Strength Design Requirements of ACI-318M-02 Code, BS8110, and EuroCode2 for Structural Concrete: A Comparative Study

Transcription

1 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN Strength Design Requireents o ACI-318M-02 Coe, BS8110, an EuroCoe2 or Structural Concrete: A Coparative Stuy Asst. Lect. Ali Abul Hussein Jawa Civil Engineering Departent, College o Engineering Al-Mustansiriya University, Bagha, Iraq Abstract This paper is intene to copare esign requireents o the structural builing coes ro saety an econoical point o view. Three ierent aous structural builing coes have been aopte. These are the ACI 318M-02, BS8110:1985, an Euro Coe2:1992. These coes have been copare in the strength esign requireents o structural eleents. The coparison inclue saety provisions, lexural esign, shear esign, an colun esign. Throughout this stuy elaborate esign oels an criteria o the consiere coes have been exhibite. Although the principles containe in these coes are basically the sae, they ier in etails. The coparison between results has shown that EC2 is ore liberal in partial saety actors an strength esign than ACI Coe. Ater ollowing this stuy, esign engineers will iscover easily that the transition aong coes is not a iicult process. الخالصة تقصد هذه الدراسة إلى أجراء مقارنة من الناحية االقتصادية واألمان للمدونات اإلنشائية لألبنية من خالل تبني ثالث مدونات مشهورة ومعتمدة عالميا. المدونات هي: المواصفة األمريكية للمتطلبات اإلنشائية للخرسانة M ACI والمواصفة القياسية البريطانية BS8110:1985 والمواصفة األوربية.Euro Coe2:1992 تمت مقارنة هذه المدونات الثالثة في إطار متطلبات القوة لكل مواصفة وقد تضمنت مقارنة معامالت األمان وتصميم االنحناء للعتبات وتصميم مقاومة القص وتصميم األعمدة. في إطار المقارنة عرضت الدراسة النماذج والمعادالت التصميمية التي تطلبها كل مواصفة تفصيليا. أفرزت الدراسة إن المواصفات الثالثة تشترك في المبادئ األساسية وتختلف في التفاصيل. كانت المواصفة األوربية أكثر كرم ا واألفضل من الناحية االقتصادية. 1. Introuction This paper is evote to ocus a spot o light on strength esign requireents or concrete structures. Three ierent coonly use structural builing coes are aopte in 636

2 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN this stuy. These are: the builing coe requireent or structural concrete ACI-318M-02 [1], the British stanar or structural use o concrete BS8110:1985 [2] ; an the Eurcoe2 or the esign o concrete structures [3]. The irst set o builing regulations or reinorce concrete was rate uner the supervision o Pro. Morsh o the University o Stuttgart an was issue in Prussia in Other countries ollowe soon ater, an toay ost countries have their own builing regulations. The ai o these regulations is to protect the public health an saety. In the Unite States the esign builing coe or concrete structures is the ACI 318M-02. This coe witnesses ajor revisions every 6 years. BS8110 has been prepare uner the irection o British Stanar Institution in It supersees CP110:1972, which was withrawn. The search or haronization o Technical Stanars across the European Counity has le to the evelopent o a series o structural Euro Coes which are the technical ocuents intene or aoption throughout all the eber states. Euro Coe2 (EC2) eals with the esign o concrete structures. Liit state principles (Ultiate Design Metho) establishe by ACI an BS is also aopte by EC2. Most Iraqi civil engineers are ailiar with ACI coe; however it is necessary to inor the about the other current British an European coes. Beore Euro Coe2 an BS8110 are involve strongly in our esign lie, ost engineers will nee to be assure that they can be aopte as a practical esign tool. Knowlege ust be extene to cover the whole aspects o each part, as well as, the econoical an the conservative results. This stuy will attept to suarize the principle esign proceures require by ACI coe, copare with their counterparts o BS8110, an EC2. The three coes are copare in the context o esign o priary structural eleents an the inoration is given broaly about the essential eatures o their esign criteria. 2. Saety Provisions 2-1 Loaing The three coes ipose partial actors o saety or loas ue to esign assuptions an inaccuracy o calculation, possible unusual loa increases, an constructional inaccuracies [4]. Design loa=characteristic loa* partial loa actor o saety ( ). The value o this actor takes into account the iportance o the liit state uner consieration an relects to soe extent the accuracy with which ierent types o loaing can be preicte, an the probability o particular loa cobinations occurring. Table (1) illustrates the values o partial actors o saety or the loaings, an a basic loa cobination stipulate by the three coes [1, 2, 3]. 631

