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Design Results of RC Members Subjected toBending Shear and Torsion Using ACI 31808

and BS 811097 Building Codes

Ali S Alnuaimi

1

Iqbal I Patel

2

and Mohammed C Al-Mohsin

3

Abstract In this research a comparative study was conducted on the amount of required reinforcement using American Concrete Institute

(ACI) and British Standards Institution (BSI) building codes The comparison included design cases of rectangular beam sections subjected to

combined loads of bending shear and torsion and punching shear at slabndashcolumn connections In addition the study included comparison of

the differencesin the amount of reinforcement requiredowing to different codesrsquo factors of safety for design loads It wasfound thatthe BScode

requires less reinforcement than the ACI code does for the same value of design load However when the load safety factors are included in

calculating the design loads the values of the resulting design loads become different for each code and in this case the ACI was found to

require less reinforcement than the BS Thepunching shear strength of 1047298at slabndashcolumnconnections calculated using theACI code was found to

be more than that calculated using the BS code for the same geometry material and loading conditions The minimum area of 1047298exural

reinforcementrequired by ACI was found to be greater than by BS while the opposite was found for the minimum area of shear reinforcement

In case both codesunify the load safetyfactors while keeping the otherdesign equations as they are now the BS code will have preference over

the ACI code owing to lower reinforcement requirements which leads to cheaper construction while maintaining safety The study showedthat both codes are good choices for design in Oman Because SI units are becoming more and more enforced internationally material that is

available in Oman is conversant more toward SI units to unify the knowledge of design among municipality and site engineers it is

recommended to use the BS code as a 1047297rst choice until a national code is established DOI 101061(ASCE)SC1943-55760000158 copy 2013

American Society of Civil Engineers

CE Database subject headings Reinforced concrete Design Bending Comparative studies

Author keywords ACI code BS code Reinforced concrete design Code comparison RC design equations

Introduction

The structural design codes for RC ACI 31808 [American Con-

crete Institute (ACI) 2008] and BS 811097 [British StandardsInstitution (BSI) 1997] are based on the limit state design How-

ever these designcodes differ on thedesignequations especiallyfor

shear and torsion They also differ on the factors of safety for

material and loads Because there is no national structural design

code in Oman a question about the most appropriate code in terms

of safety economy and suitability to the environment in Oman is

always asked Knowledge of main features of and differences be-

tween the ACI 318 and BS 8110 codes is deemed a necessity

Although both ACI 318 and BS 8110 codes agree on the live load

factor ofsafety tobe 16the factorof safetyfor the deadload inACI

is 12 whereas in BS it is14 17 greaterSubsequently this resultsin a larger value of ultimate (design) load which in turn affects theamount of reinforcement and concrete The material strength re-

duction factor f inthe ACI 318 is090 for 1047298exure and075 forshear and torsion whereas in BS 8110 the material partial safety factor is067for 1047298exure and 08for shear and torsion Further unlike the ACI318 code where the reinforcement design strength is As f y the BS8110 design strength is 095 As f y The limit of maximum strain inconcrete in ACI 318 is 0003 whereas in BS 8110 the limit is00035 Appendix I shows that the ACI 318 considers the materialand geometry in de1047297ning the minimum area of longitudinal re-inforcement Asmin whereas BS 8110 is based on geometry onlyThere is no differentiation between the sizes of bw and b in con-sidering the Asmin in ACI318 whereas BS 8110 hasdifferent valuesfor Asmin when bw=b 04 and bw=b$ 04 ACI 318 considers theeffective depth d in calculating the geometry whereas BS 8110considers the total depth h The ACI 318 equation

V c frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

bd 029

ffiffiffiffi f c9

q bd

(Section 11221) assumes that shear strength of concrete is pro-portional to the square root of concrete cylindercompressive strengthwhereas the BS 8110 equation

V c frac14

079g m

100 As

bwd

1=3400

d

1=4 f cu

25

1=3

bwd

(Section 3454) assumes that the shear strength is proportional tothe cubic rootof cube concrete compressive strength The maximum

1Associate Professor Dept of Civil and Architectural Engineering

College of Engineering Sultan Qaboos Univ PO Box 33 PC 123Muscat Oman (corresponding author) E-mail alnuaimisqueduom

alnuaimiasmgmailcom 2Structural Engineer Muscat Municipality PO Box 79 PC 100

Muscat Oman3Assistant Professor Civil Engineering Dept College of Engineering

Univ of Buarimi PO Box 890 PC 512 Buraimi OmanNote This manuscript was submitted on December 6 2011 approved

on November 28 2012 published online on December 1 2012 Discus-

sion period open until April 1 2014 separate discussions must be sub-mitted for individual papers This paper is part of the Practice Periodical

on Structural Design and Constructi on Vol 18 No 4 November 1

2013 copyASCE ISSN 1084-068020134-213ndash224$2500

PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013 213

Pract Period Struct Des Constr 201318213-224



spacing between stirrups fortorsional reinforcement in ACI 318 is thesmaller of ph=8 or 300 mm whereas BS 8110 speci1047297es the maximum spacing as the least of 08 x 1 y1eth095 f yvTHORN Asvt =T u x 1 y1=2 or 200 mm

As per Jung and Kim (2008) the response of structural concreteto the actions of bending moment is quite well understood andconsequently design procedures andprovisionsfor bendingmomentarereasonably effective and consistent between different codes Jung andKim also stated ldquoMany of shear design code provisions are principallyempirical vary greatly from code to code and do not provide uniform factors of safety against failurerdquo

Sharma and Inniss (2006) found that the slab punching shear capacity vc in ACI 318 is calculated from the concrete compressivestrength as 033

ffiffiffiffi f c9p

without any consideration to the effect of longitudinal reinforcement whereas in BS 8110

vc frac14 079g m

ffiffiffiffiffiffiffiffi400

d

4

r ffiffiffiffiffiffiffiffiffiffiffiffi100 As

bwd

3

r ffiffiffiffiffi f cu

25

3

r

which takes account of the longitudinal reinforcement in addition toconcrete strength

Subramanian (2005) pointed out that in BS 8110 the critical sectionfor checking the punching shear is 15d from edge of load pointwhereas in ACI 318 the critical section for checking punching shear is

05d from edge of load pointBari (2000) reviewed the shear strength of slabndashcolumn con-nections and concluded that the BS code predicts smaller shear strength than ACI for values of r less than 12 and larger strengthfor values of r greater than 12 However this limit may vary for differentcolumnshapes concretestrengths and effectivedepths Barialso concluded that with a ratio of column side length of 25 to 5 theBS code predictsgreater strength than theACI code whereas for ratioranges between 1 and 25 ACI predicts more shear strength than BS

Ngo (2001) stated ldquoDepending on method used the criticalsection forchecking punching shear in slabs is usually situated between05 to 2 times the effective depth from edge of load or the reactionrdquoHeconcluded that the punching shear strength values that are speci1047297ed indifferent codes vary with concrete compressive strength f c9 and are

usually expressed in terms of eth f c9THORN

n

In ACI 318 the punching shear strength is expressed as proportional to ffiffiffiffi

f c9p

whereas in BS 8110punching shear strength is assumed to be proportional to

ffiffiffiffiffi f cu

3p

Chiu et al (2007) carried out a parametric study based on ACI

31805(ACI 2005) and found that torsional strength decreases as theaspect ratio (longer dimensionshorter dimension) of specimenincreases

Bernardo and Lopes (2009) analyzed several codes of practice re-garding torsion andconcluded that the ACIcode hasclauses that imposemaximum and minimum amounts of torque reinforcement (for bothtransverse and longitudinal bars) The equations for minimum amount of reinforcement are however mainly empirical and sometimes lead toquestionable solutions namely negative minimum longitudinal rein-forcement or disproportional longitudinal reinforcement and stirrups

According to Ameli and Ronagh (2007) the area used in shear 1047298ow calculation is determined differently in different codes whichresults in different torsional shear strengths Taking the centers of longitudinal bars or center-to-center of stirrups for the calculation of this area will result in different sizes of area

Alnuaimi and Bhatt (2006) reported that ldquomost researchersbelieve that the shear stress owing to direct shear is resisted by thewhole width of cross section while the torsional shear stress isresisted by the outer skin of concrete section They differ howeveron the thickness of outer skinrdquo

Based on the literature it is clear that some research works havebeen carried out on the comparison between ACI and BS codes

However the comparisons were limited to few parameters and donot touch the effects of these differences on the amount of rein-forcement No study was found in the literature on the preference of design codes for structural design in Oman or the rest of the Gulf states In this research an intensive comparison work was carriedout to 1047297nd out the effects of design results on the amount of rein-forcement using ACI and BS codes Effects of different parameterswere studied including M u=V u ratio load safety factors requiredlength for transverse reinforcement minimum 1047298exural and shear re-inforcement etc A recommendation on a preferred code is presented

Design Equations

Bending

The design procedures in ACI 31808 and BS 811097 are based onthe simpli1047297ed rectangular stress block as given in ACI 31808ndash102and BS 811097ndash344 respectively The area of required 1047298exuralreinforcement in ACI 31808ndash1034 is given as

As frac14 M u

f f y

d 2

a

2

(1)

where

a frac14 d 2

ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffid 2 2

2 M u

085 f c9fb

r

In BS 811097ndash3444 the area of required reinforcement isgiven by

As frac14 M u095 f y z

(2)

where

z

frac14d 05

thorn ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffi0252 K

09r 095d

and K 5 M u= f cubd 2

Shear

Theconcreteshearstrength vc ina beam canbe calculated from ACI31808ndash11221 as the resulting smaller value of

vc frac14 min of

2664

016 ffiffiffiffi

f c9p

thorn 17r V ud

M u

029

ffiffiffiffi f c9

p

3775 (3)

where f c9 70 N=mm 2 and V ud = M u 1According to Table 38 of BS 811097ndash3454 the concrete

shear strength vc is calculated as

vc frac14 079

g m

100 As

bd

1=3400

d

1=4

f cu

25

1=3

(4)

with the following limitation g m 5 125 015 100 As=bd 3eth400=d THORN$ 1 and f cu 40 N=mm 2

The required shear reinforcement Asv=S for different values of shear force is calculated based on ACI 31808ndash114 as

214 PRACTICE PERIODICAL ON STRUCTURAL DESIGN AND CONSTRUCTION copy ASCE NOVEMBER 2013




Asv

S frac14

266666666664

0 for V u fV c

2

0062 ffiffiffiffi

f c9p

b

f y

035bS

f yfor

fV c

2 V u fV c

V u 2fV c

fdf yfor V u $fV c

377777777775

(5)

