Design Charts for Concrete Structures

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BS 811O :Part 3 : 1985
UDC 624.012.3/.4+691.3
@ British Standards Institution. No patt of this publicationmay be photocopied or otherwise reproduced without the prior permission inwriting of ES1
BritishStandard
Structural useof concrete
Part 3. Designchartsfor singly reinforcedbeams,
doubly reinforced beamsand rectangular columns
Utilisation du béton en construction
Partie 3. Règles de calcul des poutres à renforcement simple et double et des colonnes rectangulaires
Beton im Hochbau
Teil 3. Bernessungstafelnfür einfach und doppelt bewehrte Träger und Rechteckstützen
British Standards Institution #----
COPYRIGHT British Standards Institute on ERC Specs and Standards
Licensed by Information Handling Services

BSI BS*8LLO PART*3 85 L h 2 4 h b ï 0022354 4
BS 811Q:Part 3 :1985
Contents
Page
Foreword Inside front cover Rectangularcolumns
Committeesresponsible Back cover
fY fCu dfh Chart number
Design charts - 460 25 0.75 21
1 General i¡
1.1 Scope i¡
1.2 Symbols il
1.3 Use of charts ii
2 Design charts ii
0.80 22
0.85 23
0.90 24
0.95 25
460 30 0.75 26
0.80 27
0.85 28
fY Chart number 0.90 29
0.95 30
460 - 35 0.75 31
250 1
460 2
0.80 32
0.85 33
460 25 0.1o 3 0.95 35
0.15 4 460 40 0.75 36
0.80 37
0.85 38
0.20 5
460 30 0.10 6
0.15 7 0.90 39
0.20 8 0.95 40
460 35 Owlo 9 460 45 0.75 41
0.15 10 0.80 42
0.20 11 0.85 43
460 40 0.10 12 0.90 44
0,15 13 0.95 45
0.20 14 460 50 0.75 46
460 45 0.1o 15 0.80 47
0.1 5 16 0.85 48
0.20 17 0.90 49
460 50 0.1o 18 0.95 50
0.15 19 Page
0.20 20 Appendices
Singly reinforced beams
Doubly reinforced beams
fY fC” d’Id Chart number 0.90 34
A. Notes on the derivation of the design charts iii
B. Designexamples v
B.1 Singly reinforced beams V
6.2 Doubly reinforced beams vi
B.3 Rectangular columns vi
Figures
1 Conditions of stress and strains assumed at the
ultimate limit state iii
2 Short term design stress-straincurve for normal-
weight concrete iv
3 Short term design stress-straincurve for
reinforcement iv
____I

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1 BS 8110 : Part 3 : 1985
Designcharts
I 1 General
1.1 Scope
This Part of BS 8110 covers design charts for singly
reinforcedbeams, doubly reinforcedbeams and rectangular
columns. These design charts cannot be used to obtain the
completedetailed design of any member but they may be
used as an aid when analysing the cross section of a member
at the ultimate limit state. The charts have been based on
the assumptions laid down in BS 8110 : Part 1, use being
made of the parabolic-rectangularstress block throughout.
Full details of the derivation of the charts are given in
appendix A.
NOTE. The titles of the publications referred to in this standard are
listed on the inside back cover.
1.2 Symbols
For the purposes of this Part of BS 8110 the definitions of
the symbols given in BS 8110 : Parts 1 and 2 apply together
with the following which are used in appendix A.
f% Stress in reinforcement in compression a t the ultimate
limit state
fst
E,
Stress in reinforcement in tension at the ultimate
limit state
Strain a t the point on the parabolic-rectangular
stress-straindiagram where the parabolic section
joins the linear section (e, = 2.4 x ~{fcul*lm)).
1.3 Use of charts
Design examples illustrating the use of the charts are given
in appendix B.
The values of K indicated on the column design charts are
the additional moment reduction coefficients given by
equation 33 of BS 8110 :Part 1 : 1985.
2 Designcharts
Design charts Nos. 1 to 50 are given on the following pages.

