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Structures Index

Reinforced Concrete

Introduction..... Formwork..... Standards..... Symbols..... Concrete Elements..... Initial Sizing..... Partial Safety factors..... Design of Beams..... Design of columns..... Design of Walls.....
Design of Floor Slabs..... Design of Flat Slabs..... Reinforcement Tables..... Fire protection cover..... Characteristic Strengths..... Reinforcement bar bending.....


The building structures pages have been added over the six months to Dec. 2012.     They are very much work-in-progress and I will be updating them on a regular basis over the next six months.


Introduction

This page includes some notes on reinforced concrete as used in the construction of walls and structures.    It is important to note that I have based most of the content of this page on BS 8110 -1:1997.    This standard has now been replaced by Eurocode BS EN1992.   There are a number of differences between BS 8110 and BS EN 1992 e.g the symbols are generally different (N in BS8110 = N ED in BS EN 1992).    The notes are not intended to enable detail design to the latest codes they are simply provided to enable mechanical engineers to understand the topic and produce basic design studies.    Formal design work must be completed in accordance with the relevant codes.   

Reinforced concrete is probably the most prolific and versatile construction material .    It is composed of two distinct materials concrete and reinforcement , each of which can be varied in quality disposition and quantity to fulfill a wide range of construction requirements.

The concrete composition is an based on three constituents : aggregate, cement and water.    These are mixed together in a homogeneous mass and are then put in place and left for the chemical and physical changes to occur that result in a hard and durable material.    Information on concrete forms is provided on webpage concrete.       The strength and durability of the resulting concrete depends on the quality and quantity of each of the constituents and on any additional additives have been added to the wet mix.     Much of the mixing is now done off site by ready mix companies ..The strength of the resulting mixes is generally confirmed by a cube crushing test.   

The concrete reinforcement is generally steel although other materials are sometimes used such as glass fibre.     The main reinforcement bars are generally high yield deformed bars (  f y >= 460 N/m2 ) .    Reinforcement links are often mild steel (  f y >= 250 N/m2 ) although high yield steel is becoming more popular.    For reinforced concrete slabs and walls it is convention to use mesh reinforcement.

The reinforcement is generally located to compensate for the concrete being weak in tension e.g in spanning beams the reinforcement is primarily located in the bottom half of a section and at the midspan.    In a cantilever beam the reinforcement will generally be at the top of the beam with the maximum concentration at the support.

In the notes below the characteristic strength for concrete ( f cu ) is the value of the cube strength and the characteristic strength for the reinforcement ( f y ) is the designated proof/yield strength.    The referenced standard for these notes (BS 8110) also identifies a partial factor of safety γ m which is applied to these strengths to take into account the difference between test and practical conditions.    It should be noted that the strength of concrete related to flexure is actually accepted as 0,67. f cu.

The characteristic load regime on a structure comprises a characteristic dead load (G k) and a characteristic imposed load ( Q k ) and sometimes a characteristic wind load ( W k ) these are each modified by an appropriate partial safety margin γ f

Structures made from concrete to BS 8110 (and to the latest codes ) should be designed to transmit the design ultimate dead , wind , and imposed loads safely from the highest supported level to the foundations.    The structure and interactions between the included members should ensure a robust and stable design . The design should also be such that the structure is able to remain is service . Account should be taken of temperature, creep, shrinkage, sway, settlement and cyclic loading as appropriate.

Summary of load symbols

γ f = Partial safety factor for load
E n = Characteristic Earth Load
G k = Characteristic dead Load
Q k = Characteristic Wind Load


Summary of strength symbols

γ m = Partial safety factor for material strength
f cu = Characteristic strength of concrete
f y = Characteristic strength of reinforcement

When completing analysis of cross sections to determine the ultimate resistance to bending certain assumptions are made

1)The strain distribution in tension or compression assumes plane sections remain plane
2) The compressive stresses in concrete are derived from stress strain curve shown below with γ m = 1,5
3) The tensile strength of concrete is ignored
4) The stresses in the reinforcement are derived from the stress/strain curve as shown below γ m = 1,15
5) When the section is resisting only flexure the lever arm should not be greater than 0,95x the effective depth

The effective depth is the depth from the compression face to the centre of the area of the main reinforcement group






Formwork

The formwork is the timber , steel or plastic moulds into which the concrete is poured on site to create the various concrete components.    It is a vital part of the construction process and the formwork costs can be up to 50% of the concrete construction costs.    The reinforcement must be located in the formword prior to pouring the concrete.

The formwork must be leaktight, strong and rigid to contain and maintain dimensions of the full liquid concrete mass. It must also be designed for standardisation and reuse to reduce the construction costs to a minimum.

It is clear that the formwork should not only be designed for construction it should also include features allowing safe and convenient removal and re-use






Relevant Standards

The design notes provided on this page relate to BS 8110-1 :1997 which has been superseded by the standards referenced below.

