Concrete Frame Design Manual

Transcription

1 Conrete Frame Deign Manual

2 ETBS Integrated Three-Dimenional Stati and Dynami nalyi and Deign o Building Sytem CONCRETE FRME DESIGN MNUL COMPUTERS & STRUCTURES INC. R Computer and Struture, In. Berkeley, Caliornia, US Verion 7.0 July 2000

3 COPYRIGHT The omputer program ETBS and all aoiated doumentation are proprietary and opyrighted produt. Worldwide right o ownerhip ret with Computer and Struture, In. Unliened ue o the program or reprodution o the doumentation in any orm, without prior written authorization rom Computer and Struture, In., i expliitly prohibited. Further inormation and opie o thi doumentation may be obtained rom: Computer and Struture, In Univerity venue Berkeley, Caliornia US Tel: (510) Fax: (510) ino@iberkeley.om Web: Copyright Computer and Struture, In., The CSI Logo i a regitered trademark o Computer and Struture, In. ETBS i a regitered trademark o Computer and Struture, In.

4 DISCLIMER CONSIDERBLE TIME, EFFORT ND EXPENSE HVE GONE INTO THE DEVELOPMENT ND DOCUMENTTION OF ETBS. THE PROGRM HS BEEN THOROUGHLY TESTED ND USED. IN USING THE PROGRM, HOWEVER, THE USER CCEPTS ND UNDERSTNDS THT NO WRRNTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON THE CCURCY OR THE RELIBILITY OF THE PROGRM. THIS PROGRM IS VERY PRCTICL TOOL FOR THE DE- SIGN OF REINFORCED CONCRETE STRUCTURES. HOWEVER, THE USER MUST THOROUGHLY RED THE MNUL ND CLERLY RECOGNIZE THE SPECTS OF REINFORCED CON- CRETE DESIGN THT THE PROGRM LGORITHMS DO NOT DDRESS. THE USER MUST EXPLICITLY UNDERSTND THE SSUMP- TIONS OF THE PROGRM ND MUST INDEPENDENTLY VER- IFY THE RESULTS.

5 Table o Content CHPTER I Introdution 1 Overview...1 Organization...2 Reommended Reading....3 CHPTER II Deign lgorithm 5 Deign Load Combination...6 Deign and Chek Station...7 Identiying Beam and Column...8 Deign o Beam...8 Deign o Column...9 Deign o Joint...14 Beam/Column Flexural Capaity Ratio...18 P-D Eet...18 Element Unupported Length...19 Speial Conideration or Seimi Load...20 Choie o Input Unit...21 CHPTER III Deign or CI Deign Load Combination...23 Strength Redution Fator...26 Column Deign...27 Generation o Biaxial Interation Surae...27 Chek Column Capaity...29 Determine Fatored Moment and Fore Determine Moment Magniiation Fator...29 i

6 ETBS Conrete Deign Manual Determine Capaity Ratio...31 Deign Column Shear Reinorement...32 Determine Setion Fore...33 Determine Conrete Shear Capaity...34 Determine Required Shear Reinorement...36 Beam Deign Deign Beam Flexural Reinorement...37 Determine Fatored Moment...37 Determine Required Flexural Reinorement...37 Deign Beam Shear Reinorement Determine Shear Fore and Moment...44 Determine Conrete Shear Capaity...46 Determine Required Shear Reinorement...46 Deign o Joint...46 Determine the Panel Zone Shear Fore...47 Determine the Eetive rea o Joint...48 Chek Panel Zone Shear Stre...48 Beam/Column Flexural Capaity Ratio...49 CHPTER IV Deign or UBC Deign Load Combination...54 Strength Redution Fator...55 Column Deign...56 Generation o Biaxial Interation Surae...56 Chek Column Capaity...58 Determine Fatored Moment and Fore Determine Moment Magniiation Fator...58 Determine Capaity Ratio...60 Deign Column Shear Reinorement...61 Determine Setion Fore...62 Determine Conrete Shear Capaity...63 Determine Required Shear Reinorement...64 Beam Deign Deign Beam Flexural Reinorement...66 Determine Fatored Moment...66 Determine Required Flexural Reinorement...67 Deign Beam Shear Reinorement Determine Shear Fore and Moment...74 Determine Conrete Shear Capaity...75 Determine Required Shear Reinorement...76 Deign o Joint...76 Determine the Panel Zone Shear Fore...77 Determine the Eetive rea o Joint...78 Chek Panel Zone Shear Stre...78 ii

7 Table o Content Beam/Column Flexural Capaity Ratio...78 CHPTER V Deign or CS Deign Load Combination...84 Strength Redution Fator...84 Column Deign...85 Generation o Biaxial Interation Surae...85 Chek Column Capaity...87 Determine Fatored Moment and Fore Determine Moment Magniiation Fator...87 Determine Capaity Ratio...90 Deign Column Shear Reinorement...91 Determine Setion Fore...91 Determine Conrete Shear Capaity...93 Determine Required Shear Reinorement...94 Beam Deign Deign Beam Flexural Reinorement...97 Determine Fatored Moment...97 Determine Required Flexural Reinorement...98 Deign Beam Shear Reinorement Determine Shear Fore and Moment Determine Conrete Shear Capaity Determine Required Shear Reinorement CHPTER VI Deign or BS R Deign Load Combination Deign Strength Column Deign Generation o Biaxial Interation Surae Chek Column Capaity Determine Fatored Moment and Fore Determine dditional Moment Determine Capaity Ratio Deign Column Shear Reinorement Beam Deign Deign Beam Flexural Reinorement Determine Fatored Moment Determine Required Flexural Reinorement Deign Beam Shear Reinorement CHPTER VII Deign or Euroode Deign Load Combination Deign Strength Column Deign iii

