design of liquid retaining concrete structures third edition written pdf

Introduction

Scope

Reinforced and prestressed concrete structures are commonly utilized for the storage of water and other liquids, as well as for designing basements that require exclusion of groundwater Concrete is typically the most cost-effective construction material for these applications, offering longevity and low maintenance when properly designed and constructed The design methods outlined in this book align with the guidelines of Part 3 of Eurocode 2 and are suitable for various types of structures.

BS EN 1992-3 (2006) outlines guidelines for the design and construction of various structures, including storage tanks, reservoirs, swimming pools, elevated tanks (excluding support towers), ponds, settlement tanks, and basement walls However, it specifically excludes dams, structures exposed to dynamic forces, and any pipelines or aqueducts used for liquid conveyance.

When discussing designs for liquid retention, it is essential to consider not only water but also other aqueous liquids, including sewage tanks The structural pressures must be calculated using a specific gravity greater than one when the stored liquid is denser than water.

This book assumes that water is the primary liquid discussed, unless stated otherwise The term "structure" refers to the vessel or container that holds or prevents the liquid from escaping.

The design of structures for retaining oil, petrol, and other penetrating liquids is not covered in BS EN 1992-3 (2006), which suggests consulting specialized literature; however, the underlying principles may still be relevant Additionally, the design of tanks for containing hot liquids exceeding 200°C is not addressed in this code.

General design objectives

Structures designed to retain liquids must meet standard requirements for strength, durability, and minimal cracking or deflection Additionally, these structures must prevent any leakage or percolation through the concrete In typical building design, maintaining stability under both permanent and variable loads is crucial For liquid-retaining structures, if the design is properly proportioned and reinforced to prevent leakage (satisfying the Serviceability Limit State, SLS), it typically also meets the strength requirements of the Ultimate Limit State (ULS).

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Figure 1.2 A concrete tank (before construction of the roof) illustrating the simplicity of the structural form (Photo: M.J Kirby)

Figure 1.1 A tank under construction (Photo: J.P Forth/A.P Lowe).

To ensure a long service life for liquid-retaining structures, it is crucial to meet more stringent requirements compared to standard structures Adequate concrete cover over the reinforcement is essential, along with high-quality concrete that is properly compacted Additionally, maintaining good workmanship throughout the construction process is critical for optimal performance.

Potable water sourced from moorland areas can contain free carbon dioxide or dissolved salts that may corrode standard concrete, leading to similar issues in tanks used for sewage or industrial liquids To address these aggressive elements, it may be necessary to increase the cover and cement content of the concrete mix, utilize special cements, or, in very severe conditions as defined by BS EN 1992-1-1 (2004) and BS 8500-1 (2006), apply a special lining to the concrete tank.

Fundamental design methods

Historically, structural concrete design relied on elastic theory, which specified maximum design stresses at working loads In the 1980s, the UK adopted limit state philosophy, offering a more rational approach to safety factors The introduction of new Eurocodes in 2011, including BS 8110, marked a significant advancement in this field.

BS 8007 have been withdrawn, and in their place is a suite of new codes, including specifi cally BS EN 1992-1-1:2004 (Eurocode 2 Part 1 or EC2) and BS EN 1992-3:

2006 (Eurocode 2 Part 3 or EC2 Part 3) and their respective National Annexes

The latest Eurocodes maintain the limit state design approach, utilizing ultimate design principles In this process, characteristic actions are multiplied by partial safety factors to obtain enhanced ultimate actions These ultimate actions are then compared against the modified failure strengths of materials, which are also adjusted by their respective partial safety factors, to ensure safe and effective structural design.

Limit state design methods allow for the identification and analysis of potential failure modes in a structure, helping to prevent premature failures These limit states can be categorized into 'ultimate' states, which consider ultimate actions, and 'serviceability' states, which focus on service actions.

Historically, the design of liquid-retaining structures relied on elastic design principles outlined in BS 5337, resulting in low material stresses that prevented the development of flexural tensile cracks This approach necessitated the use of thick concrete sections with substantial mild steel reinforcement However, issues related to shrinkage and thermal cracking were inadequately addressed, with most codes of practice specifying only minimal reinforcement The alignment of design guidance for liquid-retaining structures with the Limit State code BS 8110, which governs the Structural Use of Concrete, became feasible after the development of analytical procedures to estimate flexural crack widths and compare them with specified maxima.

1966; Beeby, 1979) and a method of calculating the effects of thermal and shrinkage strains had been published (Hughes, 1976).

Before the 1980s, BS 5337 permitted designers to select between elastic and limit state design methods It is often remarked that "a structure does not know how it has been designed." Any design approach that ensures a serviceable structure can be built safely and economically is valid However, since the introduction of BS 8007 in the UK, limit state design has become the standard practice.

The design of liquid-retaining structures has seen successful advancements, particularly with the introduction of new Eurocodes that embrace the limit state design philosophy Although the previous guidelines have been withdrawn, the ongoing development in this area suggests that progress can continue effectively.

Codes of practice

For the design of water-retaining structures, BS EN 1992-3 offers specific guidance on containment structures, complementing the information provided in BS EN 1992-1-1 It is important to note that BS EN 1992-3 does not address joint details This practice aligns with the previous code, BS 8007, which also supplemented the overarching Structural Use of Concrete code, BS 8110, with additional rules.

Unlike BS 8110, which provided guidance on design philosophy and load combinations, the Eurocodes adopt a different methodology Specifically, BS EN 1992-1-1 is supported by the Eurocode framework, emphasizing a more standardized approach to design principles.

BS EN 1990:2002, known as Eurocode 0, provides essential guidelines for structural design, focusing on safety, serviceability, and durability across various construction materials Complementing this, Eurocode 1 (BS EN 1991) outlines the actions on structures and replaces the previous standards BS 6399 for loading and BS 648 for the schedule of weights of building materials Each Eurocode and its respective parts come with a National Annex (NA) to ensure localized application.

Document (NAD), which provide guidance specifi c to each individual state of the

European Union, i.e the UK National Application Document only applies to the UK

Values in these National Annexes may be different to the main body of text produced in the Eurocodes by the European Committee for Standardization (CEN).

The key differences between BS 8110/BS 8007 and the new Eurocodes are evident to designers; while Eurocodes focus on structural behavior—such as bending and shear—they do not specify member types like beams.

Also, Eurocodes are technically strong and fundamental in their approach–they do not provide a step-by-step approach on how to design a structural member.

Impermeability

For liquid-retaining structures, it is essential to use concrete with low permeability to prevent leakage and ensure durability This type of concrete also offers resistance to frost damage and protects embedded steel from corrosion A properly designed and compacted uncracked concrete slab of sufficient thickness will effectively contain liquids Detailed specifications for suitable concrete mixes can be found in Chapter 2.

For optimal performance in most structures, the minimum thickness for poured in-situ concrete should be 300 mm Thinner slabs are only suitable for structural members with restricted dimensions or when subjected to very low liquid pressures.

Liquid loss in concrete can result from poorly designed joints, cracks, or inadequately compacted surfaces Cracking is almost unavoidable in all but the simplest structures, and when a concrete slab cracks, it can lead to liquid leakage or wet patches on the surface.

Cracks of limited width typically do not permit liquid leakage, as noted by Sadgrove (1974) For designers, the challenge lies in controlling surface crack widths to a specified limit Cracks resulting from shrinkage and thermal movement usually maintain a uniform thickness, influenced by the internal restraint, while flexural cracks are shallower and supported by a compressive layer of concrete Consequently, shrinkage and thermal movement cracks pose a greater risk for leakage.

An important consideration in structural engineering is whether early thermal cracking and loading-induced cracking are additive While long-term effects may complement early thermal cracking, there is currently no established method to quantify the combined impact of early-age cracking and structural loading Although no specific issues have been identified regarding this interaction, it does not rule out its occurrence Recent research has indicated that loading can lead to both the extension of existing early-age cracks and the formation of new cracks (Forth et al., 2004).

Before evaluating the relationship between early-age cracking and cracking due to structural loading, it is essential to understand the external restraint conditions that contribute to early-age cracking This restraint can occur from either end or edge (base) constraints, as illustrated in Figure 1.3 These two forms of restraint represent the primary limiting factors affecting deformation.

In practice, the actual restraint in wall thermal movements is often a combination of two forms, with edge restraint being the more likely consideration during early movements (Beeby and Forth, 2005).

In a scenario where both edge and vertical restraint are present, consider a newly cast section of concrete positioned between two existing concrete wall segments and resting on a pre-existing concrete base In this case, edge restraint plays a dominant role at the base, influencing the overall structural behavior.

Zone 2) However, further up the wall away from the base, edge restraint will become less signifi cant and end restraint will become more infl uential At a point within the height of the wall, end restraint will dominate and edge restraint becomes insignifi cant

(see Figure 1.4–Zone 1) The position and signifi cance of the two restraint conditions

Figure 1.3 External end and edge (base) restraint.

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BS EN 1992-3 outlines restraint factors (R) for different wall and floor slab placement sequences, as illustrated in BS 8007 The document visually represents the interaction between two external restraint types: end and edge restraint However, it is important to note that the restraint factor, R, is primarily derived from a structural model that considers a member restrained at its ends, preventing overall shortening.

On the matter of whether or not early age cracking can be compounded by load cracking, consider the example of a horizontal slab between rigid end restraints

According to BS EN 1992-3, slabs constrained by rigid supports are prone to develop primary cracks, typically located midway between these restraints This positioning is often where cracks are most likely to emerge due to structural loading While additional investigations are necessary to verify the occurrence of combined cracking, the potential for such cracking is evident in this scenario.

When a wall is cast on a base and is sufficiently long, it can experience primary vertical cracking due to early age movement, even without support from adjacent wall panels This situation causes the wall to behave like a cantilever, resulting in horizontal structural cracking Consequently, early age cracking occurs independently of structural cracking.