Code Reference Number                Title
BS EN 1992-1-1:2004 General rules and rules for buildings..Replaces BS 8110-1, BS 8110-2 and BS 8110-3
BS EN 1992-1-2:2004 Eurocode 2:General rules. Structural fire design
BS EN 1992-2:2005 Eurocode 2:Concrete bridges. Design and detailing rules..Replaces BS 5400-4, BS 5400-7 and BS 5400-8
BS EN 1992-3:2006 Eurocode 2:Liquid retaining and containing structures...Replaces BS 8007
BS EN 1992-3:2006 Eurocode 2:Liquid retaining and containing structures...Replaces BS 8007
BS EN 206-1:2000 Concrete. Specification, performance, production and conformity
BS EN 206-9:2010 Concrete. Additional rules for self-compacting concrete (SCC)y





symbols
A s = Area of tension reinforcement
A' s = Area of Compression reinforcement
b = width or effective width of section
b w = average width of web
d = effective depth of section (compression face to centre of reinforcement )
d' = depth to compression reinforcement
h f = thickness of flange
L = effective span of beam
M = Design Ultimate moment at section
x = Depth to neutral axis
z = lever arm
f cu =Characteristic strength for concrete ( f cu ) = cube strength
M u = Ultimate moment capacity of unreinforced beam
βb = ratio (Moment at the section after redistribution)/ (Moment at the section before redistribution)
γ m partial factor of safety applied to characteristics strengths of concrete and reinforcement
A c = Area of concrete at section
A sv = Total cross section area of links at the neutral axis , at section
f y =Characteristic strength of reinforcement ..Proof /yield strength
f yv =Characteristic strength of links ..Proof /yield strength
s v= spacing of links along section
V = design shear force at ultimate loads
v = Design shear stress at cross section
v c = Design shear capacity

Columns..................
A c = net cross section area of concrete in column
A sc = Area of vertical reinforcement
a u = deflection at ULS
b = width of column section (smallest cross section dimension
h = depth of column section
l e = effective height of column
l o = clear height of column between restraints
l c = centre height of column between restraint centres
M 1= Smaller initial end moment due to design ultimate loads
M 2= Larger initial end moment due to design ultimate loads
N = design ultimate axial load on column
N bal = design ultimate axial load of a balanced section : (if symmetrically reinforced assume 0,25f cubd )

Walls..................
e a = additional eccentricity due to deflections
e x = resultant eccentricity of load at right angles to plane of wall
e x1 = resultant eccentricity at top of wall
e x2 = resultant eccentricity at bottom of wall
h = thickness of wall
l e = effective height of wall
l o = clear height of wall between lateral supports

Slabs
V eff = Effective shear force at ultimate loads and moments
U = Shear perimeter around column head.
U o = shear perimeter around column head at column face
U i = shear perimeter around column head location away from column face. (see notes.)





Concrete building components

Beams
Beams are horizontal structural items specifically design to support vertical loads .    Concrete beams are generally rectangular in section with width b and height h and length L.     Beams can also be of a variety of section including channel section, tee section, I section etc.     There are a number of support configurations for beams including cantilever, simply supported , continuous, etc each one tending to produce different stress and deflection characteristics.    As concrete is not able to withstand tensile stress , loaded concrete beams are generally reinforced in the area under tensile stress.

Concrete columns
Vertical structural elements of clear height = l and cross section = b x h where h < 4b are columns , otherwise they are walls.     A column should not have an unrestrained length greater than than 60b.

Concrete Walls
Vertical load bearing element with length exceeding 4 times the thickness.    The clear height is designated l o and the thickness h.    Concrete walls can be plain walls which have zero to minimum reinforcement (< 0,4% of section area ) or reinforced walls with reinforcemnt > 0,4% of area .   

Flat Slabs
Flat slabs are horizontal slabs , used for floors or upper structural surface which are supported on walls or beams.

Solid Slabs
These are horizontal slabs supported on pads or columns instead of walls






Rough preliminary sizing of concrete elements


Element Typical spans
(m)
Overall Depth or Thickness
Simply supported Continuous Cantilever
One way spanning slabs 5 - 6 L /(22-30) L/(28-36) L/(7-10)
Two way spanning slabs 6-11 L /(24-35) L/(34-40) -
Flat slabs 4-8 L /27 L/36 L/(7-10)
Rectangular beams9-10 L /12 L/15 L/6
Flanged beams5-15 L /10 L/12 L/6
Columns2,5 -8H / (10-20) H / (10-20) H/10
Walls2-4H / (30-35) H / 45 H/ (15-18)

L = effective span = smaller of distance between bearing centres or clear distance (between supports ) + depth of section






Partial Safety margins....

Typical Values of γ m for Ultimate limit state... (Persistent and transient)


Reinforcement & Pre stressing 1,15
Concrete in flexure or axially loaded 1,5
Shear strength without reinforcement 1,25
others => 1,5





Load Combinations and values γ f for Ultimate limit state.