3 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN Table (1) Basic Loa Cobinations an Partial Saety Factors ( ) at the Ultiate Liit State Coe Loa (DL) Loa (LL) ACI318M ACI318M-02 (Alternative loa actors) BS EC Both ( ea ) an ( live ) are arginally in escening anner ro ACI-318M reaching to the lowest values in EC2. For a typical eber with DL=2LL, axiu uniorly istribute esign loa in EC2 woul be 7.1% lower than that o the ACI Coe, an 4.8% lower than that o BS Materials As in BS8110, EC2 uses a basic aterial partial actor o saety ( ) [5] : Design strength aterial characteristic strength partial actor o saety ( ) The strength o the aterial will ier ro that easure in a careully prepare test specien an it is particularly true or concrete where placing, copaction an curing are so iportant to the strength. Steel, on the other han, is relatively consistent requiring a sall partial actor o saety. Recoene values or are given in Table (2). Coe Table (2) Material Partial Factors o Saety ( ) at the Ultiate Liit State Concrete in Flexure or Axial Loa Concrete in Shear Concrete in Bon Reinorceent Steel BS EC However, in ACI Coe, the strength reuction actor Φ replace the aterial partial saety actors o other coes. Φ in the ACI coe is given ierent values epening on the state o knowlege, i.e., the accuracy with which various strengths can be calculate. Thus, the value or bening is higher than that or shear or bearing. Also, the Φ values siulate the 631

4 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN ( ) values ro the sie that both relect the probable quality control achievable, an reliability o workanship an inspection [6]. In ACI coe the actors Φ or uner strength, calle strength reuction actors, are prescribe as ollows [1] : Φ Factors Φ Alternative Factors Flexure Axial tension Shear an torsion Copression ebers spirally reinorce Copression ebers tie reinorce * Bearing Design o Section uner Flexure 3-1 Design Criteria Beas ay ail by oent because o weakness in the tension steel or weakness in the copression concrete. Most beas are weaker in their reinorcing steel than in their copression concrete. Both coes an econoy require such esign. I the concrete reaches its ull copressive stress just as the steel reach its yiel-point stress, the bea is sai to be a balance bea at ailure. Such a bea which requires very heavy steel, is rarely econoical, an is not allowe by all coes. The balance bea in ultiate strength esign is unaental to the philosophy o all the consiere three coes. The Coes liit the tensile reinorceent to a axiu value ust be less than the balance reinorceent area. ACI coe liits the tensile reinorceent to a axiu o 0.75ρ b, while BS8110 an EC2 liit it to 0.76ρ b an 0.53ρ b * respectively [1, 2, 3]. 3-2 Stress Block For esign purposes real inal stress istribution ay be replace aequately by an equivalent rectangle o copression stress (pioneere in USA by Whitney) [8]. For rectangular bea section, the shae area o the rectangular stress block o Fig.(1) shoul be equal that o the real stress block an their centrois shoul be at the sae level. Figure (1) illustrates the stress block aopte by ACI coe an copare to those use by BS8110 an EC2. For cobine copression an lexure, both axial loa an bening oent are subjecte to the sae actor, which ay be variable an increase to 0.9 as the axial copression ecreases to zero. ρ ax in BS8110 an EC2 is given in ter o axiu neutral axis epth Xax perissible beore copression steel is to be provie. An the given values or ' c =30 MP a an y =420 MP a 631

5 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN Table (3) shows results o neutral axis epth against various reinorcing steel ratios or the aopte speciications. ACI oel gives the avantages in ters o reinorceent area because o the resulting increase in the lever ar coparatively with BS8110 an EC2. ACI Coe: c ' c c Neutral axis a c C h -a/2 As s T Section Strain Diagra Stress Diagra BS 8110: c 0.67 cu / c h x Neutral axis 0.9x C z As s T Section Strain Diagra Stress Diagra EC2: c ck / c h x Neutral axis x C z As s T Section Strain Diagra Stress Diagra Figure (1) Strain Distribution an Stress Block 641