The minimum transverse reinforcement Asv=S v for beam is calcu-

lated based on Table 37 of BS 811097ndash3453 and BS 811097ndash3452 as

Asv

S vfrac14

26666664

04b

095 f yv

for v ethvc thorn 04THORN

v2 vcb

095 f yvfor ethvc thorn 04THORN v vmax

resize section for v vmax

37777775

(6)

The punching shear strength in 1047298at slab is de1047297ned by ACI 31808ndash111121 as the smallest of

V c frac14 min of

017

1 thorn 2 b ffiffiffiffi

f c9p

bd 083

asd

bo

thorn 2

ffiffiffiffi f c9

q bd

033

ffiffiffiffi f c9p

bd

8gtgtgtgtgtgtgtgtgtltgtgtgtgtgtgtgtgtgt

9gtgtgtgtgtgtgtgtgt=gtgtgtgtgtgtgtgtgt

(7)

Themaximumshearstress vmax isde1047297nedin BS 811097ndash3452as

vmax frac14 08 ffiffiffiffiffi

f cu

p 5 N=mm 2 (8)

Torsion

The design provision for torsional cracking strength of RC solidbeam in ACI 31808ndash1151 is speci1047297ed as

T cr frac14 ffiffiffiffi

f c9p

3

A2

cp

Pcp

(9)

If T u fT cr =4 no torsional reinforcement is neededThe torsional strength of a member is given by ACI 31808ndash

11535 as

T n frac14 2 At Ao f yv

s cot u (10)

where Ao 5 085 Aoh and u5 45 for RC memberIn BS 8110ndash285 (BSI 1985)ndash2441 the torsional shear stress

vt for rectangular beam is computed as

vt frac14 2T u

h2min

hmax2

hmin

3

(11)

The minimum torsion stress vt min below which torsion in thesection can be ignored based on BS 8110ndash285ndash246 is given for different grades of concrete as

vt min frac14 0067 ffiffiffiffiffi

f cu

p 04 N=mm 2 (12)

If v t vt min then torsional resistance is to be provided by closed

stirrups and longitudinal barsBased on ACI 31808ndash11537 the required longitudinal re-

inforcement is calculated as

Al frac14 At

sPh

f yv

f yl

cot 2u (13)

ACI 31808ndash11553 speci1047297es the minimum longitudinal torsionalreinforcement as

Al min frac14 042 ffiffiffiffi

f c9p

Acp

f yl

2

At

s

Ph

f yv

f yl

(14)

where At =s 0175bw= f yvIn addition ACI 31808ndash11562 restricts the maximum spacing

between bars of the longitudinal reinforcement required for torsion

to 300 mm The longitudinal bars shall be inside the closed stirrups

and at least one bar is required in each corner Longitudinal bar

diameter shall not be less than 10 mmThe required longitudinal reinforcement due to torsion is given

in BS 8110ndash

285ndash

248 as

Al frac14 Asvt f yveth x 1 thorn y1THORNsv f y

(15)

BS 8110ndash285ndash249 states that the longitudinal torsion reinforce-

ment shall be distributedevenly around theperimeter of stirrups The

clear distance between these bars should not exceed 300 mm Lon-

gitudinal bar diameter shall not be less than 12 mmThe required stirrups (by assuming u5 45) is given by ACI

31808ndash11535 as

At

sfrac14 T u

17f Aoh f yv

(16)

For pure torsion the minimum amount of closed stirrup is speci1047297edby ACI 31808ndash11552 as the greater result of the following

At min frac14 larger of

266664

2 At min

s frac14 0062

ffiffiffiffi f c9

q bw

f yv

2 At min

s$ 035

bw

f yv

377775 (17)

ACI 31808ndash11561 speci1047297es the maximum spacing of stirrups as

the smaller of ph=8 or 300 mmThe shear reinforcement made of closed stirrups is calculated

based on BS 8110ndash285ndash247 as

Asvt

S v frac14 T

u08 x 1 y1

095 f yv

(18)

S v should not exceed the least of x 1 y1=2 or 200 mmTo prevent crushing of surface concrete of solid section ACI

31808ndash11531 restricts the cross-sectional dimension as ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiV u

bwd

2

thorn

T uPh

17 A2oh

2v uut f

V c

bwd thorn 066

ffiffiffiffi f c9

q (19)

where V c 5 017 ffiffiffiffiffiffiffiffiffi

f c9bd p





For section dimensions check in BS 8110ndash285ndash245 thecomputed torsional shear stress vt should not exceed the followinglimit for sections with larger center-to-center dimensions of closedlink less than 550 mm

vt vtu y1

550 (20)

In no case should the sum of the shear stresses resulting from shear force and torsion (vtu 5 vs 1 vt ) exceed the maximum shear stress

speci1047297

ed by Eq (8) If a combination of applied shear stress vs andtorsional stress vt exceeds this limit the section should be resized

Design Results and Discussions

Here design results of rectangular beams with different load com-binations and spandepth ratios are presented The ACI 31808 andBS 811097 codes were used in the design and results were judgedbased on the amount of longitudinal and transverse reinforcement requirements The characteristic cube compressive strength of con-crete was 30N=mm 2 and the cylinder compressive strength was24 N=mm 2 with concrete density of 24 kN=m 3 and the charac-teristic yield strength of the longitudinal and transverse reinforce-ment was 460 N=mm 2

Design for Combined Bending Moment and Shear Force Using ACI 31808 and BS 811097

Tables 1ndash3 and Table 4 show the design results of three groups of simply supported beams and one group of two-span continuousbeams respectively In beam numbering the 1047297rst letter denotes thetype of member considered eg B means beam the second letter denotes the variable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributedloadThe 1047297rst numeral represents the value of R and the second numeralrepresents the value of W The beam cross-sectional dimension was

selected to be 3503 700 mm with effective depth of 625 mm Dif-ferent ultimate design uniformly distributed load values were used asshownin the caption of each table It wasassumedthat 50 of bottom longitudinal bars are curtailed at 01 L from support and transversestirrups were used for shear reinforcement ie no bent-up barsconsidered to resist shear The spandepth ratio was varied among eachgroup resulting in different M u=V u ratios The design was carried out using the ACI and BS codes for the same ultimate design load values

It is clear that the two codes gave almost the same results for bendingreinforcement with minimal effect of M u=V u ratio changesgiving a maximum difference of 26 in the case of single-spansimply supported beams and 084 in the case of the continuousbeams However theresults differ largelyon theshear reinforcement with the change of M u=V u ratio using ACI and BS codes as can be

Table 1 Simply Supported Beams with Ultimate Design UDL of 75 kN=m

Beam

number

Span

(m)

L =d

Ratio

M u a t

midspan

(kNm)

V u a t d

from

support

(kN)

M u=V u

(kNm =kN)

Asethmm 2THORN Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement (m)

Difference

in length

of shear

reinforcement

()ACI BS ACI BS ACI BS

BR112W75 7 112 459 216 213 1975 1962 07 035 037 57 175 083 1108

BR12W75 75 12 527 234 225 2312 2326 06 043 042 24 190 100 900

BR128W75 8 128 600 253 237 2692 2754 23 050 047 64 225 117 923

Table 2 Simply Supported Beam with Ultimate Design UDL of 100 kN=m

Beam

number

Span

(m)

L =d

Ratio

M u at

midspan

(kNm)

V u at d

from

support

(kN)

M u=V u

(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region for

shear

reinforcement

(m)

Difference

in length

of shear

reinforcement


BR88W100 55 88 378 213 178 1591 1571 13 035 040 143 140 083 687

BR96W100 6 96 450 238 189 1931 1916 08 046 046 00 165 101 634

BR112W100 7 112 613 288 213 2762 2835 26 067 059 136 215 136 581


Beam

number

Span

(m)

L =d

Ratio

M u at

midspan

(kNm)

V u at d

from

support

(kN)

M u=V u

(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement

(m)

Difference

in length

of shear

reinforcement


BR8W125 5 8 391 234 167 1652 1624 17 045 047 44 14 095 474

BR96W125 6 96 563 297 189 2497 2532 14 072 064 125 190 130 462

BR104W125 65 104 660 328 201 3078 3089 04 085 072 181 22 15 467





seen for a typical beam in Fig 1 The differences become pronouncedwith the increase of M u=V u ratio leading to continually divergingcurves In most cases it wasfound that theBS requires less transversereinforcement than the ACI For the given geometry and loads thedifferences reached up to 181 in thecaseof simplysupported beamsand 314 in the case of continuous beams Further the length from the face of support to the point beyond which only minimum shear reinforcement is required was also investigated andis presented in thepenultimate columns of Tables 1ndash4 It was found that the length that needs shear reinforcement required by BS is less than that required

by ACI The differences become more pronounced with increaseof M u=V u ratio For the given geometry and loads the differencesreached up to 1108 in the case of simply supported beams and1533 in the case of continuous beams This indicates that with theincrease of loads the BS code becomes more economical on thetransverse reinforcement

Table 5 shows comparisonbetween theACI and BS resultson theshear strength capacity of concrete using

vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q

as extracted from Eq (3) in the case of ACI code and Eq (4) in thecase of BS code for different values of r ranging from 02 to 20

In the ACI the values of V ud = M u were varied from 0 to 10 and inthe case ofBS the value of 400=d wastaken as constant equal to 1 It is obvious that the above equations lead to highly different resultsInitially when reinforcement ratio r is 02 vc of BS is less by

about60 than that of ACI for all values of V ud = M uAsthe V ud = M uandor r increases the concrete shear capacity increases Fig 2shows that the nonlinear curve resulting from the BS equation crossesthe linearly diverging curves made by the ACI equation for variablevalues of V ud = M u at different points The1047297rst crossing point occurredat r 5 08 with V ud = M u 5 0 The succeeding crosses occurredsequentially with the increased V ud = M u curves It isalsoclear that theBS rate of increasein shear capacity is more rapid than that of the ACIAppendix II shows formulation of both ACI and BS code equationsfor required shear reinforcement to produce two similar equations with

differences in the empirical values It can be seen that even in the casewhen vc in ACI is equal to vc in BS as shown in the crosses of Fig 2the values of spacing between stirrups S as shown by the resultingequations in Appendix II will be different and the ACI code requiresapproximately 26 more shear reinforcement than the BS code Thisdifference is attributed to differences in material safety factors