8 ETBS Conrete Deign Manual Generation o Biaxial Interation Surae Chek Column Capaity Determine Fatored Moment and Fore Determine Code Total Moment Determine Capaity Ratio Deign Column Shear Reinorement Beam Deign Deign Beam Flexural Reinorement Determine Fatored Moment Determine Required Flexural Reinorement Deign Beam Shear Reinorement CHPTER VIII Deign or NZS Deign Load Combination Strength Redution Fator Column Deign Generation o Biaxial Interation Surae Chek Column Capaity Determine Fatored Moment and Fore Determine Moment Magniiation Fator Dynami Moment Magniiation Determine Capaity Ratio Deign Column Shear Reinorement Determine Setion Fore Determine Conrete Shear Capaity Determine Required Shear Reinorement Beam Deign Deign Beam Flexural Reinorement Determine Fatored Moment Determine Required Flexural Reinorement Deign Beam Shear Reinorement Determine Shear Fore and Moment Determine Conrete Shear Capaity Determine Required Shear Reinorement CHPTER IX Deign Output 185 Overview Graphial Diplay o Deign Input and Output Tabular Diplay o Deign Input and Output Member Speii Inormation Reerene 193 Index 195 iv

9 Chapter I Introdution Overview ETBS eature powerul and ompletely integrated module or deign o both teel and reinored onrete truture (CSI 1999, 2000). The program provide the uer with option to reate, modiy, analyze and deign trutural model, all rom within the ame uer interae. The program provide an interative environment in whih the uer an tudy the tre ondition, make appropriate hange, uh a reviing member propertie, and re-examine the reult without the need to re-run the analyi. ingle moue lik on an element bring up detailed deign inormation. Member an be grouped together or deign purpoe. The output in both graphial and tabulated ormat an be readily printed. The program i trutured to upport a wide variety o the latet national and international building deign ode or the automated deign and hek o onrete and teel rame member. The program urrently upport the ollowing onrete rame deign ode: U.S. CI (CI 1999), U.S. UBC (UBC 1997), Canadian (CS 1994), Overview 1

10 ETBS Conrete Deign Manual Britih (BSI 1989), European (CEN 1992), and New Zealand (NZS ). The deign i baed upon a et o uer-peiied loading ombination. However, the program provide a et o deault load ombination or eah deign ode upported in ETBS. I the deault load ombination are aeptable, no deinition o additional load ombination are required. In the deign o the olumn, the program alulate the required longitudinal and hear reinorement. However the uer may peiy the longitudinal teel, in whih ae a olumn apaity ratio i reported. The olumn apaity ratio give an indiation o the tre ondition with repet to the apaity o the olumn. Every beam member i deigned or lexure and hear at a uer deined number o tation along the beam pan. The preentation o the output i lear and onie. The inormation i in a orm that allow the engineer to take appropriate remedial meaure in the event o member overtre. Bakup deign inormation produed by the program i alo provided or onvenient veriiation o the reult. Englih a well a SI and MKS metri unit an be ued to deine the model geometry and to peiy deign parameter. Organization Thi manual i organized in the ollowing way: Chapter II outline variou apet o the onrete deign proedure o the ETBS program. Thi hapter deribe the ommon terminology o onrete deign a implemented in ETBS. Eah o ix ubequent hapter give a detailed deription o a peii ode o pratie a interpreted by and implemented in ETBS. Eah hapter deribe the deign loading ombination, olumn and beam deign proedure, and other peial onideration required by the ode. In addition Chapter IV deribe the joint deign aording to the UBC ode. Chapter III give a detailed deription o the CI ode (CI 1999) a implemented in ETBS. 2 Organization

11 Chapter I Introdution Chapter IV give a detailed deription o the UBC onrete ode (UBC 1997) a implemented in ETBS. Chapter V give a detailed deription o the Canadian ode (CS 1994) a implemented in ETBS. Chapter VI give a detailed deription o the Britih ode (BSI 1989) a implemented in ETBS. Chapter VII give a detailed deription o the Euroode 2 (CEN 1992) a implemented in ETBS. Chapter VIII give a detailed deription o the New Zealand ode (NZS 1997) a implemented in ETBS. Chapter IX outline variou apet o the tabular and graphial output rom ETBS related to onrete deign. Reommended Reading It i reommended that the uer read Chapter II Deign lgorithm and one o ix ubequent hapter orreponding to the ode o interet to the uer. Finally the uer hould read Deign Output in Chapter IX or undertanding and interpreting ETBS output related to onrete deign. I the uer interet i in the UBC onrete deign ode, it i reommended that the uer hould alo read the hapter related to CI ode. Reommended Reading 3

12 Chapter II Deign lgorithm Thi hapter outline variou apet o the onrete deign and deign-hek proedure that are ued by the ETBS program. The onrete deign and hek may be perormed in ETBS aording to one o the ollowing deign ode: The 1995 merian Conrete Intitute Building Code Requirement or Strutural Conrete, CI (CI 1999). International Conerene o Building Oiial 1997 Uniorm Building Code: Volume 2: Strutural Engineering Deign Proviion, Chapter 19 Conrete, UBC 1997 (ICBO 1997). The 1994 Canadian Standard oiation Deign o Conrete Struture or Building, CS (CS 1994). The 1989 Britih Standard Intitution Strutural Ue o Conrete, BS R1989 (BSI 1989). The 1992 European Committee or Standardization, Deign o Conrete Struture, EUROCODE 2 (CEN 1992). The 1995 Standard New Zealand Conrete Struture Standard, NZS (NZS 1995). Detail o the algorithm aoiated with eah o thee ode a implemented in ETBS are deribed in the ubequent hapter. However, thi hapter provide a bakground whih i ommon to all the deign ode. 5

