EUROPEA STADARD ORE EUROPÉEE EUROPÄISCHE OR E 1993-1-1 a 005 ICS 91.010.30; 91.080.10 Supersedes EV 1993-1-1:199 English version Eurocode 3: Design of seel srucures - Par 1-1: General rules and rules for buildings Eurocode 3: Calcul des srucures en acier - Parie 1-1: Règles générales e règles pour les bâimens This European Sandard was approved b CE on 16 April 004. Eurocode 3: Bemessung und Konsrukion von Sahlbauen - Teil 1-1: Allgemeine Bemessungsregeln und Regeln für den Hochbau CE members are bound o compl wih he CE/CEELEC Inernal Regulaions which sipulae he condiions for giving his European Sandard he saus of a naional sandard wihou an aleraion. Up-o-dae liss and bibliographical references concerning such naional sandards ma be obained on applicaion o he Cenral Secrearia or o an CE member. This European Sandard exiss in hree official versions (English, French, German). A version in an oher language made b ranslaion under he responsibili of a CE member ino is own language and noified o he Cenral Secrearia has he same saus as he official versions. CE members are he naional sandards bodies of Ausria, Belgium, Cprus, Cech Republic, Denmark, Esonia, Finland, France, German, Greece, Hungar, Iceland, Ireland, Ial, Lavia, Lihuania, Luxembourg, ala, eherlands, orwa, Poland, Porugal, Slovakia, Slovenia, Spain, Sweden, Swierland and Unied Kingdom. EUROPEA COITTEE FOR STADARDIZATIO COITÉ EUROPÉE DE ORALISATIO EUROPÄISCHES KOITEE FÜR ORUG anagemen Cenre: rue de Sassar, 36 005 CE All righs of exploiaion in an form and b an means reserved worldwide for CE naional embers. B-1050 Brussels Ref. o. E 1993-1-1:005: E
E 1993-1-1: 005 (E) Conens Page 1 General... 9 1.1 Scope... 9 1. ormaive references... 10 1.3 Assumpions... 11 1.4 Disincion beween principles and applicaion rules... 11 1.5 Terms and definiions... 11 1.6 Smbols... 1 1.7 Convenions for member axes... 0 Basis of design....1 Requiremens....1.1 Basic requiremens....1. Reliabili managemen....1.3 Design working life, durabili and robusness.... Principles of limi sae design... 3.3 Basic variables... 3.3.1 Acions and environmenal influences... 3.3. aerial and produc properies... 3.4 Verificaion b he parial facor mehod... 3.4.1 Design values of maerial properies... 3.4. Design values of geomerical daa... 3.4.3 Design resisances... 4.4.4 Verificaion of saic equilibrium (EQU)... 4.5 Design assised b esing... 4 3 aerials... 5 3.1 General... 5 3. Srucural seel... 5 3..1 aerial properies... 5 3.. Ducili requiremens... 5 3..3 Fracure oughness... 5 3..4 Through-hickness properies... 7 3..5 Tolerances... 8 3..6 Design values of maerial coefficiens... 8 3.3 Connecing devices... 8 3.3.1 Faseners... 8 3.3. Welding consumables... 8 3.4 Oher prefabricaed producs in buildings... 8 4 Durabili... 8 5 Srucural analsis... 9 5.1 Srucural modelling for analsis... 9 5.1.1 Srucural modelling and basic assumpions... 9
E 1993-1-1: 005 (E) 5.1. Join modelling... 9 5.1.3 Ground-srucure ineracion...9 5. Global analsis... 30 5..1 Effecs of deformed geomer of he srucure... 30 5.. Srucural sabili of frames... 31 5.3 Imperfecions... 3 5.3.1 Basis... 3 5.3. Imperfecions for global analsis of frames... 33 5.3.3 Imperfecion for analsis of bracing ssems... 36 5.3.4 ember imperfecions... 38 5.4 ehods of analsis considering maerial non-lineariies... 38 5.4.1 General... 38 5.4. Elasic global analsis... 39 5.4.3 Plasic global analsis... 39 5.5 Classificaion of cross secions... 40 5.5.1 Basis... 40 5.5. Classificaion... 40 5.6 Cross-secion requiremens for plasic global analsis... 41 6 Ulimae limi saes... 45 6.1 General... 45 6. Resisance of cross-secions... 45 6..1 General... 45 6.. Secion properies... 46 6..3 Tension... 49 6..4 Compression... 49 6..5 Bending momen... 50 6..6 Shear... 50 6..7 Torsion... 5 6..8 Bending and shear... 53 6..9 Bending and axial force... 54 6..10 Bending, shear and axial force... 56 6.3 Buckling resisance of members... 