According to Fig L1 (d) of BS EN 1992-3, a wall that is restrained at its base and by adjacent wall panels is likely to develop diagonal cracks at its base and near the ends The potential impact of these diagonal cracks on the formation and behavior of structural cracking remains uncertain, indicating a need for further investigation.

No specific problems have been identified related to the combination of early-age and structural cracking, possibly due to the over-estimation of steel requirements in the design of water-retaining structures In edge-restrained scenarios, crack width is influenced by the imposed strain rather than the concrete's tensile strength The horizontal reinforcement needed is primarily to manage early thermal cracking, with traditional methods using about 0.2% of anti-crack reinforcement, while BS 8007 guidelines recommend at least double this amount for improved crack control based on the structure's intended use.

Figure 1.4 Approximate regions of domination of end (Zone 1) and edge (Zone 2) restraint in an infi ll wall.

7 widths required in water-retaining structures) The Eurocodes appear to require between

0.3 and 0.4% These all relate to restraint of early thermal movement which, as discussed earlier, is based on the end restraint condition and not edge restraint

The question is one of whether this amount of steel is actually necessary.

Site conditions

When selecting a site for a reservoir or tank, factors beyond the structural designer's control often dictate the choice, yet soil conditions significantly influence the design An ideal site features well-drained soils with a uniform safe bearing pressure at the foundation level, commonly found at elevated locations like hilltops However, many sewage tank construction sites encounter poor bearing capacity and high groundwater tables, necessitating careful design to prevent flotation and manage potential settlement issues Additionally, if the subsoil strata vary within the excavation, differential settlement must also be addressed to ensure structural integrity.

A soil survey is always necessary unless an accurate record of the subsoil is available

For effective soil analysis, boreholes with a minimum diameter of 150 mm should be drilled to a depth of 10 m, allowing for the collection and testing of soil samples to assess the strata sequence and permissible bearing pressure at different depths Additionally, it is essential to enhance this data by excavating trial pits to depths of 3–4 m using a small excavator.

Soil investigations should incorporate chemical testing of both soil and groundwater to identify the presence of sulphates and other harmful chemicals that may lead to concrete deterioration and reinforcement corrosion (Newman and).

A thorough examination of the subsoil is crucial, especially for sites with a history of industrial use or those affected by groundwater from nearby landfills For additional details, refer to Chapter 2.

When mining activity is suspected, a comprehensive survey and a report from a mineral valuer or mining consultant are essential It may be necessary to conduct deeper, randomly located boreholes to identify any voids beneath the site Designing a reservoir to accommodate ground movement from future mining activities requires additional movement joints or other measures, which are beyond the scope of this book Additionally, in certain regions, it is crucial to consider the potential impact of earthquakes and to follow local practices accordingly.

Figure 1.5 Tank fl otation due to ground water. empty structure tends float ground level ground water level

Infl uence of execution methods

When designing liquid-retaining structures, it is crucial to address constructional challenges, particularly regarding construction joints, which should be clearly indicated on drawings Unlike typical building structures, these joints must be specified to ensure concrete is poured in a single operation between designated joint positions The treatment and detailing of these joints, including the incorporation of waterstops for movement joints, are essential for structural integrity The designer holds the responsibility for the detailed design and specification of joints, as the amount of distribution reinforcement and joint spacing are interconnected Additionally, casting new concrete adjacent to hardened sections generates restraining forces that can lead to cracking, making it vital to consider the degree of restraint from adjacent panels when determining reinforcement needs.

When constructing a tank in water-bearing ground, it is essential to design it to exclude groundwater during the building process This can be accomplished through general ground de-watering or by implementing sheet piling If opting for sheet piling, careful attention must be paid to the placement of necessary props and the anticipated construction sequence.

Design procedure

In structural design, determining the size and reinforcement of members is crucial before analyzing their strength and calculating crack widths under load For liquid-retaining structures, crack-width calculations significantly influence member thickness, making it challenging to estimate the required thickness without employing the limited stress design method.

An intermediate design method allows for the satisfaction of the cracking limit state by restricting reinforcement stress instead of conducting a complete calculation This approach is especially beneficial for sections experiencing both flexural and direct stresses.

Figure 1.6 Effect of varying strata on settlement.

Code requirements (UK)

BS EN 1992-3 builds upon the guidelines of BS EN 1992-1-1 for designing standard structural concrete The design and detailing of liquid-retaining structures must adhere to BS EN 1992-1-1, unless specified otherwise by BS EN 1992-3.

1992-3 (and the UK National Annex) vary the requirements The modifi cations that have been introduced into the Eurocodes mainly relate to:

• surface zones for thick sections with external restraint;

• surface zones for internal restraint only;

• the critical steel ratio, ρ crit ;

• the maximum crack spacing, S r,max ;

These modifi cations are suitably discussed by Bamforth (2007), Hughes (2008) and

Basis of design and materials

Structural action

To begin a design, it's essential to determine the type and layout of the structure Allocating preliminary sizes to each structural element allows for analysis and confirmation of these dimensions.

All liquid-retaining structures are required to resist horizontal forces due to the liquid pressures Fundamentally there are two ways in which the pressures can be contained:

(i) by forces of direct tension or compression (Figure 2.1);

(ii) by fl exural resistance (Figure 2.2).

Structures utilizing tensile or compressive forces are typically circular and may incorporate prestressing techniques In contrast, rectangular tanks or reservoirs depend on flexural action, employing cantilever walls, propped cantilever walls, or walls that span in two directions These structural elements, which flex to counteract liquid pressure, exert direct forces on the supporting elements.

2.3) is a small tank Additional reinforcement is necessary to resist such forces unless they can be resisted by friction on the soil.

Exposure classifi cation

Structural concrete elements encounter diverse environmental conditions For instance, a pumphouse roof is waterproofed with asphalt or roofing felt, remaining protected from wet conditions except during construction In contrast, the exposed legs of a water tower experience alternating wetting and drying due to rainfall, without retaining liquid The lower walls of a reservoir are consistently wet, except during maintenance, while the upper sections experience fluctuations in moisture as water levels change Additionally, the underside of a closed reservoir roof remains damp from condensation, as the waterproofing prevents complete drying These varying conditions highlight the importance of understanding the environmental impacts on structural concrete.

As exposure conditions intensify, it is crucial to implement precautions that prevent moisture and air from initiating carbonation in the concrete cover over reinforcement This carbonation can compromise the protection of steel, leading to corrosion and ultimately resulting in concrete surface spalling (Newman, 2003).

Adequate durability can normally be ensured by providing a dense well-compacted concrete mix (see Section 2.5.2) with a concrete cover (cast against formwork) in the

Figure 2.2 Direct forces of tension in wall panels of rectangular tanks. plan section elevation of one panel

2 way span reaction from next panel friction friction

Figure 2.3 Tension in fl oor of a long tank with cantilever walls.

Figure 2.1 Direct forces in circular tanks (a) Tensile forces (b) Compressive forces. section section tension plan a) b) plan compression

Figure 2.4 Exposure to environmental conditions: (a) pumphouse roof, (b) water tower and

Wide surface cracks allowing moisture and air penetration and leakage or percolation of liquid

To effectively control cracking in concrete and prevent liquid percolation through structural members, it is essential to maintain a minimum crack width of 40 mm as specified in BS 8500-1.

The classification of exposure for design has evolved from BS 8110's relative severity categories (mild, moderate, severe) to Eurocode 2's focus on specific deterioration processes such as carbonation, chloride ingress, chemical attacks, and freeze/thaw cycles Complementing Eurocode 2, BS 8500 (Parts 1 and 2) serves as a detailed guide for determining concrete cover While BS 8500 may impose less stringent requirements for less severe exposure conditions compared to BS 8110, it presents different criteria for more severe conditions This distinction is crucial, as BS EN 1992-3 mandates that all liquid-retaining structures must be designed to withstand at least 'severe' exposure conditions, addressing factors like waterproof membrane integrity, wall wetness, and varying water levels.

When designing structures like water towers, it's crucial to consider exposure categories, particularly for environments prone to harsh conditions For instance, a water tower situated near the coast, subject to saltwater spray, should be classified under the 'very severe' exposure category to ensure durability and longevity.

Durability requirements in construction are met by controlling cracking, with the maximum allowable crack width for serviceability limited to between 0.05 mm and 0.2 mm, depending on the hydrostatic pressure to wall thickness ratio These specified crack widths represent the total crack width, encompassing early age, long-term, and loading conditions This information is outlined in BS EN 1992-3.

Section 7.3 of BS EN 1992-1-1 offers general guidance on crack control, while BS EN 1992-3 provides additional insights tailored to specific structural needs Early-age thermal cracking can lead to significant issues, such as through cracks that may cause seepage or leakage, which is particularly critical in water-retaining structures where such failures are unacceptable To address this, BS EN 1992-3 includes a 'Classification of Tightness' (refer to Table 2.1), which measures leakage protection This classification ranges from 0, indicating basic crack control as per BS EN 1992-1-1, to 3, which signifies that no leakage is allowed.

Tightness class 1 is normally acceptable for water-retaining structures.

The requirement for ‘No leakage permitted’ does not mean that the structure will not crack but simply that the section is designed so that there are no through cracks

The new Eurocodes do not specify a crack width recommendation of 0.1 mm for critical aesthetic appearance, a standard previously found in BS 8110 There is no rational basis for defining the aesthetic appearance of cracking According to BS EN 1992-3, for structures classified under Tightness class 1, limiting crack widths to the appropriate range will ensure effective sealing of the cracks within a relatively short period.

The ratios indicate pressure gradients within the structural section, reinforcing the assertion that cracks measuring 0.2 mm can 'heal' as long as the pressure gradient remains below 5, a claim consistent with BS 8007 For crack widths under this threshold, the potential for self-repair is maintained.

