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This standard has now been replaced by Eurocode BS EN1992.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/m^{2} ) .
Reinforcement links are often mild steel ( f _{y} >= 250 N/m^{2} ) 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 reuse
Relevant Standards
The design notes provided on this page relate to BS 81101 :1997 which has been superseded by the standards referenced below.
Code Reference Number  Title 
BS EN 199211:2004  General rules and rules for buildings..Replaces BS 81101, BS 81102 and BS 81103 
BS EN 199212:2004  Eurocode 2:General rules. Structural fire design 
BS EN 19922:2005  Eurocode 2:Concrete bridges. Design and detailing rules..Replaces BS 54004, BS 54007 and BS 54008 
BS EN 19923:2006  Eurocode 2:Liquid retaining and containing structures...Replaces BS 8007 
BS EN 19923:2006  Eurocode 2:Liquid retaining and containing structures...Replaces BS 8007 
BS EN 2061:2000  Concrete. Specification, performance, production and conformity 
BS EN 2069:2010  Concrete. Additional rules for selfcompacting 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 _{cu}bd )
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 /(2230)  L/(2836)  L/(710) 
Two way spanning slabs  611  L /(2435)  L/(3440)   
Flat slabs  48  L /27  L/36  L/(710) 
Rectangular beams  910  L /12  L/15  L/6 
Flanged beams  515  L /10  L/12  L/6 
Columns  2,5 8  H / (1020)  H / (1020)  H/10 
Walls  24  H / (3035)  H / 45  H/ (1518) 
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 
Adverse  Beneficial 
Adverse  Beneficial 
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  1,2  1,2  1,2  1,2 
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.f_{cu} . b . x / (γ _{m} =1,5) = 0,4 . f_{cu}. 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.d^{2}
M = K.[ f _{cu}.b.d^{2} ]
Factors for lever arm (z) and neutral axis depth (x)
x  0,13.d  0,15.d  0,19.d 
0,25d 
0,32.d  0,39.d  0,45.d  0,5.d 
z  0,942.d  0,933.d  0,91.d  0,887.d  0,857.d  0,825.d 
0,798.d  0,775.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
M_{u} is simply calculated as 0,4.f_{cu}.b.h_{f}.(d  h_{f}/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/mm^{2} 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/mm^{2}  N/mm^{2} 
N/mm^{2}  N/mm^{2} 
N/mm^{2}  N/mm^{2} 
N/mm^{2}  N/mm^{2} 
= < 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/mm^{2}
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/mm^{2}) + 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.
Type  Rectangular 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 _{2}F _{3}F _{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.b^{2} /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 Top  End Condition at Bottom 
Rigidly Fixed  Fixed  Pinned with some angular restraint 
Rigidly Fixed  075  0,80  0,90 
Fixed  0,80  0,85  0,95 
Pinned with some angular restraint  0,9  0,95  1,00 
Unbraced Columns Table of effective length coefficients (β)
End Condition at Top  End Condition at Bottom 
Rigidly Fixed  Fixed  Pinned with some angular restraint 
Rigidly Fixed  1,2  1,3  1,6 
Fixed  1,3  1,5  1,8 
Pinned with some angular restraint  1,6  1,8   
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 _{a}  1,0  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 inplane 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 inplane 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 oneway 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 span  At Interior supports 
Simple Supports  Continuous 
Outer Supports  Near Middle of end span  Outer Supports  Near 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 midspan  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 midspan  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 midspan  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 midspan  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 midspan  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 midspan  0,034  0,046  0,056  0,065  0,072  0,078  0,091  0,10  0,034 
Three edges discontinuous1 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 midspan  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 midspan  0,042  0,054  0,063  0,071  0,078  0,084  0,096  0,105  0,044 
Four edges discontinuous
 Moment at midspan  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 discontinuous1 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 F_{2} 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
midstrips 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 span  At Interior supports 
Simple Supports  Continuous 
Outer Supports  Near Middle of end span  Outer Supports  Near 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/mm^{2} 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 ( mm^{2} )
Bar Size (mm)  Cross sectional area of number of bars (mm^{2}) 
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 ( mm^{2} ) 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 ( mm^{2}/mm )  2 legs
Bar Size (mm) 
Link reinforcement in beams, Asv/sv (mm^{2}/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 ( mm^{2}/mm )  3 legs
Bar Size (mm)  Link reinforcement in beams, Asv/sv (mm^{2}/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 ( mm^{2}/mm )  4 legs
>
Bar Size (mm)  Link reinforcement in beams, Asv/sv (mm^{2}/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 ( mm^{2}/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 
mm^{2(/sup> }  mm^{2(/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)
Hours  Nominal thickness cover in mm 
Beams  Floors 
Ribs  Columns 
Simply Supported  Continuous 
Simply Supported  Continuous 
Simply Supported  Continuous 
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/mm^{2})  12  16  20  25  30  35  40  45  50  55  60  70  80  90 
f _{cu}  MPa (N/mm^{2})  15  20  25  30  37  45  50  55  60  67  75  85  95  105 
f _{cm}  MPa (N/mm^{2})  20  24  28  33  38  43  48  53  58  63  68  78  88  98 
E _{cm}  GPa (N/mm^{2})  27  29  30  31  33  34  35  36  37  38  39  41  42  44 
Characteristic strength ( f _{cu )} after 28 days 
Cube strength (N/mm^{2}) at the age of: 
Flexural strength after 28 days  Indirect tensile strength at 28 days. 
Modulus of Elasticity 
(N/mm^{2})  1 days  28 days  2 month 
3 months  6 months  1 year 
(N/mm^{2})  (N/mm^{2})  (kN/mm^{2}) 
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
Designation  Characteristic strength f _{y} N/mm^{2}^{} 
Modulus of Elasticity E kN/mm^{2}^{} 
Hot rolled Mild Steel  250  200 
High Yield Steel (Hot or Cold Rolled)  500  200 
Reinforcement bar bending
Details based on BS 8666 .Normally grade H bars used f _{y} = 500 N/m^{2}
