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CHAPTER TWO

LITERATURE REVIEW2.1 REINFORCED CONCRETE STRUCTURES

Reinforced concrete structures are the most common structures available today due to their

relatively low cost and ease of construction (the materials for concrete are readily available in

almost every community). There are two types of building structures, namely:

i. Unframed buildings: load carried by load bearing wallsii. Framed buildings: building load carried by structural frames (i.e. members that

transfer loads to each other and finally to the ground); there are two types of framed

structures and there are:

Braced: frame not providing lateral stability i.e. no sway. Unbraced: frame providing lateral stability i.e. structure will sway (Allen,

1988).

A building supported on load bearing walls is limited to two-storey only and the soil bearing

pressure should be in the order of 100KN/m2 or more, otherwise, the building should be

framed (Oyenuga, 2005). A framed building is made up of the following basic structural

members, listed in order of how they transfer loads to the soil:

i. Slabsii. Beams

iii. Shear walls


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Analysis and Design of a Five Storey Hospital Complex 2013

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iv. Columnsv. Foundations.

The natural soil beneath the building is the final recipient of the loads coming from the

building and must possess a certain minimum amount of load bearing capacity for the whole

building to be safe from excessive settlement, sliding or even collapse. Prior to the

construction of any building, two stages of work are required, namely:

Analysis of structural members and the load they carry Design of the structural members, taking cognizance of the imposed load and making

provisions, by way of reinforcing steel bars and grade of concrete, to sustain the load.

Alongside these two stages of work, laboratory and field work are also carried out to ascertain

material strength and, characteristic properties and bearing capacity of the soil on the site.

Analysis of structural members as mentioned above is a task carried out to determine member

behavior under load (i.e. self weight and imposed load); the analysis provides information on

deflection or bending, shear forces, crack, compressive and tensile stresses, ultimate/yield

stresses etc.

2.2 THEORIES AND CONCEPTS IN RC STRUCTURES

The design of reinforced concrete sections has evolved through several phases as engineers

over the years attempted to provide the most stable, safe and economic design solution for

civil engineering structures. There are three major theories that have ever been used in the

design of RC structures and there are:

Permissible Stress Method


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Load Factor Method Limit State Method

PERMISSBLE STRESS METHOD: in this method the ultimate strength of the materials are

divided by an appropriate factor of safety (FOS>1.00); giving design stresses that are usually

within the elastic limit of the said material.

LOAD FACTOR METHOD: in this alternate method, the estimated load coming on the

structure is multiplied by an appropriate factor of safety (FOS>1.00) in order to increase the

load beyond a value that may cause failure. Thus design provides solution that takes into

account the failure load for the structure.

LIMIT STATE METHOD: this method is more or less a compromise of the two

aforementioned methods of design, in that the method provides two partial Factors of Safety,

one to reduce the material strength and the other to increase design load. All design codes

used in Nigeria today for almost all structural members are based on this method. This project

work shall be accomplished using this method.

2.3 LIMIT STATE DESIGNS

The basic principle of the method has been discussed above; here we shall review the

underlying concepts and contributory factors that are useful in implementing this method.


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2.3.1 LIMIT STATE REQUIREMENTS

2.3.1.1 Ultimate Limit State

The strength of the structure should be sufficient to withstand design loads (Allen, 1988), with

an adequate factor of safety against collapse to ensure the safety of the occupants and/or the

safety of the structure itself (Mosley et al, 2007). Provisions must be made against

overturning.

2.3.1.2 Serviceability Limit State

Limit state models the behavior of the structure at working loads (Allen, 1994). This

requirement is grouped under the following:

DEFLECTION: achieved by complying with the span/effective depth ratios given insection 3, BS 8110-1-1997, where the Actual span/effective depth ratio is

recommended to be less than a Limiting span/effective depth ratio. Section 3, BS

8110-2-1997 gives certain basic rules:

i. Appearance: final deflection < span/250.ii. Damage: movement of partition, cladding and finishes should not exceed the

lesser of span/350 and 20mm for non-brittle material; and the lesser of

span/500 and 20mm for brittle materials.

iii. Horizontal deflection: lateral deflection in any one storey should not exceedStorey Height/500 (Allen, 1998).

CRACKING: width of cracks should not exceed 0.3mm for appearance and corrosion;for water retaining structures, crack width < 0.3mm.


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2.3.1.3 Other Limit States

EXCESSIVE VIBRATION: such structural movement has the tendency to instillfear in the occupants leading to discomfort.

FIRE RESISTANCE: takes into account of the structures resistance to collapse, heattransfer and more importantly fire penetration.