0.05 mm, healing will occur even when the pressure gradient is greater than 35 The fact that these cracks do seal is not strictly only due to autogenous healing (i.e self-healing due to formation of hydration products) as was claimed in BS 8007, but also possibly due to the fact that the crack becomes blocked with fi ne particles As mentioned above, sealing under hydrostatic pressure is discussed in Clause 7.3.1 of BS EN 1992-3 and for serviceability conditions, the limit state appropriate for water retaining structures, crack widths are limited to between 0.05 and 0.2 mm When considering appearance and durability, further guidance with respect to crack widths and their relationship with exposure conditions can be found in Clause 7.3.1 of BS EN 1992-1-1 and its NA (Table NA.4).

Tightness class Requirements for leakage

0 Some degree of leakage acceptable, or leakage of liquids irrelevant.

1 Leakage to be limited to a small amount Some surface staining or damp patches acceptable.

2 Leakage to be minimal Appearance not to be impaired by staining.

Structural layout

Before conducting a detailed analysis, it is essential to establish the layout of the proposed structure and estimate member sizes Structural schemes must be evaluated based on strength, serviceability, construction ease, and cost, which can often conflict with one another Achieving a satisfactory design requires a compromise that is straightforward in both concept and detail In the case of liquid-retaining structures, it is crucial to avoid abrupt changes in section to prevent stress concentration and reduce the risk of cracking.

To optimize structural integrity, it is essential to transfer loads directly to the foundations while minimizing the number of structural members Designing cantilever walls as tapering slabs is more effective than using counterfort walls with slabs and beams Additionally, flat slabs can be utilized for the floors of water towers and roofs of reservoirs Underground tanks and swimming pool tanks typically feature straightforward designs with walls and floors of consistent thickness.

Designers must carefully consider construction methods and clearly indicate the locations of all construction and movement joints on the drawings This is crucial because the detailed design of structural elements relies on the level of restraint provided by adjacent sections to the section being installed.

When planning concrete casting, it's essential to include 'kickers'—short sections of upstand concrete that allow for the tightening of formwork Additionally, consider the dimensions of wall and floor panels to ensure they can be cast in a single operation.

Infl uence of construction methods

When designing a structure, it is crucial for designers to consider the construction sequence, particularly during the excavation phase In water-logged areas, it is essential that the soil profile for the foundation and floors can be easily cut by machinery Flat surfaces and long strips are more cost-effective to form than individual small excavations Additionally, the soil at the foundation level exerts a restraining force due to early thermal contraction and shrinkage, which can lead to cracking in the structure.

Figure 2.6 Cracking due to restraint by frictional forces at foundation level (a) Floor slab (b) Wall

To effectively reduce frictional forces, a 1,000 g polythene sheet or similar material should be placed on a 75 mm layer of blinding concrete Achieving a smooth and level surface finish on the blinding concrete is essential, which requires a proper screeded finish This necessitates the use of a suitable grade of concrete that meets the standards outlined in BS 8500-1 (2006) and supported by previous studies (Teychenne, 1975; Palmer, 1977).

Using the same grade of concrete for the blinding layer as that used in the structure offers several advantages This approach ensures a smooth finish for the blinding layer and allows for the assessment of concrete strength and consistency at a less critical phase of construction Additionally, it helps to minimize the nominal cover, c nom, in accordance with BS 8500-1 (2006).

Foundations and floor slabs are built in manageable sections to ensure timely completion, with each section ending at a construction or movement joint It is essential to maintain a continuous construction sequence, as illustrated in Figure 2.7(a), to achieve optimal results.

The first casting system allows each section to have one free end, enabling it to shrink freely during cooling without end restraint, although edge restraint remains In contrast, the second method generates significant tensions between the rigid adjoining slabs.

BS 8007 previously offered three design options for managing thermal contraction and restrained shrinkage: continuous (full restraint), semi-continuous (partial restraint), and total freedom of movement However, BS EN 1992-3 appears to eliminate the semi-continuous design, limiting options to full restraint (no movement joints) and free movement (minimum restraint) For free movement conditions, it recommends spacing complete joints (free contraction joints) at a minimum of 5 m or 1.5 times the wall height, aligning with the maximum crack spacing guidelines in BS EN 1992-1-1 Despite this, BS EN 1992-3 indicates that a moderate amount of reinforcement should be sufficient to accommodate movements to adjacent joints, suggesting that continuity steel less than A s, min is permissible, thus allowing for semi-continuous joints.

Figure 2.7 Construction sequence (a) Preferred sequence (b) Not recommended (c) Effect of method (b) on third slab panel (cracks shown are illustrative only)

15 m 7.5 m full contraction joint sealer timber crack inducer floor partial contraction joint cracks formed and sealed inflated, removable rubber core wall

Figure 2.8 Joints (a) Typical layout in a wall (b) Typical layout of temporary gaps in construction (c) Induced joints.

It is recommended that if partial contraction joints are used, continuity steel of at least

A s, min (or 50% of the full continuity steel) is used and in fact the recommended spacing of these partial contraction joints is similar to that proposed previously (approx 7.5 m)

BS EN 1992-3 lacks specific guidance on the spacing of full contraction joints, meaning there is no continuity steel provided The 15-meter spacing between full contraction joints, depicted in part (a) of Figure 2.8, reflects the earlier recommendations found in BS 8007.

Temporary gaps can be intentionally left in concrete to be filled after it hardens, or induced contraction joints can be created by reducing the concrete section to control crack formation at desired locations The casting sequence typically proceeds vertically, starting with foundations or floors and a short wall section, known as a kicker, to support the formwork Walls can be poured in a single operation up to approximately 8 meters in height.

Reinforcement in construction must be precisely detailed to ensure that an adequate length of bar extends from the concrete sections at each construction stage The maximum spacing between bars should not exceed 300 mm or the slab thickness, while the minimum spacing, typically no less than 100 mm, is determined by the bar size to facilitate easy concrete placement Proper distribution is essential to manage shrinkage effectively.

In concrete construction, it is essential to position reinforcement in the outer layers closest to the surface for optimal effectiveness This strategic placement enhances the structural integrity of the joint between the floor and wall, ensuring durability and stability.

To enhance effective depth, the layering of reinforcement on each face may be impacted Additionally, Figure 2.8 demonstrates common crack inducers that can be utilized at both full and partial contraction joints.

Materials and concrete mixes

In liquid-retaining structures, it is common to use high-strength steel with a ribbed or deformed surface for reinforcement, despite the service tensile stress not always being very high This practice typically involves using either single bars or mesh to ensure structural integrity.

BS EN 1992-1-1 Annex C permits a range of characteristic yield strengths between

In the UK, the specified characteristic strength of reinforcement is 500 MPa, which is a statistical measure of the yield or proof stress of the reinforcement type According to standards, 5% of bars are expected to fall below this characteristic strength level To determine the ultimate design strength, a material partial safety factor of 1.15 is applied for Persistent and Transient loading High-yield bars are supplied in compliance with BS 4449:2005 and BS 8666:2005, which are aligned with BS EN 10080:2007 BS 4449 categorizes high-yield steel into three grades (A to C), with grade C being the most ductile and suitable for seismic applications In this context, B500 steel indicates high-yield steel with a characteristic strength of 500 MPa, while B500B refers to Normal grade B steel, although it is not uncommon for manufacturers to provide Grade C steel labeled as such.

Normal grade B steel Grade B500A steel is provided for cold working.

The fact that plain round grade 250 MPa steel was excluded from BS 4449 refl ects the fact that other standards are available for the specifi cation of mild steel bars

(BS EN 10025-1, 2004; BS EN 13877-3, 2004)and the fact that this grade was being used less frequently (CARES, 2012).

Welded fabric reinforcement, as outlined in BS 4483 (2005), is categorized into four types from A to D, with Type A, or Square Mesh, being the preferred choice for water-retaining structures This type is produced using bars of 10, 8, 7, or 6 mm in diameter, arranged at 200 mm centers in both longitudinal and transverse orientations.

Reinforcement in concrete is initially safeguarded from corrosion by the cement's alkalinity; however, over time, carbon dioxide exposure leads to carbonation, which diminishes this protection In specific situations, such as limited space or heightened risk, alternative reinforcement options may be necessary Stainless steel bars, specified in BS 6722 (1986), remain a popular choice in the UK, despite their cost being 10 to 12 times higher than standard high-yield bars Hot-dipped galvanizing is also employed to protect steel in various applications, with normal grade steel typically formed into reinforcement cages before the dipping process Conversely, the use of epoxy-coated bars has significantly declined in the UK due to associated issues.

BS EN 206-1, established in 2000 and amended in 2004 and 2005, governs the specification, performance, production, and conformity of concrete In the UK, the National Annex (NA) to BS EN 1992-1-1 mandates the use of BS 8500, a complementary British Standard that includes additional provisions specific to the UK.

British Standard 8500 defines concrete strengths through 'compressive strength classes' using a notation that includes both cylinder and cube strengths (e.g., C25/30) It offers guidance on specifying concrete materials, including cement type, aggregates, and admixtures, while also assessing cover and strength for durability, effectively replacing previous standards.

BS 5328 and related sections of BS 8110-1.

Figure 2.10 Graphical defi nition of characteristic strength.

=1% to 12% depending on steel grade

While this book does not cover the intricate specifications and designs of concrete mixes, Chapter 6 offers a typical mix design specifically for water-retaining structures.