Design for Torsion Using ACI 31808 and BS 811097

Here 5003 700-mm beams with effective depth of 625 mm weresubjected to pure twisting moment Table 6 shows the design resultsof 1047297xed beams subjected to ultimate design torsion using ACI andBS codes In beam numbering the 1047297rst letter denotes the type of member eg B means beam the second letter denotes the variable

eg L means span and the numeral gives the value of L It is clear thatthe requiredlongitudinalreinforcement by ACI is 192 larger than that required by BS for most of the beams (ie BL6 BL8 andBL10) Because BL4 needs minimum steel in the ACI approach this

Table 4 Two Span Continuous Beam with Ultimate Design UDL of 60 kN=m

Beam

number

Span

(m)

L =d

Ratio

M u a t

midspan

(kNm)

V u a t d

from

support

(kN)

M u=V u(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement (m)

Difference

in length

of shear

reinforcement


BR12W60 75 12 338 221 153 1409 1375 084 036 035 29 190 075 1533

BR136W60 85 136 434 256 170 1855 1835 067 052 043 209 250 112 1232

BR152W60 95 152 542 290 187 2389 2410 056 067 051 314 300 148 1027

Fig 1 Shear reinforcement versus M u=V u using ACI and BS codes (continuous beams)





beam was not considered in the comparison The transverse re-inforcement required by ACI is approximately 19 larger than that required by BS This shows that BS is more economical than ACI inthe case of design for torsion in RC rectangular solid beams

Appendix I shows a comparison between the ACI and BS torsionequations that lead to required transverse and longitudinal reinforce-ment It is clear that the area of the shear 1047298ow Aoh is taken as 085 x 1 y1

in ACI whereas in BS it is taken as 08 x 1 y1 Further owing to dif-ferences in material safety factors ACI required about 19 moretransverse torsional reinforcement than BS Regarding longitudinal

reinforcementthederivedEqs(2)and(4)inAppendix I look identical inboth codes but since longitudinal reinforcement is dependent on theamount of transverse reinforcement the same difference of 19 that was found above for transverse reinforcement is carried to longitudinalreinforcement

DesignforCombinedBendingMomentShearForceand Twisting Moment Using ACI 31808 and BS 811097

Tables 7 and 8 show the design results of longitudinal reinforcement fortwo groupsof 1047297xed end beams withdifferent uniformly distributedload values and torsional moment of 125 kNm =m as shown in thecaption of each table The beam size considered was 400 3 700mm

with effective depth of 625 mm and design results were calculatednearthe supportIn beam numbering the1047297rstletter denotes thetypeof member considered eg B meansbeamthe second letter denotes thevariable eg R means spandepth ratio the third letter denotes thetype of loading eg W means uniformly distributed load The 1047297rst numeral represents the value of R and the second numeral representsthevalue of W It is clear that therequired topreinforcementfor ACIislarger than that for BS with a maximum difference of 84 for thegiven loads and beam geometry The bottom and face reinforcement required by ACIis largerby about 193than that required by BSNo

major changes were found in the longitudinal reinforcementdue to theincrease of L =d or M u=T u ratios However the results differ largely onthe transverse reinforcementwith the change of V u=T u ratio using ACIand BScodes ascanbe seenin Fig 3ItcanbeseenthattheACIcurveis linear whereas the BS curve is nonlinear The differences becomepronounced with increase of V u=T u ratio leading to continually di-verging curves In most cases it was found that BS requires lesstransverse reinforcement than ACI For the given geometry and loadsthe difference reached up to 193

Impactof Load SafetyFactors on DesignLoad Using ACI 31808 and BS 811097

In this section simply supported RC beams of 200-3 700-mm

cross section 625-mm effective depth and 6-m effective span withuniformly distributedlive anddead loads weredesignedusingthe ACIandBS codesThe live load waskeptconstant at 5 kN=m for all beamswhile the dead load values were varied from 20 to 40 kN=m The liveload was kept constant because the factor of safety for the live load isthe same inboth ACI and BScodes ie 16 It was assumed that50of bottom bars are curtailedat 01 L from thecenter of supportTable9shows theeffects of theACI andBS code factors of safety on requiredreinforcement In the beam numbering the1047297rst letterdenotes the typeof member eg B means a beam the second letter denotes thevariable eg R is the ratio of dead load to live load (DLLL) and thenumeral gives the value of R It is clear that because of the different values of dead load factors of safety 12 in ACI and 14 in BS thedifferences in design bending moments and shear forces between

the results from ACI and BS are linearly increasing with the increaseof the dead load For the given service loads the factored (ultimate)

Table 5 Concrete Shear Stress Capacity vc

V ud = M u Concrete shear

stress vc ( N=mm 2)

(BS 8110) with

400=d 5 1r ()

0 025 05 075 100

Concrete shear stress vc (N=mm 2) (ACI 318)

020 0784 0792 0801 0809 0818 0493

040 0784 0801 0818 0835 0852 0620

060 0784 0809 0835 0860 0886 0709

080 0784 0818 0852 0886 0920 0779

100 0784 0826 0869 0911 0954 0839

120 0784 0835 0886 0937 0988 0891

140 0784 0843 0903 0962 1022 0938

160 0784 0852 0920 0988 1056 0980

180 0784 0860 0937 1013 1090 1019200 0784 0869 0954 1039 1124 1055

Fig 2 Concrete shear stress vc versus r using ACI and BS codes





design load usingBS waslarger than that forACI having a maximum

difference of 143 As a result to these load differences therequiredlongitudinal and transverse reinforcements are differing with maxi-mum of 165 for bending and 600 for shear reinforcementsrespectively The results for the1047298exural reinforcement indicates slight

diversion due to the effect of increasing dead load while the requiredshear reinforcement shows convergence on the required transversereinforcement with the increase of the DLLL ratio Beams BR4 andBR5 required minimum stirrups in ACIand hence are notconsidered in

the discussion It is interesting to notice that as seen in Tables 1ndash4 for

the ultimate design loading the difference in 1047298exural reinforcement using ACIandBS is negligible Forservice loadinghowever shown inTable 9 the required 1047298exural reinforcement for BS was larger than for ACI with differences varying from 99 to 165 This difference isattributed to thedifferentload safetyfactors that areused in ACIandBSfor dead and live load combinations Similarly as seen in Tables 1ndash4for the ultimate design loading the shear reinforcement required by BSis less compared with ACI whereas for service loading (Table 9) theresultis reversed This reversal of resultis also attributed to thedifferent load safety factors used in ACI and BS codes for the dead load

Punching Shear Strength (at SlabndashColumn Connection) Using ACI 31808 and BS 811097

Here a parametric study of punching shear capacity at slabndashcolumnconnection using ACI and BS codes was carried out with different column aspect ratios percentagesof 1047298exural reinforcement and slabthicknesses The characteristic cube and cylindrical compressivestrengths were taken as 35 and 28 N=mm 2 respectively and thecharacteristic yield strength of reinforcementwas taken as 460N=mm 2

Table 6 Fixed Beams with Ultimate Design Torsion

Beam

number

Span

(m)

T u

(kNm)

Al

(mm 2)Difference

in Al ()

At =s

(mm 2=mm)Difference

in At =s ()ACI BS ACI BS

BL4 4 50 min 583 mdash 068 057 193

BL6 6 75 1043 875 192 102 086 186

BL8 8 100 1391 1167 192 136 114 193

BL10 10 125 1738 1458 192 17 143 189

Table 7 Fixed End Beams with Ultimate Design UDL of 100 kN=m and Torsion of 125kNm =m

Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d

(kNm) M u=V u V u=T u

Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface

bars ()ACI BS ACI BS ACI BS

BR8W100 5 8 208 188 66 317 286 1200 1107 84 365 306 365 306 193

BR96W100 6 96 300 238 67 447 353 1598 1498 67 371 311 371 311 193

BR112W100 7 112 408 288 68 598 421 2084 1986 49 376 315 376 315 194

Table 8 Fixed End Beams with Ultimate Design UDL of 125kN=m and Torsion of 125kNm =m

Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W125 5 8 260 234 66 397 357 1420 1323 73 365 306 365 306 193

BR96W125 6 96 375 297 67 558 442 1929 1830 54 371 311 371 311 193BR112W125 7 112 510 359 68 747 526 2563 2483 32 376 315 376 315 194

Fig 3 Transverse reinforcement versus V u=T u (for UDL5100and125kN=m)





From Eqs (4) and (7) it can be seen that unlike BS 8110 ACI 318does not consider dowel action of 1047298exural reinforcement in thecalculation of shear capacity Fig 4 shows punching shear strengthof a 250-mm-thick slab with effective depth of 220 mm at interior column having r 5 10 with column sizes of 3003 3003003 600 3003 900 and 3003 1200 mm resulting in different aspectratios usingACI andBS codesThe concrete cube compressivestrength f cu was 35 Nmm 2 with concrete cylinder compressivestrength as 08 f cu and steel yield strength of 460 N=mm 2 It can beseen that punching shearstrength forACI is larger than for BS for all

aspect ratios This means that for the same ultimate design punchingshear force ACI requires less slab thickness than BS The largest difference is368 when column aspect ratio is 2 It canalsobe seenthat in BS code punching shear strength increases linearly ascolumn aspect ratio increases whereas in ACI code the curve isnonlinear having a larger rate of increase of punching shear strengthbetween column aspect ratio of 1 and 2 than between 2 and 4 Fig 5shows punching shear strength of 250-mm-thick slab at interior columnof size 3003 300 mm with different percentages of 1047298exural re-inforcement ranging between 015 and 3 using ACI and BS codesThe material strengths and effective depths of slab were the same as inthe previous slab It can be seen that in ACI code the punching shear strength is constant at 773 kN without any effect of the percentage of 1047298exural reinforcement whereas in BS code punching shear strength

increases with increase of reinforcement TheBS curve is nonlinear and

it crosses the ACI horizontal line at r 5 17 This shows that with thegiven data untilr 5 17 ACI leads to largerpunching shear strengththan BS with the largest difference of 1314 when r 5 015

Fig 6 shows punching shear strengthof slabat interiorcolumnof size3003 300 mm with area of 1047298exural reinforcement As 5 2 050 mm 2

with varying depth The material strengths were the same as in theprevious slab The effective depth of each slab is 35 mm less than theoverall thickness It can be seen that ACIestimates more punchingshear strength than BS The differences with the given data ranged between148 and 233 Both ACI and BS curves vary linearly with increase of

depth however the rate ofincreaseinthe ACIresults ismorethan inBSleading to diverging curves This shows that the difference in V c usingboth codes increases as depth increases