Load combinations Load type
Dead ( G k) Imposed ( Q k) Earth + Water Pressure Wind Pressure
AdverseBeneficial AdverseBeneficial
Dead and Imposed (+ earth and water pressure) 1,4 1,0 1,6 0 1,6 1,2
Dead and Wind (+ earth and water pressure) 1,4 1,0 - - 1,2 1,4
Dead + Imposed + Wind (+ earth and water pressure) 1,2 1,2 1,21,2 1,21,2





Simple Reinforced beam design

The theory supporting the relationships in this section,in outline, is covered on web page Reinforced concrete beams theory

The sketch below identifies the types of simple reinforced beams that are relevant to the notes provided

Condition of strain and stress in a rectangular section at ultimate limit state of loading is shown in the figure below

Note: The factor 0,67 is not a partial safety margin it relates to the direct relationship between the cube strength as indicated by f cu and the strength in flexure of the concrete.
The total compressive force generated within the concrete at the ultimate moment capacity is

0,9 . 0,67.fcu . b . x / (γ m =1,5)    =     0,4 . fcu. b. x

The ultimate moment capacity of a unreinforced concrete beam section where there is less than 10% moment distribution is

M u = 0,156 .F cu.b.d2

M = K.[ f cu.b.d2 ]

Factors for lever arm (z) and neutral axis depth (x)

x0,13.d0,15.d0,19.d 0,25d 0,32.d0,39.d0,45.d0,5.d
z0,942.d0,933.d0,91.d0,887.d0,857.d0,825.d 0,798.d0,775.d
K 0,05 0,057 0,070 0,090 0,110 0,130 0,145 0,156

Area of Reinforcement bars

If the applied moment is less than M u then the area of tension reinforcement =

If the applied moment is greater than M u ( K > 0,156 ) then tension  and compression reinforcement is necessary
The tension reinforcement required is.

Compression reinforcement required is



Application of equations to concrete tees

Mu is simply calculated as 0,4.fcu.b.hf.(d - hf/2) if this is greater than M then the neutral axis is within the flange and the tee can be assessed using the equations above..



Shear Strength of concrete beams

The design shear capactity (v) in a concrete beam at any section is calculated from

v = V / (b v.d )

V is the Shear force at a section
v should never exceed 0,8 f cu or 5 N/mm2 if lower.

Values of concrete shear capacity v c related to % reinforcement and effective depth (d) of section

% Reinforcement
=
100 A s /b v.d
Effective Depth (mm) - d
125 150 175 200 225 250 300 400
N/mm2 N/mm2 N/mm2 N/mm2 N/mm2 N/mm2 N/mm2 N/mm2
= < 0,15 0,45 0,43 0,41 0,40 0,39 0,38 0,36 0,34
0,25 0,53 0,51 0,49 0,47 0,46 0,45 0,43 0,40
0,50 0,67 0,64 0,62 0,60 0,58 0,56 0,54 0,50
0,75 0,77 0,73 0,71 0,68 0,66 0,65 0,62 0,57
1,00 0,84 0,81 0,78 0,75 0,73 0,71 0,68 0,63
1,50 0,97 0,92 0,89 0,86 0,83 0,81 0,78 0,72
2,0 1,06 1,02 0,98 0,95 0,92 0,89 0,86 0,80
>= 3,0 1,22 1,16 1,12 1,08 1,05 1,02 0,98 0,91


Form of Shear Reinforcement

If the applied shear stress is less than 0,5 v c throughout the beam then

Minimum links should be provided, and in elements of low importance e.g lintels then no links need be included

Suggested shear area provided = A sv > 0,2 b v.s v / (0,87 .f yv)

If the applied shear stress is greater than 0,5 v c and less than (0,4 + v c) throughout the beam then

Minimum links should be provided for the whole length of beam to provide shear resistance of 0,4 N/mm2

Suggested shear are provided = A sv > 0,4 b v.s v / (0,87 . f yv)

If the applied shear stress is greater than (0,4 + v c) and less than (0,8 Sqrt(F cu or 5 N/mm2) + v c) throughout the beam then

Links should be provided for the whole length of beam to provide shear resistance at no more than 0,75d spacing .    No tension bar should be more the 150 mm for a vertical shear link.

Suggested shear are provided = A sv > b v.s v (v - v c) / (0,87 . f yv)

>





Stiffness and Deflection

A table is provided below which gives the basic span/ depth ratio for beams which limit the total deflection to span/250 or 20mm (if less) , for spans up to 10m.

TypeRectangular Section Flanged Section
b w/b =1,0 b w/b =< 0,3
Cantilever 7 5,6
Simply support 20 16,0
Continuous 26 20,8

For b w/b >0,3 interpolation between the rectangular and flanged values is acceptable



Allowable span/depth ratio

The allowable span/depth = F 1.F 2F 3F 4. Basic span/depth ratio

F 1 For long spans exceeding 10m the values in the table should be multiplied by 10/span.
F 2= A factor to allow for tension reinforcement. See chart below
F 3= A factor to allow for compression reinforcement. See chart below
F 4= A factor to allow for stair waists where the staircase occupies over 60% of the span






Simple Column design


Cross section of a typical simple column.