56 6.3.1 Uniform members in compression... 56 6.3. Uniform members in bending... 60 6.3.3 Uniform members in bending and axial compression... 64 6.3.4 General mehod for laeral and laeral orsional buckling of srucural componens... 65 6.3.5 Laeral orsional buckling of members wih plasic hinges... 67 6.4 Uniform buil-up compression members... 69 6.4.1 General... 69 6.4. Laced compression members... 71 6.4.3 Baened compression members... 7 6.4.4 Closel spaced buil-up members... 74 7 Serviceabili limi saes... 75 7.1 General... 75 7. Serviceabili limi saes for buildings... 75 7..1 Verical deflecions... 75 7.. Horional deflecions... 75 7..3 Dnamic effecs... 75 Annex A [informaive] ehod 1: Ineracion facors k ij for ineracion formula in 6.3.3(4)... 76 3
E 1993-1-1: 005 (E) Annex B [informaive] ehod : Ineracion facors k ij for ineracion formula in 6.3.3(4)... 79 Annex AB [informaive] Addiional design provisions...81 Annex BB [informaive] Buckling of componens of building srucures... 8 4
Foreword E 1993-1-1: 005 (E) This European Sandard E 1993, Eurocode 3: Design of seel srucures, has been prepared b Technical Commiee CE/TC50 «Srucural Eurocodes», he Secrearia of which is held b BSI. CE/TC50 is responsible for all Srucural Eurocodes. This European Sandard shall be given he saus of a aional Sandard, eiher b publicaion of an idenical ex or b endorsemen, a he laes b ovember 005, and conflicing aional Sandards shall be wihdrawn a laes b arch 010. This Eurocode supersedes EV 1993-1-1. According o he CE-CEELEC Inernal Regulaions, he aional Sandard Organiaions of he following counries are bound o implemen hese European Sandard: Ausria, Belgium, Cprus, Cech Republic, Denmark, Esonia, Finland, France, German, Greece, Hungar, Iceland, Ireland, Ial, Lavia, Lihuania, Luxembourg, ala, eherlands, orwa, Poland, Porugal, Slovakia, Slovenia, Spain, Sweden, Swierland and Unied Kingdom. Background of he Eurocode programme In 1975, he Commission of he European Communi decided on an acion programme in he field of consrucion, based on aricle 95 of he Trea. The objecive of he programme was he eliminaion of echnical obsacles o rade and he harmoniaion of echnical specificaions. Wihin his acion programme, he Commission ook he iniiaive o esablish a se of harmonied echnical rules for he design of consrucion works which, in a firs sage, would serve as an alernaive o he naional rules in force in he ember Saes and, ulimael, would replace hem. For fifeen ears, he Commission, wih he help of a Seering Commiee wih Represenaives of ember Saes, conduced he developmen of he Eurocodes programme, which led o he firs generaion of European codes in he 1980s. In 1989, he Commission and he ember Saes of he EU and EFTA decided, on he basis of an agreemen 1 beween he Commission and CE, o ransfer he preparaion and he publicaion of he Eurocodes o he CE hrough a series of andaes, in order o provide hem wih a fuure saus of European Sandard (E). This links de faco he Eurocodes wih he provisions of all he Council s Direcives and/or Commission s Decisions dealing wih European sandards (e.g. he Council Direcive 89/106/EEC on consrucion producs CPD and Council Direcives 93/37/EEC, 9/50/EEC and 89/440/EEC on public works and services and equivalen EFTA Direcives iniiaed in pursui of seing up he inernal marke). The Srucural Eurocode programme comprises he following sandards generall consising of a number of Pars: E 1990 Eurocode: Basis of srucural design E 1991 Eurocode 1: Acions on srucures E 199 Eurocode : Design of concree srucures E 1993 Eurocode 3: Design of seel srucures E 1994 Eurocode 4: Design of composie seel and concree srucures E 1995 Eurocode 5: Design of imber srucures E 1996 Eurocode 6: Design of masonr srucures E 1997 Eurocode 7: Geoechnical design E 1998 Eurocode 8: Design of srucures for earhquake resisance 1 Agreemen beween he Commission of he European Communiies and he European Commiee for Sandardisaion (CE) concerning he work on EUROCODES for he design of building and civil engineering works (BC/CE/03/89). 5
