casting. Identify the evidence needed to distinguish plastic shrinkage, thermal cracking and settlement cracking.

3. A bridge deck is subjected to variable truck-load cycles in a humid environment. Propose a fatigue-assessment workflow, identifying the data, models, uncertainties and inspection decisions required.

Multiple Choice Questions with Answers

Question 1

Which property primarily describes resistance to deformation rather than failure?

A. Compressive strength

B. Elastic modulus

C. Fracture energy

D. Splitting tensile strength

Correct Answer: B. Elastic modulus

Question 2

For a cylindrical splitting test, the nominal tensile stress is calculated using which expression?

A. P/A

B. PL/4bd²

C. 2P/(πLD)

D. Eε

Correct Answer: C. 2P/(πLD)

Question 3

What is the main characteristic of quasi-brittle fracture in concrete?

A. No damage occurs before peak load

B. A finite fracture process zone develops

C. The material remains perfectly elastic after cracking

D. Failure is independent of specimen size

Correct Answer: B. A finite fracture process zone develops

Question 4

In the fatigue stress ratio R = σmin/σmax, what does σmax represent?

A. Average stress only

B. Minimum cyclic stress

C. Maximum cyclic stress

D. Fracture energy

Correct Answer: C. Maximum cyclic stress

Question 5

Which mechanism is especially associated with low water–binder-ratio concrete?

A. Autogenous shrinkage

B. Plastic settlement only

C. Aggregate swelling in all environments

D. Elimination of creep

Correct Answer: A. Autogenous shrinkage

Question 6

A concrete member is fully restrained and has an imposed strain of 0.0002. If its effective modulus is 15,000 MPa, the elastic restraint stress is:

A. 0.30 MPa

B. 3.0 MPa

C. 30 MPa

D. 75 MPa

Correct Answer: B. 3.0 MPa

Question 7

Which action most directly reduces plastic-shrinkage cracking risk?

A. Increasing surface evaporation

B. Delaying curing until the next day

C. Providing prompt protection and curing

D. Removing all reinforcement

Correct Answer: C. Providing prompt protection and curing

Question 8

Why can creep be beneficial in a restrained concrete member?

A. It increases tensile strength instantly

B. It can relax restraint stress over time

C. It eliminates drying shrinkage

D. It prevents all crack formation

Correct Answer: B. It can relax restraint stress over time

Question 9

What is a principal limitation of Miner’s linear fatigue damage rule?

A. It cannot represent any cyclic loading

B. It ignores possible load-sequence effects

C. It requires no fatigue data

D. It applies only to static strength

Correct Answer: B. It ignores possible load-sequence effects

Question 10

A temperature change in a free, uniform concrete element is most simply related to strain by which equation?

A. εT = αΔT

B. εT = P/A

C. εT = σ/E²

D. εT = φE/σ

Correct Answer: A. εT = αΔT