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Reinforced Concrete Design

2.2.1 Introduction

A structure is an assembly of members each of which is subjected to bending or direct force (either tensile or compressive) or to a combination of both. These primary influences may be accompanied by shearing forces and sometimes by torsion – all of which cannot be adequately resisted by concrete, thus the concept of reinforced concrete.

Reinforced Concrete is a combination of two dissimilar but complementary materials, namely: concrete and steel (Oyenuga, 2001). Concrete has considerable crushing strength, is durable, has good fire resistance; but has a poor tensile stress, and fair strength in shear. On the other hand, steel has good tensile properties, poor resistance to fire (due to rapid loss of strength under high temperature), and is very good both in shear and compression. Thus, a combination of these materials results in good tensile and compressive strength, durability and good resistance to fire and shear.

To every action of loading on any member of a structure, there is a consequential reaction as a result of the combination of concrete and steel. The method of combining these materials (concrete and steel) in the most economical way on one hand, and safety on the other hand, is referred to as reinforced concrete design (commonly referred to as design or structural design). This means that, according to Reynolds and Steedman (1988), design entails the calculation of, or by other means of assessing, and providing resistance against the moments, forces, and other effects on the members (i.e. analysis of structures).



      1. Design Objectives

The aim of structural design is the achievement of an acceptable probability that structures being designed will perform satisfactorily during their intended life (British Standards Institution (BSI), 1997). With an appropriate degree of safety, they should sustain all the loads and deformations of normal construction and use, and have adequate durability and resistance to the effects of misuse and fire.

From the foregoing, according to Oyenuga (op. cit.), a good structural design must satisfy the following functional objectives:



  • Under the worst combination of loading, the structure must be safe.

  • Under the working condition, the deformation of the structure must not impair the appearance, durability and/or performance of the structure – i.e. fits for its intended use.

  • The structure must be economical – the factor of safety should not be too large to the extent that the cost of the structure becomes prohibitive with no additional advantage(s).

Achieving these potentially conflicting objectives calls for experience and good sense of engineering, as well as leads to an efficiently designed structure.

An efficiently-designed structure is one in which the members are arranged in such a way that the weights, loads, and forces are transmitted to the foundation by the cheapest means consistent with the intended use of structure and the nature of the site (Reynolds and Steedman, op.cit.). Efficient design means more than providing suitable sizes for the concrete member and the provision of the calculated amount of reinforcement in an economical manner. It implies that the bars can be easily placed, that reinforcement is provided to resist the secondary forces inherent in monolithic construction, and that resistance is provided against all likely causes of damage to the structure. That is to say, experience and good judgement may do as much towards the production of safe and economical structures as calculations.

In summary, these objectives call for good assessment/estimation of the intending loads, right choice, quality, and proportion of materials, and sound workmanship. The realisation of these requires conformity to clearly defined criteria for materials, production, workmanship, and, also, maintenance and use of the structure in service. All these requirements are borne out of experience—from a study of existing structures and from comparison of alternative designs.


      1. Design Methods

To achieve the objectives of design, according to Ojo (2000), the following methods can be adopted:

(a) By dividing the ultimate strengths of materials with certain factor (factor of safety) to provide design stress (strength). This method is called elastic method of design (or permissible stress method/modular-ratio method).

(b) By multiplying the load that the structure can withstand with certain factor of safety to give the working load. This is called the load-factor method.

(c) Limit state method combines the advantages of the two methods above by applying factor of safety to both the materials and loads. This method also allows a varied factor of safety for various types of loading conditions.

The limit state design is based on the limit state approach or philosophy – the achievement of acceptable probabilities that the structure being designed will not become unfit for its intended use. This means that all criteria relevant to both safety and serviceability are considered in the design process so as to make sure that the structure does not reach a limit state. An easy and usual approach is to design on the most critical limit state, and then to check that the remaining limit states will not be reached.

There are two types of limit state in structural design, namely:

(i) Ultimate limit state (ULS) – the limit state that ensures that the structure is safe under the worst loading condition. This ensures resistance against collapse, buckling, stability or overturning, and other accidental/special hazards such as earthquake, explosion or fire.

(ii) Serviceability limit state (SLS) – the limit state that ensures that the structure is fit for normal use, i.e. serviceable. This is to ensure that the structure will not fail during service. It takes care of deflection, cracking, fatigue, vibration, durability, lightning, etc.