E 1993-1-1: 005 (E) E 1999 Eurocode 9: Design of aluminium srucures Eurocode sandards recognie he responsibili of regulaor auhoriies in each ember Sae and have safeguarded heir righ o deermine values relaed o regulaor safe maers a naional level where hese coninue o var from Sae o Sae. Saus and field of applicaion of Eurocodes The ember Saes of he EU and EFTA recognie ha Eurocodes serve as reference documens for he following purposes : as a means o prove compliance of building and civil engineering works wih he essenial requiremens of Council Direcive 89/106/EEC, paricularl Essenial Requiremen 1 - echanical resisance and sabili - and Essenial Requiremen - Safe in case of fire; as a basis for specifing conracs for consrucion works and relaed engineering services; as a framework for drawing up harmonied echnical specificaions for consrucion producs (Es and ETAs) The Eurocodes, as far as he concern he consrucion works hemselves, have a direc relaionship wih he Inerpreaive Documens referred o in Aricle 1 of he CPD, alhough he are of a differen naure from harmonied produc sandard 3. Therefore, echnical aspecs arising from he Eurocodes work need o be adequael considered b CE Technical Commiees and/or EOTA Working Groups working on produc sandards wih a view o achieving a full compaibili of hese echnical specificaions wih he Eurocodes. The Eurocode sandards provide common srucural design rules for everda use for he design of whole srucures and componen producs of boh a radiional and an innovaive naure. Unusual forms of consrucion or design condiions are no specificall covered and addiional exper consideraion will be required b he designer in such cases. aional Sandards implemening Eurocodes The aional Sandards implemening Eurocodes will comprise he full ex of he Eurocode (including an annexes), as published b CE, which ma be preceded b a aional ile page and aional foreword, and ma be followed b a aional annex (informaive). The aional Annex (informaive) ma onl conain informaion on hose parameers which are lef open in he Eurocode for naional choice, known as aionall Deermined Parameers, o be used for he design of buildings and civil engineering works o be consruced in he counr concerned, i.e. : values for parial facors and/or classes where alernaives are given in he Eurocode, values o be used where a smbol onl is given in he Eurocode, geographical and climaic daa specific o he ember Sae, e.g. snow map, he procedure o be used where alernaive procedures are given in he Eurocode, references o non-conradicor complemenar informaion o assis he user o appl he Eurocode. Links beween Eurocodes and produc harmonied echnical specificaions (Es According o Ar. 3.3 of he CPD, he essenial requiremens (ERs) shall be given concree form in inerpreaive documens for he creaion of he necessar links beween he essenial requiremens and he mandaes for hes and ETAGs/ETAs. 3 According o Ar. 1 of he CPD he inerpreaive documens shall : a) give concree form o he essenial requiremens b harmoniing he erminolog and he echnical bases and indicaing classes or levels for each requiremen where necessar ; b) indicae mehods of correlaing hese classes or levels of requiremen wih he echnical specificaions, e.g. mehods of calculaion and of proof, echnical rules for projec design, ec. ; c) serve as a reference for he esablishmen of harmonied sandards and guidelines for European echnical approvals. The Eurocodes, de faco, pla a similar role in he field of he ER 1 and a par of ER. 6
