CHAPTER ONE

1.0 INTRODUCTION

For the award of a higher national diploma (HND), students in their final year of study are

required to present or produce a project work report to their various departments which will then

be accessed and grades awarded for performance and quality of work.

In the view of this, we choose a project work titled “design of concrete structural elements from

a two (2) storey classroom block”

Almost all tall rise buildings, storey buildings consist of reinforced concrete elements such as

beams; roof, floor, main and secondary beams, slabs, stairs columns and foundations. These

elements during their life span will be subjected to various kinds of loads which it will be require

of them to transmit the loads successfully without any impair or failure of the element.

Reinforced concrete design has different methods in which various concrete elements can be

designed, example are the working stress method and the ultimate load method of design. But it

is most recommended that limit state method of design which is in accordance with the British

standard code 8110 must be used in reinforced concrete design and in fact, it is the most widely

used.

During the design of reinforced concrete elements, there are various serviceability requirements

which must be satisfied and this could also determine whether the element or the building as a

whole is safe, this serviceability includes deflection, cracking, fire resistance durability, shear

and others.

With the above statement and the requirements in reinforced concrete design, we will go on with

the design work and make sure all requirements are satisfied and controlled where necessary.

1.1 BACKGROUND OF THE STUDY

Civil engineers design and construct major structures and facilities that are essential in our

everyday lives. Civil engineering is perhaps the broadest of the engineering fields, for it deals

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with the creation, improvement and protection of the communal environment providing facilities

for living, industry and transportation including roads, bridges, canals, water supply systems,

dams etc.

The design and assessment of structures is the main activity of many civil engineers, the study of

the structural behavior, analysis and design is therefore a principal party of most civil

engineering works and is essential for professional accreditation.

Many structural engineering works are of such an ordered reference standard or complexity that

they require extensive management for their procurement, maintenance and later reuse for

demolition.

1.2 STATEMENT OF THE PROBLEM

Since buildings are subjected to various kinds of loads such as dead loads, live loads, wind loads,

seismic loads and etc. the need of structural design is necessary in able to determine by

calculation the sizes of structural components and members. This will enable the building to

serve it intended purpose or function for which it was designed for.

1.2 AIMS OF THE STUDY

To produce a structure which satisfies an appropriate safety and serviceability

requirement, keep within the budget and pleasing the eye

To develop understanding of the structural behavior

Gain competence in the method of analysis and design.

Understand the various procedures during the design

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1.3 OBJECTIVES OF THE STUDY

To complete our aims as stated above, this project will lay emphasis on the design of reinforced

concrete structural elements from a two (2) storey classroom block proposed to be a civil

engineering department. The design of the structural elements will include: the slab, the beam,

the column, stair and foundation.

1.4 LIMITATIONS

Likewise every situation, there are some problems which hinder the progress of every work in

almost all situations in this world. During the design work, few hindrances which were

encountered are summarized below.

Financial difficulties embraced us which did not permit us to have a well detailed and up

to date architectural drawing for the design work.

Combining class duties and the project work at the same time was very hectic and

challenging, it made it difficult for us to go the extra mile in this project work.

The library is not well equipped with the necessary handbooks about real life reinforced

concrete design problems.

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CHAPTER TWO

2.0 LITERATURE REVIEW

2.1 INTRODUCTION

This chapter presents an overview of previous work on related topics that provide the necessary

background for the purpose of this research. The literature review concentrates on a range of

reinforced concrete design topics which help in the overall design of concrete structural

elements. These topics will include the aim or the necessity of reinforced concrete design,

structural detailing, and the behavior of loads on structures and also about concrete elements

such as beam, slab, column and foundation.

2.2 THE AIMS OF REINFORCED CONCRETE DESIGN

This project is concerned with reinforced concrete and since structural engineering is dominated by

design, it is appropriate to begin by stating the aims of structural design and briefly describe the process

by which structural engineers seeks to achieve them.