Except in water-retaining structures, the ULS is generally critical for reinforced concrete structures, while SLS conditions are checked. However, in prestressed concrete2 design, serviceability conditions are the basis for designing with checks on the ULS conditions (BSI, op.cit.).

Structural design is largely controlled by regulations or codes (but, even within such bounds, the designer must exercise good judgement in his interpretation of the requirements, endeavouring to grasp the spirit of the requirements rather than to design to the minimum allowed by the clauses of the codes). The various methods of design highlighted above formed the basis of these codes. In Nigeria, the most prominent of these codes is ‘Structural Use of Concrete’ (BS 8110: Parts 1, 2, and 3), which is based on the limit state design method as stated in clause 2.1.2 of the code. Others include ‘The Structural Use of Normal Reinforced Concrete in Buildings’ (CP 114), which is partly based on the load-factor method, and ‘The Structural Use of Concrete’ (CP 110: Parts 1, 2, and 3).





      1. Reinforced Concrete Members

A reinforced concrete structural member may be subjected to any (or all, in worst condition) of the structural failures – flexural, buckling, shear or torsion – depending on the type of member it is and its location in the structure. Thus, it is imperative to understand the importance/necessity of the various structural members, which are briefly outlined in this section as follows:

(a) Beam: This is a horizontal member of the whole structure with a rectangular cross-section usually. It, in most cases, supports the loads on the slab, the self-weight of the slab, and its own self-weight – all of which are transmitted to the nearest vertical member, such as column or wall (load-bearing). Beams, generally, resist flexural loading.

The fundamental principle involved in the design of a reinforced concrete beam, according to Nilsor (1997), is that, at any cross-section, there exist internal forces that can be resolved into components normal and tangential to the section. Those components that are normal to the section are the bending stresses (tension on one side of the neutral axis and compression on the other) – their function is to resist bending moments at the section. The tangential components are known as the shear stresses (they resist the transverse or shear forces).

In reinforced concrete beams, the concrete usually resists the compressive forces and the steel the tensile forces. Hence, the longitudinal reinforcing steels are located close to the tension face to resist the tension force; and, usually, additional steel bars (shear links) are used to resist inclined tensile stresses caused by the shear force in the beam. However, reinforcement is also used for resisting compressive forces primarily where it is desired to reduce the cross-sectional dimensions of compression members. Even if no such necessity exists, a minimum amount of reinforcement must be placed in all compression members to safeguard them against the effects of accidental bending moments (Nilsor, op. cit.).

In general, for the most effective reinforcing action, it is essential that steel and concrete deform together, i.e. that there be a sufficiently strong bond between the two materials to ensure that no relative movements of the steel bars and the surrounding concrete occur.

Design of reinforced concrete beams can be classified based on various factors. Based on reinforcement type, it could either be singly reinforced (only tension reinforcement is provided) or doubly reinforced (tension as well as compression reinforcement is provided). Based on structural shape and role, it may be classified into simply supported, continuous, flanged, and cantilever.

(b) Column: Primarily, columns are compression members, although some may be subjected to bending either due to their slenderness or due to their asymmetric loading from beams (Oyenuga, op. cit.). Reinforced concrete columns are generally either rectangular in cross-section with separate links, or circular – and, in some cases, polygonal.

Fundamentally, columns can be categorised as:


  • Axially loaded column – when it supports approximately symmetrical beam arrangement.

  • Uniaxial column – when it supports direct loading and bending in one direction.

  • Biaxial column – when it supports a concentric loading and bending acting about two axes that are mutually at right angles.

Also, columns can be classified based on its end conditions as:

  • Braced column – when wall, bracing or buttressing, designed to resist all lateral forces in that plane, laterally supports it.

  • Unbraced column – when it is not laterally supported by wall, bracing or buttressing.

Furthermore, columns can be categorised, based on the ratio of its effective length to its cross-sectional dimensions, as:

  • Short column – when the ratios lex/h and/or ley/b are/is less than 15 (braced) and 10 (unbraced), where:

lex = effective height in respect of the major axis

ley = effective height in respect of the minor axis

h = depth of cross-section measured in the plane under consideration

b = width of a column (i.e. dimension of the cross-section perpendicular to h).



  • Slender column – when both the ratios lex/h and/or ley/b are/is greater than 15 (braced) and 10 (unbraced).