and ETAs) E 1993-1-1: 005 (E) There is a need for consisenc beween he harmonied echnical specificaions for consrucion producs and he echnical rules for works 4. Furhermore, all he informaion accompaning he CE arking of he consrucion producs which refer o Eurocodes should clearl menion which aionall Deermined Parameers have been aken ino accoun. Addiional informaion specific o E 1993-1 E 1993 is inended o be used wih Eurocodes E 1990 Basis of Srucural Design, E 1991 Acions on srucures and E 199 o E 1999, when seel srucures or seel componens are referred o. E 1993-1 is he firs of six pars of E 1993 Design of Seel Srucures. I gives generic design rules inended o be used wih he oher pars E 1993- o E 1993-6. I also gives supplemenar rules applicable onl o buildings. E 1993-1 comprises welve subpars E 1993-1-1 o E 1993-1-1 each addressing specific seel componens, limi saes or maerials. I ma also be used for design cases no covered b he Eurocodes (oher srucures, oher acions, oher maerials) serving as a reference documen for oher CE TC s concerning srucural maers. E 1993-1 is inended for use b commiees drafing design relaed produc, esing and execuion sandards, cliens (e.g. for he formulaion of heir specific requiremens) designers and consrucors relevan auhoriies umerical values for parial facors and oher reliabili parameers are recommended as basic values ha provide an accepable level of reliabili. The have been seleced assuming ha an appropriae level of workmanship and quali managemen applies. 4 See Ar.3.3 and Ar.1 of he CPD, as well as clauses 4., 4.3.1, 4.3. and 5. of ID 1. 7
E 1993-1-1: 005 (E) aional annex for E 1993-1-1 This sandard gives values wih noes indicaing where naional choices ma have o be made. Therefore he aional Sandard implemening E 1993-1 should have a aional Annex conaining all aionall Deermined Parameers o be used for he design of seel srucures o be consruced in he relevan counr. aional choice is allowed in E 1993-1-1 hrough he following clauses:.3.1(1) 3.1() 3..1(1) 3..(1) 3..3(1) 3..3(3)B 3..4(1)B 5..1(3) 5..(8) 5.3.(3) 5.3.(11) 5.3.4(3) 6.1(1) 6.1(1)B 6.3..() 6.3..3(1) 6.3..3() 6.3..4(1)B 6.3..4()B 6.3.3(5) 6.3.4(1) 7..1(1)B 7..(1)B 7..3(1)B BB.1.3(3)B 8
E 1993-1-1: 005 (E) 1 General 1.1 Scope 1.1.1 Scope of Eurocode 3 (1) Eurocode 3 applies o he design of buildings and civil engineering works in seel. I complies wih he principles and requiremens for he safe and serviceabili of srucures, he basis of heir design and verificaion ha are given in E 1990 Basis of srucural design. () Eurocode 3 is concerned onl wih requiremens for resisance, serviceabili, durabili and fire resisance of seel srucures. Oher requiremens, e.g. concerning hermal or sound insulaion, are no covered. (3) Eurocode 3 is inended o be used in conjuncion wih: E 1990 Basis of srucural design E 1991 Acions on srucures Es, ETAGs and ETAs for consrucion producs relevan for seel srucures E 1090 Execuion of Seel Srucures Technical requiremens E 199 o E 1999 when seel srucures or seel componens are referred o (4) Eurocode 3 is subdivided in various pars: E 1993-1 Design of Seel Srucures : General rules and rules for buildings. E 1993- Design of Seel Srucures : Seel bridges. E 1993-3 Design of Seel Srucures : Towers, mass and chimnes. E 1993-4 Design of Seel Srucures : Silos, anks and pipelines. E 1993-5 Design of Seel Srucures : Piling. E 1993-6 Design of Seel Srucures : Crane supporing srucures. (5) E 1993- o E 1993-6 refer o he generic rules in E 1993-1. The rules in pars E 1993- o E 1993-6 supplemen he generic rules in E 1993-1. (6) E 1993-1 General rules and rules for buildings comprises: E 1993-1-1 E 1993-1- E 1993-1-3 E 1993-1-4 E 1993-1-5 E 1993-1-6 E 1993-1-7 E 1993-1-8 E 1993-1-9 Design of Seel Srucures : General rules and rules for buildings. Design of Seel Srucures : Srucural fire design. Design of Seel Srucures : Cold-formed hin gauge members and sheeing. Design of Seel Srucures : Sainless seels. Design of Seel Srucures : Plaed srucural elemens. Design of Seel Srucures : Srengh and sabili of shell srucures. Design of Seel Srucures : Srengh and sabili of planar plaed srucures ransversel loaded. Design of Seel Srucures : Design of joins. Design of Seel Srucures : Faigue srengh of seel srucures. E 1993-1-10 Design of Seel Srucures : Selecion of seel for fracure oughness and hrough-hickness properies. E 1993-1-11 Design of Seel Srucures : Design of srucures wih ension componens made of seel. E 1993-1-1 Design of Seel Srucures : Supplemenar rules for high srengh seel. 9