FATIGUE: provisions against the action of cyclic loading.In every project, there may be certain characteristics needing special requirements for the

adequate performance of the structure; such requirements may not be covered by any of the

aforementioned limit states, examples are seismic actions, radioactivity resistant structures

etcetera.

Limit state design method is disadvantaged in that it is quite impossible to design for all the

limit states. The convention is to design for the highest limit state and then check for the

adequacy of other limit states. In the case of Reinforced Concrete Design, the Ultimate Limit

State (ULS) is used.

2.3.2 CHARACTERISTIC RESISTANCE

This is the resistance which takes account of the statistical variation of the resistance of the

material (Hughes, 1978); this material strength may also be defined as the strength below

which only 1 in 20 test results are likely to fall, the criterion is defined by the following

equation:

(2.1)Where,= characteristic resistance


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= mean resistances = standard deviation

z = coefficient, say 1.64, implying that 5% of the test result will be below 2.3.3 CHARACTERISTIC MATERIAL STRENGTH

STEEL STRENGTH,This refers to the minimum yield strength (or 0.2% proof stress) of the reinforcing steel.

According to BS 4449, refer to the 0.2% proof stress as the stress at the point where the

stress-strain curve deviates from the initial tangent modulus by 02% strain. The characteristic

strength of steel reinforcing bars, commonly used in Nigeria, are listed on page 9, of chapter

one. Steel has an elastic modulus of 200N/mm2.

CONCRETE (CUBE) STRENGTH,The characteristic strength of concrete,, is the cube strength of concrete at 28 days. Note, insome codes (e.g. EC2), it is the cylinder strength of concrete at 28 days a 150 300mmcylinder.

MATERIAL FACTOR

In the design of structural members, the exact strength of materials obtained from laboratory

tests is not used; for safety requirements, these strengths are usually divided by a material

factor, . The material factors as specified by BS8110 for the Ultimate Limit State are givenby S. S. Ray (1995:4) as:

Reinforcement 1.15


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Concrete in flexure or axial load 1.50

Concrete in shear 1.25

Bond strength in concrete 1.40

Bearing stress 1.50

For exceptional loads and for localized damage,

= 1.30, for concrete= 1.00, for reinforcement

MATERIAL STRESS-STRAIN RELATIONSHIP

The figure shown in Fig. 1.1 (see chapter 1), illustrates the (compressive) stress-strain

relationship for normal weight concrete in the short term; from the curve the following

can be deduced:

The Initial Elastic Modulus the initial tangent to the parabolic curve:

2.2 The Ultimate Stress:

2.3


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The Ultimate Strain: 2.4 2.5

Equation 2.4, gives the strain for general design purposes; while equation 2.5 gives strain

when the curve reaches ultimate stress levels, Ray (1995:4-5).

LOAD FACTOR

For safe load on any structure, the code specifies a percentage increment in permanent and

variable loads such that the final structure possess the capacity to sustain load under

favorable and adverse conditions. The table below gives a typical outlay of these factors

used to increase the calculated loads on a structure by a percentage as recommended by

the code

(Table 2.1 of BS8110-1-1997, abri dged here as Table 2.1):

Load combination

Dead Imposed Wind

Adverse Beneficial Adverse Beneficial

Dead and Imposed 1.4 1.0 1.6 0

Dead and Wind 1.4 1.0 1.4

Dead, Imposed

and wind

1.2 1.2 1.2 1.2 1.2


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Typical load combinations used are:

2.6 2.7 2.8 2.9Where,

Design load Dead load Imposed load Wind loadThese characteristic factors recommended by the code are the factor of safety (f) applied to

the loads imposed on a structure and used here in several computations. A more

comprehensive tabulation of these factors is in Table 2.1 of BS8110-1997.

2.4 ANALYSIS AT THE ULTIMATE LIMIT STATE

The critical limit for reinforced concrete structures will usually be the Ultimate (ULS), thus

most design procedures for RC structures are based on analysis at the Ultimate Limit State

(Allen, 1988:22).


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This analysis involves the determination of the distribution moments and forces in the

structure. A structure of several storeys may be analyzed as frames with the aid of

computer programs1.

All methods that may be used for the analysis of a structure require that an assessment

of section sizes must be carried out. Generally, slabs spanning in one direction, a minimum

span/depth ratio of 30 and 12 to 15 for beams will be satisfactory, provided durability and fire

requirements are satisfied (Allen, 1988:22).