13 ETBS Conrete Deign Manual For reerring to pertinent etion o the orreponding ode, a unique preix i aigned or eah ode. Reerene to the CI ode ha the preix o CI Reerene to the UBC 1997 ode ha the preix o UBC Reerene to the Canadian ode arry the preix o CS Reerene to the Britih ode arry the preix o BS Reerene to the Euroode 2 arry the preix o EC2 Reerene to the New Zealand ode arry the preix o NZS In writing thi manual it ha been aumed that the uer ha an engineering bakground in the general area o trutural reinored onrete deign and amiliarity with at leat one o the above mentioned deign ode. Deign Load Combination The deign load ombination are ued or determining the variou ombination o the load ae or whih the truture need to be deigned/heked. The load ombination ator to be ued vary with the eleted deign ode. The load ombination ator are applied to the ore and moment obtained rom the aoiated load ae and the reult are then ummed to obtain the atored deign ore and moment or the load ombination. For multi-valued load ombination involving repone petrum, time hitory, and multi-valued ombination (o type enveloping, quare-root o the um o the quare or abolute) where any orrepondene between interating quantitie i lot, the program automatially produe multiple ub ombination uing maxima/minima permutation o interating quantitie. Separate ombination with negative ator or repone petrum ae are not required beaue the program automatially take the minima to be the negative o the maxima or repone petrum ae and the above deribed permutation generate the required ub ombination. When a deign ombination involve only a ingle multi-valued ae o time hitory or moving load, urther option are available. The program ha an option to requet that time hitory ombination produe ub ombination or eah time tep o the time hitory. For normal loading ondition involving tati dead load, live load, wind load, and earthquake load, and/or dynami repone petrum earthquake load, the program ha built-in deault loading ombination or eah deign ode. Thee are baed on 6 Deign Load Combination

14 Chapter II Deign lgorithm the ode reommendation and are doumented or eah ode in the orreponding hapter. For other loading ondition involving time hitory, pattern live load, eparate onideration o roo live load, now load, et., the uer mut deine deign loading ombination either in lieu o or in addition to the deault deign loading ombination. The deault load ombination aume all tati load ae delared a dead load to be additive. Similarly, all ae delared a live load are aumed additive. However, eah tati load ae delared a wind or earthquake, or repone petrum ae, i aumed to be non additive with eah other and produe multiple lateral load ombination. lo wind and tati earthquake ae produe eparate loading ombination with the ene (poitive or negative) revered. I thee ondition are not orret, the uer mut provide the appropriate deign ombination. The deault load ombination are inluded in deign i the uer requet them to be inluded or i no other uer deined ombination i available or onrete deign. I any deault ombination i inluded in deign, then all deault ombination will automatially be updated by the program any time the uer hange to a dierent deign ode or i tati or repone petrum load ae are modiied. Live load redution ator an be applied to the member ore o the live load ae on an element-by-element bai to redue the ontribution o the live load to the atored loading. The uer i autioned that i time hitory reult are not requeted to be reovered in the analyi or ome or all the rame member, then the eet o thee load will be aumed to be zero in any ombination that inlude them. Deign and Chek Station For eah load ombination, eah beam, olumn, or brae element i deigned or heked at a number o loation along the length o the element. The loation are baed on equally paed egment along the lear length o the element. By deault there will be at leat 3 tation in a olumn or brae element and the tation in a beam will be at mot 2 eet (0.5m i model i reated in SI unit) apart. The number o egment in an element an be overwritten by the uer beore the analyi i made. The uer an reine the deign along the length o an element by requeting more egment. See the etion Frame Output Station igned to Line Objet in the ETBS Uer Manual Volume 1 (CSI 1999) or detail. Deign and Chek Station 7

15 ETBS Conrete Deign Manual When uing 1997 UBC deign ode, requirement or joint deign at the beam to olumn onnetion are evaluated at the topmot tation o eah olumn. The program alo perorm a joint hear analyi at the ame tation to determine i peial onideration are required in any o the joint panel zone. The ratio o the beam lexural apaitie with repet to the olumn lexural apaitie onidering axial ore eet aoiated with the weak beam-trong olumn apet o any beam/olumn interetion are reported. Identiying Beam and Column In ETBS all beam and olumn are repreented a rame element. But deign o beam and olumn require eparate treatment. Identiiation or a onrete element i done by peiying the rame etion aigned to the element to be o type beam or olumn. I there i any brae element in the rame, the brae element would alo be identiied a either a beam or a olumn element baed on the aigned etion to the brae element. Deign o Beam In the deign o onrete beam, in general, ETBS alulate and report the required area o teel or lexure and hear baed upon the beam moment, hear, load ombination ator, and other riteria whih are deribed in detail in the ode peii hapter. The reinorement requirement are alulated at a uer-deined number o tation along the beam pan. ll the beam are only deigned or major diretion lexure and hear. Eet due to any axial ore, minor diretion bending, and torion that may exit in the beam mut be invetigated independently by the uer. In deigning the lexural reinorement or the major moment at a partiular etion o a partiular beam, the tep involve the determination o the maximum atored moment and the determination o the reinoring teel. The beam etion i deigned or the maximum poitive M u + and maximum negative M ū atored moment envelope obtained rom all o the load ombination. Negative beam moment produe top teel. In uh ae the beam i alway deigned a a retangular etion. Poitive beam moment produe bottom teel. In uh ae the beam may be deigned a a retangular- or a T-beam. For the deign o lexural reinorement, the beam i irt deigned a a ingly reinored beam. I the beam etion i not adequate, then the required ompreion reinorement i alulated. 8 Identiying Beam and Column

16 Chapter II Deign lgorithm In deigning the hear reinorement or a partiular beam or a partiular et o loading ombination at a partiular tation due to the beam major hear, the tep involve the determination o the atored hear ore, the determination o the hear ore that an be reited by onrete, and the determination o the reinorement teel required to arry the balane. Speial onideration or eimi deign are inorporated in ETBS or CI, UBC, Canadian, and New Zealand ode. Deign o Column In the deign o the olumn, the program alulate the required longitudinal teel, or i the longitudinal teel i peiied, the olumn tre ondition i reported in term o a olumn apaity ratio, whih i a ator that give an indiation o the tre ondition o the olumn with repet to the apaity o the olumn. The deign proedure or the reinored onrete olumn o the truture involve the ollowing tep: Generate axial ore-biaxial moment interation urae or all o the dierent onrete etion type o the model. typial interation urae i hown in Figure II-2. Chek the apaity o eah olumn or the atored axial ore and bending moment obtained rom eah loading ombination at eah end o the olumn. Thi tep i alo ued to alulate the required reinorement (i none wa peiied) that will produe a apaity ratio o 1.0. Deign the olumn hear reinorement. The generation o the interation urae i baed on the aumed train and tre ditribution and ome other impliying aumption. Thee tre and train ditribution and the aumption vary rom ode to ode. typial aumed train ditribution i deribed in Figure II-1. Here maximum ompreion train i limited to e. For mot o the deign ode, thi aumed ditribution remain valid. However, the value o e varie rom ode to ode. For example, e = or CI, UBC and New Zealand ode, and e = or Canadian, Britih and European ode. The detail o the generation o interation urae dier rom ode to ode. Thee are deribed in the hapter peii to the ode. Deign o Column 9