E 1993-1-1: 005 (E) 1.1. Scope of Par 1.1 of Eurocode 3 (1) E 1993-1-1 gives basic design rules for seel srucures wih maerial hicknesses 3 mm. I also gives supplemenar provisions for he srucural design of seel buildings. These supplemenar provisions are indicaed b he leer B afer he paragraph number, hus ( )B. OTE For cold formed hin gauge members and plae hicknesses < 3 mm see E 1993-1-3. () The following subjecs are deal wih in E 1993-1-1: Secion 1: General Secion : Basis of design Secion 3: aerials Secion 4: Durabili Secion 5: Srucural analsis Secion 6: Ulimae limi saes Secion 7: Serviceabili limi saes (3) Secions 1 o provide addiional clauses o hose given in E 1990 Basis of srucural design. (4) Secion 3 deals wih maerial properies of producs made of low allo srucural seels. (5) Secion 4 gives general rules for durabili. (6) Secion 5 refers o he srucural analsis of srucures, in which he members can be modelled wih sufficien accurac as line elemens for global analsis. (7) Secion 6 gives deailed rules for he design of cross secions and members. (8) Secion 7 gives rules for serviceabili. 1. ormaive references This European Sandard incorporaes b daed or undaed reference, provisions from oher publicaions. These normaive references are cied a he appropriae places in he ex and he publicaions are lised hereafer. For daed references, subsequen amendmens o or revisions of an of hese publicaions appl o his European Sandard onl when incorporaed in i b amendmen or revision. For undaed references he laes ediion of he publicaion referred o applies (including amendmens). 1..1 General reference sandards E 1090 E ISO 1944 E 1461 Execuion of seel srucures Technical requiremens Pains and varnishes Corrosion proecion of seel srucures b proecive pain ssems Ho dip galvanied coaings on fabricaed iron and seel aricles specificaions and es mehods 1.. Weldable srucural seel reference sandards E 1005-1:004 E 1005-:004 Ho-rolled producs of srucural seels - Par 1: General deliver condiions. Ho-rolled producs of srucural seels - Par : Technical deliver condiions for nonallo srucural seels. E 1005-3:004 Ho-rolled producs of srucural seels - Par 3: Technical deliver condiions for normalied / normalied rolled weldable fine grain srucural seels. 10
E 1993-1-1: 005 (E) E 1005-4:004 Ho-rolled producs of srucural seels - Par 4: Technical deliver condiions for hermomechanical rolled weldable fine grain srucural seels. E 1005-5:004 Ho-rolled producs of srucural seels - Par 5: Technical deliver condiions for srucural seels wih improved amospheric corrosion resisance. E 1005-6:004 E 10164:1993 Ho-rolled producs of srucural seels - Par 6: Technical deliver condiions for fla producs of high ield srengh srucural seels in he quenched and empered condiion. Seel producs wih improved deformaion properies perpendicular o he surface of he produc - Technical deliver condiions. E 1010-1:1994 Ho finished srucural hollow secions of non-allo and fine grain srucural seels Par 1: Technical deliver requiremens. E 1019-1:1997 Cold formed hollow secions of srucural seel - Par 1: Technical deliver requiremens. 