Recent advancements in concrete sustainability have focused on optimizing the manufacturing process of cements, selecting appropriate aggregates, and reducing the use of CEM 1 (Portland cement) This reduction is achieved by replacing Portland cement or blending it with alternative materials, enabling the creation of concrete with enhanced properties such as reduced heat of hydration, faster strength gain, and improved frost resistance However, enhancing one property may compromise another, requiring designers to carefully weigh the technical and economic benefits of these new cements For example, specifying lower strength requirements does not necessarily lead to decreased durability; in fact, concrete with cement replacement materials like fly ash or ground granulated blast-furnace slag (GGBS) may provide superior rebar protection compared to traditional CEM 1 concretes.

(2004); more information can also be obtained from Bamforth (2007).

When selecting the maximum size of aggregate for concrete, it is essential to consider the thickness of the structural member For members with a thickness of approximately 300–400 mm, a maximum aggregate size of 20 mm is typically recommended, although larger sizes may be used if necessary In very thick members, a maximum size of 40 mm can be specified if available Utilizing larger aggregate sizes can lead to a reduction in cement content while maintaining workability, which in turn minimizes the risk of shrinkage cracking.

When selecting aggregates, it is crucial to opt for those with low drying shrinkage, ideally below 0.075% as per BS 8500: Part 2, and low absorption rates While most quartz aggregates typically meet these criteria, it is advisable to assess the porosity of limestone aggregates before use.

Certain aggregates obtained from igneous rocks exhibit high shrinkage properties and are quite unsuitable for use in liquid-retaining structures.

The type of aggregate used in concrete significantly influences early thermal cracking Crushed rock, a preferred normal weight coarse aggregate, offers higher tensile strain capacity compared to rounded aggregates and typically has a low coefficient of thermal expansion, often seen in many limestones Designers must carefully weigh these factors to balance the benefits and drawbacks Lightweight aggregates, which exhibit even lower coefficients of thermal expansion, are gaining popularity for their superior tensile strain capacities Additionally, recycled concrete aggregates (RCA) and recycled aggregates (RA), as specified in BS 8500 Parts 1 and 2, are becoming increasingly favored in concrete applications.

Local suppliers can provide evidence of prior usage that meets the specifier's requirements, particularly under BS 8500 Utilizing locally sourced aggregates is more cost-effective and sustainable, but caution is advised when sourcing from new quarries, and testing the aggregate properties is recommended.

Admixtures play a crucial role in enhancing the strength and durability of concrete Common types include plasticisers and super-plasticisers, which improve workability and allow for easier placement while reducing water content, thus functioning as water-reducing agents Additionally, air-entraining agents introduce air bubbles into the concrete, boosting freeze-thaw resistance and overall durability, though they may lead to a reduction in compressive strength—approximately 5% for every 1% of entrained air Moreover, certain admixtures can slow down the hydration process, which is beneficial for large pours to prevent premature setting However, admixtures containing calcium chloride should be avoided due to the potential risk of reinforcing steel corrosion.

The design of a concrete mix involves several key stages, starting with the identification of relevant exposure conditions Each face of the structure and its individual elements must be assessed and assigned an appropriate exposure class to ensure durability and performance.

BS 8500 addresses the deterioration processes of concrete, focusing on carbonation (XC classes), freeze/thaw cycles (XF classes), chloride ingress (XD and XS classes), and chemical attacks, including sulphate attack from aggressive ground conditions The standard directs designers to consult the BRE for further guidance.

Special Digest 1(2005), which gives guidance on the assessment of the aggressive chemical environment for concrete class (ACEC), rather than the XA classes used in

BS EN 206-1.) All of these X classes are sub-divided; it is likely that there will always be at least one relevant exposure class for each element.

Once the relevant exposure condition(s) have been identifi ed, a strength class and cover (including permitted deviations) are chosen that will ensure a minimum 50-year working life of the structure.

Loading

According to BS EN 1991 (Eurocode 1: Actions on Structures), characteristic values for loads are essential for assessing liquid-retaining structures, which primarily experience pressure from the retained liquid The standard also outlines the nominal densities of materials relevant to these structures.

As of January 1, 1992, the guidelines do not specify the densities of all materials suitable for storage in liquid-retaining structures However, Table 2.2 lists the nominal densities for commonly stored liquids.

BS EN 1991 also provides specifi c guidance for Silos and Tanks (BS EN 1991-4)

Guidance on Thermal actions (BS EN 1991-1-5) and Execution actions (BS EN

1991-1-6) can also be particularly relevant to the design of water-retaining structures.

External reservoir walls must be designed to withstand soil fill pressures, which are influenced by various factors including the water table level, the compaction state of the backfill, and the use of native soil Understanding these soil loading conditions is crucial for ensuring structural integrity over time, as pressures are expected to increase as conditions stabilize.

In an 'at-rest' condition, clay backfill may take years to mobilize, necessitating careful design considerations When the reservoir is empty, it is crucial to account for both the 'at rest' or active earth pressure and any surcharge pressures from vehicles, applying appropriate partial safety factors Proper control of the backfill is essential to ensure structural integrity during this phase.

In the 'reservoir full' scenario, it is essential to assume at least the active earth pressure during design Importantly, no relief from the soil fill's passive pressure should be considered, due to the differing moduli of elasticity between soil and concrete This discrepancy prevents the soil's passive resistance from developing until the concrete is fully subjected to the pressure of the contained liquid Consequently, insufficient strain may be generated in the soil to produce passive pressure, although the method of backfill and potential over-compaction can lead to pseudo passive conditions.

Eurocode 0 specifies three distinct load combinations for ultimate limit state analysis in persistent and transient situations: (i) EQU, for assessing loss of equilibrium; (ii) STR, for evaluating internal structural failure based on material strength, applicable regardless of geotechnical actions; and (iii) GEO, for analyzing ground failure or soil strength resistance Typically, in normal conditions, both ULS (STR) and SLS limit states should be taken into account.

When designing a reservoir, it is essential for the designer to account for the possibility of some sections being empty while others are full Each structural element should be engineered to withstand the maximum bending moments and forces resulting from hydrostatic pressures, as well as lateral earth, groundwater, and potential surcharge pressures, or a combination of these factors.

Table 2.2 Nominal density of retained liquids.

Digested sludge aerobic 10.4 Digested sludge anaerobic 11.3 Sludge from vacuum fi lters 12.0

The Eurocodes, following the guidance of BS 8110, design to limit states by combining permanent (dead) and variable (imposed) actions, with characteristic actions multiplied by appropriate partial safety factors (psfs) To ensure structural elements meet ultimate limit state requirements, it is essential to apply psfs alongside characteristic actions, providing a necessary safety margin against potential failure These psfs account for the expected variability in loading and the implications of structural failure.

For the case where the pressure is derived from the stored liquid alone (i.e (a) above), the ULS (STR) operational safety factor, γ F = 1.2, as provided in BS EN 1991-4

(Actions on Silos and Tanks) (Water = permanent action.) Under test, γ F = 1.0.

In structural design, the operational safety factors are typically set at γ F = 1.35 for permanent actions and γ Q = 1.5 for variable actions To account for the low probability of multiple variable actions reaching their maximum simultaneously, a multiplier, ψ 0, is applied to the variable action partial safety factor Additionally, multipliers ψ 1 and ψ 2 are used to represent frequent and quasi-permanent load values, respectively, particularly in Ultimate Limit State (ULS) scenarios involving accidental actions The quasi-permanent multiplier also aids in assessing long-term effects such as creep and settlement, with specific numerical values for ψ 1 and ψ 2 detailed in BS EN 1990.

Designers must conduct structural analysis to assess the arrangement of permanent and variable loads on a structure, ensuring they identify the most critical effects of these loads.

A few fi nal design comments: as the roofs of partially buried and underground reservoirs are covered with a solar attenuating layer composed of soil or gravel, any

Figure 2.11 Design loadings for external walls with soil fi ll (a) Reservoir full (b) Reservoir empty

When designing a roof slab, it is crucial to recognize that the imposed loads from vehicles will be distributed before reaching the structural elements Typically, a single load analysis case is sufficient for roof design For monolithic roofs attached to reservoir walls, thermal expansion may exert additional stress on the perimeter walls While BS EN 1991-1-5 (Thermal Actions) offers some guidance on this issue, it is primarily tailored for bridge design Ongoing research is being conducted on a partially buried reinforced concrete service reservoir in North to further investigate these effects.

Yorkshire and full-scale laboratory testing) to quantify this type of thermal effect

(Forth et al., 2005; Muizzu, 2009; Forth, 2012) BS EN 1991-4 (Actions–Silos and

Thermal expansion stresses can be disregarded if the number of expansion cycles poses no risk of fatigue or cyclic plastic failure However, despite the relatively low number of thermal cycles, caution is advised when designing monolithic roof-to-wall joints in buried or partially buried structures due to the additional moments caused by thermal creep.

For a reservoir with height of wall, H and an operating depth of water, h, BS EN

According to the 1991-4 guidelines for silos and tanks, a partial safety factor of γ F = 1.2 should be applied to determine the design load at Ultimate Limit State (ULS) under normal operational conditions, calculated as 1.2ρh, where ρ represents the density of the liquid In contrast, for accidental scenarios, a safety factor of γ F = 1.0 is recommended, utilizing the full depth of the wall in the calculation, expressed as 1.0ρH.

Foundations

For optimal performance, liquid-retaining structures should be built on stable, uniform soil to prevent differential settlements However, achieving this ideal condition can be challenging due to varying soil conditions, which must be assessed to estimate potential settlement issues (Barnes, 2000) To accommodate some movement, joints can be incorporated, but in cases of significant soil variability, it may be necessary to construct the structure in entirely separate sections Alternatively, employing cut-and-fill techniques can create a consistent foundation for the structure.

Figure 2.12 Propped cantilever walls on a cohesive soil (a) Structure (b) Basic structural assumptions (c) Rotation due to soil movement

Soils that contain bands of peat or other very soft strata may not allow normal support without very large settlements, and piled foundations are required (Barnes,

Designing structures in mining regions necessitates incorporating additional joints, segmenting the structure into smaller units, or utilizing rafts to accommodate significant settlements To enhance resistance to cracking during movement, prestressed tendons can be integrated into standard reinforced concrete designs.