Comparison for Minimum Area of Flexural Reinforcement Using ACI 31808 and BS 811097

The equations of minimum required 1047298exural reinforcement basedon the ACI and BS codes are shown in Appendix I Fig 7 was de-veloped based on those equations for different values of f c9 which istakenas08 f cu Thebeamcross-sectional dimension is 3503 700 mm with effective depth of 625 mm The yield strength of reinforcement was taken as 460 N=mm 2 It can be seen that the minimum area of 1047298exural reinforcement required by ACI is much larger than that re-

quired by BS The BS curve is constant with all grades of concrete

Table 9 Parametric Study to Compare Steel Required for Bending and Shear with DL 1 LL Combination Using ACI and BS

Beam

number

Ratio

DL

LL

Service

UDL

(kN=m)

Ultimate

design UDL

(wu) (kN=m)Difference

in wu

()

Ultimate

design

moment

at midspan

M u (kNm)

Ultimate

design

shear

at d V u

(kN)

Flexural

reinforcement

As (mm 2)Difference

in As

()

Shear

reinforcement

Asv=s

(mm 2=mm)Difference

in Asv=s

()Dead Live

ACI

(12D1 16L)

BS

(14D1 16L) ACI BS ACI BS ACI BS ACI BS

BR4 4 20 5 32 36 125 144 162 76 86 588 646 99 min 018 mdash

BR5 5 25 5 38 43 132 171 194 90 102 706 789 118 min 018 mdash

BR6 65 33 5 47 535 138 212 241 112 127 891 1014 138 015 024 600

BR7 7 35 5 50 57 140 225 257 119 135 951 1094 150 018 026 444BR8 8 40 5 56 64 143 252 288 133 152 1079 1257 165 024 031 292

Fig 4 Punching shear strength versus column aspect ratio using ACI and BS codes





while the ACI curve changes from being constant for concretegrades of 30ndash40 N=mm 2 to nonlinear for concrete grades larger than40 N=mm 2 The difference is constant at the value of 106 for theconcrete strengths of 30ndash40 N=mm 2 then it increases with the in-crease in the concrete strength The maximum difference for thegiven beam geometry and concrete strengths was 1335

Comparison for Minimum Area of Shear Reinforcement Using ACI 31808 and BS 811097

Fig 8 was developed based on Eqs (5) and (6) for different values of f c9 which is taken as 08 f cu The beam cross-sectional dimension is3503 700 mm with effective depth of 625 mm The yield strengthof reinforcement was taken as 460 N=mm 2 It can be seen that theminimum area of shear reinforcement required by BS is larger thanrequired by ACI The BS curve is constant for all grades of concretewhereas theACI curveis constant forconcretegrades of 30ndash40 N=mm 2

then reduces linearly for grades larger than 40 N=mm 2 The dif-ference is constant at the value of 185 for the concrete strengths

between 30 and 40 N=mm 2 then decreases with the increase in theconcretestrength Theminimum difference forthegiven beamgeometryand concrete strengths was 67 at concrete grade of 50 N=mm 2

Concluding Remarks and Recommendations

In this research design results of rectangular RC beams subjected to

bending shear and torsion and punching shear at the slabndashcolumnconnection using ACI 31808 and BS 811097 were comparedConclusions can be drawn as follows

Design for Combined Bending Moment Twisting Moment and Shear Force

bull Therequired 1047298exural reinforcementsfor thesame designbendingmoment using ACI and BS codes are almostthe same regardlessof M u=V u ratio

bull In most cases the required shear reinforcement by ACI code islargerthan that by BS code forthesame design load This difference

Fig 5 Punching shear strength versus percentage of r using ACI and BS codes

Fig 6 Punching shear strength versus slab thickness using ACI and BS codes





becomes morepronounced with the increase of M u=V u ratio It wasfound that empirical equations of shear capacity in BS and ACIcodes have led to highlydifferent results It wasalso established that owing to differences in material safety factors ACI equations leadto more required shear reinforcement than BS

bull The beam length that needs shear reinforcement (beyond whichonly minimum shear reinforcement is needed) required by BS

code is shorter than that for ACI code The difference becomesmore pronounced with the increase of M u=V u ratio

bull The longitudinal and transverse torsional reinforcement requiredby ACI was found to be larger than that required by BS and thedifference in value betweenthe reinforcementof the two codesisalmost constant It was found that these differences are due todifferences in material safety factors

Impact of Safety Factors on Ultimate Design Load

bull The difference in the factor of safety for the dead load betweenthe ACI and BS resulted in larger design bending moments

and shear forces by the BS equations than the ACI ones Thediverging difference increases linearly with the increase of thedead load

bull For the resulting different design loads it wasfound that both thelongitudinal and transverse reinforcements required by the ACIare lower than the BS in all beams

Punching Shear Strength (at SlabndashColumn Connection)

bull For different column aspect ratios the punching shear strength of 1047298at slabndashcolumn connections calculated using the ACI code wasfound to be larger than that calculated using the BS code for thesame geometry materials and loading conditions

bull In the ACI code punching shear strength remains constant for different percentages of 1047298exural reinforcement whereas in theBS code punching shear strength increases with increase of 1047298exural reinforcement

bull For different slab thicknesses ACI code estimates more punch-ing shear strength than BS code

Fig 7 Minimum area of 1047298exural reinforcement with different f cu

Fig 8 Minimum area of shear reinforcement with different f cu





Minimum Area of Flexural Reinforcement

Minimum area of 1047298exural reinforcement required by ACI code is

larger than BS code for RC rectangular beams

Minimum Area of Shear Reinforcement

Minimum area of shear reinforcement required by ACI code is

smaller than BS code for RC rectangular beams

Recommendation

From the results of this research it was found that the BS code

requires less reinforcement than the ACI for the same design load

Contrarily when the load safety factors are used in calculating the

design loads from the service loads the resulting factored loads

using BS code are larger than the ACI code loads which results in

larger area of reinforcementby BSthanthe ACI Henceit isnot easy

to give preference of one code over the other for use in Oman and

other countries that do not have national codes and allow both ACI

and BS codes to be used However because SI units are becoming

more and more enforced internationally materials and references

available in Oman andother Gulf states markets are conversant moretoward SI units To unify the knowledge of the design municipality

and site engineers it is recommended to use the BS code as a 1047297rst

choice until national codes are established This will reduce the dis-

crepancies between the design and construction phases in terms of

standards speci1047297cations and materials In the case that both ACI and

BS codes unify the load safety factors while keeping the other design

equations as they are now the BS code will have preference over the

ACI owing to fewer reinforcement requirements which leads to

cheaper construction

Appendix I Equations of Minimum FlexuralReinforcement in Beams

Appendix II Comparison of Formulas forShear Reinforcement

ACI 31808

V c 5fV n and f5 075 (for shear)

V n frac14 V c thorn V s

V u frac14 fethV c thorn V sTHORN frac14 fV c thorn fV s

V s frac14 V u 2wV cf

Asv

s frac14 V s

df y

ACI 31808e11472

[ Asv

s frac14 V u 2fV c

fdf y

Multiply the RHS with b=b

[ Asv

s frac14V u 2fV c

fdf ytimes

bw

bw

[ Asv

sfrac14 ethvu 2fvcTHORNbw

f f y

where

vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q

[ Asv

s frac14 ethvu 2 075vcTHORNbw

075 f y

[ s frac14 075 f yv Asv

ethvu 2 075vcTHORNbw

BS 811097

Asv

s frac14

vu 2

vc

g m conc in shear

bw

f y

g m steel

where

vc frac14

079

100 As

bwd

1 3

400d

1 4

f cu

25

1 3

g m conc in shear frac14 125

g m steel frac14 105

[ Asv

sfrac14

vu 2

vc

125

bw

f yv

105

Situation ACI 31808 (Section 105)

BS 811097

(Table 325)

Flanged beams web in tension

bw

b 04 Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00018bwh

bw

b $ 04 Larger of

0

025

ffiffiffiffi f c9p

f ybwd

1

Aor

14

f ybwd

00013bwh

Flanged beams 1047298ange in tension

T-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00026bwh

L-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00020bwh

Rectangular

beams

Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00013bwh





[ Asv

sfrac14 ethvu 2 08vcTHORNbw

095 f yv


ethvu 2 08vcTHORNbw

Notation

The following symbols are used in this paper

Acp 5 area enclosed by outside perimeter of concrete

cross section

Al 5 area of longitudinal reinforcement to resist torsion

Al min 5 minimum area of longitudinal reinforcement to

resist torsion

Ao 5 gross area enclosed by shear 1047298ow path

Aoh 5 area enclosed by centerline of the outermost closed

transverse torsional reinforcement

As 5 area of longitudinal tension reinforcement to resist

bending moment

Asmin 5 minimum area of 1047298exural reinforcement to resist

bending moment

Asv 5 area of shear reinforcement to resist shear

Asvt 5 area of two legs of stirrups required for torsion At 5 area of one leg of a closed stirrup resisting torsion

At min 5 minimum area of shear reinforcement to resist

torsion

a 5 depth of equivalent rectangular stress block

b 5 width of section 1047298ange

bw 5 width of section web

d 5 effective depth of tension reinforcement (distance

from extreme compression 1047297ber to centroid of

longitudinal tension reinforcement)

f 9c 5 characteristic cylinder compressive strength of

concrete (150 mm 3 300 mm)

f cu 5 characteristic strength of concrete

(1503

1503

150 mm concrete cube strength) f y 5 characteristic yield strength of longitudinal

reinforcement for 1047298exure

f yl 5 characteristic yield strength of longitudinal

reinforcement for torsion

f yv 5 characteristic yield strength of transverse

reinforcement

h 5 overall depth of section

hmax 5 larger dimension of rectangular cross section

hmin 5 smaller dimension of rectangular cross section

L 5 effective beam span

M u 5 ultimate 1047298exural moment

ph 5 perimeter of centerline of outermost closed


S 5 center-to-center spacing of transverse reinforcement

S v 5 spacing of stirrups

T cr 5 torsional cracking moment

T n 5 nominal torsional moment strength

T u 5 ultimate design twisting moment

V c 5 nominal shear strength provided by concrete

V u 5 ultimate shear force

v 5 design shear stress

vc 5 concrete shear strength

vt 5 torsional shear stress

vt min 5 minimum torsional shear stress above which

reinforcement is required

vtu 5 maximum combinedshear stress (shear plustorsion)

x 1 5 smaller center to center dimension of rectangular

stirrups y1 5 larger center to center dimension of rectangular

stirrups

Z 5 lever arm

g m 5 partial safety factor for strength of material

u 5 angle between axis of strut compression diagonal

and tension chord of the member

r 5 reinforcement ratio ( As=bd ) and

f 5 strength reduction factor

References

Alnuaimi A S and Bhatt P (2006) ldquo

Design of solid reinforced concretebeamsrdquo Structures Buildings 159(4) 197ndash216Ameli M and Ronagh H R (2007) ldquoTreatment of torsion of reinforced

concrete beams in current structural standardsrdquo Asian J Civil Eng

(Building Housing) 8(5) 507ndash519American Concrete Institute (ACI) (2005) ldquoBuilding code requirements

for structural concrete and commentaryrdquo 318-05 Farmington Hills

MIAmerican Concrete Institute (ACI) (2008) ldquoBuilding code requirements


MIBari MS(2000)ldquoPunching shear strength of slab-column connectionsmdashA

comparative study of different codesrdquo J Inst Engineers (India) 80(4)163ndash168