6 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN Table (3) Neutral Axis Depth against Dierent Steel Ratios (Rectangular Section b*h, c'=30 MPa, y=420 MPa) ρ ACI Coe BS EC Concrete Graes ACI Coe an EC2 allow the beneits o eriving a orula by using high strength concretes, while BS oes not. The value o cu shoul not be taken greater than (40 MPa) as stipulate by BS8110. Concrete strengths are reerre in EC2 an ACI by cyliner strengths, which are (10-20%) less than the corresponing cube strengths use in BS Design Forula A rectangular section was analyze uner bening oent to avoi the necessity o using the ultiate concrete strain. Application o the unique two equilibriu equations at the section prouces the esign oent capacity criteria. Eq. (1), Eq. (2), an Eq.(3) represent esign oent capacity orula proucing by ACI Coe, BS8110 an EC2 oel respectively [1,2, 3] : 2 y M b (1 ) ACI y '.. (1) y c y M b (1 ) BS (2) 1.33 cu (3) 2 y y M b (1 ) EC ck The only uner reinorce beas are peritte by the consiere three speciications. The resulting stretching o the steel will raise the neutral axis until the inal seconary copression ailure occurs at the copression strain which has been taken in ACI Coe as ε c =0.003, an ε c = in BS8110, an EC2. The coeicient R is use to convert cyliner strength to cube, where R= log( c ' /20) 646

7 M/b^2 MPa Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN Eect o ρ on Moent Capacity To trace the ultiate oent capacity prouce ro equations 1,2, an 3, a rectangular section with c ' =30 MP a an y =420 MP a has been analyze. Figure (2) shows the results o analysis. It was oun that the results showe siilar behavior or BS8110 an EC2 ue to the siilarity o oeling an convergence o saety actors. On the other han, the atter was ierent in ACI orula. ACI orula gives higher oent capacity or lower steel ratios, while this virtue becoes o seconary eect coparatively with BS an EC when the steel ratio increase over ρ ax in oubly reinorce sections because o the eect o copression steel ratio which has contribute highly in increasing oent capacity ACI Coe 4.00 BS8110 EC Reinoceent ratio Figure (2) Eect o ρ on Ultiate Moent Capacity (c'=30 MPa an y=420 MPa) 4. Design o Shear 4-1 Concrete Shear Strength The shear in a reinorce concrete bea without reinorceent is carrie by a cobination o three ain coponents. These are concrete in copression zone, owelling 641

8 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN action o tensile reinorceent, an aggregate interlock across lexural crack. The actual behavior is coplex, an iicult to analyze theoretically but by applying the results o any experiental investigations, reasonable sipliie proceures or estiating concrete shear strength can be evelope. In EC2 as in the other two coes, the concrete shear strength epens on concrete copressive strength, eective bea epth, with an tension steel ratio. The recoene esign shear strength o the concrete alone or coparison aong the aopte three coes is as given in the ollowing equations: EC2 [3] : V R k(1.2 40) b EC2 (4) ck w where: k= (1.6-) >1 or 1 where ore than 50% o tension reinorceent is cut, in eter, 0.02 BS8110 [2,4] : where: V As 0.03 b w c cu 40 MPa cu 3 4 (100 ) ( ) BS b (5) w c While ACI Coe [1] suggests two equations to estiate concrete shear strength: ' V c 6 b c w ACI Coe (6) or ' c 120 Vu V c 7 7 bw w M u ACI Coe... (7) ' V 0.3 b c c w ACI Coe where: epth shear span ratio Vu 1.0 M u 643

9 Concrete shear Strength MPa Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN The engineer ay use either Eq. (6) or Eq. (7) an will soon note that only a ew situations give large ierences between the [8]. Fro the above concrete shear strength, it ay be seen that the shear stress o concrete increases or shallower sections an or section with larger percentage o tensile reinorceent. The longituinal tension bars contribute to shear resistance by their owelling action an they help to prevent shear cracks ro coencing at sall tension cracks, also they increase the epth o copression concrete zone [4, 8]. It is obvious that concrete shear strength Equations (4), (5), (6), or (7) is relate epirically to the concrete copressive strength. The principal stresses at iagonal shear cracks are incline. I the iagonal tension excees the liit tensile strength o concrete, then concrete, is not aequate alone to carry the applie shear orce. Concrete tensile strength has eterine epirically by correlation between various easures o tensile strength an square or thir root o the copressive strength [9]. Figure (3) shows the increasing in the allowable shear stress o concrete as the concrete copressive strength increases. For noral strength concrete, BS8110 shear strength orula Eq. (5) gives 20-55% over the strength calculate by EC2 Eq.4, while it is o 20-30% over values o ACI Coe Eq. (7) ACI Coe Eq BS8110 (40MPa liit is reove) EC Cyliner Concrete Copressive Strength MPa Figure (3) Eect o Concrete Copressive Strength on Allowable Concrete Shear Strength (ρ=0.02) 644