The process of design involves the determination of the worst effect due to the

calculated imposed loads. The maximum moment in a continuous beam and in carry

maximum design loads; while in obtaining maximum moments in a span, that span carries the

maximum load with adjacent spans carrying the minimum load.

Buildings with multiple floors are best analyzed as frames, since the interconnection

between beams and columns allow the imposed moments to be shared between the beams and

columns, thus reducing the design moments on each member which in turn reduces the

reinforcement required for each member effectively lowering the construction cost. The

code provides options for frame analysis depending on whether allocation is made for lateral

stability2 or not. Clause 3.2.1.2 of the BS8110-1-1997 is for frames without provision for

lateral stability whereas clause 3.2.1.3 serves frames providing for lateral stability.

1This project work involved a partial frame analysis by manual computations, while the complete analysis and design was

done using ORION software2Lateral stability implies provision to support vertical and lateral loads or actions.


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This project work was concerned with the design of a structure with provision for

lateral stability3. It must be stated at this juncture that a building may sway under vertical

loads only if the load is asymmetrical loading arrangement (Allen, 1988:22).

2.4.1 UNBRACED FRAMES

The analysis and subsequent design of an unbraced (frame) structure is quite complex, tedious

and time consuming, thus in this project work the analysis was done partially by hand and

completed using a computer program (i.e. ORION).

Lateral loads causing sway input in a structure, is usually a relatively small amount of

effect on the behavior of a structure under load and in time past unbraced framed structures

were designed with this effect ignored (Allen, 1988:22); though in some cases the magnitude

may be large enough to cause concern therefore in this work the analysis shall be carried out

to ensure that the variations do not exceed acceptable limits. The analysis that shall be carried

out later, based on recommendations of the code, shall be broken into:

Frame analysis with vertical loads only (Clause 3.2.1.3.2(a)) Frame analysis with horizontal loads only (Clause 3.2.1.3.2(b))The procedure and typical frame analysis are discussed in detail kin chapters 3 and 4

respectively.

3Wind action assumed to occur at the eastern wing of the structure.


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2.4.2 SLABS

Types

The choice of slabs for any structure may depend on the following as stated by Oyenuga

(2007):

i. The span of the slabii. The use of the space which may determine the span

iii. The load to be carried, andiv. Architectural aesthetics that are required

The following are the basic types of slabs:

Solid slab4 Ribbed slab Flat slab Waffle slab5

Analysis

There are four available methods for the analysis of slabs and there are as follows (Ray,

1995):

i. Code: BS8110-1-1985 Clauses 3.5.2 and 3.5.3, Table 3.15ii. Yield line method (non linear)

iii. Finite difference (linear elastic)4This may be cantilever, simply-supported, continuous, and two-way spanning slabs, (Oyenuga, 2007)

5With beams, or mushroom waffle


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iv. Finite element analysisThe detailed analysis of slabs are beyond the scope of this work, nevertheless, a brief analogy

of the yield line method shall be given here while its application shall be used (limitedly) in

chapter 4.

THE YIELD LINE METHOD

The yield line theory gives an upper-bound solution which ensures that the most critical

collapse mechanism has been selected, if the load-carrying capacity of the slab is not to be

over-estimated (Hughes, 1976). These collapse mechanisms can be represented by

superimposed yield line patterns, creating rigid regions between the yield lines which are also

uncracked assumed (Mosley et al, 2007). Rotation along the yield lines will occur at a

constant moment equal to the ultimate moment of resistance of the section, and will absorb

energy (Mosley et al, 2007). This allows the application of the virtual work method for

applied load undergoing displacement (Khurmi, 2010).

The virtual work method gives the following applicable expressions (Paraphrased

from Mosley et al, 2007):

2.10

2.11For a square one-way slab, as shown below with,Displacement, d


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Rotation, r

Moment, m, and

Load, w

Therefore,

( ) , and 2.12 , also 2.13 2.14

equating 2.12 and 2.13

2.15rearranging,

2.16

L

L rd

a. slab b. Collapse mechanismFigure 2.2: Collapse Mechanism for Slabs


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Equation 2.16 gives the ultimate moment of resistance of a slab when load is maximum

(i.e. critical).

Design

The design of a slab is basically rudimentary as the designer already has a clear

knowledge of the failure pattern of a slab based on its dimensions and ultimate moment of

resistance6.

The object of design is to provide reinforcement for the slab such that the imposed

load on the slab is less likely to cause a moment exceeding the ultimate moment of

resistance. The details for the design of slabs peculiar to this project work are in chapters 3

and 4.