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Appendices
Appendix A. Noteson the derivation of the
design charts
All the charts have been derived using the assumptions
given in 3.4.4.1 of'BS 8110 : Part 1 :1985 for the analysis
of cross sections. These assumptions are shown diagram-
matically in figures 1 to 3. Figure 2 shows the stress-strain
curvesassumedfor the concreteand figure 3 the stress-strain
relationshipfor the reinforcement at the ultimate limit
state, In derivingthe charts from these stress-straincurves,
rrnhas been taken as 1.5 and 1.15 for concrete and
reinforcement, respectively. For rectangular cross sections
where the neutralaxis remainswithin thesection, expressions
can easily be derived to give the total compressiveforce
developed in the concrete and the position of the centroid
of this force at failure. These are as follows.
Concrete compressiveforce at failure is given by:
0.0035
Distance from compressive face of section to centroid of
concrete compressive force is given by:
(2- eo/0.0035)' + 2
x=kzx
[ 4 (3- ~0/0.0035)1These expressions were used in the production of all the
design charts for rectangular cross sections. For rectangular
column cross sections where the eccentricity of the load is
sufficiently small to cause the neutral axis to lie outside the
section, the result obtained from the expressions is reduced
to allow for the effect of the part of the parabola lying
outside the section,
The figures from which the charts were drawn were'
producedby solution of the equations for equilibrium of
moments and forces for successive values of neutral axis
depth. For a doubly reinforced rectangular cross section
with the neutral axis within the section, these equations are
as follows.
Equilibrium of axial forces, N, is given by:
Equilibrium of moments, M, is given by:
For the beam charts, areas of tension steel and moments
were calculatedfor specifiedareas of compression steel and
neutral axis depth. For the column charts, moments and
axial loads were calculated for specifiedsteel areas and
neutral axis depths.
Three assumptions of a minor nature have been introduced
in the production of the charts in addition to those given in
BS8110: Part 1.
N = k l b x + A , ' f , , + A , f ~
M=kl bx(h/2- ~ Z X )+A,' fsc(h/2 - d'l +A,fs,(h/2- d )
(a) No solutions have been producedfor situations
where x <d'. For the beam chartsthe first point
calculated is for x = d'. This point was joined to the
- origin by a straight line. This is conservative,
(b) Where compression reinforcement is present the full
area of concrete in compression has still been assumed
active, thusno reduction has beenmade inthe calculations
for the concretedisplaced by the reinforcement.
(cl There should, rigorously, be a slight deviation from a
smooth curve of the interaction diagrams for columns in
the region of low moments. This arises where the neutral
axis liesjust outside the section and part of the parabolic
section of the stress-straincurve is curta,iled. The curves
havebeen'smoothed' inthis region. The error introduced
is negligible.
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Stress in Stress in
concrete reinforcement
Figure 1. Conditions of stress and strains assumed a t the ultimate limit state
.------

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0,67 fCu
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0.67 takes account of the relation between the cube strength and the bending strength in a flexural member. It is
simply a coefficient and nor a partial safety factor.
NOTE. f,, is in N/mm2,
Figure 2. Short term design stress-straincurve for normal-weight concrete
Figure 3. Short term design stress-straincurve for reinforcement

*- I BSI BS*83i10 PART*3 85 LbZ4bbî 0022908 I I
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Appendix B. Designexamples
NOTE. The use of each type of chart is illustrated by an example.
B.1 Singlyreinforcedbeams
Design the cross section of a slab for the ultimate moment
given. Designdetails:
fCu= 25 N/mmz;
fv = 250 N/mmz;
h = 160 mm;
cover = 30 mm to main reinforcement;
M per metre width = 27.6 kN.m.
BS 8110 : Part 3 : 1985
Issue 2,May 1989
Assume 16 mm bars
Therefore
d - 1 6 0 - [30 t T]16
= 122 mm
M 2 7 . 6 ~lo6
bd2 1000 x 1222
-I
= 1.E6 N/mm2'per metre width
From Chart No. 1
Therefore
A, =
0.94 x 1000 x 122
1O0
= 1145 mm2 per metrewidth
Therefore a suitable solution is to use 16 mm bars at
175 mm centres (¡.e. 1150 mm2 per metre width).
7-1 1