10 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN Miniu Shear Reinorceent When checking a noral shear, EC2 is the sae as ACI Coe an BS8110 in that noinal shear stresses below which only iniu shear reinorceent to be provie. The iniu shear reinorceent requeste by the coes is as suarize in the ollowing equations: where: where: A b 0.48 S w EC2. (8) v 0.87 ck MPa S 0.65,300 cu A v A b y 0.4 S w BS (9) v MPa c bws 16 but not less than: where: A y b y y 0.33 S w ACI Co (10) v S 0.5, 600 The EC2 liitation given by Eq. (8) is ore conservative than those given by Eqs. (9) an (10) o BS8110 an ACI Coe respectively. 4-3 Maxiu Applie Shear Force Large shearing orces are liable to cause crushing o the concrete along the irection o the principal copression stresses. EC2 an BS8110 liit the axiu applie shear stress at section close to support to certain values calculate by using the ollowing Eq. (11) an Eq. (12) respectively [3,5] : where: ck V 0.3 EC 2 (11) 0.7 ck

11 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN cu V 0.8 or 5 MPa BS8110 (12) While the ACI Coe liits the axiu applie shear stress at section in another way. It has liite the shear strength provie by shear reinorceent in orer to ensure that the aount o shear reinorceent is not too high [1, 4] : V 2 ' ACI Coe s 3 c bw (13) This eans that the axiu allowe shear stress at a section ay be written in this orula: ' c V 0.83 ACI Coe.. (14) The values prouce ro the three ierent coes orulae are so close, i.e. or a section with 'c=30 MPa, the axiu liiting allowe shear strength shoul be less than: 4.95 MPa accoring to EC2 orulae 4.90 MPa accoring to BS8110 orulae 4.56 MPa accoring to ACI Coe orulae 5. Design o Eleent uner Bening Plus Axial Copression 5-1 Basic Equations As in ACI Coe, BS8110 an EC2 o not give separate guiance on the approach to be use in esigning a colun uner a oent an axial orce. For practical purposes as with ACI the rectangular stress block that use or the esign o beas ay also be use or the esign o coluns. Figure (4) represents the cross-section o a eber with typical strain an stress istribution or varying positions o neutral axis. c h ' A s s C or x a or s NA A s s s A s y A s s b x Section Strains Stresses Strains Stresses X or c < h X or c >= h A s y s A s y Figure (4) Bening Plus Axial Copression with Varying Position o the Neutral Axis 646

12 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN Moes o Failure The relative agnitue o the oent (M) an the axial copression orce (P) govern whether the section will ail in tension or in copression. M-P interaction iagras can be constructe or any shape o cross-section by applying the basic equilibriu equations an strain copatibility. Three types o ailure will appear on the interaction iagra. With large eective eccentricity (e=m/p) a tensile ailure is likely, but with a sall eccentricity a copression ailure is ore likely. M-P interaction charts or a (500*300) section with esign ata shown in Fig.(5) have been plotte taking stress istribution blocks aopte by the three coes Fig.(2). A urther liitation on colun strength is ipose by ACI Coe as well as the two others, in orer to allow or acciental eccentricities o loaing. This woul be inclue by iposing an upper liit o pure axial colun capacity less than the calculate ultiate strength. This upper liit is taken as 0.80 ties the calculate strength o tie colun as state by ACI Coe an 0.87 as requeste by BS8110. This reuction in ultiate strength belongs to that all consiere coes orere that each colun shoul not be esigne or a oent less than (P o * e in ), where e in is the iniu eccentricity o the axial loa an has the ollowing value or tie colun: e in = in( 0.05h, 20) BS8110 & EC2 While the ACI coe requires soething siilar by setting an upper liit on the axiu axial loa Pu, as shown by the horizontal line in Fig.(5). The paraeter h represents the overall size o the colun-cross section in the plane o bening. The interaction iagras or actore esign colun strength uner a provision o each coe have been calculate an plotte, as shown in Fig.(5). The horizontal line appears within each chart belonging to the reuction o pure axial copression orce ue to the iniu ipose eccentricity [4]. The charts o the actore esign strength or the aopte exaple give close agreeent between EC2 an BS8110 because the siilarity in strain istribution iagras an stress blocks, on the other han, the closeness in aterial partial saety actors. While the chart o ACI Coe oves away ro others. ACI Coe esign criteria see obviously less econoical an wiely conservative. 641