There are three main aims in structural design; firstly, the structure must be safe for society demands

security in the structure it inhabits. Secondly, the structure must fulfill it intended purpose during its

intended life span. Thirdly, the structure must be economical with regards to frost cost and to

maintenance cost: indeed, most design decisions are implicit or explicit; economic decisions.

A structural project is initiated by the client, who states his requirements of the structure; his

requirements are usually vague, because he is not aware of the possibilities and limitations of

structural engineering. In fact, his most important requirements are not often explicit stated, for

instance, he will assume that the structure will be safe and that it will remain serviceable during

its intended life.

2.2.1 THE DESIGN PROCEDURE

The process of structural design begins with the structural engineer appreciation of the clients

requirements. After collecting and assimilating relevant facts, he develops concepts of general

structural schemes, appraises them, and then, having considered the use of materials and

methods, he makes the important decisions of choosing the final structural scheme (after

consultation with the client if necessary). This is followed by a full structural analysis and

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detailed design which form the subject matter of this project. Having checked through such

analysis and design, that the final structure is adequate under service conditions and during

erection, the engineer then issues the specifications and detail drawings to the contractor. These

documents are the engineer’s instructions, which will erect the structure under the engineer’s

supervision.

2.3 CODE OF PRACTICE (BS8110)

Codes of practice are intended as guides or references to the structural engineer and should to be

as such; they should never be allowed to replace his conscience and competence.

While the structural engineer will be striving to achieve good design and be creative, he must

appreciate the dangers inherent in revolutionary concepts. Ample experience in the past and in

recent times has shown that uncommon designs or unfamiliar constructional methods do increase

the risk of failures. The Reinforced concrete design is based on the BS8110 code.

2.4 THE STRUCTURAL BEHAVIOUR OF CONCRETE ELEMENTS

One should be aware of the implications of loads applied to structural building elements and

understanding the terminology associated with the structure behavior of building and the

elements within them. One should also appreciate the implications of the structural performance

upon the selection of materials. Included in this section are: the nature of loads acting on

buildings and the nature of building components

2.4.1 The nature of loads acting on buildings

Vertically applied loads, such as the dead loading of the building structure and some live

loadings act to give rise to a tendency for the structure to move in a downward direction that is to

sink into the ground. The extent of any such movement depends upon the ability of the building

to spread the building load over a sufficient area to ensure stability on ground of a given bearing

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capacity. The load bearing capacities of different soil types vary considerably and the function of

the foundation to building is to ensure that the bearing capacity of the ground is not exceeded by

the loading of the structure. In most instances, the bearing capacity of the ground normally

expressed in KN/m2 is very much less than the pressure likely to be exerted by the building

structure if placed directly onto the ground. The pressure is reduced by utilizing foundation to

increase the interface area between the building and the ground, thus reducing the pressure

applied to the ground. Heavy loadings on components may give rise to deflection resulting from

the establishment of moments or in extreme cases puncturing of the component resulting from

excessive shear at a specific point. When subjected to deflections, beam and floor sections are

forced into compression at the upper regions and tensions at the lower regions. This may limit

the design feasibility of some materials, such as concrete which performs well in compression

but not in tension. Hence the use of composite units is common such as concrete reinforced in

the tension zones with steel.

2.4.2 the nature of building components

Reinforced concrete is one of the common materials used for the construction of supporting

structures for multi-storey or large span industrial and commercial buildings

Reinforced concrete combines the compressive strength of concrete and the tensile strength of

steel to allow for efficient and cost effective frame design. When considering the structural

behavior of building elements, the following must be noticed:

The direction of the applied load is important which normally dictates the effect upon the

building.