Partially buried cantilever walls rely on passive resistance against sliding between the base and the foundation soil However, when groundwater saturates the soil, achieving the necessary resistance under the footing can be challenging due to elevated water pressures In such cases, additional lateral support, like a toe, may be needed, or a cantilever design might be unsuitable Instead, overturning and sliding forces could be countered with a system of beams balanced by the opposite wall or by designing the wall to span horizontally if feasible When walls are fully buried, the resistance they provide should also be taken into account.

Walls that are designed as propped cantilevers, and where the roof structure can act as a tie, are often considered to have no rotation at the footing (Figure 2.12)

In cohesive soils, the strain can facilitate rotation and the redistribution of forces and moments, impacting the stability of structures As the groundwater level rises, the weight of the soil on the heel surrounding the tank increases, leading to a greater downward load Additionally, increasing the floor thickness can further add weight at ground level, influencing the overall load distribution.

Figure 2.13 Methods of preventing fl otation (a) Additional dead weight (b) Provision of a heel

Flotation

An empty tank in water-bearing soil can experience upward movement or floating due to groundwater pressure To ensure stability, designers must compare the permanent stabilizing forces, such as the tank's weight and side friction, against the permanent and variable destabilizing forces from groundwater and other sources In essence, the tank's weight must exceed the upward force created by the displaced groundwater to prevent uplift.

According to BS EN 1997-1:2004 (Eurocode 7), the stabilizing actions required to ensure structural stability must exceed the destabilizing actions, particularly in the context of hydraulic uplift assessment This code serves as a critical guideline for designers evaluating the stability of structures.

According to BS EN 1997-1 and its National Annex, the partial safety factors for assessing the uplift limit state related to buoyancy and flotation are specified The stabilizing action of water is assigned a partial safety factor of 0.9 (γ G;stb = 0.9), while the destabilizing action is given a factor of 1.1 (γ G;dst = 1.1).

To enhance the weight of a tank, one can either thicken the floor or add a perimeter heel to utilize additional weight from the surrounding soil Regardless of the chosen method, it is crucial to ensure that the floor is designed to withstand uplift caused by groundwater pressure When calculating the weight of the soil over the heel, it is essential to consider that the soil is submerged in groundwater.

Thickening the floor reduces the effective density of the soil, allowing for construction in two separate layers linked by ties This method offers the benefit of using reduced thermal reinforcement suitable for the upper layer's thickness.

Designers must account for construction conditions alongside the final state of the structure It is essential to outline a construction sequence that guarantees stability throughout each phase of the building process.

Chapter 6 provides a design example that illustrates the use of the basic design materials and parameters presented in this chapter, including a UPL design check for stability against hydraulic uplift.

[1] Typically, owing to the more stringent cover requirements of BS EN 1992-1-1 and

BS 8500, the required cover has increased compared to that required previously in

BS 8110 and BS 8007 influence the calculated crack widths in concrete structures, particularly where crack spacing is regulated by reinforcement This affects the necessary steel area to manage these crack widths effectively For a more in-depth discussion on cracking, refer to Chapters 3 and 5.

Design of reinforced concrete

General

The basic design philosophy of liquid-retaining structures is discussed in Chapter 2

In this chapter, detailed design methods are described to ensure compliance with the basic requirements of strength and serviceability.

Unlike conventional structural design, which primarily focuses on strength, the design of liquid-retaining structures is predominantly governed by serviceability considerations Consequently, the design procedure must prioritize these serviceability factors to ensure optimal performance.

(ii) calculate the reinforcement required to limit the design crack widths to the required value;

(iv) check other limit states;

The calculation of crack widths in a member subjected to fl exural loading can be carried out once the overall thickness and the quantity of reinforce ment have been determined.

Wall thickness

When designing liquid-retaining structures, it is essential to start by estimating the overall wall thickness in relation to the height The wall thickness should be optimized to prevent excessive thermal stresses during the concrete hardening process, as unnecessary thickness can lead to increased stress levels.

The principal factors that govern the wall thickness are:

(iii) avoidance of excessive defl ections;

(v) avoidance of excessive crack widths.

The fi rst estimate of minimum section thickness is conveniently made by considering

For a simple cantilever, a wall thickness of approximately 1/10 of the span is recommended, while a slightly reduced thickness is suitable for walls restrained on multiple edges Each of these factors will be elaborated upon in the subsequent sections.

When designing liquid-retaining structures, it is crucial to ensure that wall thickness is adequate in relation to height, as thin walls can hinder the proper placement and compaction of concrete Typically, walls up to 8 meters high are cast in a single operation; however, for panels exceeding a 7-meter span, adjustments to the limiting span-to-depth ratios must be considered.

Section 3.2.5), and to enable this to be successfully carried out, the minimum thickness of a wall over 2 metres high should be not less than 250–300 mm Walls less than

2 metres high may have a minimum thickness of 200 mm A wall thickness less than

200 mm is not normally possible, as the necessary four layers of reinforcement cannot be accommo dated with the appropriate concrete cover on each face of the wall

To optimize material usage, the wall's thickness may gradually decrease with height, and a uniform tapering throughout the entire wall enhances the ease of setting out.

Lateral pressure on a wall slab is countered by bending moments and shear forces that transfer applied loads to the supports In the most straightforward scenario, the wall acts as a simple cantilever, experiencing peak shear force and bending moment at its fixed end.

Table 3.1 Approximate minimum thickness h (mm) of R C Cantilever wall subjected to water pressure.

Height of wall (m) Minimum wall thickness h (mm)

Figure 3.1 Typical section through a wall. designed thickness h minimum thickness uniform taper

In structural design, the wall panel's support at all four edges allows for a continuous structure, enabling the slab to span in two directions This arrangement significantly reduces the bending moments compared to a simple cantilever, allowing for the use of thinner walls with less reinforcement to prevent cracking The optimal design will vary based on the relative spans in each direction and the necessity for movement joints along the panel's edges.

3.2.4 Shear resistance of reinforced concrete

Theoretically, shear in reinforced concrete fl exural members is resisted by a combination of four factors:

(i) concrete in the compression zone;

(ii) dowell action of main reinforcement;

(iii) aggregate interlock across fl exural (tension) cracks;

Eurocode 2 respects the above theory and as such, the shear stress depends on the concrete strength, effective depth and tension steel ratio As before in BS 8110, the recommended design guidance in BS EN 1992-1-1 is (i) that there is a shear stress below which only minimum shear reinforcement need be provided (shear reinforcement is provided in all structural elements) and (ii) the design shear stress should be less than the shear capacity of the section.

The design approach in BS EN 1992-1-1 differs subtly from that in BS 8110, consisting of three stages for shear design The first stage involves assessing the capacity of the concrete alone If this capacity is inadequate to handle the design shear force, the second stage focuses on determining the required steel reinforcement without considering the concrete's shear capacity Consequently, in most structural beams, shear capacity is primarily calculated based on the steel, overlooking the concrete's contribution The final stage, stage three, specifies the area and spacing of the shear reinforcement needed.

Using shear reinforcement in slabs can be inconvenient due to the difficulty of installation and its interference with concrete placement, making it an inefficient use of steel.

In water-retaining structures, shear design focuses on ensuring that the shear capacity of the concrete slab surpasses the applied design shear force While stages 2 and 3 of the design process are not discussed in detail, they are based on established theories and are adequately covered in relevant codes and general texts on reinforced concrete.

According to BS EN 1992-1-1, the concrete shear force capacity, V Rd,c is given as:

V Rd,c = b w d [(0.18/ c ) k (100 1 f ck ) 1/3 + 0.15 cp ] (units are N) (3.1)

(0.18/ c ) = C Rd.c where  c = 1.5 (partial factor for concrete) k = (1 + (200/d) 1/2 ) 2.0 (with d expressed in mm)

 1 = A s1 / b w d ≤ 0.02 where A s1 = the area of tension reinforcement that extends beyond the section being considered by at least a full anchorage length plus one effective depth, d

 cp is only included if there are axial forces within the member (discussed later)

In recognition of the fact that a member still possesses some shear strength even without any reinforcement, the minimum value for the concrete shear force capacity is:

To ensure adequate capacity in concrete structures, the wall thickness must be adjusted so that the concrete shear force capacity (V Rd,c) exceeds the applied shear force (V Ed) Alternatively, the concrete shear stress capacity (v Rd,c) should surpass the applied shear stress (v Ed), calculated as v Ed = V Ed / 0.9 b w d, with the factor of 0.9 applicable only when using the Variable Strut Inclination Method The National Annex provides essential values for C Rd,c, k 1, and v min, where v min is defined as [0.035k 3/2 f ck ẵ] Additionally, it offers guidance for concrete strength classes above C50/60 Unlike BS 8110, which limited design shear stress to the lesser of 0.8√f cu or 5 N/mm², BS EN 1992-1-1 mandates that the applied shear force V Ed must always meet specific conditions for structural integrity.

V Ed ≤ 0.5 b w d v f cd (3.2a) where v = 0.6 [1–f ck /250] ( f ck in MPa)

The capacity of concrete to resist shear is influenced by longitudinal tension steel, indicating that the applied shear force, V Ed, generates additional forces in the tension steel that must be considered in the design While BS EN 1992-1-1 does not mandate this check for members that do not require shear reinforcement, it does require this consideration for those that do necessitate shear reinforcement.

This additional longitudinal tension force, ∆F td for sections reinforced with vertical links

(i.e links perpendicular to the horizontal or longitudinal axis of the section) is defi ned:

∆F td = 0.5V Ed cot (3.3) where  is the angle between the concrete compression strut and the beam axis perpendicular to the shear force (1 ≤ cot ≤ 2.5; 22° ≤  ≤ 45°).