(c) Slab: A slab is a reinforced concrete member that, more often than not, is subjected to shear (Oyenuga, op. cit.). Because slab is generally a horizontal member, its design centres more on flexure rather than direct shear.

Generally, slabs are similar to beams except that:



  • a width of 1.0m is generally assumed to as to make for a simplified design
  • the section is usually rectangular, hence no flanges


  • shear is generally not considered unless where concentrated or point loads predominate, and the slab is thicker than 200mm.

There are various types of slab, and the type to be preferred may depend on: (i) the span of the slab, (ii) the use of the space, which may determine the span, (iii) the load to be carried, and (iv) the architectural aesthetics required.

The various types include:



  • Solid slab (cantilever, simply-supported, continuous, one-way, and two-way)

  • Ribbed slab

  • Flat slab

  • Waffle slab

Slab directly carries the load imposed on it and its own self-weight (all in the form of uniformly distributed loads) and is supported by walls, beams and/or columns. Solid slabs are the commonest, especially in residential areas.

(d) Wall: Generally, this is a vertical load-bearing member whose length exceeds four times its thickness. A reinforced concrete wall is one with a minimum reinforcement not less than 0.4% of the area of concrete (BSI, op. cit.). According to Reynolds and Steedman (op. cit.), a braced wall is one where lateral stability of entire structure, at right angles to plane of wall being considered, is provided by walls (or other means) designed to resist all lateral forces; otherwise, the wall is unbraced. Whether braced or unbraced, a wall can further be classified as either being slender or stocky based on its slenderness ratio3. Thus, a stocky wall is one whose slenderness ratio does not exceed 15 (braced) or 10 (unbraced); while a slender wall is any one other than stocky, i.e. greater than 15 (braced) and greater than 10 (unbraced).

(e) Foundation: They are horizontal or vertical members supporting the entire structure and transmitting the loads to the soil below. They are sub-structures supporting the superstructures of columns, beams, walls, slabs, and roofs (Oyenuga, op. cit.). Generally, foundations can be broadly classified as either shallow or deep. These encompass the various types, namely: pad footing, strip footing, raft foundation, pile foundation, displacement foundation, strap foundation, e.t.c. The choice of foundation type depends, primarily, on the magnitude of load to be transmitted from the superstructure and the permissible bearing capacity of the soil. The selected foundation type must satisfy two fundamental and independent requirements:


  • The factor of safety against shear failure of the supporting soil must be adequate.

  • The settlement should neither cause any unacceptable damage nor interfere with function/use of the structure.

(i) Pad footing: This is most common of all the reinforced concrete footings. It supports columns and transmits the loads to the soil evenly. It is usually square in plan, but where there is a large moment acting about one axis, it may be more economical to have a rectangular base. It may be axially or eccentrically loaded. When axially loaded, the reactions to design ultimate loads may be assumed to be uniformly distributed (i.e. load per unit area). When eccentrically loaded, the reactions may be assumed to vary linearly across the base. It should be noted that the actual pressure distribution depends on the soil type, and the critical section is taken as that at the face of the column being supported (MacGinley and Choo, 1990).

(ii) Strip footing: Mosley et al (1999) states that strip foundation is commonly used under walls or under a line of closely spaced columns. Even if it were possible to have individual bases, it is often simpler and more economical to excavate and construct the formwork for a continuous base. In the general case of a wall footing in which the load is uniformly distributed throughout its length, the principal bending moments are due to the transverse cantilever action of the projecting portion of the footing (Reynolds and Steedman, op. cit.).

For a reinforced concrete wall, the critical section occurs at the face of the wall; hence, the thickness of the footing should be such that the safe shearing stress is not exceeded. Whether the footing is designed for transverse bending or not, if the safe ground pressure is low, longitudinal reinforcement should be inserted to resist possible longitudinal bending moments due to unequal settlement and non-uniformity of the load. One method of providing the amount of longitudinal reinforcement required for unequal settlement is to design the footing to span over a cavity (or area of soft ground) from 1m to 1.5m according to the nature of the ground.

Generally, the loads for foundation design must be expressed both in the SLS and ULS. The ground bearing capacity is generally expressed in working state (SLS); hence, the area of foundation required to sustain the load must be defined based on working state. Once the area has been obtained, the net pressure exerted on the soil is calculated based on the ULS. All loads are obtained from ULS approach.