Failure of building elements can occur in a variety of ways such as:

Buckling of slender columns

Bending of beams and slabs

Shear at support points

Crushing of localized areas

Individual structural elements can act together to create a stronger form

Some deflection of elements is essential and acceptable, but an element is allowed to reach its

elastic limit due to overloading, the structural element may f

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2.4.3 STRUCTURAL DETAILING

Simple and practical detailing should always be aimed for during design. Aesthetically, detailing

should be presentable and must avoid clumsy joints. Special emphasis has to be put on seismic

detailing in order to provide ductile behavior. Column –beam junctions will need additional care

to ensure flow of concrete between bars especially when ductile detailing has been done for

joints are not shown fully in the drawings. Injections grouting, replacement or anticorrosive

treatment to rebar, use of bonding aids, jacketing to structural members, patch repair, applying

special casting/ treatment to protect structures against harmful exposures/environment, water

proofing etc. are often adopted. Various materials are available and the engineers have to be

careful to select the right one after detailed investigation and as per the requirement.

2.5 REINFORCED CONCRETE STRUCTURAL ELEMENTS

2.5.1 SLABS

Slabs are plate elements forming floors and roofs in building which normally carry uniform distributed

loads. Slabs maybe simply supported or continuous over one or more supports and are classified

according to the method of supports as follows:

Spanning one way between beams or walls

Spanning two ways between the support beams or walls

Flat slabs carried on columns and edge beams or walls with no interior beams.

Slabs may be analyzed using the following methods

The elastic analysis

For the method of design coefficients use is made of the moment and she coefficient

given in the code, which have been obtained from yield line analysis

The yield line and Hillerborg strip methods are limit design or collapse loads method.

Simply supported slabs: these are slabs which rest on a bearing and for design purpose are not

considered to be fixed to the support and are therefore, in theory, free to lift. In practice however

they are restrained from unacceptable lifting by their own self weight plus any loadings. A

simply supported slab spanning two ways will deflect about both axis under load and the corners

will tend to lift and curl up from the supports causing tortional moments. When not provision has

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been made to prevent this lifting or resist the torsional then moment coefficients in BS8100

maybe be used.

Solid slabs spanning in one direction: these slabs are designed as if they consist of a series of

beams of one meter breadth .The main steel is in the direction of the span and or distribution

steel is required in the transverse direction. The main steel should form the outer layer of

reinforcement to give it the maximum lever arm. The calculation for bending reinforcement

follows a similar procedure to that used in beam design.

2.5.2 COLUMNS

These are the vertical load bearing members of the structural frame which transmits the beam

loads down to the foundation. They are usually constructed in storey heights and therefore the

reinforcement must be lapped to provide structural continuity.

Braced and unbraced columns

An essential step in the design of a column is to determine whether the proposed dimension and

frame arrangement will make it short or a slender column. If the column is slender additional

moments due to deflection must be added to the moments from the primary analysis. In general

columns in buildings are short. Clause 3.8.1.3 of the code defines short columns as follows:

For a braced structure, the column is considered as short if both the slenderness ratios lex/h and

ley/b are less than 15. If either ratio is greater than 15, the column is considered slender.

For an unbraced structure, the column is considered as short if both the slenderness ratios lex/h

and ley/b are less than 10. If either ratio is greater than 10, the column is considered slender.

Effective height of column

The effective height of a column depends on

The actual height between floor beams, base and floor beams or lateral supports

The column section dimensions

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The end conditions such as the stiffness of beams framing into the columns or whether

the column to base connection is designed to resist moment

Whether the column is braced or unbraced.

The effective height of a pin ended column is the actual height. The effective height of a general

column is the height of an equivalent pined ended column of the same strength as the actual

member. Theoretically the effective height is the distance between the points of inflexion along

the member length

2.5.3BEAMS

These are horizontal load bearing members which are classified as either main beams which

transmit floor and secondary floor loads to the main beams. Concrete being a material which has

little tensile strength needs to be reinforced to resist the induced tensile stresses which can be in

the form of ordinary or diagonal tension (shear). Beams can sub divided into singly reinforced or

doubly reinforced.

2.5.3.1 Singly reinforced beam

Reinforced concrete beams are non homogeneous in nature and, therefore, an exact theory of

bending cannot be developed.

2.5.3.2 BENDING THEORY

Assumptions made in the design of reinforced concrete beam are given bellow:

Cross section remains plane before and after bending, this means that the unit strain in a

beam above and below the neutral axis is proportional to the distance from that axis.