Owing to the method of design introduced in BS EN 1992-1-1 (the Variable Strut

The Inclination Method highlights the necessity of balancing the compressive force in inclined concrete struts with a horizontal tension force, as mandated by design codes These codes specify that only half of the horizontal tension force resulting from shear is to be accounted for by the reinforcement in the tension zone Typically, this additional tension force is not substantial; thus, the extra steel area required to address it is unlikely to exceed the area already determined for bending steel to meet serviceability limit states Moreover, this additional force can often be effectively managed through modifications to the existing design.

In Chapter 3, the authors emphasize the importance of detailing steel by increasing the curtailment lengths of the tension reinforcement They recommend conducting a thorough check, as illustrated in Chapter 6, and advise that the angle θ in Equation (3.3) should be appropriately considered for optimal outcomes.

Whereas in BS 8110, values of design concrete shear stress were tabulated in terms of percentage area of tension steel and effective depth for a concrete of 25 MPa strength,

BS EN 1992-1-1 lacks specific guidance on this topic; however, an equivalent table can be created using Eqs (3.1) and (3.2) This derived table, presented as Table 3.2, offers values of v Rd,c for slabs made with C30/35 concrete and without any axial loads.

A comparison between the guidance provided in BS 8110 and the current BS EN

Cracking

When a reinforced concrete slab experiences lateral loading, the concrete on the tension reinforcement side tends to extend, leading to cracking as the load increases Initially, a crack will form with a positive width, and subsequent loading will result in additional cracks and the widening of existing ones, potentially creating a stabilized crack pattern However, this stabilization is rare in practice, and as cracks develop, the stress in the reinforcement increases By using a concrete section with a higher quantity of reinforcement, the service stresses in the steel can be reduced, which may result in narrower crack widths.

In structural design, the applied load is predetermined, and using limit state design principles, designers must select appropriate slab thickness and reinforcement quantities to ensure that crack widths under service loads remain within acceptable limits based on the exposure class Achieving compliance with the ultimate limit state is also essential However, there is no one-size-fits-all design that can meet all criteria simultaneously, allowing for multiple viable solutions even for a specific design crack width.

In Sections 3.4 and 3.5, the methods for calculating limit state design are outlined, emphasizing the importance of identifying the predominant force system when both direct tensile and flexural forces are present For vertical walls, horizontal tension occurs near lateral walls, while circular deep tanks primarily experience tensile forces without significant flexure at the top When flexural forces dominate, additional tensile forces can be accounted for by increasing the calculated reinforcement for flexure based on the service stress in the flexural steel In cases where both flexure and direct tension are significant, a modified strain diagram should be utilized for accurate calculations, including flexural crack width It is crucial to ensure that reinforcement is evenly distributed on both faces of the section when substantial tensile forces are present, promoting best practices by either maintaining equal steel arrangements or implementing clearly distinct reinforcement patterns to minimize on-site errors.

Calculating stress and strain diagrams for combined bending and tension leads to a complex cubic equation Designers often refer to handbooks with charts for solutions, while another option is utilizing computer programs for accurate results.

In some circumstances, it is possible in the fi rst instance to choose a section and

Figure 3.5 Flexural cracking (a) Concrete uncracked with low steel stress (b) Fine cracks and increased steel stress (c) Wide cracks and high steel stress. a) b) c)

To optimize the design for reinforcement, focus on bending alone initially, then adjust the calculations using the formulas from Section 3.6 This allows for accurate recalculation of strain based on the neutral axis depth relevant to the actual bending and tension applied Iteration of these results continues until a satisfactory solution is achieved.

Calculation of crack widths due to fl exure

3.4.1 Stress limitations in the concrete and steel

To ensure the limit state of cracking is satisfied, the maximum calculated surface crack width must not exceed the specified value, which varies based on the member's exposure degree A proper procedure is required to check the surface crack width effectively.

(i) calculate the service bending moment;

(ii) calculate the depth of the neutral axis, lever arm and steel stress by elastic theory;

(iii) calculate the average surface strain allowing for the stiffening effect of the concrete;

(iv) calculate the crack spacing;

The maximum service bending moment is calculated using characteristic loads with

 f = 1.0 The calculation for a slab is based on a unit width of 1 metre.

The depth of the neutral axis x is calculated (see Section 3.8.1) using the usual assumptions for modular ratio design (Figure 3.6): x / d =  e  {(1 + (2 /  e ) 1/2 –1} (3.11) where

 e is the modular ratio = E s / E c,eff

Alternative formulas for calculating the depth of the neutral axis are discussed in Chapter 6 on design calculations, and a more complex formula can be applied when compression reinforcement is included.

E c,eff (long-term or effective elastic modulus) above has traditionally in many cases been taken as half of the instantaneous or short-term modulus of elasticity of concrete,

The short-term modulus of concrete, as outlined in Table 3.1 of BS EN 1992-1-1, applies to concrete strengths ranging from 20 MPa to about 100 MPa (cube strength) For a more precise definition of the effective modulus, it is advisable to utilize the nomograms in Figure 3.1 of BS EN 1992-1-1 to determine the creep coefficient, φ.

(∞, t 0 ) for a particular strength concrete; the effective modulus is then calculated from:

Figure 3.1 of BS EN 1992-1-1 relates the tangent modulus, E c to the creep coeffi cient;

The effective modulus of elasticity (E c) can be considered as 1.05 times the modulus of elasticity for concrete in compression (E cm), as referenced in Clause 3.1.4 (2) According to Table 3.1 of BS EN 1992-1-1, the E cm values apply to compressive stresses ranging from 0 to 0.4 times the concrete's characteristic compressive strength (f cm) and specifically for concretes made with quartzite aggregates It is recommended to apply a 10% reduction to these values.

Cross Section Strain Distribution Stress Distribution

Figure 3.6 Assumed stress and strain diagrams – cracked section – elastic design. applied if the concrete is manufactured using limestone aggregates (see Cl 3.1.3 (2))

Current research is examining the application of a long-term or effective modulus, as initial findings indicate that long-term moments caused by creep in a monolithic roof-wall joint significantly exceed predictions made using a reduced or effective modulus (Forth, 2012; Muizzu, 2009).

Once x has been determined from Eq (3.11) above, the lever arm, z can be found from z = d–x / 3 (3.13)

The tensile steel and concrete compressive stresses are then given using: f st = M sls / zA s f cc = 2M sls / zbx

According to BS EN 1992-1-1 Clause 7.2 (3) and (5), for the linear creep assumption and crack width formula to be applicable, the compressive stress in concrete under quasi-permanent loads and the tensile stress in steel under service conditions must not exceed specified limits These limits are defined as k2 multiplied by the characteristic compressive strength of concrete (fck) for concrete, where k2 is 0.45, and k3 multiplied by the characteristic yield strength of steel (fyk) for steel, with k3 set at 0.8.

As with BS 8007, BS EN 1992-3 also provides guidance for the design of reinforcement to control early-age thermal and shrinkage cracking and fl exural cracking

Early-age thermal cracking is considered in Chapter 5 (which also considers long- term cracking due to shrinkage) This section deals with fl exural cracking.

To best illustrate the format of the guidance offered in BS EN 1992-3 it is worth recapping the approach presented in BS 8007 Previously, BS 8007 defi ned the design

The formula for calculating the surface crack width in sections experiencing flexure or a combination of flexure and tension, with the neutral axis depth (x) ranging from 0 to the effective depth (d), is given by: w = 3a cr  m / [1 + 2((a cr –c min ) / (h–x))] In this equation, the average strain at the cracking level, denoted as  m, is determined by the difference between two strains,  1 and  2.

 1 is the strain at the level considered (ignoring the stiffening effect of the concrete in the tension zone) (see Figure 3.7).

The strain, denoted as ε1, is calculated using the formula ε1 = [(h–x) / (d–x)] · (f_st / E_s) Additionally, ε2 represents the strain caused by the stiffening effect of concrete between cracks, which is defined based on the maximum allowable design surface crack widths of 0.2 mm or 0.1 mm.

(BS 8007: Appendix B; Equations 2 and 3, respectively).

The hyperbola outlined in Equation 3.14 illustrates the relationship between crack width, crack spacing, and distance from the bar, approaching the maximum crack width, denoted as w lim At the point where crack spacing equals the minimum value (c min), specifically directly above the bar, the crack width is calculated as w = 3c min ε m.

BS 8007 presents a distinct equation format for calculating crack width in members subjected to flexure, differing from the equation used for assessing crack width due to early thermal and shrinkage movements Notably, Equation 7.8 of BS EN 1992-1-1 provides additional guidance on this topic.

(here as Equation 3.16) describes the crack width for both cases: w k = s r,max ( sm −  cm ) (3.16) where s r,max = is the maximum crack spacing; x h d ε cc ε 1 ε st = f st / E s

Figure 3.7 Crack calculation – strain diagram.

 sm = is the mean strain in the reinforcement under the relevant combination of loads, including the effects of imposed deformations and taking into account the effects of tension stiffening;

 cm = the mean strain in the concrete between cracks (often ignored).

It must be noted that the approach adopted in BS EN 1992-1-1 (as was the case with

BS 8110) does not predict the maximum crack width but a crack width that in practice has a 20% chance of being exceeded (Beeby, 1979).

For the fl exural case, ( sm −  cm ) can be calculated using Equation 7.9 of BS EN

( sm −  cm ) =  s –k t ( f ct,eff /  p,eff )(1 +  e  p,eff ) / E s ≥ 0.6 ( s / E s ) (3.17) where

 s = the stress in the tension reinforcement assuming a cracked section;

A p ’ = 0 (reinforcement only; no pre or post-tensioned tendons);

A c,eff = the effective area of concrete surrounding the reinforcement of depth h c,eff

(where h c,eff is defi ned in Figure 3.8);

 1 = 0 (only consider if prestressing cables present); k t = a factor dependent on the duration of load (0.6 for short term; 0.4 for long term).