(f) Retaining Wall: Retaining wall is usually required to resist a combination of earth and hydrostatic loads (Mosley et al, op. cit.). Simply put, retaining wall is a structure used to retain earth, which could not be able stand vertically unsupported (MacGinley and Choo, op. cit.). According to Oyenuga (op. cit.), they are useful within the built environment, especially at bridge sites, riverbank areas, ground with sloppy terrain, e.t.c.

A retaining wall is essentially a vertical, cantilever structure, and when it is constructed in reinforced concrete, it can be a cantilevered slab, a wall with counterforts, or a sheet-pile wall (Reynolds and Steedman, op. cit.). In general, concrete retaining walls may be considered in terms of three basic categories:


  • Gravity wall – usually constructed of mass concrete, and relies on self-weight to satisfy stability requirements both in respect of overturning and sliding.

  • Counterfort wall – it is the combination of a wall and counterforts. Stability is provided by the weight of the wall and the backfill of the retained material.

  • Cantilever wall – it is a vertical cantilever spanning from a rigid base and relies on the bending strength of the cantilevered slab above the base, as well as the weight of backfill on the base, where applicable, to provide stability.

The principal factors to be considered, generally, are stability against overturning, bearing pressures on the ground, resistance to sliding, and internal resistance to bending moments, and shearing forces. Mosley et al (op. cit.) advises that the back faces of retaining walls will usually be subjected to hydrostatic forces from groundwater. This can be reduced by the provision of drainage path at the face of the wall. It is usual practice to provide such drain by a layer of porous medium with pipes to remove the water, or by providing ‘weep-holes’ at regular intervals in the wall.

(g) Drainage Channel: This is an open box culvert-like structure used to transport water or liquid from an unwanted area to a point of discharge. The channel must be strong enough to resist vertical and horizontal pressures from the earth and other superimposed loads. Generally, there are only two conditions to considered:



  • When the channel is empty, full load and surcharge on the channel walls’ sides, the weight of the walls, and maximum earth pressure on the walls.

  • When the channel is full, minimum load on the walls, minimum earth pressure on the walls, the weight of the walls, maximum horizontal pressure from water in the channel.

In some circumstances, these conditions may not produce the maximum positive or negative bending moments at any particular section; hence, the effect of every probable combination should be considered.


2.2.5 Design Process

This is, generally, a series of steps that are taken to realise the design objective(s) of a structure. It considers design as a whole, including design for durability, construction and use in service. The realisation of the design objectives, through the design process, requires conformity to clearly defined criteria for materials, production, workmanship and, also, maintenance and use of the structure in service. The design process, chronologically, involves careful estimation of foreseeable loads, analysis of the structure, design procedures to be followed in arriving at concrete and reinforcement parameters, production of a good clear detail drawing and preparation of reinforcement schedule. Each of the series of steps is concisely explained as follows:



2.2.5.1 Load Estimation: The loads acting on a structure are permanent (or dead) loads, and imposed (live) loads, which include wind load.

  • Dead Loads include the self-weights of the structure being considered, and any permanent fixtures, partitions, finishes, superstructures and so on.

  • Live loads include any external loads imposed upon the structure when it is serving its normal purpose. They vary in magnitude. They are moving loads that would be supported by the structure. They include weights of occupants, furniture, etc. Also, they include wind load caused by the effect of wind on the structure. The accurate assessment of the actual and probable loads is an important factor in the production of an efficient structural design (Reynolds and Steedman, op. cit.).

To arrive at the dead load of a member, Oyenuga (op. cit.) notes that preliminary sizing has to be done and the weight is calculated such that a slight change in the member size will not attract a re-design of the structure. All given values should represent the actual forces, weights of materials. The primary dead load is usually the weight of the concrete, which literatures generally agree to be 24kN/m3. The weight of the other materials to be included as dead loads can be obtained from appropriate texts. Appendix A gives the weights of common construction materials. The sum of all the individual weights of the construction materials to be used permanently in the structure gives the characteristic dead load (Gk). Likewise, the sum of all the individual intensity of expected moving loads on the structure gives the characteristic imposed load (Qk).

In accordance with the philosophy of the ULS, so as to ensure adequate safety of structure, partial factors of safety are applied to the characteristic loads. These factors are not rigid because of the dynamic nature of various load combinations. The standard factors for various combinations of loads are as outlined in Table 2.1. It is seen from the


Table 2.1 Load Combinations and their Values of Partial Factor of Safety for the ULS

(Source: BSI, op. cit.)