The concrete in tension cracked and all tensile stressed are taken by the reinforcement

There is good bond between the reinforcement and the concrete, the strain in the

reinforcement is given by the theoretical strain in the adjacent concrete.

The stress in all the bars are equal, therefore the resultant tensile act at the centroid of the

bar

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2.5.3.3 Doubly reinforced beams

It had been since that the balanced section of a beam is the most economical section from the

requirement of steel point of view. If the area of tensile steel reinforcement is doubled, the

moment of resistance of the beam is increased only about 22%.if a beam is required to resist a

moment much greater, there are two alternatives: one is to use an over reinforced section, which

is always uneconomical since the increase in the moment of resistance is not in proportion to the

increase in the area of tensile reinforcement since the concrete, having reached maximum

allowable stress cannot take more additional load without adding compression steel. The second

alternative is to provide reinforcement in the compression side of the beam and thus to increase

the moment of resistance of the beam beyond the value for a singly reinforced balance section.

Doubly reinforced sections are required when the applied moment is larger than the limiting

moment. Sections reinforced with steel in compression and tension is known as doubly

reinforced sections.

2.5.3.4 T AND L BEAMS

In actual practices T-sections are common than rectangular sections since the part of reinforced

concrete slab, monolithic with the beam, participates with the structural behavior of the beam.

The slab, which forms the upper part of the T- beam, is stressed laterally in compression, but this

does not reduce it capacity to care for longitudinal compression as a part of the beam

2.5.4 FOUNDATION

Foundations transfer the load from the floor, beams, and columns to the ground. The type of

ground and its strength must play an important role in the selection of the type of foundation.

Thus prior to the engineer deciding on the foundation system, he must have results of site

investigation. This may vary from a trial hole, in a small contract, to large number of deep

boreholes in a large contract. This is the work of a specialist and is carried out in order to

determine the nature of ground and the contours of its strata. No matter how extensive the

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ground exploration is, there will always be the unknown factor and so special care must be taken

with foundations.

Not only is the strength of the ground important, but the type of ground will also play a part in

deciding the type of foundation. Example, it is difficult to drive piles through boulder clay, or

keep bored pile casings dry where water table is high and which could attack the concrete.

2.5.4.1 TYPES OF FOUNDATION

2.5.4.2 STRIP FOUNDATION

Where the ground is good and the loads are light and continuous (e.g. A block/brick wall) strip

foundation is all that may be required. If the load is less than or equal to the depth of foundation,

then there is no transverse bending in the strip and if any reinforcement is required it will only be

a light mesh to enable the foundation to span across local soft spots. It should be noted that at

large door openings, there is possibilities in this foundation of a reversal of bending. Thus

putting the top section into tension. Here again reinforcement may be required.

2.5.4.3 PAD FOUNDATION

If the load is not continuous and the structure is supported on columns, the most economical

foundation is often an isolated pad foundation. However if the ground property to load

relationship is such that the area is covered by the pad is more than half the total area, then a strip

foundation design as a continuous beam may be the answer, but if this is unsatisfactory, a raft

foundation may provide the answer.

2.5.4.4 RAFT FOUNDATION

A raft can provide the answer where pads become so large that they are almost touching. If the

ground is so poor that the raft could not spread the load sufficiently, we can consider buoyant

raft. This is a cellular raft, which in itself is lighter than the soil removed. This gives the

supporting strata a relief of load which can thus be available to support the load from the

superstructure.

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2.5.4.5 PILED FOUNDATION

If there is a good load bearing strata at a reasonable depth, piled foundation then provide a

satisfactory solution. These are series of columns constructed or inserted into the ground to

transmit the loads of a structure to a lower level of subsoil. Piled foundations can be used when

suitable foundation conditions are not present at or near ground level making the use of deep

traditional foundation uneconomic.

2.5.5 STAIR CASE

Stairs consist of a succession of steps and landing that make it possible to pass on foot to other

levels .whereas staircase or stair way is often applied to the complete system of treads, risers,

strings, landings, balustrades and other component parts in one or more successive flights of

stairs. The space occupied by a stair case is termed as stairwell.