The maximum final crack spacing is determined using Expression 7.11 from BS EN 1992-1-1, represented as s r,max = k 3 c + k 1 k 2 k 4  /  p,eff In this equation, k 3 and k 4, which are specified in the National Annex, have values of 3.4 and 0.425, respectively Additionally, k 1 is a coefficient reflecting the bond properties of the bonded reinforcement, set at 0.8 for high bond bars, while k 2 accounts for the distribution of strain, with a value of 0.5 for bending scenarios.

In Chapter 2, it was highlighted that the new codes may necessitate higher cover values, leading to increased percentages of steel required for effective crack width control, as demonstrated in Equation (3.18).

The maximum crack width at the concrete surface is directly influenced by the specified parameters, as indicated by industry codes Research indicates that while cracks appear parallel at the surface, they taper to about 25% of the surface width at a depth of half the cover This raises the question of whether designers should focus solely on the surface crack width or consider minimum durability requirements instead To address this, the UK National Annex Document (NAD) has implemented a simplified method for predicting surface crack widths, aiming to provide reassurance to designers when determining adequate cover thickness for durability.

Kaethner (2011) critically examines whether BS EN 1992-1-1 has improved the prediction of crack widths, highlighting several key factors such as the influence of effective reinforcement ratio (ρp, eff) and bar layout, particularly noting that these factors are less significant for water-retaining structures due to their more uniform detailing She also addresses the implications of excessive concrete cover on predicted crack widths, especially in relation to flexural cracking, referencing the findings of Tammo and Thelandersson (2009), who analyze Equation (3.18) concerning 'cover zone cracking' (k3c).

Research indicates that the width of cracks near reinforcement bars is influenced by both cover and bond slip theory, with findings suggesting that the slip theory alone does not fully account for cracking in this area Kaethner recommends reducing surface crack width predictions by 50 to 60%, reflecting the actual residual opening at the bar surface Additionally, studies confirm that for flexural elements, the value of k3 should be set at 2.1, which is 1.7 times lower than the k3 value of 3.4 used for axial members, representing a significant reduction of 62% (Kong et al., 2007).

Strength calculations

The ultimate flexural strength of a structural section is analyzed using design formulas applicable to standard structures, with a partial safety factor for liquid pressure loads set at γf = 1.2 The calculations for the ultimate limit state condition are derived from equilibrium forces and the configuration of the concrete stress block at failure, following the guidelines outlined in BS EN 1992-1-1.

The partial safety factor for concrete is taken as  c = 1.5 and for steel  s = 1.15

In UK practice, after applying the partial safety factor for concrete and considering the testing of concrete strength with cubes, a stress block width of 0.57 f ck is utilized, along with a depth (s) equal to 0.8 times the depth to the neutral axis for concrete classes up to C50/60.

Using the rectangular stress block as illustrated in Figure 3.8, the following equations may be derived:

Lever arm factor z 1 = 1 – 0.40x 1 (3.27) Force of tension = force of compression

Therefore, A s f yk / 1.15 = 0.57f ck b0.8x 1 d (3.28) and x 1 = 2.42A s f yk / f ck bd (3.29)

Moment of resistance based on steel

For concrete classes up to C50/60, the maximum permissible value of x is set at 0.45d, which ensures a ductile section and gradual tension failure of the steel at the ultimate limit state Consequently, the maximum moment of resistance is determined based on the concrete section.

M u represents the maximum ultimate moment that can be applied to the section without using compression reinforcement (a singly reinforced section) The actual applied ultimate moment M should be less than M u

To determine the area of reinforcement needed for a specific ultimate moment of resistance, it is essential to rearrange equations (3.27) to (3.32) to express the depth of the neutral axis in relation to the applied ultimate moment and the maximum ultimate moment By rearranging equations (3.31) and (3.32) for A_s f_yk and f_ck bd in terms of M and M_u, respectively, and substituting these into equation (3.28), we can then rearrange to solve for x_1 Utilizing equation (3.27) to replace z_1 allows us to form a quadratic equation with x_1 as the variable The solution to this quadratic equation is given by equation (3.33): x_1 = [1 − √(1 – 0.59(M / M_u ))] / 0.8.

This value may be substituted in Eqs (3.27) and (3.31) to calculate the required area of reinforcement.

After the arrangement of reinforcement has been decided, the ultimate shear stress should be rechecked (see Section 3.2.4).

Calculation of crack widths due to combined tension and bending (compression present)

tension and bending (compression present)

Estimating crack widths requires careful judgment due to the combined effects of direct tension and bending The calculation of the neutral axis depth in a bending section is straightforward, as outlined in Section 3.4 However, when tensile forces are introduced, the neutral axis shifts, resulting in a reduced portion of the concrete section being in compression If tension continues to increase, the neutral axis may move outside the section, leading to the entire section being in tension This transition from pure flexure to pure tension is illustrated in Figure 3.9.

Where minimum reinforcement is provided, BS EN 1992-3 provides guidance, d

Design stress in compression = 0.85 f ck /γ c = 0.85f ck /1.5 = 0.567 f ck z = lever arm (= d–0.40x) Fcc = b.0.8x.0.85f ck /γ c

Figure 3.8 Assumed stress diagrams – ultimate fl exural limit state design.

This article discusses the maximum bar diameters and spacings for various design crack widths in scenarios where the entire section is subjected to tension, superseding the guidance in BS EN 1992-1-1 It presents tables that help control axial tension cracking using simplified detailing rules, which are based on the crack width formulae outlined in clause 7.3.4 of BS EN 1992-1-1 A key practical example of pure tension is found in cylindrical structures featuring a sliding joint at the base, with Chapter 4 focusing on the design considerations for cylindrical tanks.

When analyzing combined tension and bending, it's crucial to understand the relationship between the bending moment (M) and the tensile force (T) The ratio M/T reveals the necessary eccentricity of the tensile force to generate the bending moment A high M/T ratio relative to the section thickness suggests that bending is the dominant factor, while a low ratio indicates that tension is more significant In cases where one of the forces is minimal, the most effective design strategy is to focus on the predominant force and then make adjustments using approximate methods.

To derive formulae for a section under applied tension and bending with both tensile and compressive stresses, principles of strain compatibility and the modular ratio method of elastic design are utilized This method results in cubic equations, making direct design challenging, particularly when the tensile force is not excessively high Initially, it is advisable to design for bending alone and subsequently enhance the design with a modest amount of reinforcement The resulting equations can then be employed to verify the permissible values of applied loads, noting that the formulae require assumptions about the concrete section and the amount of reinforcement used.

To address the three variables involved, an additional equation is required This equation is derived from the crack width formula, as satisfying the crack width is essential.

Example in the next section) The formulae for calculating the applied tensile force

(N ) and service bending moment (M ) are derived below.

The section geometry, strain distribution and the forces acting on a section in combined tension and fl exure with the section in part compression are shown in Figure 3.9.

From strain compatibility (refer to Figure 3.10), the strain in the compression reinforcement  sc is given by sc cc x a x ε = ε −

Figure 3.9 Section with compressive stress.

In structural engineering, the depth to the neutral axis from the extreme compression fiber is denoted as 'x', while 'a' represents the distance from the axis to the centroid of the reinforcement Understanding these measurements is crucial for analyzing the behavior of reinforced concrete structures.

 cc is the strain in the extreme compression fi bre of the concrete

As both the reinforcement and concrete behaviour may be considered linear elastic, then the stress in the reinforcement  sc can be written as

 sc = E s  sc (3.35) and the stress in the concrete  cc as

 cc = E c  cc (3.36) where E s and E c are the elastic moduli of the steel and concrete, respectively Thus

 sc is given by s sc cc e cc c

⎛ ⎞ ⎛ ⎞ σ = σ ⎜⎝ − ⎟⎠= α σ ⎜⎝ − ⎟⎠ (3.37) where  e is the modular ratio.

The force F s ′ in the compression steel is given by s s sc s e cc 1 a h

A' s is the area of the compression steel x a h – a ε cc ε sc ε st

Figure 3.10 Strain distribution across a doubly reinforced section.

Note, in deriving the compression reinforcement, the area of the concrete displaced by the steel has been ignored.

The strain in the tension reinforcement, denoted as ε_st, can be expressed in terms of the strain in the concrete, ε_cc, and the depth to the neutral axis, x, from the extreme compression fiber, using the formula ε_st = ε_cc * (h - x) / a Here, 'a' represents the distance from the axis to the centroid of the reinforcement.

 cc is the strain in the extreme compression fi bre of the concrete

As both the reinforcement and concrete behaviour may be considered linear elastic, then the stress in the reinforcement  st can be written as σ st = E s  st (3.40)

Thus  s is given by s st cc e cc c

The force F s in the tension steel is given by s = s st= s e cc h a h 1

A s is the area of the tension steel

The force in the concrete F c is given by cc c 2

− = + − (3.44) where N the axial tension force applied at the centroid of the section

Rewriting Eq (3.44) gives cc s e cc 1 s e cc 1

Defi ning a compression steel ratio  c as s c= ′ ρ A bh (3.47)

Chapter_3.indd 51 5/9/2014 12:15:36 PM 5/9/2014 12:15:36 PM www.EngineeringEbooksPdf.com and a tension steel ratio  t as s t ρ A bh (3.48) then Eq (3.46) may be rewritten as

− cc = + c e ⎜⎝ − ⎟⎠− t e ⎜⎝ − − ⎟⎠ (3.49) Taking moments about the centre-line (or mid-depth) of the section, c s s

When dealing with reversible moments, consistent reinforcement is essential across all faces However, if the moment is unidirectional, it may be feasible to design with varying levels of reinforcement on each face.