1.3 Assumpions (1) In addiion o he general assumpions of E 1990 he following assumpions appl: fabricaion and erecion complies wih E 1090 1.4 Disincion beween principles and applicaion rules (1) The rules in E 1990 clause 1.4 appl. 1.5 Terms and definiions (1) The rules in E 1990 clause 1.5 appl. () The following erms and definiions are used in E 1993-1-1 wih he following meanings: 1.5.1 frame he whole or a porion of a srucure, comprising an assembl of direcl conneced srucural elemens, designed o ac ogeher o resis load; his erm refers o boh momen-resising frames and riangulaed frames; i covers boh plane frames and hree-dimensional frames 1.5. sub-frame a frame ha forms par of a larger frame, bu is be reaed as an isolaed frame in a srucural analsis 1.5.3 pe of framing erms used o disinguish beween frames ha are eiher: semi-coninuous, in which he srucural properies of he members and joins need explici consideraion in he global analsis coninuous, in which onl he srucural properies of he members need be considered in he global analsis simple, in which he joins are no required o resis momens 1.5.4 global analsis he deerminaion of a consisen se of inernal forces and momens in a srucure, which are in equilibrium wih a paricular se of acions on he srucure 11
E 1993-1-1: 005 (E) 1.5.5 ssem lengh disance in a given plane beween wo adjacen poins a which a member is braced agains laeral displacemen in his plane, or beween one such poin and he end of he member 1.5.6 buckling lengh ssem lengh of an oherwise similar member wih pinned ends, which has he same buckling resisance as a given member or segmen of member 1.5.7 shear lag effec non-uniform sress disribuion in wide flanges due o shear deformaion; i is aken ino accoun b using a reduced effecive flange widh in safe assessmens 1.5.8 capaci design design mehod for achieving he plasic deformaion capaci of a member b providing addiional srengh in is connecions and in oher pars conneced o i 1.5.9 uniform member member wih a consan cross-secion along is whole lengh 1.6 Smbols (1) For he purpose of his sandard he following smbols appl. () Addiional smbols are defined where he firs occur. Secion 1 x-x - - u-u v-v b h d w f r r 1 r Secion P k G k 1 OTE Smbols are ordered b appearance in E 1993-1-1. Smbols ma have various meanings. axis along a member axis of a cross-secion axis of a cross-secion major principal axis (where his does no coincide wih he - axis) minor principal axis (where his does no coincide wih he - axis) widh of a cross secion deph of a cross secion deph of sraigh porion of a web web hickness flange hickness radius of roo fille radius of roo fille oe radius hickness nominal value of he effec of presressing imposed during erecion nominal value of he effec of permanen acions
X K X n R d R k γ γ i γ f η a d Secion 3 f f u R eh R m A 0 ε ε u Z Z Rd E G ν α Secion 5 α cr F F cr H V characerisic values of maerial proper nominal values of maerial proper design value of resisance characerisic value of resisance general parial facor paricular parial facor parial facor for faigue conversion facor design value of geomerical daa ield srengh ulimae srengh ield srengh o produc sandards ulimae srengh o produc sandards original cross-secion area ield srain ulimae srain E 1993-1-1: 005 (E) required design Z-value resuling from he magniude of srains from resrained meal shrinkage under he weld beads. available design Z-value modulus of elasici shear modulus Poisson s raio in elasic sage coefficien of linear hermal expansion facor b which he design loads would have o be increased o cause elasic insabili in a global mode design loading on he srucure elasic criical buckling load for global insabili mode based on iniial elasic siffnesses design value of he horional reacion a he boom of he sore o he horional loads and ficiious horional loads oal design verical load on he srucure on he boom of he sore δ H, horional displacemen a he op of he sore, relaive o he boom of he sore h λ φ φ 0 α h h sore heigh non dimensional slenderness design value of he axial force global iniial swa imperfecion basic value for global iniial swa imperfecion reducion facor for heigh h applicable o columns heigh of he srucure 13