Stairs maybe divided into two categories, depending upon the direction in which the stair slab

spans.

Stair slab spanning horizontal: in this category, the slab is supported on each side by side wall or

stringer beam on one side and beam on the other side. Sometimes as in the case of straight flight

stair, the slab may also be supported on both the sides by the two side walls.

Stair slab spanning longitudinally: in this category, the slab is supported at bottom and top of the

flight and remain unsupported on the sides. Each flight of stairs is continuous, supported on

beams at top and bottom or on landings.

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CHAPTER THREE

3.0METHODOLOGY

3.1INTRODUCTION

The design of reinforced concrete structures is achievable with different kinds of methods and

code of practices. The design work was done using the limit state design concept according to

BS8110. Below is the other method of design description and concise description of the method

used.

3.2DESCRIPTION OF DESIGN METHODS

3.2.1WORKING STRESS METHOD

In this method, the structures are analyzed by the classical elastic theory. The stresses in the

members are considered for normal working loading condition, and no attention is given to the

condition that arises at the time of structural collapse. The working loads are fixed by limiting

the stresses in concrete and steel to a fraction of the stresses at which the material fails when

tested as cubes and cylinders for concrete and bars in steel.

3.2.2ULTIMATE LOAD METHOD OF DESIGN

An alternative method of design that was developed was the ultimate load method or the load

factor method, in which the ultimate load is some known multiple of the maximum working load

which the structure is likely to carry. The ration of the collapse load to the working load is

known as the load factor. The load factor gives the exact margin of safety against collapse

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3.2.3LIMIT STATE METHOD DESIGN

The design of an engineering structure must ensure that (1) under the worst loadings, the

structure is safe, and (2) during normal working conditions the deformation of the members does

not detract from the appearance, durability or performance of the structure. The Limit State

method involves applying partial factors of safety, both to the loads and to the material strengths.

The magnitude of the factors may be varied so that they may be used either with the plastic

conditions in the ultimate state or with the more elastic stress range in the working loads. The

two principal type s of limit state are the ultimate limit state and the serviceability limit state.

This is the method used in the design of the various reinforced structural elements of the design

work.

Ultimate Limit State (ULS)

This requires that the structure must be able to withstand, with an adequate factor of safety

against collapse, the loads for which it is designed. The possibility of buckling or overturning

must also be taken into account, as must the possibility of accidental damage as caused, for

example, by an internal explosion.

Serviceability Limit State (SLS)

This requires that the structural elements do not exhibit any preliminary signs of failure.

Generally, the most important serviceability limit states are: Deflection (appearance or efficiency

of any part of the structure must not be adversely affected by deflections), Cracking (local

damage due to cracking and spalling must not affect the appearance, efficiency or durability of

the structure) and Durability (in terms of the proposed life of the structure and its conditions of

exposure). Other Limit States that may be reached include: Excessive Vibration, Fatigue & Fire

Resistance

3.3CHARACTERISTIC LOADS

Since it is not yet possible to express loads in statistical terms, the following characteristic loads

are used in the design;

Dead loads (GK) - the weight of the structure complete, with finishes, partitions etc.

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Imposed loads (QK) - the weight due to furniture, occupants etc.

3.3.1DESIGN LOADS

The design load is the characteristic loads times the partial safety factor. The partial safety factor

varies according to the circumstances under which the loads are considered. Below is the

mathematical representation of the design load used in this design work.

n=1.4 GK+1.6 QK

3.3.2CHARACTERISTIC STRENGTH OF MATERIALS

The characteristic strength of materials used in the design work is stated below

High yield steel with fy equal to 460N/mm3

Concrete grade C30 with a characteristic strength of 30N/m2

3.4 SUMMARY OF DESIGN PROCEDURES

3.4.1SLAB

The slab will be determined whether it is a one way or two way.

We will then decide on the material stresses to be used, i.e. fy and fcu.