17 ETBS Conrete Deign Manual Varying Linear Strain Plane 0 Reinorement Bar DIRECTION 1 Varying Linear Strain Plane 0 Neutral xi Diretion DIRECTION 2 Reinorement Bar 3 2 Neutral xi Diretion a a 1 0 Varying Linear Strain Plane DIRECTION 3 Reinorement Bar Neutral xi Diretion Figure II-1 Idealized Strain Ditribution or Generation o Interation Surae typial interation urae i hown in Figure II-2. The olumn apaity interation volume i numerially deribed by a erie o direte point that are generated on the three-dimenional interation ailure urae. The oordinate o thee point are determined by rotating a plane o linear train in three dimenion on the etion o the olumn a deribed in Figure II-1. The area aoiated with eah rebar i plaed at the atual loation o the enter o the bar and the algorithm doe not aume any impliiation in the manner in whih the area o teel i ditributed over the ro etion o the olumn. The interation algorithm provide orretion to aount or the onrete area that i diplaed by the reinoring in the ompreion zone. 10 Deign o Column

18 Chapter II Deign lgorithm xial ompreion +P 0 P max Curve #1 Curve #2 P by P bx Curve #NRCV M bx M by M y M x -P 0 xial tenion Figure II-2 Typial Column Interation Surae The eet o ode peiied trength redution ator and maximum limit on the axial apaity are inorporated in the interation urae. The ormulation i baed onitently upon the general priniple o ultimate trength deign, and allow or retangular, quare or irular, doubly ymmetri olumn etion. In addition to axial ompreion and biaxial bending, the ormulation allow or axial tenion and biaxial bending onideration a hown in Figure II-2. Deign o Column 11

19 ETBS Conrete Deign Manual xial Compreion Line Deining Failure Surae C L P M x M y o M X M Y xial Tenion Figure II-3 Geometri Repreentation o Column Capaity Ratio The apaity hek i baed on whether the deign load point lie inide the interation volume in a ore pae, a hown in Figure II-3. I the point lie inide the volume, the olumn apaity i adequate, and vie vera. The point in the interation volume (P, M x, and M y ) whih i repreented by point L i plaed in the interation pae a hown in Figure II-3. I the point lie within the interation volume, the olumn apaity i adequate; however, i the point lie outide the interation volume, the olumn i overtreed. a meaure o the tre ondition o the olumn, a apaity ratio i alulated. Thi ratio i ahieved by plotting the point L, deined by P, M x and M y, and determining the loation o point C. The point C i deined a the point where the line OL (i extended outward) will interet the ailure urae. Thi point i determined by three-dimenional linear interpolation between the point that deine the ailure urae. The apaity ratio, CR, i given by the ratio OL OC. 12 Deign o Column

20 Chapter II Deign lgorithm Figure II-4 Moment Capaity M u at a Given xial Load P u I OL = OC (or CR=1) the point lie on the interation urae and the olumn i treed to apaity. I OL < OC (or CR<1) the point lie within the interation volume and the olumn apaity i adequate. I OL > OC (or CR>1) the point lie outide the interation volume and the olumn i overtreed. The apaity ratio i baially a ator that give an indiation o the tre ondition o the olumn with repet to the apaity o the olumn. In other word, i the axial ore and biaxial moment et or whih the olumn i being heked i ampliied by dividing it by the reported apaity ratio, the point deined by the reulting axial ore and biaxial moment et will lie on the ailure (or interation volume) urae. Deign o Column 13

21 ETBS Conrete Deign Manual The hear reinorement deign proedure or olumn i very imilar to that or beam, exept that the eet o the axial ore on the onrete hear apaity need to be onidered. For ertain peial eimi ae, the deign o olumn or hear i baed on the apaity-hear. The apaity-hear ore in a partiular diretion i alulated rom the moment apaitie o the olumn aoiated with the atored axial ore ating on the olumn. For eah load ombination, the atored axial load i alulated, uing the ETBS analyi load ae and the orreponding load ombination ator. Then, the moment apaity o the olumn in a partiular diretion under the inluene o the axial ore i alulated, uing the uniaxial interation diagram in the orreponding diretion a hown in Figure II-4. Deign o Joint To enure that the beam-olumn joint o peial moment reiting rame poee adequate hear trength, the program perorm a rational analyi o the beamolumn panel zone to determine the hear ore that are generated in the joint. The program then hek thi againt deign hear trength. Only joint having a olumn below the joint are deigned. The material propertie o the joint are aumed to be the ame a thoe o the olumn below the joint. The joint analyi i done in the major and the minor diretion o the olumn. The joint deign proedure involve the ollowing tep: h Determine the panel zone deign hear ore,v u Determine the eetive area o the joint Chek panel zone hear tre The ollowing three etion deribe in detail the algorithm aoiated with the above mentioned tep. Determine the Panel Zone Shear Fore For a partiular olumn diretion, major or minor, the ree body tre ondition o a typial beam-olumn interetion i hown in Figure II-5. The ore V h u i the horizontal panel zone hear ore that i to be alulated. The ore that at on the joint are P u, V u, M L u and M R u. The ore P u and V u are axial ore and hear ore, repetively, rom the olumn raming into the top o the L joint. The moment M u and M R u are obtained rom the beam raming into the 14 Deign o Joint