E 1993-1-1: 005 (E) α m m e 0 L η ini η cr e 0,d reducion facor for he number of columns in a row number of columns in a row maximum ampliude of a member imperfecion member lengh ampliude of elasic criical buckling mode shape of elasic criical buckling mode design value of maximum ampliude of an imperfecion Rk characerisic momen resisance of he criical cross secion Rk characerisic resisance o normal force of he criical cross secion α imperfecion facor EI η bending momen due o η cr a he criical cross secion " cr χ reducion facor for he relevan buckling curve α ul,k minimum force amplifier o reach he characerisic resisance wihou aking buckling ino accoun α cr minimum force amplifier o reach he elasic criical buckling q equivalen force per uni lengh δ q q d in-plane deflecion of a bracing ssem equivalen design force per uni lengh design bending momen k facor for e 0,d ε srain σ sress σ com, maximum design compressive sress in an elemen l lengh ε coefficien depending on f c widh or deph of a par of a cross secion α porion of a par of a cross secion in compression ψ sress or srain raio k σ plae buckling coefficien d ouer diameer of circular ubular secions Secion 6 γ 0 γ 1 γ parial facor for resisance of cross-secions whaever he class is parial facor for resisance of members o insabili assessed b member checks parial facor for resisance of cross-secions in ension o fracure σ x, design value of he local longiudinal sress σ, design value of he local ransverse sress τ design value of he local shear sress design normal force, design bending momen, - axis, design bending momen, - axis Rd design values of he resisance o normal forces 14
,Rd design values of he resisance o bending momens, - axis,rd design values of he resisance o bending momens, - axis s p n d 0 e E 1993-1-1: 005 (E) saggered pich, he spacing of he cenres of wo consecuive holes in he chain measured parallel o he member axis spacing of he cenres of he same wo holes measured perpendicular o he member axis number of holes exending in an diagonal or ig-ag line progressivel across he member or par of he member diameer of hole shif of he cenroid of he effecive area A eff relaive o he cenre of gravi of he gross cross secion addiional momen from shif of he cenroid of he effecive area A eff relaive o he cenre of gravi of he gross cross secion A eff effecive area of a cross secion,rd design values of he resisance o ension forces pl,rd design plasic resisance o normal forces of he gross cross-secion u,rd design ulimae resisance o normal forces of he ne cross-secion a holes for faseners A ne ne area of a cross secion ne,rd design plasic resisance o normal forces of he ne cross-secion c,rd design resisance o normal forces of he cross-secion for uniform compression c,rd design resisance for bending abou one principal axis of a cross-secion W pl plasic secion modulus W el,min minimum elasic secion modulus W eff,min minimum effecive secion modulus A f area of he ension flange A f,ne ne area of he ension flange V design shear force V c,rd design shear resisance V pl,rd plasic design shear resisance A v η S I A w A f T T Rd shear area facor for shear area firs momen of area second momen of area area of a web area of one flange design value of oal orsional momens design resisance o orsional momens T, design value of inernal S. Venan orsion T w, design value of inernal warping orsion τ, design shear sresses due o S. Venan orsion τ w, design shear sresses due o warping orsion σ w, design direc sresses due o he bimomen B B bimomen V pl,t,rd reduced design plasic shear resisance making allowance for he presence of a orsional momen 15