2.4.3 BEAMS

Beams are structural elements primarily designed to provide adequate resistance to the

ultimate bending moments, shear forces and torsional moments (Mosley et al, 2007). Beams

also carry the lateral loads in roofs and floors, whose design stages may be condensed as

(from Mosley, et al 2007:169):

Preliminary analysis and member sizing Detailed analysis and design of reinforcement Serviceability checks

6Research over the years has enabled engineers to satisfactorily define the critical failure patterns of most slab

shapes.


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Types

Beams may be grouped and classified as follows (Arya):

i. Cross-section: Rectangular T-section beams L-section beams

ii. Position of reinforcement Singly Reinforced beams Doubly reinforced beams

iii. Support conditions Simply supported Continuous beams

The aforementioned parameters help to define the behaviour of the beam section in relation to

bending, shear and deflection (Oyenuga, 2005). Following the analysis of the beam, Draycott

(1990) stated the following dimensional restraints and limitations as applicable to the design:

Effective span of beams Deep and/or slender beams Main reinforcement areas Minimum spacing of reinforcement Maximum spacing of reinforcement


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Analysis

Beams may be analyzed as simply supported where the end moments are zero and the span

moment is:

For beams spanning over several supports they are analyzed as continuous with the end fixed

(i.e. rigid) or more simply with the ends free. The beams are analyzed and designed in this

work were analyzed as rigid members of braced frames (see chapters 3 and 4). The Moment

Distribution Method is the common method used in the analysis of frames. This analysis is

very tedious and most were accomplished using Orion analysis and design software.

Design

The beams designed in this project work were all of the continuous type and were designed

following a strict regimen of sequential operations as recommended by several textbooks:

Preliminary sizing Analysis of loads obtaining moments (and reactions) at the spans and support

connections respectively

Checking that imposed moments does not exceed ultimate bending moment of thebeam, otherwise adequate provisions were made for sustenance (in the form

compression steel).

Design of reinforcement at span and at support (against bending and shear) Checks were also instituted to ensure that shear, deflection, and area of reinforcements

were all adequate.


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Regions of the structure lacking walls for lateral resistance were designed withadditional moment and shear from wind load analysis.

2.4.4 COLUMN

Columns are largely compression members which may be subjected to bending due to their

slenderness and/or asymmetrical loading from beams (Oyenuga, 2005:201). Columns are the

vertical sections of a structure and are best analyzed as part of a frame enabling the

determination of the imposed moment and in turn ensuring design provisions are adequate and

economic.

The code (in clause 3.8) makes provision solely for columns whose greater overall

dimensions does not exceed four times its smaller dimensions. Columns may be grouped into

(see clause 3.8.1.5):

Braced: when stability of the structure as a whole is provided by wall, bracing, orbuttressing designed to resist all lateral forces in that plane.

Unbraced: column provides lateral support for the entire structure (lateral loadanalysis required).

A further classification of columns is:

Short column: lex/h and ley/b less than 15 (braced)lex/h and ley/b less than 10 (unbraced)

It should be noted that columns may not possess reinforcement (i.e. plain columns), if the

cross section is large enough to provide support for the ultimate loads.


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Analysis

The bending moment and forces acting on a column are:

Imposed moment (from frame analysis) Moments from column deflection (if the column is slender) Axial forces (from frame analysis) Imposed axial load (or force) from area of beam, wall and slab controlled by

the column

The type and number of moments and forces acting on a column determine if the column is to

be designed as axial, uniaxial, or biaxial column (see typical frame analysis in chapter 4).

The analysis of columns as recommended by the code, clause 3.8.2.4 requires

that a nominal eccentricity of vertical loads equal to 0.05 times the overall dimensions in the

plane of bending, not to exceed 20mm. biaxial bending only requires minimum eccentricity

checks about one axis at a time.

Design

The design of columns (as with all RC members) follows a strict regimen controlled by codes

BS8110 mostly. In this work, the manual analysis and design of biaxial columns were

considered as the structural analysis data was readily available7.

7Design for other types of columns would have required a manual analysis of the whole structure an

impractical and time-consuming venture.


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PRELIMINARY DETERMINATION OF IMPORTANT PARAMETERS

The following parameters are vital to the design of a column:

a. Sizing: based on durability, fire resistance and architectural aesthetics.b. Effective Height: Table 3.19 and 3.20 of the code makes provision of multiplication

factors used to reduce or increase the clear distance between floors to give its effective

value at each axis column end conditions are taken into account.

c. Slenderness Limit: the clear distance between floors is expected not to exceed 60times the minimum thickness of the column clause 3.8.1.7.

d. Minimum eccentricity, as stated above.e. Procedures for the design of biaxial columns are available in chapter 3f. Typical biaxial column analysis (i.e. frame analysis) are available in chapter 4

2.4.5 WALLS

A wall is a vertical load-bearing member, whose length exceeds four times its thickness

(Ray,). Walls may be categorized as

Unbraced: designed to carry lateral loads Braced: does not carry any lateral loads, and Reinforced walls: contains at least the minimum quantities of reinforcement

Plain walls: contains no reinforcement or less than the minimum quantity of

reinforcement (Ray,).