22 Chapter II Deign lgorithm joint. The joint hear orev h u i alulated by reolving the moment into C and T ore. Figure II-5 Beam-Column Joint nalyi The loation o C or T ore i determined by the diretion o the moment uing bai priniple o ultimate trength theory. Noting that T = C and T = C, h V = T + T -V u L R u L L R R Deign o Joint 15

23 ETBS Conrete Deign Manual The moment and thec andt ore rom beam that rame into the joint in a diretion that i not parallel to the major or minor diretion o the olumn are reolved along the diretion that i being invetigated, thereby ontributing ore omponent to the analyi. In the deign o peial moment reiting onrete rame, the evaluation o the deign hear ore i baed upon the moment apaitie (with reinoring teel overtrength ator,, and no ator) o the beam raming into the joint, (CI , UBC ). The C and T ore are baed upon thee moment apaitie. The olumn hear orev u i alulated rom the beam moment apaitie a ollow: V = M L + M u u H R u See Figure II-6. It hould be noted that the point o inletion hown on Figure II-6 are taken a midway between atual lateral upport point or the olumn. The eet o load reveral, a illutrated in Cae 1 and Cae 2 o Figure II-5 are invetigated and the deign i baed upon the maximum o the joint hear obtained rom the two ae. Determine the Eetive rea o Joint The joint area that reit the hear ore i aumed alway to be retangular in plan view. The dimenion o the retangle orrepond to the major and minor dimenion o the olumn below the joint, exept i the beam raming into the joint i very narrow. The eetive width o the joint area to be ued in the alulation i limited to the width o the beam plu the depth o the olumn. The area o the joint i aumed not to exeed the area o the olumn below. The joint area or joint hear along the major and minor diretion i alulated eparately (CI R21.5.3). It hould be noted that i the beam rame into the joint eentrially, the above aumption may be unonervative and the uer hould invetigate the aeptability o the partiular joint. Chek Panel Zone Shear Stre The panel zone hear tre i evaluated by dividing the hear orev h u by the eetive area o the joint and omparing it with the ollowing deign hear trength (CI , UBC ) : 16 Deign o Joint

24 Chapter II Deign lgorithm v ì 20 j, or joint onined on all our ide, 15 j, or joint onined on three ae or on two oppoite ae, 12 j or all other joint, ï = í ï, î where j = (CI , UBC , ) For joint deign, the program report the joint hear, the joint hear tre, the allowable joint hear tre and a apaity ratio. POINT OF INFLECTION V u COLUMN BOVE COLUMN HEIGHT (H) TOP OF BEM PNEL ZONE L Mu TL h V u C R C L T R R Mu COLUMN BELOW V u POINT OF INFLECTION ELEVTION Figure II-6 Column Shear Fore,V u Deign o Joint 17

25 ETBS Conrete Deign Manual Beam/Column Flexural Capaity Ratio t a partiular joint or a partiular olumn diretion, major or minor, the program will alulate the ratio o the um o the beam moment apaitie to the um o the olumn moment apaitie, (CI , UBC ). M e ³ 6 5 M g (CI , UBC ) The apaitie are alulated with no reinoring overtrength ator,, and inluding ator. The beam apaitie are alulated or revered ituation (Cae 1 and 2) a illutrated in Figure II-5 and the maximum ummation obtained i ued. The moment apaitie o beam that rame into the joint in a diretion that i not parallel to the major or minor diretion o the olumn are reolved along the diretion that i being invetigated and the reolved omponent are added to the ummation. The olumn apaity ummation inlude the olumn above and the olumn below the joint. For eah load ombination the axial ore, P u, in eah o the olumn i alulated rom the ETBS analyi load ondition and the orreponding load ombination ator. For eah load ombination, the moment apaity o eah olumn under the inluene o the orreponding axial load P u i then determined eparately or the major and minor diretion o the olumn, uing the uniaxial olumn interation diagram, ee Figure II-4. The moment apaitie o the two olumn are added to give the apaity ummation or the orreponding load ombination. The maximum apaity ummation obtained rom all o the load ombination i ued or the beam/olumn apaity ratio. The beam/olumn lexural apaity ratio are only reported or Speial Moment-Reiting Frame involving eimi deign load ombination. P- Eet The ETBS deign algorithm require that the analyi reult inlude the P-D eet. The P-D eet are onidered dierently or braed or nonway and unbraed or way omponent o moment in rame. For the braed moment in rame, the eet o P-D i limited to individual member tability. For unbraed omponent, lateral drit eet hould be onidered in addition to individual member tability eet. In ETBS, it i aumed that braed or nonway moment are ontributed rom the dead or live load. Wherea, unbraed or way moment are ontributed rom all other type o load. 18 Beam/Column Flexural Capaity Ratio

26 Chapter II Deign lgorithm For the individual member tability eet, the moment are magniied with moment magniiation ator a in the CI, UBC, Canadian, and New Zealand ode or with additional moment a in the Britih and European ode. For lateral drit eet, ETBS aume that the P-D analyi i perormed and that the ampliiation i already inluded in the reult. The moment and ore obtained rom P-D analyi are urther ampliied or individual olumn tability eet i required by the governing ode a in the CI, UBC, Canadian, and New Zealand ode. The uer o ETBS hould be aware that the deault analyi option in ETBS or P-D eet i turned OFF. The deault number o iteration or P-D analyi i 1. The uer hould turn the P-D analyi ON and et the maximum number o iteration or the analyi. For urther reerene, the uer i reerred to ETBS Uer Manual Volume 2 (CSI 1999). The uer i alo autioned that ETBS urrently onider P-D eet due to axial load in rame member only. Fore in other type o element do not ontribute to thi eet. I igniiant ore are preent in other type o element, or example, large axial load in hear wall modeled a hell element, then the additional ore omputed or P-D will be inaurate. Element Unupported Length To aount or olumn lenderne eet the olumn unupported length are required. The two unupported length are l 33 and l 22. Thee are the length between upport point o the element in the orreponding diretion. The length l 33 orrepond to intability about the 3-3 axi (major axi), and l 22 orrepond to intability about the 2-2 axi (minor axi). Normally, the unupported element length i equal to the length o the element, i.e., the ditane between END-I and END-J o the element. See Figure II-7. The program, however, allow uer to aign everal element to be treated a a ingle member or deign. Thi an be done dierently or major and minor bending. Thereore, extraneou joint, a hown in Figure II-8, that aet the unupported length o an element are automatially taken into onideration. In determining the value or l 22 and l 33 o the element, the program reognize variou apet o the truture that have an eet on thee length, uh a member onnetivity, diaphragm ontraint and upport point. The program automatially loate the element upport point and evaluate the orreponding unupported element length. Element Unupported Length 19