A column should not have a clear distance between restraints which exceeds 60.b ( b being the small cross section dimension ).    If one end of a column is not restrained (a cantilever column) then its clear height must be the smaller of 60.b or 100.b2 /h .

It is important early in the design process to determine if the column is a stocky design and if there is significant bracing associated with the columns.    The effective length of a column l e = l o.β where β is the effective length constant which is dependent on the end support conditions (see tables below).     A column is considered a stocky column if its effective length divided by b = l e/b is less than 15.     A longer column must be assessed in the design for risk of buckling.

Some simple rules for column reinforcement.
A sc should by more than 1% and less than 6% of gross cross section area of column (b x h)
The minimum dia of bars should be 12mm.
Lateral binders/ties should be arranged to restrain each bar from buckling and the end of the binders should be anchored.     The pitch of the binder should not exceed b or 12 times the dia of the longitudinal bars, nor 300 mm . The diameter of the binders should not be less than 25% of the diameter of the longitudinal bars


Typical column head designs. (columns and associated heads can also be circular.






Braced Columns -Table of effective length coefficients (β)

A column is considered to be braced if lateral stability is provided by walls or buttresses. The column is effectively only taking axial loads and moments resulting from eccentricity of lateral loads



End Condition at TopEnd Condition at Bottom
Rigidly FixedFixedPinned with some
angular restraint
Rigidly Fixed0750,800,90
Fixed0,800,850,95
Pinned with some
angular restraint
0,90,951,00


Unbraced Columns -Table of effective length coefficients (β)



End Condition at TopEnd Condition at Bottom
Rigidly FixedFixedPinned with some
angular restraint
Rigidly Fixed1,21,31,6
Fixed1,31,51,8
Pinned with some
angular restraint
1,61,8-
Free 2,2--


Rigidly Fixed
The end of the column is connected monolithically (solidly) to beams on either side which are at least as deep as the overall dimension of the column in the plane considered.    Where the column is connected to a foundation structure, this should be of a form specifically designed to carry moments.

Fixed.
The end of the column is connected monolithically to beams or slabs on either side which are shallower than the overall dimension of the column in the plane considered

Pinned with some angular restraint
The end of the column is connected to members which, while not specifically designed to provide restraint to rotation of the column will, nevertheless, provide some nominal restraint.

Free.
The end of the column is unrestrained against both lateral movement and rotation. e.g the free end of a cantilever column in an unbraced structure

Design Calculations

When a stocky column is subject to a simple axial loads with induced moments , assuming a well balanced load scenario , it need only be design for the ultimate design axial force + a nominal allowance for an eccentricity of force (e c ) of h/20 (with a maximum of 20mm).

When a stocky column is subject Axial forces and bending stresses it is generally necessary to use design charts .Reference Column Design charts.

Stocky beams resisting moments
Following equations include provision for γ m.

When a stocky column cannot be subjected to significant moments,it is sufficient to design the column such that the design ultimate load is less than

N = 0,4 f cu.A c + 0,75 A sc.f y

When a stocky column is supporting to a reasonably symmetrical arrangement of beams of similar spans and which are for uniformly distributed loads , it is sufficient to design the column such that the design ultimate load is less than

N = 0,35 f cu.A c + 0,67 A sc.f y

Biaxial bending in columns
When it is necessary to consider biaxial moments, the design moment about one axis is enhanced to allow for the biaxial loading condition and the column is designed around the enhanced axis.    Consider the column as loaded below.

The relevant moment is modified as below

N/( b.h.F cu )0 0,10 0,20 0,30 0,40 0,50 >=0,60
β a1,0 0,88 0,77 0,65 0,53 0,42 0,3





Design of Walls

The design axial forces in a reinforced wall may be calculated on the assumption that the beam and floor slabs being supported are simply supported.

The effective length of a wall l e should be obtained as if the wall was a column which is subject to moments in the plane normal to the wall.    The determination if a wall is stocky or slender is also obtained using the same criteria as for a column.

Stocky reinforced walls

A stocky braced reinforced wall supporting reasonably symmetrical load should be designed such than..

n w = 0,55.f cu.A c + f y.0,67A SC.

n w = total design axial load on wall due to design ultimate loads :providing the slab loads are uniform in loading and relatively evenly distributed.

Except for short braced walls loaded symmetrically the eccentricity in the direction at right angles to a wall should not be less than h/20 or 20mm if less.

When the eccentricity results from only transverse moments the design axial load may be assumed to be evenly distributed along the length of the wall.    The cross section should be designed to resist the design ultimate load and the transverse moment .   The assumptions made for the calculation of beam sections apply.

When a wall is subject to in-plane moments and uniform axial forces the cross section of the wall should be designed to support the ultimate resulting axial loads and inplane moments.