The overall thickness h of the slab will be assumed.

Estimate the characteristic loads Gk and Qk per unit area.

Calculate the design load using this equation: n=1.4 Gk +1.6 Qk

Determine the ultimate bending moments in the short and long spans from the following

equations:

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Short span Msx =αsxnlx²

Long span Mxy=αsynlx²

Choose the appropriate concrete cover and determine d.

The cover will be Check whether it is appropriate for fire resistance

Determine the ultimate moment of resistance based on the concrete section for the short span.

Check the span/depth ratio (deflection):

Calculate M/bd2 and obtain a modification factor from the table 3.10 of the code. Select the basic

ratio, then calculate the allowable ratio from basic ratio×modification factor, then calculate the

actual ratio which is equal to effective span/effective depth.

Actual ratio should be less then allowable ratio

The reinforcement areas will be calculated using the design formula stated below.

AS=Msx/ (0.95fy z) for the short span

AS=Msy/ (0.95fy z) for the long span

Select the reinforcement required

Check for shear will be done in accordance with the equation 21 of BS8110.

v=V/bd and in not case will v exceeds 0.8√fcu or 5N/mm2 which ever is lesser.

Check the minimum area of reinforcement in either direction should not be less than the

following: 0.0013bh for high yield steel; 0.0024bh for mild steel, where b =1000mm and h=

overall depth of slab (mm

3.4.2BEAM

Decide on the material stresses to be used, that is, the characteristic strength of concrete fcu and

the characteristic strength of steel fy.

Assume a beam size, could be d=the effective span/12 and breath=d/2

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Estimate the characteristic loads Gk and Qk per unit length of beam.

Calculate the design loads 1.4 Gk +1.6 Qk per unit length of beam

The ultimate bending moment M will be determine from the bending moment diagram.

Choose the appropriate concrete cover and determine the overall depth of beam

Check the cover is appropriate for fire resistance if necessary.

Determine the ultimate resistant moment based on the concrete section (this must be equal to or

greater than the ultimate bending moment. Otherwise a larger section or compression

reinforcement must be considered). It was determined using Microsoft excel program developed

by Techno consult and university of Portsmouth in UK

Check the span/depth ratio:

M/bd2 will be calculated and the modification factor will be obtain a from table 3.10 of the

BS8110 .Select the basic ratio from table 3.9, then calculate the allowable ratio from: basic

ratio×modification factor, then calculate the actual ration which is equal to effective

span/effective depth.

Actual ratio should be less then allowable ratio

Calculate the reinforce area by either:

Use of the design charts: in which case calculate M/bd2 and determine 100As/bd from

appropriate design chart in BS8100.Part 3 or

Used the design formula: in which calculate

K=M/fcubd2 will be used to determine if the section is singly reinforce or double reinforced.

Therefore, when: M/fcubd2 = K >0.156

Compression reinforcement is required to supplement the moment of resistance of the concrete.

The lever arm will be Calculated by the equation: Z= (0.5+√0.25-k/0.9)d

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Calculate the reinforcement area As=M/0.95fyz for singly reinforced section

Tension reinforcement area will calculated with the equation below

As’=M-0.156fcu bd2/0.95fy (d-d’)

Compression reinforcement area is calculated with the equation below

As=0.156 fcubd2/0.95 fyz + As’

Check the minimum reinforcement required

Calculating the shear reinforcement:

The actual shear stress v will be determine from V/bd as in BS8110 cl.3.4.5.2

100As/bd will be determined and vc will be selected from a table 3.8 of the code. If vc+0.4<v,

shear reinforcement will be provided in accordance with table 3.7 of BS 8110, that is, and a bar

size will be determined and spacing for nominal links.

3.4.3COLUMN DESIGN

The column was considered as braced since it is supported by walls or other form of bracing

which is in accordance to BS8110 part 3. Clause 3.8.1.5

The column was determined to be either a short or slender as stated in BS8110 .part 3, clause

3.8.1.3 by the following formulae.