The analysis and design of walls was performed via computer application.


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2.4.6 FOUNDATION

Foundations serve the primary function of transferring and spreading the loads from a

structures columns and walls to the ground (Mosley, et al,). The ground must possess a

bearing capacity that reasonably exceeds the load transferred to it per meter square. An

effective foundation provides resistance against sliding, uplift, and overturning.

The design of foundations takes into account of both structural and geotechnical

failure. Foundation structures are founded on soils, thus soil mechanics plays a vital role in

the selection of footing types, sizing of footing base, founding depth, thickness of footing.

The following are the basic types of footing and a description of situations in which they are

used (Arya, 1994):

a) CONTINOUS STRIP FOOTING:To support load-bearing walls or under a line of closely spread columns

b) PAD FOOTING:To support a single column; it may be reinforced or plain concrete form depending

on magnitude of loading.

c) RAFT FOOTING:Used where ground conditions are relatively poor. This type of footing distributes the

load over a large area and allows the uniform settlement of the structure.

d) PILE FOOTING:Applicable where the ground conditions are so poor that it is impractical to use strip or

pad footing, as well as where better soil is present at lower depths.


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2.4.7 STAIRCASE

These are structural members added to a structure to bridge the gap between two (say, floors)

levels by breaking up the distance into smaller vertical distances spread out in a slope length

between these levels.

Staircases may be classified into transverse spanning stairs and longitudinal spanning

stairs.

TRANSVERSE SPAN STAIRS

This type of stairs allow for smaller thickness of slab waist. Allen () categorized this type of

stairs as:

a. Cantilever stairs spanning from walls at one sideb. Stairs spanning between support at each side, with support provided by walls or

stringer beams

c. Cantilever stairs across a central spine beam; no lateral distribution between adjacenttreads so that each tread must be designed for concentrated loads.

Categories (a) and (b) above requires minimal waist thickness for adequate and effective

lateral distribution of load only uniformly distributed load are thus considered in the

design.

LONGITUDINAL SPAN STAIRS

These stairs span between supports at the top and bottom of the flight and are unsupported at

the sides (Allen,). The supports are provided by beams or walls cast monolithically with the


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stairs, or spanning across the edges of the landing. The span of the stairs will be taken as the

distance between the centers of the beam or walls.

The staircases designed in this project work are three flights surrounding an elevator

opening (or well). They were designed individually with their spans taken as the distance

between half the landing on both ends of the stairs, as recommended by MacGinley, (1990).

2.4.8 WIND LOAD ON TALL STRUCTURES

Wind is a source of lateral action on high rise buildings and must be taken into account for

any (unbraced building) structure rising above 4 storeys or above 12 metres at least.

Fig 2.3: typical structure subjected to wind action

(Source: Smith and coull, 1991. Page 49)


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Failure to take wind actions into consideration during design may lead to excessive sway or

even catastrophic failure due to overturning or flutter from aero-elastic effects (Ameen-Ikoyi,

2005).

Wind action is not constant with height of structure or duration of impact. Thus wind

load (or action) on the side of a building is not uniform and its effect may be favorable or

unfavourable to the amount of imposed load to which a structure is subjected (Ameen-Ikoyi,

2005). However in executing this project work, for simplicity, the wind load was assumed to

vary uniformly across the entire height of the structure8.

WIND VELOCITY PROFILE

The earths rough surface causes turbulence and frictional drag which reduces the wind speed

at lower levels; these turbulence and friction decreases with height, allowing the wind

velocity to increase towards a maximum value. But for simplification purposes again, this

work involved the application of a constant wind velocity, v = 43m/s, as was recommended

for North-central Nigeria (Aguwa, 2013)9.

It should be noted that a wind design load of 1.2Wk was applied to the building

(lateral) frame analysis process prior to the design. The conventional vertical load factor of

safety remained unchanged.

8The accurate determination of the variation of wind action on the structure would have required intensive

test simulation and wind speed evaluations, which both exceed the scope of work for this project.9Authority obtained from supervisors verbal communication to student.

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