Even if, as is usual, the tension reinforcement and the compression reinforcement are set equal, i.e.

Equations (3.49) and (3.52) involve three variables and cannot be solved without an additional equation, which is provided by the crack width equation The design crack width must be satisfied and is influenced by crack spacing and the mean strain in the reinforcement, accounting for tension stiffening Consequently, a closed-form solution for a specific design is unattainable, necessitating the use of an iterative method, such as a simple spreadsheet, to obtain results.

The simplest manner of proceeding is:

To begin, estimate the height (h) if it is not already known, along with the axis distance (a) It is advisable to work with the axis distance for simplicity, while ensuring that the cover remains within acceptable limits for the specific scenario.

• Estimate the bar size and spacing.

To determine the moment capacity (M) using the value of σcc from Eq (3.52), compare M with the applied moment If M is less than the applied moment, increase the reinforcement or the section size as needed Conversely, if M exceeds the applied moment, reduce the reinforcement or section size until M is only slightly greater than the applied moment.

• The stress in the tension reinforcement may then be determined from Eq (3.41) and the crack width calculated.

• If the crack width is unsatisfactory, it will be necessary to iterate through the complete calculations.

Determine the reinforcement required (assumed equal in each face) for a section 300 mm thick carrying actions of a tensile force of 78 kN/m and a moment of

57 kNm/m at serviceability limit state assuming an axis distance of 50 mm to the centroid of the reinforcement and an allowable crack width of 0.2 mm.

For a long-term loading scenario, consider the value of αe as 15 and the span length b as 1,000 mm Utilizing C30/37 concrete, the effective tensile strength fct,eff can be approximated as fctm.

The calculations given below are the fi nal iteration only.

From Table 3.1 (BS EN 1992-1-1) determine f ctm :

Assume reinforcement of B20 at 200 mm centres (A s = 1570 mm 2 /m) s 1570

For a value of x = 72 mm, or x h of 0.24, determine cc

Chapter_3.indd 53 5/9/2014 12:15:36 PM 5/9/2014 12:15:36 PM www.EngineeringEbooksPdf.com c e t e 2 cc

This is satisfactory as far as equilibrium is concerned (applied moment is 57 kNm/m).

Determine  st from Eq (3.41) e cc

⎛ ⎞ ⎛ ⎞ σ = α σ st ⎜⎝ − − ⎟⎠ ⎜⎝ − − ⎟⎠ Limiting spacing of reinforcement is 5(c + /2):

Actual spacing is 200 mm, therefore use Eq (3.18) to determine s r,max : k 1 = 0.8 (high bond bars) k 2 = 0.5 (fl exure) k 3 = 3.4 (UK National Annexe to BS EN 1992-1-1) k 4 = 0.425 (UK National Annexe to BS EN 1992-1-1)

The cover c is given by

A c,eff is the minimum of 2.5(h − d)b, (h − x)b/3 and hb/2.

The least value is 76 000 mm 2 , thus A c,eff = 76 000 mm 2

The effective reinforcement ratio  p,eff (in the absence of prestressing tendons) is given by s p,eff c,eff

( ) ct,eff s 1 e p eff p eff s sm cm s s

The parameter k 1 is the load duration factor ( = 0.4 for long-term load) It is not to be confused with the k 1 factor in the crack spacing formula.

Also,  s is the stress in the tension reinforcement assuming a cracked section, which is the same as  st in Eq (3.41).

The value of  sm –  cm to be used to calculate the crack width is therefore 593×10 -6

From Eq (3.16), the characteristic crack width w k is given by

Note, within practical bar spacings it is not possible to get closer to the allowable limit of 0.2 mm.

The study examined the impact of varying reinforcement levels on each face of the structure Tension reinforcement was maintained at B20 with 200 mm spacing, totaling 1570 mm²/m, while compression reinforcement was reduced to approximately half, using B16.

The calculations revealed a compression zone depth of 74.4 mm, a moment capacity of 57.3 kNm/m, a concrete stress of 5.4 MPa, a tensile steel stress of 191 MPa, and a final crack width of 0.177 mm Consequently, there is potential for cost savings by reducing reinforcement in the compression face, provided that the applied moment acts in a single direction.

Detailing

The reinforcement detailing requirements for water-retaining structures follow the usual rules for normal structures Guidance can be found in Sections 7, 8 and 9 of

EC2 Part 1, along with BS EN 1992-3, focuses on prestressed members and emphasizes controlling cracking to ensure sufficient bond through adequate concrete cover, proper placement, and compaction It highlights the importance of transverse reinforcement to address potential tensile stresses in high bond stress areas To maintain continuity, reinforcement bars should be detailed on the liquid faces, avoiding sudden changes in reinforcement ratios For maximum effectiveness, distribution reinforcement in walls should be positioned in the outer layers, and spacers must be used to maintain the correct concrete cover.

Guidance is provided on the minimum clear distance between horizontal or vertical bars or between layers of parallel bars Three minimum limits to spacing are provided:

20 mm, maximum aggregate size plus 5 mm (k 2 in the NAD), and bar diameter × k 1

(where k 1 = 1 in the UK NAD).

For slabs with an overall thickness of greater than 200 mm, Cl 7.3.3 of EC2 con- trols cracking without direct calculation for specifi ed crack widths of either 0.2 mm,

0.3 mm or 0.4 mm depending on the specifi c requirements of the structure With the crack widths fi xed, the rules for determining crack widths are presented in tabular form in BS EN 1992-1-1 for bar size (Table 7.2N) and bar spacing (Table 7.3N) for a range of steel stresses from 160 to 450 MPa For cases where cracks are caused mainly by loading, bar diameter or bar spacing tables can be used; for cracking caused predominantly by restraint of imposed strain, only the bar size table can be utilised The maximum bar diameters obtained from Table 7.2N are then modifi ed by Eq 7.6N for cases where bending forces dominate (i.e at least part of the section is in compression) and Eq 7.7N where the section is subject to uniform axial tension. spacers at

Figure 3.11 Detailing of spacer reinforcement.

BS EN 1992-3 further modifi es Eq 7.7N to refl ect the fact that the basic guidance in

BS EN 1992-1-1 has been obtained from studies of elements subjected to pure fl exure

According to BS EN 1992-3 (7.122), smaller maximum bar diameters are theoretically required at closer spacings, and the relevant data on bar diameters and spacings is presented graphically rather than in a tabular format (see Figures 7.103N and 7.104N).

Tables 3.4 and 3.5 compare the maximum bar diameter and spacing, respectively, of tension bars for a crack width of 0.3 mm as suggested by BS EN 1992-1-1 and BS

EN 1992-3 and Narayanan and Beeby (2005).

Some of the data contained within Tables 3.4 and 3.5 are extracted from fi gures

The values presented from BS EN 1992-1-1 pertain specifically to bending scenarios, while the bar diameter values from Narayanan and Beeby also focus on bending, though their maximum bar spacing values apply to both bending and pure tension Notably, BS EN 1992-3 provides values for pure tension, suggesting larger bar diameters than BS EN 1992-1-1, except under high steel stresses, which contradicts the intent of Expression 7.122 advocating for smaller bar sizes Furthermore, the bar spacings recommended in BS EN 1992-3 for pure tension are generally less than those in BS EN 1992-1-1 for flexural cases, yet they exceed the recommendations by Narayanan and Beeby In flexural scenarios, the concrete area in tension just before the first crack, A ct, is roughly half the overall depth of the section, whereas in pure tension, the entire section is in tension, making A ct equal to the overall depth Additionally, for pure flexure, the stress distribution constant, k c, is defined.

In structural design, the coefficient for pure tension is k c = 1.0, while it is 0.4 for other cases Narayanan and Beeby recommend that the maximum bar spacing for pure tension should be 50% of the spacing suggested for flexural scenarios, which appears to be a reasonable guideline Additionally, when considering a fixed crack width of 0.2 mm, the values outlined in BS EN 1992-3 are generally more appropriate, particularly at higher stress levels, although they may not be as accurate at low stresses.

Steel stress (MPa) BS EN 1992-1-1 Narayanan and Beeby BS EN 1992-3

Clear guidance on anchorage of reinforcement and laps in reinforcement can be found in BS EN 1992-1-1: Sections 8 and 9.Very little additional guidance is provided in

According to BS EN 1992-3, it is essential for bars to be adequately anchored to achieve their design stresses The bond between the bar and concrete determines the necessary anchorage length, which is influenced by the bar's angle of inclination and the depth of the concrete The design anchorage length, denoted as l bd, is derived by adjusting the basic required anchorage length, l b,red, through the application of five specific α factors.

The shape of the bar, concrete cover, and confinement by transverse reinforcement—whether welded or not—play crucial roles in structural integrity When lapping is necessary to transfer stresses between bars, it is essential to stagger the laps and avoid high-stress areas The lap length is determined by the minimum anchorage length, which is adjusted using five specific α factors along with an additional consideration for optimal performance.

 factor, which accounts for the percentage of lapped bars relative to the total cross- section area.

Table 3.5 Maximum bar spacing Narayanan and Beeby (2005).

Steel stress (MPa) BS EN 1992-1-1 Narayanan and Beeby BS EN 1992-3

Design of prestressed concrete

Distribution reinforcement and joints: Design for thermal

Design calculations

Testing and rectifi cation

Vapour exclusion

Tiêu đề	Design of Liquid Retaining Concrete Structures
Tác giả	J.P. Forth, A.J. Martin
Người hướng dẫn	J.P. Forth, Senior Lecturer in Structures
Trường học	University of Leeds
Chuyên ngành	Civil Engineering
Thể loại	book
Năm xuất bản	2014
Thành phố	Dunbeath

Định dạng
Số trang	187
Dung lượng	1,96 MB