Load Combination

Load Type

Dead

Imposed

Earth and Water Pressure

Wind

Adverse4

Beneficial5

Adverse

Beneficial

1. Dead and Imposed (and earth and water pressure)

1.4

1.0

1.6

0

1,4

--


2. Dead and Wind (and earth and water pressure)

1.4

1.0

--

--

1.4

1.4


3. Dead and wind and imposed (and earth and water pressure)

1.2

1.2

1.2

1.2

1.2

1.2


table that adequate factor is provided for various load combinations in order to achieve the ULS requirements.

Thus the design load, for a given type of loading, can be obtained from the sum of Gkγ and Qkγ, where γ is the appropriate factor of safety (BSI, op. cit.). This is true, generally, for beams, columns, slabs and walls. In general, Oyenuga (op. cit.) points out that γ is introduced to take account of unconsidered possible increase in load, inaccurate assessment of load effects, unforeseen stress distribution and variations in dimensional accuracy, and the impression of the limit state being considered.


2.2.5.2 Analysis of Structure: This is the determination of the forces and moments as well as deformation that results from the action of loads (Oladepo, 2001). Tebedge (1983) defines it as the “process of determining the response of a structure due to specific loadings in order to satisfy the essential requirements of function, safety, economy and, sometimes, aesthetics. This response is usually measured by calculating the reactions, internal forces in the members and the displacements of the structures.” Since the structure is made up of different members joined together, the analysis that must be carried out to justify the design of a structure can be broken into two stages as follows:

  • Analysis of the structure (the structure as a unit)

  • Analysis of the structure (parts of the structure)

The analysis of the structure, as a whole component, is very tedious and laborious, and the advantages may not worth the efforts (Oyenuga, op. cit.). Thus, the analysis is easily dealt with by considering the various sections.

The primary objective of structural analysis is to obtain a set of internal forces and moments throughout the structure that are in equilibrium with the design loads for the required loading combinations (BSI, op. cit.). To obtain this set of internal forces and moments, the determination of the static determinacy of the structure is an essential pre-requisite. A structure can either be statically determinate6 or statically indeterminate7.

Basically, the static determinacy of a structure is determined by the following equation:

n = r – e (2.12)

where n = number of redundants

r = number of reactions

e = number of equations of static equilibrium (e = 3)

Hence, if a section of the structure is found to be statically determinate (such as in the case of beams, lintels, e.t.c.), the internal forces and moments are obtained from basic equations of static equilibrium. However, if the section(s) is (are) found to be statically indeterminate, the internal forces and moments are obtained from appropriate method(s) of analysis of indeterminate structures.

Oladepo (op. cit.) explains that there are, generally, two methods of solving

indeterminate structures, namely: (a) the plastic method, and (b) the elastic method. The elastic method of analysis of indeterminate structures can further be divided into:

(i) Classic methods, and

(ii) Matrix methods.

Under the classical methods, we have the moment-area method, virtual work method, moment distribution method, slope-deflection method (SDM), three-moment equations' method, column analogy method, e.t.c. Under the matrix method, we have flexibility (force) method, and stiffness (displacement) method.

The choice of method to be used depends on its suitability to the type of problem concerned and, to some extent, on its appeal to the particular designer involved (Reynolds and Steedman, op. cit.). Moreover, the method(s) of analysis to be used should be based on as accurate a representation of the structure as is reasonably practicable. For the author of this report, the SDM is the easiest. It forms the basis of the stiffness matrix method. In the SDM, the rotations (i.e. slopes) and relative joint translations/displacements constitute the unknowns. The moments at the joints are expressed in terms of these quantities in the form of the slope deflection equations. These moments are obtained as the solutions of the resulting slope deflection equations, and back-substitution of the rotation and displacement into the original slope-deflection equations. The slope deflections, for two ends A & B of a section of the structure, are:

MAB = MFAB + 2EI/L (2θA + θB - 3∆/L) (2.13)

MBA = MFBA + 2EI/L (θA + 2θB - 3∆/L) (2.14)

where MAB and MBA are the end moments produced at ends A and B respectively,

MFAB and MFBA are the fixed end moments (FEM8)

EI = flexural rigidity of the member

L = length of the member

θA= slope of deformed member AB at A = ∫A M/EI

θB = slope of deformed member AB at B = ∫B M/EI

E = modulus of elasticity of the material

I = moment of inertia of member AB at section

∆ = relative movement of supports

Reynolds and Steedman (op. cit.) points out that the principles of the SDM for analysing a restrained (indeterminate structural) member are that the difference in slope between any two points in the length of the member is equal to the area of the M/EI diagram between these two points. Moreover, that the distance of any point on the member from a line drawn tangentially to the elastic curve at any other point, the distance being measured normal to the moment (taken about the first point) of the M/EI diagram between these two points.