Slender reinforced walls

The maximum slenderness ratio l e/h should be 40 for braced walls with <1% reinforcement: 45 for braced walls with => 1% reinforcement: 30 for unbraced walls

A suitable design procedure is to first consider axial forces and in-plane moments to obtain the distribution of forces along the wall assuming the concrete does not resist tension.    The transverse moments are then calculated.    At various points along the wall the results are combined.

Walls subject to significant transverse moments additional to the ones allowed for by assuming a minimum eccentricity are considered by assuming such walls are slender columns bent about the minor axis .    If the wall is reinforced with only one central layer of reinforcement the additional moments should be doubled

Plain walls

Plain walls include less than 0,4% reinforcement.

The effective height of plain unbraced concrete walls is assessed as ( l e = 1,5 l o ) if the wall is supporting a roof or floor slab, otherwise it is calculated as (l e = 2 l o).

When a plain concrete wall is braced with lateral supports resisting both rotation and movement then ( l e = 0,75 l o )
Where the lateral support only resists lateral movement then ( l e = l o )or if relevant ( l e = 2,5 (distance between support and a free edge )





Design of solid slabs

Solid slabs can be simply one-way loaded plates or two way loaded plates depending on the support arrangements


Design Moments and shear forces in simple one way spanning continuous slabs
Uniformly Distributed Loads

F = Total Design Ultimate load on one slab (1,4 G k + 1,6 Q k)
l s = is effective span of slab

G k = Dead Load
Q k = Imposed load)



Design Moments and shear forces in simple one way spanning continuous slabs

  End support/ Slab connection At First Support At Middle of interior spanAt Interior supports
Simple SupportsContinuous
Outer SupportsNear Middle of end spanOuter SupportsNear Middle of end span
Moment 0 F.l s /11,5 -F.l s /25 F.l s /13 -F.l s /11,5 FL /15,5 -F.l s /15,5
Shear F / 2,5 - 6 F /13 - 3 F /5 - F/2




Design Moments and shear forces in two way spanning continuous slabs
Uniformly Distributed Loads





Type of Panel and Location Short span coefficient β sx Long span coefficient β sy
For values of l y/l x
1,0 1,1 1,2 1,3 1,4 1,5 1,75 2,0
Interior Panels
Moment at continuous edge -0,031 -0,037 -0,042 -0,046 -0,050 -0,053 -0,059 -0,063 -0,032
Moment at mid-span 0,024 0,028 0,032 0,035 0,037 0,040 0,044 0,048 0,024
One short edge discontinuous
Moment at continuous edge -0,039 -0,044 -0,048 -0,052 -0,055 -0,058 -0,063 -0,067 -0,037
Moment at mid-span 0,029 0,033 0,036 0,039 0,041 0,043 0,047 0,050 0,028
One long edge discontinuous
Moment at continuous edge -0,039 -0,049 -0,056 -0,062 -0,068 -0,073 -0,082 -0,089 -0,037
Moment at mid-span 0,030 0,036 0,042 0,047 0,051 0,055 0,062 0,067 0,028
Two adjacent edges discontinuous
Moment at continuous edge -0,047 -0,056 -0,063 -0,069 -0,074 -0,078 -0,087 -0,093 -0,045
Moment at mid-span 0,036 0,042 0,047 0,051 0,055 0,059 0,065 0,070 0,034
Two short edges discontinuous
Moment at continuous edge -0,046 -0,050 -0,054 -0,057 -0,060 -0,062 -0,067 -0,070 -
Moment at mid-span 0,034 0,038 0,040 0,043 0,045 0,047 0,050 0,053 0,034
Two long edges discontinuous
Moment at continuous edge - - - - - - - - -0,045
Moment at mid-span 0,034 0,046 0,056 0,065 0,072 0,078 0,091 0,10 0,034
Three edges discontinuous-1 long edge discontinuous
Moment at continuous edge -0,057 -0,065 -0,071 -0,076 -0,081 -0,084 -0,092 -0,098 -
Moment at mid-span 0,043 0,048 0,053 0,057 0,060 0,063 0,069 0,074 0,044
Three edges discontinuous- 1 short discontinuous
Moment at continuous edge - - - - - - - - -0,058
Moment at mid-span 0,042 0,054 0,063 0,071 0,078 0,084 0,096 0,105 0,044
Four edges discontinuous
Moment at mid-span 0,055 0,065 0,074 0,081 0,087 0,092 0,103 0,111 0,056