Lex/h and ley/b

Where

lex is the effective height in respect of the major axis

ley is the effective height in respect of the minor axis

h is depth of cross section

b is width of column

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The effective height le of the column was determined by the equation

le=βlo

Where

lo is the clear height of the column between end restraints

β are values obtain from table 3.19 of BS8110

When both ratios are less than 15 (braced) and 10(unbraced), it is considered as short. It should

otherwise be considered as slender.

The end conditions which are selected to determine the value of β is given in clause 3.8.1.6.2 of

BS8110.

If the column is axially loaded, the column design for compressive ULS is done by using

BS8110 equation 38.

N=0.4fcuAc+0.75Ascfy

When eccentricity is allowed due to construction tolerance, only a column that cannot be

subjected to significant moments for pure axial load, the ultimate capacity of the column is given

in BS8110 clause 3.8.3.1 as:

Nuz=0.45fcuAc+0.87Ascfy

If the column supports an approximately symmetrical arrangement of beams, the column is

design for compressive ULS using BS8110 equation 39.

N=0.35fcuAc+0.67Ascfy

If the column is subjected to uniaxial or biaxial bending design for combined ULS of

compression and bending by reference to BS8110 part 3 design charts.

There will be a check for shear ULS for columns subjected to vertical loading and bending. No

check will be required if the column is axially loaded.

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The reinforcement area could also be determined by using the design chart, in which case, the

following must be calculated:

N/bh and M/bh2

Then determine 100Asc/bh from the design chart in BS8100: Part 3 and as provided in appendix

B in this design work.

Minimum reinforcement will be check by;

100Asc/bh≤0.4

Maximum reinforcement will be check by:

6%bh

Minimum size of links which will be provided will be ¼ of the biggest longitudinal bar.

Maximum spacing between links which will be provided will be 12 times the size of smallest

longitudinal bar.

3.4.4FOUNDATION DESIGN

The plan size of the footing was determined by using the permissible bearing pressure and the

critical loading arrangements for the serviceability limit state. The bearing value was chosen

from a soil type of “medium sand or medium dense sand and gravel of bearing value between

200-600 kN/m2”. The equation below was used:

A=N/bearing pressure value

The bearing pressure associated with the critical loading arrangement at the ultimate limit state

was then determined using the formula below:

Bearing pressure=ultimate load (N)/area of base (A)

The thickness h of the pad base will be assumed which will lead to the determination of the

effective depth d.

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A check will be carried out to make sure that the shear stress at the column face is less than

0.8√fcu or 5N/mm2.

Shear stress vc= N/ (column perimeter×d)

Punching shear will be calculated to check the thickness, assuming a probable value for the

ultimate shear stress vc from table of code. The formulae below were used;

Critical perimeter=column perimeter+12d

Area within perimeter= (b+3d) 2

Punching shear V=earth pressure (l2-area within perimeter)

Punching shear stress =V/ (perimeter × d)

Reinforcement will be calculated to resist bending using the following equation.

K=M/fcubd2

Z= (0.5+√0.25-k/0.9)d

As=M/0.95fyz

A final check of the punching shear will be done again having established vc precisely and a

check on the shear stress at the critical section must be carried out too.

3.4.5DESIGN OF STAIR CASE

Dimensions:

Rise

According to BS5395 part 1, the rise should not be less than 100mm and not greater than 220mm

for any category of stairs. Based on this, 150mm was chosen as the rise for the steps in the

design.

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Going

Again according to BS5395 part 1, it recommends that going should not be less than 225mm and

not greater than 350mm for any category of stair. Based on this, 300mm was chosen as the going

for steps in the design work.

Loading

The estimated dead load of the stair will consist of the dead weight of the waist slab which will

be calculated at right angle to the slope and the weight of the steps which will be calculated by

treating the steps to be equivalent horizontal slab of thickness equal to half the rise.

Reinforcement area

Reinforced area of the stair will be determined or calculated using the formulae as used in

beams and slabs.

Serviceability checks

Deflection and shear will be determined and controlled as stated in the code and the same as used

in beams and slabs.

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