It may suffice to round off this section in this way: calculating the shearing forces, bending moments, slopes and deflections caused by a load in a structural member, by any method of structural analysis, ensures that the design loads are in equilibrium. The analytical procedure involves transforming the whole section to line diagrams in such a way that, under ultimate load conditions, the inelastic deformations at the critical sections remain within the limits that the sections can withstand. While, under working loads, the deformations are insufficient to cause excessive deflection or cracking or both.

2.2.5.3 Design Procedure: This section gives the procedures of design methods that will, in general, ensure that for reinforced concrete structures, the objectives set out in section 2.2.2 above are met. These procedures assume the use of normal-weight aggregate, and are extracts of the provisions in BS 8110 1997: Part 1. However, in certain cases, the recommendations of the appropriate clauses of the code may be inappropriate, it is thus incumbent on the engineer to adopt a more suitable method having regard to, and satisfactorily for, the nature of the member in question (BSI, op. cit. – clause 3.1.1.).

The most important characteristic of any structural member is its actual strength, which must be large enough to resist all foreseeable loads that may act on it during the life of the structure without failure or other distresses (Nilsor, op. cit.). It is logical therefore to proportion members (i.e. to select concrete dimensions and reinforcement) so that members’ strengths are adequate to resist certain hypothetical design loads, significantly above loads expected actually to occur in service. This is the perspective of the limit state method of design.

Reynolds and Steedman (op. cit.) explains that, when designing in accordance with limit-state principles as embodied in BS 8110, each reinforced concrete section is first designed to meet the most critical limit state and then checked to ensure that the remaining limit states are not reached. For the majority of sections, the critical condition considered is the ULS – at which the strength of each section is assessed on the basis of conditions at failure. When the member has been designed to meet this limit-state, it should be checked to ensure compliance with the requirements of the various SLS such as deflection and cracking.

However, since certain serviceability requirements (e.g. the selection of an adequate span/effective depth ratio to prevent excessive deflection and choice of a suitable bar spacing to prevent excessive cracks occurring) clearly also influence the strength of the section, the actual design process eventually involves the simultaneous consideration of requirements for various limit states. Nevertheless, the normal process in preparing a design is to ensure that the actual strength of each section at failure is adequate, while also complying with the necessary requirements for serviceability.

Having identified the critical limit state that governs the design procedures, another vital consideration in the design process is the durability of the concrete. According to BSI (op. cit), as contained in clause 3.1.5.1, a durable concrete element is one that is designed and constructed to protect the embedded metal from corrosion and to perform satisfactorily in the working environment for the life-time of the structure. To achieve this, it is necessary to consider many interrelated factors at various stages in the design process (even construction process), particularly in formulating the design procedures.

The factors influencing durability of concrete, inter alia, include:


  • Design and detailing of the structure (clause 3.1.5.2.1)

  • The cover to the embedded steel (clauses 3.3)

  • Exposure conditions (clause 3.3.4)

Specifically important is the depth of concrete cover provided to protect the steel in concrete against corrosion. The code provisions for nominal cover limiting values to meet durability requirements is outlined in Table 2.2 below, as contained in Table 3.3 of the code. It would be seen from the table that various degree of exposure for concrete has corresponding nominal cover requirement so as to provide an acceptable durability properties in the concrete.

Having explained the general preambles to design procedures, it is pertinent to outline specific design steps of the various reinforced concrete structural members, which are dealt with as follows:



Table 2.2 Nominal Cover to all Reinforcement (including links) to meet Durability Requirements (See Note 1)

(Excerpted from: BSI, op. cit.).


Conditions of Exposure

Nominal Cover

(Dimensions in millimetres)

Mild

25

20

20

20


25

Moderate

__

35

30

25

20

Severe

__

__

40

30

25

Very Severe

__

__

50

40

30

Most Severe

__

__

__

__

50

Abrasive

__

__

__

See Notes 2

See Notes 2

Maximum free water/cement ratio

0.65

0.60

0.55

0.50

0.45

Minimum cement content (kg/m3)

275

300


325

350

400

Lowest grade of strength

C30

C35

C40

C45

C50

(a) Rectangular Beam: A rectangular beam can be simply supported or continuous. Simply supported beams are often encountered as lintels, braces between walls, e.t.c. The design procedures include:

  • Choose beam dimensions – In most cases, the working drawings would have specified these dimensions.