Design Moments and shear forces in two way spanning continuous slabs




Shear Force coefficients

Type of Panel and Location Short span coefficient βsx Long span coefficient βvy
For values of ly/lx
1,0 1,1 1,2 1,3 1,4 1,5 1,75 2,0
Interior Panels Four Edges continuous
Continuous edge 0,33 0,36 0,39 0,41 0,43 0,45 0,48 0,50 0,33
One short edge discontinuous
Continuous edge 0,36 0,39 0,42 0,44 0,45 0,47 0,50 0,52 036
Discontinuous Edge - - - - - - - - 0,24
One long edge discontinuous
Continuous edge 0,36 0,40 0,44 0,49 0,51 0,55 0,59 0,36 -0,037
Discontinuous Edge 0,24 0,27 0,29 0,32 0,34 0,36 0,38 - 0,028
Two adjacent edges discontinuous
Continuous edge 0,40 0,44 0,47 0,50 0,52 0,54 0,57 0,60 0,40
Discontinuous Edge 0,26 0,29 0,31 0,33 0,34 0,35 0,38 0,40 0,26
Two short edges discontinuous
Continuous edge 0,40 0,43 0,45 0,47 0,48 0,49 0,52 0,54 -
Discontinuous Edge - - - - - - - - 0,26
Two long edges discontinuous
Continuous edge - - - - - - - - 0,40
Discontinuous Edge 0,26 0,30 0,33 0,36 0,38 0,40 0,44 0,47 -
Three edges discontinuous-1 long edge discontinuous
Continuous edge 0,45 0,48 0,51 0,53 0,55 0,57 0,60 0,63 -
Discontinuous Edge 0,30 0,32 0,34 0,35 0,36 0,37 0,39 0,41 0,29
Three edges discontinuous- 1 short discontinuous
Continuous edge - - - - - - - - 0,45
Discontinuous Edge 0,29 0,33 0,36 0,38 0,40 0,42 0,45 0,48 0,30
Four edges discontinuous
Discontinuous Edge 0,33 0,36 0,39 0,41 0,43 0,45 0,48 0,50 0,33


Deflection .

The deflection can be limited by the application of the span/depth ratio as indicated in the table for beams and modified by the use of F2 as shown in the relevant graph Design of Beams...... Only conditions at the centre of slab in the width of the should be used to influence the deflection.

For two way spanning slabs the ratio should be based on the shorter span.








Design of Flat Slabs

Flat slabs should be designed to satisfy deflection requirements and to resist the shear load around the column supports.


BS 8110 allows for a simplified method for determining moments subject to certain provisions

1) design is based on a single load case of all spans being loaded with the maximum design ultimate load.
2) There are at least three rows of panels of approx equal span in the direction under consideration
4)The ratio of imposed to dead load does not exceed 1,25
5)The characteristic imposed load does not exceed 5kN/m2

This method involve simply using the table provided for design moments in simple one way spanning continuous slabs as provided above as copied below.
Moments at supports resulting from the table below are reduced by 0,15F.h c
The design moments resulting should be divided between the column strips and mid-strips as shown in the figure below in proportions as shown in table below

F = Total Design Ultimate load (1,4 G k + 1,6 Q k)        l s = is effective span of slab        G k = Dead Load        Q k = Imposed load)

  End support/ Slab connection At First Support At Middle of interior spanAt Interior supports
Simple SupportsContinuous
Outer SupportsNear Middle of end spanOuter SupportsNear Middle of end span
Moment (M) - F.l s /11,5 -F.l s /25 F.l s /13 -F.l s /11,5 FL /15,5 -F.l s /15,5


Distribution of design moments across panels in flat slabs
Design Moment apportionment between strips
as a percentage of total negative
or positive moments
Column strip % Middle Strip strip %
negative 75 25
positive 55 45



Punching shear forces in Flat Slabs

The critical shear condition for flat slabs is punching shear around the column heads.    The shear load supported by a column is the basic calculated shear force (V) uprated to account for moment transfer.    For slabs with approximately equal spans the uprated shear force, designated the effective shear force V eff ,can be simply estimated using the following rules.

For internal columns V eff = 1,15 V
For corner columns V eff = 1,15 V
For corner columns V eff = 1,15 V
For edge columns with the moment parallel to the edge V eff = 1,25 V
For edge columns with the moment normal to the edge V eff = 1,4 V

The slab shear at the column face is calculated as

d = thickness of slab and U o is the perimeter of the slab at the column head edge

ν o should be less than 0,8 f cu or 5 N/mm2 if less

Perimeters U i radiating out from the column edge should be checked with the first perimeter (i =1) at a distance 1,5.d from the column face and subsequent perimeters i = 2,3... with intervals of 0,75.d

successive perimeters are checked until the applied shear stressν i is less than the allowable shear stress ν c.    Reinforcement links are required between the perimeters at which the shear stress is greater than ν c.   



Deflection .

When the gross width of drops in both directions exceed 1/3 the respective span the deflection can be limited by the application of the span/depth ratio as indicated in the table for beams Design of Beams...... Otherwise the resulting span/effective depth should be multiplied by 0,9.

The assessment should be completed for the most critical direction.