27 ETBS Conrete Deign Manual l 33 Element xi END J END I l 22 Figure II-7 xe o Bending and Unupported Length Thereore, the unupported length o a olumn may atually be evaluated a being greater than the orreponding element length. I the beam rame into only one diretion o the olumn, the beam i aumed to give lateral upport only in that diretion. The uer ha option to peiy the unupported length o the element on an element-by-element bai. Speial Conideration or Seimi Load The CI ode impoe a peial dutility requirement or rame in eimi region by peiying rame either a Ordinary, Intermediate, or Speial moment reiting rame. The Speial moment reiting rame an provide the required dutility and energy diipation in the nonlinear range o yli deormation. The UBC ode require that the onrete rame mut be deigned or a peii Seimi Zone whih i either Zone 0, Zone 1, Zone 2, Zone 3, or Zone 4, where Zone 4 i deignated a the zone o evere earthquake. The Canadian ode require that the onrete rame mut be deigned a either an Ordinary, Nominal, or Dutile moment reiting 20 Speial Conideration or Seimi Load

28 Chapter II Deign lgorithm rame. The New Zealand ode alo require that the onrete rame mut be deigned a either an Ordinary, Elatially reponding, rame with Limited dutility, or Dutile moment reiting rame. Figure II-8 Unupported Length and Interior Node Unlike the CI, UBC, Canadian, and New Zealand ode, the urrent implementation o the Britih ode and the Euroode 2 in ETBS doe not aount or any peial requirement or eimi deign. Choie o Input Unit Englih a well a SI and MKS metri unit an be ued or input. But the ode are baed on a peii ytem o unit. ll equation and deription preented in the ubequent hapter orrepond to that peii ytem o unit unle otherwie noted. For example, the CI ode i publihed in inh-pound-eond unit. By deault, all equation and deription preented in the hapter Deign or CI orrepond to inh-pound-eond unit. However, any ytem o unit an be ued to deine and deign the truture in ETBS. Choie o Input Unit 21

29 Chapter III Deign or CI Thi hapter deribe in detail the variou apet o the onrete deign proedure that i ued by ETBS when the uer elet the CI Deign Code (CI 1999). Variou notation ued in thi hapter are lited in Table III-1. The deign i baed on uer-peiied loading ombination. But the program provide a et o deault load ombination that hould atiy requirement or the deign o mot building type truture. ETBS provide option to deign or hek Ordinary, Intermediate (moderate eimi rik area), and Speial (high eimi rik area) moment reiting rame a required or eimi deign proviion. The detail o the deign riteria ued or the dierent raming ytem are deribed in the ollowing etion. Englih a well a SI and MKS metri unit an be ued or input. But the ode i baed on Inh-Pound-Seond unit. For impliity, all equation and deription preented in thi hapter orrepond to Inh-Pound-Seond unit unle otherwie noted. Deign Load Combination The deign load ombination are the variou ombination o the preribed load ae or whih the truture need to be heked. For the CI ode, i a Deign Load Combination 23

30 ETBS Conrete Deign Manual v rea o onrete ued to determine hear tre, q-in g Gro area o onrete, q-in rea o tenion reinorement, q-in rea o ompreion reinorement, q-in ( required) rea o teel required or tenion reinorement, q-in t Total area o olumn longitudinal reinorement, q-in v rea o hear reinorement, q-in a Depth o ompreion blok, in a b Depth o ompreion blok at balaned ondition, in b Width o member, in b Eetive width o lange (T-Beam etion), in b w Width o web (T-Beam etion), in C m Coeiient, dependent upon olumn urvature, ued to alulate moment magniiation ator Depth to neutral axi, in b Depth to neutral axi at balaned ondition, in d Ditane rom ompreion ae to tenion reinorement, in d Conrete over to enter o reinoring, in d Thikne o lab (T-Beam etion), in E Modulu o elatiity o onrete, pi E Modulu o elatiity o reinorement, aumed a 29,000,000 pi (CI 8.5.2) Speiied ompreive trength o onrete, pi y Speiied yield trength o lexural reinorement, pi y 80, 000 pi (CI 9.4) y Speiied yield trength o hear reinorement, pi h Dimenion o olumn, in I g Moment o inertia o gro onrete etion about entroidal axi, negleting reinorement, in 4 I e Moment o inertia o reinorement about entroidal axi o member ro etion, in 4 Table III-1 Lit o Symbol Ued in the CI ode 24 Deign Load Combination

31 Chapter III Deign or CI k L M 1 M 2 M M n M M u M ux M uy P b P P max P 0 P u r V V E V D V u V p a b 1 b d d d n e e j Eetive length ator Clear unupported length, in Smaller atored end moment in a olumn, lb-in Larger atored end moment in a olumn, lb-in Fatored moment to be ued in deign, lb-in Nonway omponent o atored end moment, lb-in Sway omponent o atored end moment, lb-in Fatored moment at etion, lb-in Fatored moment at etion about X-axi, lb-in Fatored moment at etion about Y-axi, lb-in xial load apaity at balaned train ondition, lb Critial bukling trength o olumn, lb Maximum axial load trength allowed, lb xial load apaity at zero eentriity, lb Fatored axial load at etion, lb Radiu o gyration o olumn etion, in Shear reited by onrete, lb Shear ore aued by earthquake load, lb + L Shear ore rom pan loading, lb Fatored hear ore at a etion, lb Shear ore omputed rom probable moment apaity, lb Reinoring teel overtrength ator Fator or obtaining depth o ompreion blok in onrete bolute value o ratio o maximum atored axial dead load to maximum atored axial total load Moment magniiation ator or way moment Moment magniiation ator or nonway moment Strain in onrete Strain in reinoring teel Strength redution ator Table III-1 Lit o Symbol Ued in the CI ode (ontinued) Deign Load Combination 25