Bernardo L F A and Lopes S M R (2009) ldquoTorsion in high strengthconcrete hollow beamsmdashStrength and ductility analysisrdquo ACI Struc-

tural J 106(1) 39ndash48British Standards Institution(BSI) (1985)ldquoStructuraluse of concrete Code

of practice for special circumstancesrdquo BS 811085 Part-2 London

British Standards Institution(BSI) (1997)ldquoStructuraluse of concrete Codeof practice for design and constructionrdquo BS 811097 London

Chiu H J Fang I K Young W T and Shiau J K (2007) ldquoBehavior

of reinforced concrete beams with minimum torsional reinforcementrdquo Eng Structures 29(9) 2193ndash2205

Jung S and Kim KS (2008) ldquoKnowledge-based prediction on shear strength of concrete beams without shear reinforcementrdquo Eng Struc-

tures 30(6) 1515ndash1525Ngo D T (2001) ldquoPunching shear resistance of high-strength concrete

slabsrdquo Electron J Structural Eng 1(1) 2ndash14

Sharma A K and Innis B C (2006) ldquoPunching shear strength of slab-column connectionmdashA comparative study of different codesrdquo ASCE

Conf Proc Structural Engineering and Public Safety 2006 StructuresCongress ASCE Reston VA 1ndash11

Subramanian N (2005) ldquoEvaluation and enhancing the punching shear resistance of 1047298at slabs using high strength concreterdquo Indian Concr J79(4) 31ndash37




spacing between stirrups fortorsional reinforcement in ACI 318 is thesmaller of ph=8 or 300 mm whereas BS 8110 speci1047297es the maximum spacing as the least of 08 x 1 y1eth095 f yvTHORN Asvt =T u x 1 y1=2 or 200 mm

As per Jung and Kim (2008) the response of structural concreteto the actions of bending moment is quite well understood andconsequently design procedures andprovisionsfor bendingmomentarereasonably effective and consistent between different codes Jung andKim also stated ldquoMany of shear design code provisions are principallyempirical vary greatly from code to code and do not provide uniform factors of safety against failurerdquo

Sharma and Inniss (2006) found that the slab punching shear capacity vc in ACI 318 is calculated from the concrete compressivestrength as 033

ffiffiffiffi f c9p

without any consideration to the effect of longitudinal reinforcement whereas in BS 8110

vc frac14 079g m

ffiffiffiffiffiffiffiffi400

d

4

r ffiffiffiffiffiffiffiffiffiffiffiffi100 As

bwd

3

r ffiffiffiffiffi f cu

25

3

r

which takes account of the longitudinal reinforcement in addition toconcrete strength

Subramanian (2005) pointed out that in BS 8110 the critical sectionfor checking the punching shear is 15d from edge of load pointwhereas in ACI 318 the critical section for checking punching shear is

05d from edge of load pointBari (2000) reviewed the shear strength of slabndashcolumn con-nections and concluded that the BS code predicts smaller shear strength than ACI for values of r less than 12 and larger strengthfor values of r greater than 12 However this limit may vary for differentcolumnshapes concretestrengths and effectivedepths Barialso concluded that with a ratio of column side length of 25 to 5 theBS code predictsgreater strength than theACI code whereas for ratioranges between 1 and 25 ACI predicts more shear strength than BS

Ngo (2001) stated ldquoDepending on method used the criticalsection forchecking punching shear in slabs is usually situated between05 to 2 times the effective depth from edge of load or the reactionrdquoHeconcluded that the punching shear strength values that are speci1047297ed indifferent codes vary with concrete compressive strength f c9 and are

usually expressed in terms of eth f c9THORN

n

In ACI 318 the punching shear strength is expressed as proportional to ffiffiffiffi

f c9p

whereas in BS 8110punching shear strength is assumed to be proportional to

ffiffiffiffiffi f cu

3p

Chiu et al (2007) carried out a parametric study based on ACI

31805(ACI 2005) and found that torsional strength decreases as theaspect ratio (longer dimensionshorter dimension) of specimenincreases

Bernardo and Lopes (2009) analyzed several codes of practice re-garding torsion andconcluded that the ACIcode hasclauses that imposemaximum and minimum amounts of torque reinforcement (for bothtransverse and longitudinal bars) The equations for minimum amount of reinforcement are however mainly empirical and sometimes lead toquestionable solutions namely negative minimum longitudinal rein-forcement or disproportional longitudinal reinforcement and stirrups

According to Ameli and Ronagh (2007) the area used in shear 1047298ow calculation is determined differently in different codes whichresults in different torsional shear strengths Taking the centers of longitudinal bars or center-to-center of stirrups for the calculation of this area will result in different sizes of area

Alnuaimi and Bhatt (2006) reported that ldquomost researchersbelieve that the shear stress owing to direct shear is resisted by thewhole width of cross section while the torsional shear stress isresisted by the outer skin of concrete section They differ howeveron the thickness of outer skinrdquo

Based on the literature it is clear that some research works havebeen carried out on the comparison between ACI and BS codes

However the comparisons were limited to few parameters and donot touch the effects of these differences on the amount of rein-forcement No study was found in the literature on the preference of design codes for structural design in Oman or the rest of the Gulf states In this research an intensive comparison work was carriedout to 1047297nd out the effects of design results on the amount of rein-forcement using ACI and BS codes Effects of different parameterswere studied including M u=V u ratio load safety factors requiredlength for transverse reinforcement minimum 1047298exural and shear re-inforcement etc A recommendation on a preferred code is presented

Design Equations

Bending

The design procedures in ACI 31808 and BS 811097 are based onthe simpli1047297ed rectangular stress block as given in ACI 31808ndash102and BS 811097ndash344 respectively The area of required 1047298exuralreinforcement in ACI 31808ndash1034 is given as

As frac14 M u

f f y

d 2

a

2

(1)

where

a frac14 d 2

ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffid 2 2

2 M u

085 f c9fb

r

In BS 811097ndash3444 the area of required reinforcement isgiven by

As frac14 M u095 f y z

(2)

where

z

frac14d 05

thorn ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffi0252 K

09r 095d

and K 5 M u= f cubd 2

Shear

Theconcreteshearstrength vc ina beam canbe calculated from ACI31808ndash11221 as the resulting smaller value of

vc frac14 min of

2664

016 ffiffiffiffi

f c9p

thorn 17r V ud

M u

029

ffiffiffiffi f c9

p

3775 (3)

where f c9 70 N=mm 2 and V ud = M u 1According to Table 38 of BS 811097ndash3454 the concrete

shear strength vc is calculated as

vc frac14 079

g m

100 As

bd

1=3400

d

1=4

f cu

25

1=3

(4)

with the following limitation g m 5 125 015 100 As=bd 3eth400=d THORN$ 1 and f cu 40 N=mm 2

The required shear reinforcement Asv=S for different values of shear force is calculated based on ACI 31808ndash114 as





Asv

S frac14

266666666664

0 for V u fV c

2

0062 ffiffiffiffi

f c9p

b

f y

035bS

f yfor

fV c

2 V u fV c

V u 2fV c

fdf yfor V u $fV c

377777777775

(5)



Asv

S vfrac14

26666664

04b

095 f yv


v2 vcb



37777775

(6)


V c frac14 min of

017


f c9p

bd 083

asd

bo

thorn 2

ffiffiffiffi f c9

q bd

033

ffiffiffiffi f c9p

bd



(7)



f cu

p 5 N=mm 2 (8)

Torsion



f c9p

3

A2

cp

Pcp

(9)


11535 as


s cot u (10)



vt frac14 2T u

h2min

hmax2

hmin

3

(11)



f cu

p 04 N=mm 2 (12)




Al frac14 At

sPh

f yv

f yl

cot 2u (13)



f c9p

Acp

f yl

2

At

s

Ph

f yv

f yl

(14)






in BS 8110ndash

285ndash

248 as


(15)





31808ndash11535 as

At

sfrac14 T u

17f Aoh f yv

(16)



266664

2 At min

s frac14 0062

ffiffiffiffi f c9

q bw

f yv

2 At min

s$ 035

bw

f yv

377775 (17)




Asvt

S v frac14 T

u08 x 1 y1

095 f yv

(18)



bwd

2

thorn

T uPh

17 A2oh

2v uut f

V c

bwd thorn 066

ffiffiffiffi f c9

q (19)


f c9bd p






vt vtu y1

550 (20)


speci1047297









Beam

number

Span

(m)

L =d

Ratio

M u a t

midspan

(kNm)

V u a t d

from

support

(kN)

M u=V u

(kNm =kN)


in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement (m)

Difference

in length

of shear

reinforcement


BR112W75 7 112 459 216 213 1975 1962 07 035 037 57 175 083 1108

BR12W75 75 12 527 234 225 2312 2326 06 043 042 24 190 100 900

BR128W75 8 128 600 253 237 2692 2754 23 050 047 64 225 117 923


Beam

number

Span

(m)

L =d

Ratio

M u at

midspan

(kNm)

V u at d

from

support

(kN)

M u=V u

(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region for

shear

reinforcement

(m)

Difference

in length

of shear

reinforcement


BR88W100 55 88 378 213 178 1591 1571 13 035 040 143 140 083 687

BR96W100 6 96 450 238 189 1931 1916 08 046 046 00 165 101 634

BR112W100 7 112 613 288 213 2762 2835 26 067 059 136 215 136 581


Beam

number

Span

(m)