13 Factore Axial Copression orce Pu KN Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN c=ck=25 MPa cu=31 MPa,y=420 MPa ACI BS EC Factore Bening Moent Mu KN-M Figure (5) Interaction Diagras or Ultiate Factore Design Strengths in Cobine Bening an Axial Copression Loa 5-3 Coluns Longituinal Reinorceent The iniu or axiu aount o longituinal reinorceent shoul not violate the liits stipulate by coes. Table (4); gives iniu an axiu steel ratio requeste by ACI coe, BS 8110, an EC2 [1, 2,3]. Table (4) Miniu an Maxiu Colun Longituinal Steel Ratio Coe Min. Steel Ratio Max. Steel Ratio ACI 318M BS EC Coes also require a iniu o our bars in a rectangular colun (one bar in each corner) an six bars in a circular colun. 641

14 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN Conclusions The ain conclusions ro this stuy can be suarize as ollow: 1. Although the principles containe in the consiere builing regulations are generally the sae, they ier in etails. 2. In general EC2 an BS8110 are not very ierent ro ACI Coe in ters o the esign approach. They give siilar answers an oer scope or ore econoical concrete structures. 3. A true actor o saety can only be eterine by coparing esign loaing with that at collapse. While partial saety actors or aterials an loaings are not saety actors; they only relect egrees o conience in aterial properties an accuracy o loa preiction. 4. EC2 an ACI Coe are ore extensive or esign requireents point o view than BS8110. For exaple in peritting using higher concrete strength. 5. Ater stuy soe nuerical exaples; EC2 an BS8110 show close agreeent in lexure plus axial copression results, while ACI Coe results iverge in a less econoical sie. 7. BS8110 exhibits larger allowable esign shear strength o concrete. 8. ACI Coe, EC2, an BS8110 give a very close esign oent capacity or steel ratios within or less than balance steel ratio. But EC2 is ore generous in oubly reinorce sections. 7. Reerences 1. ACI 318M-02, Builing Coe Requireents or Structural Concrete, ACI Coittee 318, Aerican concrete institute, Michigan, BS8110, Structural Use o Concrete, Part 1, 2 British Stanar Institute, W. H., Mosley, R., Husle, an J. H., Bungey, Reinorce Concrete Design to Euro Coe 2, Macillan Press Lt, A. H., Nilson, an G., Winter, Design o Concrete Structures, 12 th Eition, McGraw-Hill, C. E., Reynols, an J. C., Steean, Reinorce Concrete Designer's Hanbook, 10 th Eition, E& FN Spon, Lonon, R., Husle, W. H., Mosley, Reinorce Concrete Design by Coputer, Macillan Press Lt, C. K., Wang, an C. G., Salon, Reinorce Concrete Design, 4 th Eition, Harper & Row Publisher Inc, P. M., Ferguson, Reinorce Concrete Funaentals, 4 th Eition, Wiley,

15 Journal o Engineering an Developent, Vol. 10, No.1, March (2006) ISSN A. W., Astill, an L. H., Martin, Eleentary Structural Design in Concrete to CP110, Arnol Publisher Lt, Notations A: Depth o equivalent rectangular ACI Coe stress block bw: Web with c or x: Distance ro extree copression iber to neutral axis : Distance ro extree copression iber to centroi o tension reinorceent s: Depth o equivalent rectangular EC2 an BS8110 stress block As: Area o tension reinorceent Av: Area o shear reinorceent within a istance S M: EC2 an BS8110 oent at section Mu: Factore ACI Coe oent at section S: Spacing o stirrups V: Noinal shear strength o section Vc: VR1: Vs: c ' : ck: cu: y: Noinal shear strength provie by concrete EC2 concrete shear strength Noinal shear strength provie by shear reinorceent Speciie ACI Coe cyliner copressive strength o concrete Speciie EC2 cyliner copressive strength o concrete Characteristic BS8110 cube copressive strength o concrete Speciie yiel strength o reinorceent : EC2 paraeter or the rectangular stress block, =0.85 1: Concrete ACI Coe stress block epth actor c: s: s ' : Ultiate strain o concrete Tension steel strain Copression steel strain : ACI Coe strength reuction actor : ACI Coe paraeter or the rectangular stress block, =0.85 : : c: s: Partial saety actor or loa EC2 an BS8110 partial saety actor or strength o aterials Partial saety actor or strength o concrete Partial saety actor or strength o steel : Concrete EC2 stress block epth actor : Steel ratio o longituinal tension reinorceent 651