  • Determine the effective depth, d, from:

d = h – cover – Ǿ/2 – link diameter (2.15)

where d = effective depth of beam

h = overall depth of beam

Ǿ = diameter of steel reinforcement



  • Compare the design ultimate moment, M (obtained from the analysis of sections) with the ultimate moment of resistance of concrete, Mu.

Mu = 0.156fcubd2 (2.16)

where fcu = characteristic strength of concrete after 28 days

If M > Mu (or M = Mu), then compression and tension reinforcements are both provided; else, only tension reinforcement is required – subsequent steps are for this case.


  • Obtain the lever arm, z from:

Z = d {0.5 + √( 0.25 – K/0.9)} (2.17)

where z ≤ 0.95d

K = M/bd2fcu (2.18)


  • Calculate the area of steel reinforcement in tension, As from:

As = M/0.95fyz (2.19)

  • A check is then made to ensure that the area of steel reinforcement provided conforms to the provisions for minimum percentage of reinforcement required by the code as stated in clause 3.12.5.3, as well as that for maximum percentage of reinforcement as stated in clause 3.12.6.1.

  • Check for shear stress and design for shear reinforcement where found inadequate. The design shear stress, ν, at any cross-section is calculated from

ν = V/bd (2.20)

where V = maximum shear force

b = breadth of section

According to clause 3.4.5.2, in no case should ν exceed 0.8√ fcu or 5N/mm2, whichever is the lesser of the two values. Then, the value of ν is checked against the design concrete shear stress, νc obtained from:

νc = [0.79 {100As/(bvd)1/3{400/d}1/4]/ λm (2.21)

where λm= 1.25 (partial factor of safety for material)

100As/(bvd) should not be taken as greater than 3

400/d should not be taken as less than 1.

Thus, shear reinforcement should be provided in accordance with clause 3.4.5.3 and Table 3.7 of the code.


  • Check for local or anchorage bond stresses as required by provisions of clauses 3.12.8.1 – 3.12.8.4. The bond stress, fb, is calculated from

fb = Fs/(∏ǾeL) (2.22)

where Fs = force in the bar or group of bars

Ǿe = effective bar size

L = anchorage length

Values for design ultimate bond stress, fbu, may be obtained from

fbu = ß√fcu (2.23)

where ß = coefficient dependent on bar type (Table 3.26 of code).

(b) Axially loaded Column: The design procedure for a rectangular, short, unbraced, axially loaded column is as follows:



  • Determine the ultimate axial load, N, from the analysis of sections

  • Calculate the area of steel reinforcement from

N = 0.4fcubh + (0.8fy0.4fcu)Asc (2.24)

where h = depth of cross-section measured in the plane under consideration

fy = characteristic strength of steel

Asc = area of vertical reinforcement

Therefore, Asc = (N – 0.4fcubh)/(0.8fy0.4fcu) (2.25)

Should equation 2.25 results in a negative value (i.e. 0.4fcubh exceeds N), then the minimum reinforcement required by clause 3.12.5.3 is provided.


  • No check for shear is required, provided that M/N does not exceed 0.6h, and ν does not exceed the maximum value given in clause 3.4.5.12.


  • Also, no check is necessary if, in the direction and at the level considered, the average value of le/h is not more than 30 for all columns (clause 3.8.5.6).

(c) Simply supported one-way Slab: This is a slab carrying predominantly uniform loads. It is designed on the assumption that it consists of a series of rectangular beams 1m wide spanning between supporting beams or walls. Having satisfied the conditions of clause 3.5.2.3, the deign load obtained from structural analysis is turned to a uniformly distributed loads (kN/m), then the design procedure is as follows:

  • Determine the ultimate moment, M from

M = wl2/8 (2.26)

where w = uniformly distributed load along the shorter span (kN/m)

l = effective span of slab (the same as that for beam in clause 3.4.1.2)


  • Determine the effective depth, d from equation 2.15, if the dimensions have been specified in the working drawings.

  • Determine M/bd2

  • Determine K = M/(bd2fcu)

  • Determine z from the lever arm equation



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