Reinforcement Data
Cross sectional area of number of bars ( mm2 )

Bar Size (mm)Cross sectional area of number of bars (mm2)
1 2 3 4 5 6 7 8 9 10 11 12
6 28 57 85 113 141 170 198 226 254 283 311 339
8 50 101 151 201 251 302 352 402 452 503 553 603
10 79 157 236 314 393 471 550 628 707 785 864 942
12 113 226 339 452 565 679 792 905 1018 1131 1244 1357
16 201 402 603 804 1005 1206 1407 1608 1810 2011 2212 2413
20 314 628 942 1257 1571 1885 2199 2513 2827 3142 3456 3770
25 491 982 1473 1963 2454 2945 3436 3927 4418 4909 5400 5890
32 804 1608 2413 3217 4021 4825 5630 6434 7238 8042 8847 9651
40 1257 2513 3770 5027 6283 7540 8796 10053 11310 12566 13823 15080
50 1963 3927 5890 7854 9817 11781 13744 15708 17671 19635 21598 23562


Cross sectional area of number of bars ( mm2 ) per metre spacing

Bar Size ( mm )Bar Spacing
50 75 100 125 150 175 200 225 250 275 300 400
6 565 377 283 226 188 162 141 126 113 103 94 71
8 1005 670 503 402 335 287 251 223 201 183 168 126
10 1571 1047 785 628 524 449 393 349 314 286 262 196
12 2262 1508 1131 905 754 646 565 503 452 411 377 283
16 4021 2681 2011 1608 1340 1149 1005 894 804 731 670 503
20 6283 4189 3142 2513 2094 1795 1571 1396 1257 1142 1047 785
25 9817 6545 4909 3927 3272 2805 2454 2182 1963 1785 1636 1227
32 - 10723 8042 6434 5362 4596 4021 3574 3217 2925 2681 2011
40 - - 12566 10053 8378 7181 6283 5585 5027 4570 4189 3142
50 - - 19635 15708 13090 11220 9817 8727 7854 7140 6545 4909


Link reinforcement in beams, Asv/sv ( mm2/mm ) - 2 legs

Bar Size (mm) Link reinforcement in beams, Asv/sv (mm2/mm) - 2 legs
Spacing of Links (mm)
50 75 100 125 150 175 200 225 250 275 300 400
6 1.13 0.75 0.57 0.45 0.38 0.32 0.28 0.25 0.23 0.21 0.19 0.14
8 2.01 1.34 1.01 0.80 0.67 0.57 0.50 0.45 0.40 0.37 0.34 0.25
10 3.14 2.09 1.57 1.26 1.05 0.90 0.79 0.70 0.63 0.57 0.52 0.39
12 4.52 3.02 2.26 1.81 1.51 1.29 1.13 1.01 0.90 0.82 0.75 0.57
16 8.04 5.36 4.02 3.22 2.68 2.30 2.01 1.79 1.61 1.46 1.34 1.01


Link reinforcement in beams, Asv/sv ( mm2/mm ) - 3 legs

Bar Size (mm) Link reinforcement in beams, Asv/sv (mm2/mm) - 3 legs
Spacing of Links (mm)
50 75 100 125 150 175 200 225 250 275 300 400
6 1.70 1.13 0.85 0.68 0.57 0.48 0.42 0.38 0.34 0.31 0.28 0.21
8 3.02 2.01 1.51 1.21 1.01 0.86 0.75 0.67 0.60 0.55 0.50 0.38
10 4.71 3.14 2.36 1.88 1.57 1.35 1.18 1.05 0.94 0.86 0.79 0.59
12 6.79 4.52 3.39 2.71 2.26 1.94 1.70 1.51 1.36 1.23 1.13 0.85
16 12.06 8.04 6.03 4.83 4.02 3.45 3.02 2.68 2.41 2.19 2.01 1.51


Link reinforcement in beams, Asv/sv ( mm2/mm ) - 4 legs

>
Bar Size (mm) Link reinforcement in beams, Asv/sv (mm2/mm) - 4 legs
Spacing of Links (mm)
50 75 100 125 150 175 200 225 250 275 300 400
6 2.26 1.51 1.13 0.90 0.75 0.65 0.57 0.50 0.45 0.41 0.38 0.28
8 4.02 2.68 2.01 1.61 1.34 1.15 1.01 0.89 0.80 0.73 0.67 0.50
10 6.28 4.19 3.14 2.51 2.09 1.80 1.57 1.40 1.26 1.14 1.05 0.79
12 9.05 6.03 4.52 3.62 3.02 2.59 2.26 2.01 1.81 1.65 1.51 1.13
16 16.08 10.72 8.04 6.43 5.36 4.60 4.02 3.57 3.22 2.92 2.68 2.01