L =d

Ratio

M u at

midspan

(kNm)

V u at d

from

support

(kN)

M u=V u

(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement

(m)

Difference

in length

of shear

reinforcement


BR8W125 5 8 391 234 167 1652 1624 17 045 047 44 14 095 474

BR96W125 6 96 563 297 189 2497 2532 14 072 064 125 190 130 462

BR104W125 65 104 660 328 201 3078 3089 04 085 072 181 22 15 467








vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q









Beam

number

Span

(m)

L =d

Ratio

M u a t

midspan

(kNm)

V u a t d

from

support

(kN)

M u=V u(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement (m)

Difference

in length

of shear

reinforcement


BR12W60 75 12 338 221 153 1409 1375 084 036 035 29 190 075 1533

BR136W60 85 136 434 256 170 1855 1835 067 052 043 209 250 112 1232

BR152W60 95 152 542 290 187 2389 2410 056 067 051 314 300 148 1027




















stress vc ( N=mm 2)

(BS 8110) with

400=d 5 1r ()

0 025 05 075 100


020 0784 0792 0801 0809 0818 0493

040 0784 0801 0818 0835 0852 0620

060 0784 0809 0835 0860 0886 0709

080 0784 0818 0852 0886 0920 0779

100 0784 0826 0869 0911 0954 0839

120 0784 0835 0886 0937 0988 0891

140 0784 0843 0903 0962 1022 0938

160 0784 0852 0920 0988 1056 0980

180 0784 0860 0937 1013 1090 1019200 0784 0869 0954 1039 1124 1055














Beam

number

Span

(m)

T u

(kNm)

Al

(mm 2)Difference

in Al ()

At =s

(mm 2=mm)Difference


BL4 4 50 min 583 mdash 068 057 193

BL6 6 75 1043 875 192 102 086 186

BL8 8 100 1391 1167 192 136 114 193

BL10 10 125 1738 1458 192 17 143 189


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W100 5 8 208 188 66 317 286 1200 1107 84 365 306 365 306 193

BR96W100 6 96 300 238 67 447 353 1598 1498 67 371 311 371 311 193

BR112W100 7 112 408 288 68 598 421 2084 1986 49 376 315 376 315 194


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W125 5 8 260 234 66 397 357 1420 1323 73 365 306 365 306 193

BR96W125 6 96 375 297 67 558 442 1929 1830 54 371 311 371 311 193BR112W125 7 112 510 359 68 747 526 2563 2483 32 376 315 376 315 194

















Beam

number

Ratio

DL

LL

Service

UDL

(kN=m)

Ultimate

design UDL


in wu

()

Ultimate

design

moment

at midspan

M u (kNm)

Ultimate

design

shear

at d V u

(kN)

Flexural

reinforcement

As (mm 2)Difference

in As

()

Shear

reinforcement

Asv=s

(mm 2=mm)Difference

in Asv=s

()Dead Live

ACI

(12D1 16L)

BS


BR4 4 20 5 32 36 125 144 162 76 86 588 646 99 min 018 mdash

BR5 5 25 5 38 43 132 171 194 90 102 706 789 118 min 018 mdash

BR6 65 33 5 47 535 138 212 241 112 127 891 1014 138 015 024 600

BR7 7 35 5 50 57 140 225 257 119 135 951 1094 150 018 026 444BR8 8 40 5 56 64 143 252 288 133 152 1079 1257 165 024 031 292















































Recommendation






















ACI 31808





Asv

s frac14 V s

df y

ACI 31808e11472

[ Asv

s frac14 V u 2fV c

fdf y


[ Asv

s frac14V u 2fV c

fdf ytimes

bw

bw

[ Asv


f f y

where

vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q

[ Asv


075 f y



BS 811097

Asv

s frac14

vu 2

vc

g m conc in shear

bw

f y

g m steel

where

vc frac14

079

100 As

bwd

1 3

400d

1 4

f cu

25

1 3



[ Asv

sfrac14

vu 2

vc

125

bw

f yv

105


BS 811097

(Table 325)


bw

b 04 Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00018bwh

bw

b $ 04 Larger of

0

025

ffiffiffiffi f c9p

f ybwd

1

Aor

14

f ybwd

00013bwh


T-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00026bwh

L-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00020bwh

Rectangular

beams

Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00013bwh





[ Asv


095 f yv


ethvu 2 08vcTHORNbw

Notation



cross section



resist torsion





bending moment


bending moment




torsion










(1503

1503






reinforcement























stirrups

Z 5 lever arm






References

























Asv

S frac14

266666666664

0 for V u fV c

2

0062 ffiffiffiffi

f c9p

b

f y

035bS

f yfor

fV c

2 V u fV c

V u 2fV c

fdf yfor V u $fV c

377777777775

(5)



Asv

S vfrac14

26666664

04b

095 f yv


v2 vcb



37777775

(6)


V c frac14 min of

017


f c9p

bd 083

asd

bo

thorn 2

ffiffiffiffi f c9

q bd

033

ffiffiffiffi f c9p

bd



(7)



f cu

p 5 N=mm 2 (8)

Torsion



f c9p

3

A2

cp

Pcp

(9)


11535 as


s cot u (10)



vt frac14 2T u

h2min

hmax2

hmin

3

(11)



f cu

p 04 N=mm 2 (12)




Al frac14 At

sPh

f yv

f yl

cot 2u (13)



f c9p

Acp

f yl

2

At

s

Ph

f yv

f yl

(14)






in BS 8110ndash

285ndash

248 as


(15)





31808ndash11535 as

At

sfrac14 T u

17f Aoh f yv

(16)



266664

2 At min

s frac14 0062

ffiffiffiffi f c9

q bw

f yv

2 At min

s$ 035

bw

f yv

377775 (17)




Asvt

S v frac14 T

u08 x 1 y1

095 f yv

(18)



bwd

2

thorn

T uPh

17 A2oh

2v uut f

V c

bwd thorn 066

ffiffiffiffi f c9

q (19)


f c9bd p






vt vtu y1

550 (20)


speci1047297









Beam

number

Span

(m)

L =d

Ratio

M u a t

midspan

(kNm)

V u a t d

from

support

(kN)

M u=V u

(kNm =kN)


in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement (m)

Difference

in length

of shear

reinforcement


BR112W75 7 112 459 216 213 1975 1962 07 035 037 57 175 083 1108

BR12W75 75 12 527 234 225 2312 2326 06 043 042 24 190 100 900

BR128W75 8 128 600 253 237 2692 2754 23 050 047 64 225 117 923


Beam

number

Span

(m)

L =d

Ratio

M u at

midspan

(kNm)

V u at d

from

support

(kN)

M u=V u

(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region for

shear

reinforcement

(m)

Difference

in length

of shear

reinforcement


BR88W100 55 88 378 213 178 1591 1571 13 035 040 143 140 083 687

BR96W100 6 96 450 238 189 1931 1916 08 046 046 00 165 101 634

BR112W100 7 112 613 288 213 2762 2835 26 067 059 136 215 136 581


Beam

number

Span

(m)

L =d

Ratio

M u at

midspan

(kNm)

V u at d

from

support

(kN)

M u=V u

(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement

(m)

Difference

in length

of shear

reinforcement


BR8W125 5 8 391 234 167 1652 1624 17 045 047 44 14 095 474

BR96W125 6 96 563 297 189 2497 2532 14 072 064 125 190 130 462

BR104W125 65 104 660 328 201 3078 3089 04 085 072 181 22 15 467








vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q









Beam

number

Span

(m)

L =d

Ratio

M u a t

midspan

(kNm)

V u a t d

from

support

(kN)

M u=V u(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement (m)

Difference

in length

of shear

reinforcement


BR12W60 75 12 338 221 153 1409 1375 084 036 035 29 190 075 1533

BR136W60 85 136 434 256 170 1855 1835 067 052 043 209 250 112 1232

BR152W60 95 152 542 290 187 2389 2410 056 067 051 314 300 148 1027




















stress vc ( N=mm 2)

(BS 8110) with

400=d 5 1r ()

0 025 05 075 100


020 0784 0792 0801 0809 0818 0493

040 0784 0801 0818 0835 0852 0620

060 0784 0809 0835 0860 0886 0709

080 0784 0818 0852 0886 0920 0779

100 0784 0826 0869 0911 0954 0839

120 0784 0835 0886 0937 0988 0891

140 0784 0843 0903 0962 1022 0938

160 0784 0852 0920 0988 1056 0980

180 0784 0860 0937 1013 1090 1019200 0784 0869 0954 1039 1124 1055














Beam

number

Span

(m)

T u

(kNm)

Al

(mm 2)Difference

in Al ()

At =s

(mm 2=mm)Difference


BL4 4 50 min 583 mdash 068 057 193

BL6 6 75 1043 875 192 102 086 186

BL8 8 100 1391 1167 192 136 114 193

BL10 10 125 1738 1458 192 17 143 189


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W100 5 8 208 188 66 317 286 1200 1107 84 365 306 365 306 193

BR96W100 6 96 300 238 67 447 353 1598 1498 67 371 311 371 311 193

BR112W100 7 112 408 288 68 598 421 2084 1986 49 376 315 376 315 194


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W125 5 8 260 234 66 397 357 1420 1323 73 365 306 365 306 193

BR96W125 6 96 375 297 67 558 442 1929 1830 54 371 311 371 311 193BR112W125 7 112 510 359 68 747 526 2563 2483 32 376 315 376 315 194

















Beam

number

Ratio

DL

LL

Service

UDL

(kN=m)

Ultimate

design UDL


in wu

()

Ultimate

design

moment

at midspan

M u (kNm)

Ultimate

design

shear

at d V u

(kN)

Flexural

reinforcement

As (mm 2)Difference

in As

()

Shear

reinforcement

Asv=s

(mm 2=mm)Difference

in Asv=s

()Dead Live

ACI

(12D1 16L)

BS


BR4 4 20 5 32 36 125 144 162 76 86 588 646 99 min 018 mdash

BR5 5 25 5 38 43 132 171 194 90 102 706 789 118 min 018 mdash

BR6 65 33 5 47 535 138 212 241 112 127 891 1014 138 015 024 600

BR7 7 35 5 50 57 140 225 257 119 135 951 1094 150 018 026 444BR8 8 40 5 56 64 143 252 288 133 152 1079 1257 165 024 031 292















