32 ETBS Conrete Deign Manual truture i ubjeted to dead load (DL) and live load (LL) only, the tre hek may need only one load ombination, namely 1.4 DL LL (CI 9.2.1). However, in addition to the dead and live load, i the truture i ubjeted to wind (WL) and earthquake (EL) load, and onidering that wind and earthquake ore are reverible, then the ollowing load ombination have to be onidered (CI 9.2). 1.4 DL 1.4 DL LL (CI 9.2.1) 0.9 DL ± 1.3 WL 0.75 (1.4 DL LL ± 1.7 WL) (CI 9.2.2) 0.9 DL ± 1.3 * 1.1 EL 0.75 (1.4 DL LL ± 1.7 * 1.1 EL) (CI 9.2.3) Thee are alo the deault deign load ombination in ETBS whenever the CI ode i ued. The uer i warned that the above load ombination involving eimi load onider ervie-level eimi ore. Dierent load ator may apply with trength-level eimi ore (CI R9.2.3). Live load redution ator an be applied to the member ore o the live load ondition on an element-by-element bai to redue the ontribution o the live load to the atored loading. Strength Redution Fator The trength redution ator, j, are applied on the nominal trength to obtain the deign trength provided by a member. The j ator or lexure, axial ore, hear, and torion are a ollow: j = 0.90 or lexure, (CI ) j = 0.90 or axial tenion, (CI ) j = 0.90 or axial tenion and lexure, (CI ) j =0.75or axial ompreion, and axial ompreion and lexure (pirally reinored olumn), (CI ) j =0.70or axial ompreion, and axial ompreion and lexure (tied olumn), and (CI ) j = 0.85 or hear and torion. (CI ) 26 Strength Redution Fator

33 Chapter III Deign or CI Column Deign The uer may deine the geometry o the reinoring bar oniguration o eah onrete olumn etion. I the area o reinoring i provided by the uer, the program hek the olumn apaity. However, i the area o reinoring i not provided by the uer, the program alulate the amount o reinoring required or the olumn. The deign proedure or the reinored onrete olumn o the truture involve the ollowing tep: Generate axial ore/biaxial moment interation urae or all o the dierent onrete etion type o the model. typial biaxial interation urae i hown in Figure II-2. When the teel i undeined, the program generate the interation urae or the range o allowable reinorement 1 to 8 perent or Ordinary and Intermediate moment reiting rame (CI ) and 1 to 6 perent or Speial moment reiting rame (CI ). Calulate the apaity ratio or the required reinoring area or the atored axial ore and biaxial (or uniaxial) bending moment obtained rom eah loading ombination at eah tation o the olumn. The target apaity ratio i taken a one when alulating the required reinoring area. Deign the olumn hear reinorement. The ollowing three ubetion deribe in detail the algorithm aoiated with the above-mentioned tep. Generation o Biaxial Interation Surae The olumn apaity interation volume i numerially deribed by a erie o direte point that are generated on the three-dimenional interation ailure urae. In addition to axial ompreion and biaxial bending, the ormulation allow or axial tenion and biaxial bending onideration. typial interation diagram i hown in Figure II-2. The oordinate o thee point are determined by rotating a plane o linear train in three dimenion on the etion o the olumn. See Figure II-1. The linear train diagram limit the maximum onrete train, e, at the extremity o the etion to (CI ). The ormulation i baed onitently upon the general priniple o ultimate trength deign (CI 10.3), and allow or any doubly ymmetri retangular, quare, or irular olumn etion. Column Deign 27

34 ETBS Conrete Deign Manual The tre in the teel i given by the produt o the teel train and the teel modulu o elatiity, e E, and i limited to the yield tre o the teel, y (CI ). The area aoiated with eah reinoring bar i aumed to be plaed at the atual loation o the enter o the bar and the algorithm doe not aume any urther impliiation in the manner in whih the area o teel i ditributed over the ro etion o the olumn, uh a an equivalent teel tube or ylinder. See Figure III ' d' = C C a= 1 2 C 3 T 3 4 T 4 (i) Conrete Setion (ii) Strain Diagram (iii) Stre Diagram Figure III-1 Idealization o Stre and Strain Ditribution in a Column Setion The onrete ompreion tre blok i aumed to be retangular, with a tre value o 0.85 (CI ). See Figure III-1. The interation algorithm provide orretion to aount or the onrete area that i diplaed by the reinorement in the ompreion zone. The eet o the trength redution ator, j, are inluded in the generation o the interation urae. The maximum ompreive axial load i limited to jp n(max), where j P = j g - t + y t n(max) 0.85 [0.85 ( ) ] j P = j g -t y t piral olumn, (CI ) 0.80 [ 0.85 ( ) + ] tied olumn, (CI ) n(max) j = 0.70 or tied olumn, and (CI ) j = 0.75 or pirally reinored olumn. (CI ) 28 Column Deign