mesh reinforcement in beams, Asv/sv ( mm2/mm ) - 4 legs

BS4483 Fabric Mesh size nominal pitch of wires Diameter of wire Cross section area per metre width Nominal mass No. of sheets
Main Cross Main Cross Main Cross per tonne -
mm mm mm mm mm2(/sup> mm2(/sup> kg/mē -
Square mesh
A393 200 200 10 10 393 393 6.16 15
A252 200 200 8 8 252 252 3.95 22
A193 200 200 7 7 193 193 3.02 22
A142 200 200 6 6 142 142 2.22 40
A98 200 200 5 5 98 98 1.54 57
Structural mesh
B1131 100 200 12 8 1131 252 10.9 8
B785 100 200 10 8 785 252 8.14 11
B503 100 200 8 8 503 252 5.93 15
B385 100 200 7 7 385 193 4.53 20
B283 100 200 6 7 283 193 3.73 24
B196 100 200 5 7 196 193 3.05 29
Long mesh
C785 100 400 10 6 785 70.8 6.72 13
C636 100 400 9 6 636 70.8 5.55 16
C503 100 400 8 5 503 49 4.34 21
C385 100 400 7 5 385 49 3.41 26
C283 100 400 6 5 283 49 2.61 34
Wrapping mesh
D98 200 200 5 5 98 98 1.54 57
D49 100 100 2.5 2.5 49 49 0.77 113





Nominal thick cover *(mm)of reinforcement bars for fire resistance (hours)

HoursNominal thickness cover in mm
BeamsFloors RibsColumns
Simply SupportedContinuous Simply SupportedContinuous Simply SupportedContinuous Simply Supported
0,5 20 20 20 20 20 20 20
1 20 20 20 20 20 20 20
1,5 20 20 25 20 35 20 20
2 40 30 35 25 45 35 25
3 60 40 45 35 55 45 25
4 70 50 55 45 65 55 25


Minimum Section width for fire resistance.

Fire Resistance Maximum beam width Rib Width Min floor Thickness Column width Minimum Wall Thickness
Fully Exposed 50% exposed One Face Exposed p < 0,4% 0,4% < p < 1% p > 1%
h mm mm mm mm mm mm mm mm mm
0,5 200 125 75 150 125 100 150 100 75
1,0 200 125 95 200 160 120 150 120 75
1,5 20 125 110 250 200 140 175 140 100
2,0 20 125 125 300 200 160 - 160 100
3,0 240 150 150 400 300 200 - 200 150
4,0 280 175 170 450 350 240 - 240 180





Characteristic strength of concrete

Concrete strength classes
f ck MPa (N/mm2) 12 16 20 25 30 35 40 45 50 55 60 70 80 90
f cu MPa (N/mm2) 15 20 25 30 37 45 50 55 60 67 75 85 95 105
f cm MPa (N/mm2) 20 24 28 33 38 43 48 53 58 63 68 78 88 98
E cm GPa (N/mm2) 27 29 30 31 33 34 35 36 37 38 39 41 42 44



Characteristic
strength ( f cu )
after 28 days
Cube strength (N/mm2) at the age of: Flexural strength after 28 days Indirect tensile strength at 28 days. Modulus of Elasticity
(N/mm2) 1 days 28 days 2 month 3 months 6 months 1 year (N/mm2) (N/mm2) (kN/mm2)
15 - 15 ------ -
20 13.5 20 22 23 24 25 2.3 1.5 24
25 16.5 25 27.5 29 30 31 2.7 1.8 25
30 20 30 33 35 36 37 3.1 2.1 26
40 28 40 44 45.5 47.5 50 3.7 2.5 30
50 36 50 54 55.5 57.5 60 4.2 2.8 32


Characteristic strength of Reinforcement

DesignationCharacteristic strength f y
N/mm2
Modulus of Elasticity E
kN/mm2
Hot rolled Mild Steel250200
High Yield Steel (Hot or Cold Rolled)500200







Reinforcement bar bending

Details based on BS 8666 .Normally grade H bars used f y = 500 N/m2



Useful relevant Links
  1. Eurocode 2 worked examples.... A 120 page document include a large number of worked examples for reinforced concrete systems..important
  2. Eurocode 2 Design of concrete structures EN 1992-1-1... A very detailed document providing notes on the code content and examples .. important
  3. Mechanical programs....Includes Framework download - an advanced struct. analysis program
  4. Concrete beam strength -Strucsoft.... An applet used for determining strength of reinforced concrete beams
  5. C Capriani.. reinforced concrete beams... Extremely clear notes with worked examples
  6. C Capriani.. concrete flat slabs... Extremely clear notes with worked examples
  7. C Capriani..reinforced concrete columns... Extremely clear notes with worked examples
  8. Design of slabs beams and foundations using SAFE...Background theory for a software package ( including many codes)
  9. Design of centric loaded column...Detailed explanation including reference to Eurocode
  10. xcalcs... Section information and Calculations
  11. Free CD offer from reinforced Concrete Council... A comprehensive set of calculators on CD to BS 8110
  12. Reinforcement bar bending - kbrebar... Detailed dimensions for bar bending to BS8666
  13. National Structural Concrete Specification... Extremely detailed and authoritative Guidance notes : Not to Eurocodes


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Last Updated 28/10/2011