Recommendation






















ACI 31808





Asv

s frac14 V s

df y

ACI 31808e11472

[ Asv

s frac14 V u 2fV c

fdf y


[ Asv

s frac14V u 2fV c

fdf ytimes

bw

bw

[ Asv


f f y

where

vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q

[ Asv


075 f y



BS 811097

Asv

s frac14

vu 2

vc

g m conc in shear

bw

f y

g m steel

where

vc frac14

079

100 As

bwd

1 3

400d

1 4

f cu

25

1 3



[ Asv

sfrac14

vu 2

vc

125

bw

f yv

105


BS 811097

(Table 325)


bw

b 04 Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00018bwh

bw

b $ 04 Larger of

0

025

ffiffiffiffi f c9p

f ybwd

1

Aor

14

f ybwd

00013bwh


T-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00026bwh

L-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00020bwh

Rectangular

beams

Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00013bwh





[ Asv


095 f yv


ethvu 2 08vcTHORNbw

Notation



cross section



resist torsion





bending moment


bending moment




torsion










(1503

1503






reinforcement























stirrups

Z 5 lever arm






References


























vt vtu y1

550 (20)


speci1047297









Beam

number

Span

(m)

L =d

Ratio

M u a t

midspan

(kNm)

V u a t d

from

support

(kN)

M u=V u

(kNm =kN)


in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement (m)

Difference

in length

of shear

reinforcement


BR112W75 7 112 459 216 213 1975 1962 07 035 037 57 175 083 1108

BR12W75 75 12 527 234 225 2312 2326 06 043 042 24 190 100 900

BR128W75 8 128 600 253 237 2692 2754 23 050 047 64 225 117 923


Beam

number

Span

(m)

L =d

Ratio

M u at

midspan

(kNm)

V u at d

from

support

(kN)

M u=V u

(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region for

shear

reinforcement

(m)

Difference

in length

of shear

reinforcement


BR88W100 55 88 378 213 178 1591 1571 13 035 040 143 140 083 687

BR96W100 6 96 450 238 189 1931 1916 08 046 046 00 165 101 634

BR112W100 7 112 613 288 213 2762 2835 26 067 059 136 215 136 581


Beam

number

Span

(m)

L =d

Ratio

M u at

midspan

(kNm)

V u at d

from

support

(kN)

M u=V u

(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement

(m)

Difference

in length

of shear

reinforcement


BR8W125 5 8 391 234 167 1652 1624 17 045 047 44 14 095 474

BR96W125 6 96 563 297 189 2497 2532 14 072 064 125 190 130 462

BR104W125 65 104 660 328 201 3078 3089 04 085 072 181 22 15 467








vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q









Beam

number

Span

(m)

L =d

Ratio

M u a t

midspan

(kNm)

V u a t d

from

support

(kN)

M u=V u(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement (m)

Difference

in length

of shear

reinforcement


BR12W60 75 12 338 221 153 1409 1375 084 036 035 29 190 075 1533

BR136W60 85 136 434 256 170 1855 1835 067 052 043 209 250 112 1232

BR152W60 95 152 542 290 187 2389 2410 056 067 051 314 300 148 1027




















stress vc ( N=mm 2)

(BS 8110) with

400=d 5 1r ()

0 025 05 075 100


020 0784 0792 0801 0809 0818 0493

040 0784 0801 0818 0835 0852 0620

060 0784 0809 0835 0860 0886 0709

080 0784 0818 0852 0886 0920 0779

100 0784 0826 0869 0911 0954 0839

120 0784 0835 0886 0937 0988 0891

140 0784 0843 0903 0962 1022 0938

160 0784 0852 0920 0988 1056 0980

180 0784 0860 0937 1013 1090 1019200 0784 0869 0954 1039 1124 1055














Beam

number

Span

(m)

T u

(kNm)

Al

(mm 2)Difference

in Al ()

At =s

(mm 2=mm)Difference


BL4 4 50 min 583 mdash 068 057 193

BL6 6 75 1043 875 192 102 086 186

BL8 8 100 1391 1167 192 136 114 193

BL10 10 125 1738 1458 192 17 143 189


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W100 5 8 208 188 66 317 286 1200 1107 84 365 306 365 306 193

BR96W100 6 96 300 238 67 447 353 1598 1498 67 371 311 371 311 193

BR112W100 7 112 408 288 68 598 421 2084 1986 49 376 315 376 315 194


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W125 5 8 260 234 66 397 357 1420 1323 73 365 306 365 306 193

BR96W125 6 96 375 297 67 558 442 1929 1830 54 371 311 371 311 193BR112W125 7 112 510 359 68 747 526 2563 2483 32 376 315 376 315 194

















Beam

number

Ratio

DL

LL

Service

UDL

(kN=m)

Ultimate

design UDL


in wu

()

Ultimate

design

moment

at midspan

M u (kNm)

Ultimate

design

shear

at d V u

(kN)

Flexural

reinforcement

As (mm 2)Difference

in As

()

Shear

reinforcement

Asv=s

(mm 2=mm)Difference

in Asv=s

()Dead Live

ACI

(12D1 16L)

BS


BR4 4 20 5 32 36 125 144 162 76 86 588 646 99 min 018 mdash

BR5 5 25 5 38 43 132 171 194 90 102 706 789 118 min 018 mdash

BR6 65 33 5 47 535 138 212 241 112 127 891 1014 138 015 024 600

BR7 7 35 5 50 57 140 225 257 119 135 951 1094 150 018 026 444BR8 8 40 5 56 64 143 252 288 133 152 1079 1257 165 024 031 292















































Recommendation






















ACI 31808





Asv

s frac14 V s

df y

ACI 31808e11472

[ Asv

s frac14 V u 2fV c

fdf y


[ Asv

s frac14V u 2fV c

fdf ytimes

bw

bw

[ Asv


f f y

where

vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q

[ Asv


075 f y



BS 811097

Asv

s frac14

vu 2

vc

g m conc in shear

bw

f y

g m steel

where

vc frac14

079

100 As

bwd

1 3

400d

1 4

f cu

25

1 3



[ Asv

sfrac14

vu 2

vc

125

bw

f yv

105


BS 811097

(Table 325)


bw

b 04 Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00018bwh

bw

b $ 04 Larger of

0

025

ffiffiffiffi f c9p

f ybwd

1

Aor

14

f ybwd

00013bwh


T-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00026bwh

L-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00020bwh

Rectangular

beams

Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00013bwh





[ Asv


095 f yv


ethvu 2 08vcTHORNbw

Notation



cross section



resist torsion





bending moment


bending moment




torsion










(1503

1503






reinforcement























stirrups

Z 5 lever arm






References




























vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q









Beam

number

Span

(m)

L =d

Ratio

M u a t

midspan

(kNm)

V u a t d

from

support

(kN)

M u=V u(kNm =kN)

As (mm 2)Difference

in As ()

Asv=s at

support

(mm 2=mm)Difference

in Asv=s ()

Length of

region

for shear

reinforcement (m)

Difference

in length

of shear

reinforcement


BR12W60 75 12 338 221 153 1409 1375 084 036 035 29 190 075 1533

BR136W60 85 136 434 256 170 1855 1835 067 052 043 209 250 112 1232

BR152W60 95 152 542 290 187 2389 2410 056 067 051 314 300 148 1027




















stress vc ( N=mm 2)

(BS 8110) with

400=d 5 1r ()

0 025 05 075 100


020 0784 0792 0801 0809 0818 0493

040 0784 0801 0818 0835 0852 0620

060 0784 0809 0835 0860 0886 0709

080 0784 0818 0852 0886 0920 0779

100 0784 0826 0869 0911 0954 0839

120 0784 0835 0886 0937 0988 0891

140 0784 0843 0903 0962 1022 0938

160 0784 0852 0920 0988 1056 0980

180 0784 0860 0937 1013 1090 1019200 0784 0869 0954 1039 1124 1055














Beam

number

Span

(m)

T u

(kNm)

Al

(mm 2)Difference

in Al ()

At =s

(mm 2=mm)Difference


BL4 4 50 min 583 mdash 068 057 193

BL6 6 75 1043 875 192 102 086 186

BL8 8 100 1391 1167 192 136 114 193

BL10 10 125 1738 1458 192 17 143 189


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W100 5 8 208 188 66 317 286 1200 1107 84 365 306 365 306 193

BR96W100 6 96 300 238 67 447 353 1598 1498 67 371 311 371 311 193

BR112W100 7 112 408 288 68 598 421 2084 1986 49 376 315 376 315 194


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W125 5 8 260 234 66 397 357 1420 1323 73 365 306 365 306 193

BR96W125 6 96 375 297 67 558 442 1929 1830 54 371 311 371 311 193BR112W125 7 112 510 359 68 747 526 2563 2483 32 376 315 376 315 194

















Beam

number

Ratio

DL

LL

Service

UDL

(kN=m)

Ultimate

design UDL


in wu

()

Ultimate

design

moment

at midspan

M u (kNm)

Ultimate

design

shear

at d V u

(kN)

Flexural

reinforcement

As (mm 2)Difference

in As

()

Shear

reinforcement

Asv=s

(mm 2=mm)Difference

in Asv=s

()Dead Live

ACI

(12D1 16L)

BS


BR4 4 20 5 32 36 125 144 162 76 86 588 646 99 min 018 mdash

BR5 5 25 5 38 43 132 171 194 90 102 706 789 118 min 018 mdash

BR6 65 33 5 47 535 138 212 241 112 127 891 1014 138 015 024 600

BR7 7 35 5 50 57 140 225 257 119 135 951 1094 150 018 026 444BR8 8 40 5 56 64 143 252 288 133 152 1079 1257 165 024 031 292















































Recommendation






















ACI 31808





Asv

s frac14 V s

df y

ACI 31808e11472

[ Asv

s frac14 V u 2fV c

fdf y


[ Asv

s frac14V u 2fV c

fdf ytimes

bw

bw

[ Asv


f f y

where

vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q

[ Asv


075 f y



BS 811097

Asv

s frac14

vu 2

vc

g m conc in shear

bw

f y

g m steel

where

vc frac14

079

100 As

bwd

1 3

400d

1 4

f cu

25

1 3



[ Asv

sfrac14

vu 2

vc

125

bw

f yv

105


BS 811097

(Table 325)


bw

b 04 Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00018bwh

bw

b $ 04 Larger of

0

025

ffiffiffiffi f c9p

f ybwd

1

Aor

14

f ybwd

00013bwh


T-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00026bwh

L-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00020bwh

Rectangular

beams

Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00013bwh





[ Asv


095 f yv


ethvu 2 08vcTHORNbw

Notation



cross section



resist torsion





bending moment


bending moment




torsion










(1503

1503






reinforcement























stirrups

Z 5 lever arm






References







































stress vc ( N=mm 2)