BS 8110 : Part 3 : 1985
B,2 Doublyreinforcedbeams
Designthe centre cross section of a recta.ngular beam to
comply with the following requirementsat the ultimate
limit state.
Designdetails:
feu = 40 Nlmm’ ;
f, = 460 N/mm2;
M = 127 kN*m;
cover = 30 mm to main reinforcement.
The critical cross section under consideration is given
below and the bending moment a t the ultimate limit state
has been obtained by redistribution involving a reduction
equal to 30 % of the numerically largest moment given by
the elastic maximum momentsdiagramfor the beam,
h=4OOrL
O
t30
Assume 10 mm bars for compression reinforcement and
25 mm bars for tension reinforcement.
- - 35 0.10 therefore use Chart No. 18
d’
d 357.5
- -
Mlbd2 = 4,97
A reduction of.30 % due to redistribution requiresthat the
neutral axis depth should be limited such that xld Q 0.3.
Thus a solution must be sought on or to the left of the line
markedxld = 0.3 on Chart No. 18. A suitable solution is:
100AJbd = 1,42;
100A,’lbd = 0.3 (by interpolation).
Therefore A, = 1015 mm2
and A,’ = 214 mm2
Therefore reinforcementto be provided
A,: 2 No. 20 -t 2 No, 16 (area 1030 mm’)
A’$:2 No. 12 (area226 mm2)
The use of 12 mm compression reinforcement means that
d’/dis now 0.101 thus the use of Chart No. 18 is still
justified,
B.3 Rectangularcolumns
Design the cross section of a rectangularcolumn to comply
with the following requirementsat the ultimate limit state.
Design details:
feu= 50 N/mmz;
f, = 460 N/mm2;
cover = 40 mm to main reinforcement;
M = 91.2 kNmmabout major axis
O kN*mabout minor axis
N = 2460 kN
The cross section of the column is as follows:
h=45i
t+40
Assume 32 mm bars
- = - 394 =0.88 therefore use Chart No, 49 where
h 450
dlh = 0.90
Mlbh’ r2.25
Nlbh = 27.4
From Chart No. 49
100AJbh = 2.6
ThereforeA, 2340 mm2
Therefore a suitable solution is to use 4 No. 32 mm cold
worked bars (Le. 3220 mmz1,
r
ViCOPYRIGHT British Standards Institute on ERC Specs and Standards

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Publicationsreferredto
BS 8110 Structural use of concrete
Part 1 Cade of practice for design and construction
Part 2 Code of practice for special circumstances

8 BS 8110:Part 3: 1985
This British Standard, having been prepared under the direction of
the Civil Engineering and Building Structures Standards Commit.tge,
was published under the authority of the Board of BSI and com& ., Contract requirements
into effect on 31 December 1985.
O British Standards Institution, 1985
ISBN O 580 14781 9
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Committees responsible for this British Standard
The preparation of this British Standard was entrusted by the Civil
Engineeringand Building Structures Standards Committee (CSB/-)
to Technical Committee CSB139, uponwhich the following bodies
were represented:
Association of Consulting Engineers
British Aggregate Construction Materials Industries
British Precast Concrete Federation Ltd.
British Railways Board
British Ready Mixed Concrete Association
British Reinforcement Manufacturers' Association
British Steel Industry
Building Employers' Confederation
Cement Admixtures Association
Cement and Concrete Association
Cement Makers' Federation
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Draft (ref 84/14533) announced BSI News October 1985
Concrete Society
Departmentof the Environment (Building Research Establishment)
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Departmentof the Environment (Property Services Agency)
District Surveyors' Association
Federationof Civil Engineering Contractors
Greater London Council
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Institution of Structural Engineers
Precast Flooring Federation
Royal Institute of British Architects
Sand and Gravel Association Limited
Industries)
Institution of Civil Engineers a
Amd, No. Date of issue Text affected
A
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8606-1-4k-B ,------- CSB/39

BSI. l i
AMD 5918
May 1989
-------
BSm811O P A R T r 3 85 a 1b24bb7 O022412 3
Amendment No. 1
published and effective from 31 May 1989
to BS 8110 : Part 3 : 1985
Structural use of concrete
Part 3. Design charts for singly reinforcedbeams,
doubly reinforced beams and rectangular columns
Instructionsfor the insertionof revised pages
AMD 5918
Replace pages ¡i¡ and iv and v and vi by new pages i¡¡ and iv and v and vi (pages iv and vi
unchanged).
8905-2-4k-B- --
La-. -,’
CSEU39

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