35 Chapter III Deign or CI The value o j ued in the interation diagram varie rom j(ompreion) to j(lexure) baed on the axial load. For low value o axial load, j i inreaed linearly rom j(ompreion) to j(lexure) a the jp n dereae rom the maller o jp b or 0.1 g to zero, where jp b i the axial ore at the balaned ondition. The j ator ued in alulating jp n and jp b i the j(ompreion). In ae involving axial tenion, j i alway j(lexure) whih i 0.9 by deault (CI ). Chek Column Capaity The olumn apaity i heked or eah loading ombination at eah hek tation o eah olumn. In heking a partiular olumn or a partiular loading ombination at a partiular tation, the ollowing tep are involved: Determine the atored moment and ore rom the analyi load ae and the peiied load ombination ator to give Pu, M ux,and M uy. Determine the moment magniiation ator or the olumn moment. pply the moment magniiation ator to the atored moment. Determine whether the point, deined by the reulting axial load and biaxial moment et, lie within the interation volume. The atored moment and orreponding magniiation ator depend on the identiiation o the individual olumn a either way or non-way. The ollowing three etion deribe in detail the algorithm aoiated with the above-mentioned tep. Determine Fatored Moment and Fore The atored load or a partiular load ombination are obtained by applying the orreponding load ator to all the load ae, giving Pu, M ux,and M uy. The atored moment are urther inreaed or non-way olumn, i required, to obtain minimum eentriitie o ( h) inhe, where h i the dimenion o the olumn in the orreponding diretion (CI ). Determine Moment Magniiation Fator The moment magniiation ator are alulated eparately or way (overall tability eet), d and or non-way (individual olumn tability eet), d n. lo the moment magniiation ator in the major and minor diretion are in general dierent (CI 10.0, R10.13). Column Deign 29

36 ETBS Conrete Deign Manual The moment obtained rom analyi i eparated into two omponent: the way ( M ) and the non-way (M n ) omponent. The non-way omponent whih are identiied by n ubript are predominantly aued by gravity load. The way omponent are identiied by the ubript. The way moment are predominantly aued by lateral load, and are related to the aue o ide way. For individual olumn or olumn-member in a loor, the magniied moment about two axe at any tation o a olumn an be obtained a M = M n +d M. (CI ) The ator d i the moment magniiation ator or moment auing ide way. The moment magniiation ator or way moment, d, i taken a 1 beaue the omponent moment M and M n are obtained rom a eond order elati (P-D) analyi (CI R10.10, , R10.13, ). The program aume that a P-D analyi ha been perormed in ETBS and, thereore, moment magniiation ator d or moment auing ideway i taken a unity (CI ). For the P-D analyi the load hould orrepond to a load ombination o 1.4 dead load live load (CI ). See alo White and Hajjar (1991). The uer hould ue redution ator or the moment o inertia in ETBS a peiied in CI The moment o intertia redution or utained lateral load involve a ator b d (CI 10.11). Thi b d or way rame in eond-order analyi i dierent rom the one that i deined later or non-way moment magniiation (CI 10.0, R , R ). The deault moment o inertia ator in ETBS i 1. The omputed moment are urther ampliied or individual olumn tability eet (CI , ) by the nonway moment magniiation ator, d n,aollow: M =d M, where (CI ) n M i the atored moment to be ued in deign. The non-way moment magniiation ator, d n, aoiated with the major or minor diretion o the olumn i given by (CI ) d n = 1 - C m P u 0.75 P ³ 1.0, where (CI ) M a C m = ³ 0.4, (CI ) M b 30 Column Deign

37 Chapter III Deign or CI M a and M b are the moment at the end o the olumn, and M b i numerially larger than M a. M a M i poitive or ingle urvature bending and negative b or double urvature bending. The above expreion oc m i valid i there i no tranvere load applied between the upport. I tranvere load i preent on the pan, or the length i overwritten,c m =1. C m an be overwritten by the uer on an element by element bai. P = EI p 2 2 ( kl ) u, where (CI ) k i onervatively taken a 1, however ETBS allow the uer to override thi value (CI ), l u i the unupported length o the olumn or the diretion o bending onidered. The two unupported length are l 22 and l 33 orreponding to intability in the minor and major diretion o the element, repetively. See Figure II-7. Thee are the length between the upport point o the element in the orreponding diretion. EI i aoiated with a partiular olumn diretion: EI = 0.4 E I + 1 b d g, where (CI ) b d = maximum atored axial utained (dead) load maximum atored axial total load.(ci 10.0,R ) The magniiation ator, d n, mut be a poitive number and greater than one. Thereore P u mut be le than 0.75P.IP u i ound to be greater than or equal to 0.75P, a ailure ondition i delared. The above alulation are done or major and minor diretion eparately. That mean that d, d n,c m, k, l u, EI, and P aume dierent value or major and minor diretion o bending. I the program aumption are not atiatory or a partiular member, the uer an expliitly peiy value o d and d. Determine Capaity Ratio n a meaure o the tre ondition o the olumn, a apaity ratio i alulated. The apaity ratio i baially a ator that give an indiation o the tre ondition o the olumn with repet to the apaity o the olumn. Column Deign 31

38 ETBS Conrete Deign Manual Beore entering the interation diagram to hek the olumn apaity, the moment magniiation ator are applied to the atored load to obtain Pu, M ux,and M uy. The point (Pu, M ux, M uy) i then plaed in the interation pae hown a point L in Figure II-3. I the point lie within the interation volume, the olumn apaity i adequate; however, i the point lie outide the interation volume, the olumn i overtreed. Thi apaity ratio i ahieved by plotting the point L and determining the loation o point C. The point C i deined a the point where the line OL (i extended outward) will interet the ailure urae. Thi point i determined by threedimenional linear interpolation between the point that deine the ailure urae. See Figure II-3. The apaity ratio, CR, i given by the ratio OL OC. I OL = OC (or CR=1) the point lie on the interation urae and the olumn i treed to apaity. I OL < OC (or CR<1) the point lie within the interation volume and the olumn apaity i adequate. I OL > OC (or CR>1) the point lie outide the interation volume and the olumn i overtreed. The maximum o all the value o CR alulated rom eah load ombination i reported or eah hek tation o the olumn along with the ontrolling Pu, M ux,and M uy et and aoiated load ombination number. I the reinoring area i not deined, ETBS ompute the reinorement that will give an interation ratio o unity. Deign Column Shear Reinorement The hear reinorement i deigned or eah loading ombination in the major and minor diretion o the olumn. In deigning the hear reinoring or a partiular olumn or a partiular loading ombination due to hear ore in a partiular diretion, the ollowing tep are involved: Determine the atored ore ating on the etion, P u andv u. Note that P u i needed or the alulation o V. Determine the hear ore,v, that an be reited by onrete alone. Calulate the reinorement teel required to arry the balane. 32 Column Deign