(BS 8110) with

400=d 5 1r ()

0 025 05 075 100


020 0784 0792 0801 0809 0818 0493

040 0784 0801 0818 0835 0852 0620

060 0784 0809 0835 0860 0886 0709

080 0784 0818 0852 0886 0920 0779

100 0784 0826 0869 0911 0954 0839

120 0784 0835 0886 0937 0988 0891

140 0784 0843 0903 0962 1022 0938

160 0784 0852 0920 0988 1056 0980

180 0784 0860 0937 1013 1090 1019200 0784 0869 0954 1039 1124 1055














Beam

number

Span

(m)

T u

(kNm)

Al

(mm 2)Difference

in Al ()

At =s

(mm 2=mm)Difference


BL4 4 50 min 583 mdash 068 057 193

BL6 6 75 1043 875 192 102 086 186

BL8 8 100 1391 1167 192 136 114 193

BL10 10 125 1738 1458 192 17 143 189


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W100 5 8 208 188 66 317 286 1200 1107 84 365 306 365 306 193

BR96W100 6 96 300 238 67 447 353 1598 1498 67 371 311 371 311 193

BR112W100 7 112 408 288 68 598 421 2084 1986 49 376 315 376 315 194


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W125 5 8 260 234 66 397 357 1420 1323 73 365 306 365 306 193

BR96W125 6 96 375 297 67 558 442 1929 1830 54 371 311 371 311 193BR112W125 7 112 510 359 68 747 526 2563 2483 32 376 315 376 315 194

















Beam

number

Ratio

DL

LL

Service

UDL

(kN=m)

Ultimate

design UDL


in wu

()

Ultimate

design

moment

at midspan

M u (kNm)

Ultimate

design

shear

at d V u

(kN)

Flexural

reinforcement

As (mm 2)Difference

in As

()

Shear

reinforcement

Asv=s

(mm 2=mm)Difference

in Asv=s

()Dead Live

ACI

(12D1 16L)

BS


BR4 4 20 5 32 36 125 144 162 76 86 588 646 99 min 018 mdash

BR5 5 25 5 38 43 132 171 194 90 102 706 789 118 min 018 mdash

BR6 65 33 5 47 535 138 212 241 112 127 891 1014 138 015 024 600

BR7 7 35 5 50 57 140 225 257 119 135 951 1094 150 018 026 444BR8 8 40 5 56 64 143 252 288 133 152 1079 1257 165 024 031 292















































Recommendation






















ACI 31808





Asv

s frac14 V s

df y

ACI 31808e11472

[ Asv

s frac14 V u 2fV c

fdf y


[ Asv

s frac14V u 2fV c

fdf ytimes

bw

bw

[ Asv


f f y

where

vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q

[ Asv


075 f y



BS 811097

Asv

s frac14

vu 2

vc

g m conc in shear

bw

f y

g m steel

where

vc frac14

079

100 As

bwd

1 3

400d

1 4

f cu

25

1 3



[ Asv

sfrac14

vu 2

vc

125

bw

f yv

105


BS 811097

(Table 325)


bw

b 04 Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00018bwh

bw

b $ 04 Larger of

0

025

ffiffiffiffi f c9p

f ybwd

1

Aor

14

f ybwd

00013bwh


T-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00026bwh

L-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00020bwh

Rectangular

beams

Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00013bwh





[ Asv


095 f yv


ethvu 2 08vcTHORNbw

Notation



cross section



resist torsion





bending moment


bending moment




torsion










(1503

1503






reinforcement























stirrups

Z 5 lever arm






References

































Beam

number

Span

(m)

T u

(kNm)

Al

(mm 2)Difference

in Al ()

At =s

(mm 2=mm)Difference


BL4 4 50 min 583 mdash 068 057 193

BL6 6 75 1043 875 192 102 086 186

BL8 8 100 1391 1167 192 136 114 193

BL10 10 125 1738 1458 192 17 143 189


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W100 5 8 208 188 66 317 286 1200 1107 84 365 306 365 306 193

BR96W100 6 96 300 238 67 447 353 1598 1498 67 371 311 371 311 193

BR112W100 7 112 408 288 68 598 421 2084 1986 49 376 315 376 315 194


Beam

number

Span

(m)

L =d

ratio

M u

(kNm)

V u at d

(kN)

T u at d


Top steel

(mm 2) Difference

in top

bars ()

Bottom

steel (mm 2)

Face bars

(mm 2) Difference

in topface


BR8W125 5 8 260 234 66 397 357 1420 1323 73 365 306 365 306 193

BR96W125 6 96 375 297 67 558 442 1929 1830 54 371 311 371 311 193BR112W125 7 112 510 359 68 747 526 2563 2483 32 376 315 376 315 194

















Beam

number

Ratio

DL

LL

Service

UDL

(kN=m)

Ultimate

design UDL


in wu

()

Ultimate

design

moment

at midspan

M u (kNm)

Ultimate

design

shear

at d V u

(kN)

Flexural

reinforcement

As (mm 2)Difference

in As

()

Shear

reinforcement

Asv=s

(mm 2=mm)Difference

in Asv=s

()Dead Live

ACI

(12D1 16L)

BS


BR4 4 20 5 32 36 125 144 162 76 86 588 646 99 min 018 mdash

BR5 5 25 5 38 43 132 171 194 90 102 706 789 118 min 018 mdash

BR6 65 33 5 47 535 138 212 241 112 127 891 1014 138 015 024 600

BR7 7 35 5 50 57 140 225 257 119 135 951 1094 150 018 026 444BR8 8 40 5 56 64 143 252 288 133 152 1079 1257 165 024 031 292















































Recommendation






















ACI 31808





Asv

s frac14 V s

df y

ACI 31808e11472

[ Asv

s frac14 V u 2fV c

fdf y


[ Asv

s frac14V u 2fV c

fdf ytimes

bw

bw

[ Asv


f f y

where

vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q

[ Asv


075 f y



BS 811097

Asv

s frac14

vu 2

vc

g m conc in shear

bw

f y

g m steel

where

vc frac14

079

100 As

bwd

1 3

400d

1 4

f cu

25

1 3



[ Asv

sfrac14

vu 2

vc

125

bw

f yv

105


BS 811097

(Table 325)


bw

b 04 Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00018bwh

bw

b $ 04 Larger of

0

025

ffiffiffiffi f c9p

f ybwd

1

Aor

14

f ybwd

00013bwh


T-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00026bwh

L-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00020bwh

Rectangular

beams

Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00013bwh





[ Asv


095 f yv


ethvu 2 08vcTHORNbw

Notation



cross section



resist torsion





bending moment


bending moment




torsion










(1503

1503






reinforcement























stirrups

Z 5 lever arm






References




































Beam

number

Ratio

DL

LL

Service

UDL

(kN=m)

Ultimate

design UDL


in wu

()

Ultimate

design

moment

at midspan

M u (kNm)

Ultimate

design

shear

at d V u

(kN)

Flexural

reinforcement

As (mm 2)Difference

in As

()

Shear

reinforcement

Asv=s

(mm 2=mm)Difference

in Asv=s

()Dead Live

ACI

(12D1 16L)

BS


BR4 4 20 5 32 36 125 144 162 76 86 588 646 99 min 018 mdash

BR5 5 25 5 38 43 132 171 194 90 102 706 789 118 min 018 mdash

BR6 65 33 5 47 535 138 212 241 112 127 891 1014 138 015 024 600

BR7 7 35 5 50 57 140 225 257 119 135 951 1094 150 018 026 444BR8 8 40 5 56 64 143 252 288 133 152 1079 1257 165 024 031 292















































Recommendation






















ACI 31808





Asv

s frac14 V s

df y

ACI 31808e11472

[ Asv

s frac14 V u 2fV c

fdf y


[ Asv

s frac14V u 2fV c

fdf ytimes

bw

bw

[ Asv


f f y

where

vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q

[ Asv


075 f y



BS 811097

Asv

s frac14

vu 2

vc

g m conc in shear

bw

f y

g m steel

where

vc frac14

079

100 As

bwd

1 3

400d

1 4

f cu

25

1 3



[ Asv

sfrac14

vu 2

vc

125

bw

f yv

105


BS 811097

(Table 325)


bw

b 04 Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00018bwh

bw

b $ 04 Larger of

0

025

ffiffiffiffi f c9p

f ybwd

1

Aor

14

f ybwd

00013bwh


T-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00026bwh

L-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00020bwh

Rectangular

beams

Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00013bwh





[ Asv


095 f yv


ethvu 2 08vcTHORNbw

Notation



cross section



resist torsion





bending moment


bending moment




torsion










(1503

1503






reinforcement























stirrups

Z 5 lever arm






References


































































Recommendation






















ACI 31808





Asv

s frac14 V s

df y

ACI 31808e11472

[ Asv

s frac14 V u 2fV c

fdf y


[ Asv

s frac14V u 2fV c

fdf ytimes

bw

bw

[ Asv


f f y

where

vc frac14

016

ffiffiffiffi f c9

q thorn 17r

V ud

M u

029

ffiffiffiffi f c9

q

[ Asv


075 f y



BS 811097

Asv

s frac14

vu 2

vc

g m conc in shear

bw

f y

g m steel

where

vc frac14

079

100 As

bwd

1 3

400d

1 4

f cu

25

1 3



[ Asv

sfrac14

vu 2

vc

125

bw

f yv

105


BS 811097

(Table 325)


bw

b 04 Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00018bwh

bw

b $ 04 Larger of

0

025

ffiffiffiffi f c9p

f ybwd

1

Aor

14

f ybwd

00013bwh


T-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00026bwh

L-beam Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00020bwh

Rectangular

beams

Larger of

0025

ffiffiffiffi f c9p

f ybwd

1A or

14

f ybwd

00013bwh





[ Asv


095 f yv


ethvu 2 08vcTHORNbw

Notation



cross section



resist torsion





bending moment


bending moment




torsion










(1503

1503






reinforcement























stirrups

Z 5 lever arm






References

























[ Asv


095 f yv


ethvu 2 08vcTHORNbw

Notation



cross section



resist torsion





bending moment


bending moment




torsion










(1503

1503






reinforcement























stirrups

Z 5 lever arm






References























Compare BS and ACI Code

Documents

Transcript of Compare BS and ACI Code