E 1993-1-1: 005 (E) ρ reducion facor o deermine reduced design values of he resisance o bending momens making allowance for he presence of shear forces V,,Rd reduced design values of he resisance o bending momens making allowance for he presence of shear forces,,rd reduced design values of he resisance o bending momens making allowance for he presence of normal forces n a α β e, e, raio of design normal force o design plasic resisance o normal forces of he gross cross-secion raio of web area o gross area parameer inroducing he effec of biaxial bending parameer inroducing he effec of biaxial bending shif of he cenroid of he effecive area A eff relaive o he cenre of gravi of he gross cross secion (- axis) shif of he cenroid of he effecive area A eff relaive o he cenre of gravi of he gross cross secion (- axis) W eff,min minimum effecive secion modulus b,rd design buckling resisance of a compression member χ Φ reducion facor for relevan buckling mode value o deermine he reducion facor χ a 0, a, b, c, d class indexes for buckling curves cr i λ 1 λ T elasic criical force for he relevan buckling mode based on he gross cross secional properies radius of graion abou he relevan axis, deermined using he properies of he gross cross-secion slenderness value o deermine he relaive slenderness relaive slenderness for orsional or orsional-flexural buckling cr,tf elasic orsional-flexural buckling force cr,t elasic orsional buckling force b,rd design buckling resisance momen χ LT Φ LT α LT reducion facor for laeral-orsional buckling value o deermine he reducion facor χ LT imperfecion facor λ LT non dimensional slenderness for laeral orsional buckling cr elasic criical momen for laeral-orsional buckling λ LT,0 plaeau lengh of he laeral orsional buckling curves for rolled secions β correcion facor for he laeral orsional buckling curves for rolled secions χ LT,mod modified reducion facor for laeral-orsional buckling f k c ψ L c λ f i f I eff,f modificaion facor for χ LT correcion facor for momen disribuion raio of momens in segmen lengh beween laeral resrains equivalen compression flange slenderness radius of graion of compression flange abou he minor axis of he secion effecive second momen of area of compression flange abou he minor axis of he secion 16
A eff,f effecive area of compression flange A eff,w,c effecive area of compressed par of web λ c0 slenderness parameer k fl modificaion facor momens due o he shif of he cenroidal - axis momens due o he shif of he cenroidal - axis χ χ k k k k reducion facor due o flexural buckling (- axis) reducion facor due o flexural buckling (- axis) ineracion facor ineracion facor ineracion facor ineracion facor λ op global non dimensional slenderness of a srucural componen for ou-of-plane buckling χ op reducion facor for he non-dimensional slenderness λ op E 1993-1-1: 005 (E) α ul,k minimum load amplifier of he design loads o reach he characerisic resisance of he mos criical cross secion α cr,op minimum amplifier for he in plane design loads o reach he elasic criical resisance wih regard o laeral or laeral orsional buckling Rk characerisic value of resisance o compression,rk characerisic value of resisance o bending momens abou - axis,rk characerisic value of resisance o bending momens abou - axis Q m local force applied a each sabilied member a he plasic hinge locaions L sable sable lengh of segmen L ch h 0 a α i min A ch buckling lengh of chord disance of cenrelines of chords of a buil-up column disance beween resrains of chords angle beween axes of chord and lacings minimum radius of graion of single angles area of one chord of a buil-up column ch, design chord force in he middle of a buil-up member I design value of he maximum momen in he middle of he buil-up member I eff S v n A d d A V I ch I b effecive second momen of area of he buil-up member shear siffness of buil-up member from he lacings or baened panel number of planes of lacings area of one diagonal of a buil-up column lengh of a diagonal of a buil-up column area of one pos (or ransverse elemen) of a buil-up column in plane second momen of area of a chord in plane second momen of area of a baen µ efficienc facor 17
E 1993-1-1: 005 (E) i Annex A C m C m radius of graion (- axis) equivalen uniform momen facor equivalen uniform momen facor C mlt equivalen uniform momen facor µ facor µ facor cr, elasic flexural buckling force abou he - axis cr, elasic flexural buckling force abou he - axis C C C C w w n pl facor facor facor facor facor facor facor λ max maximum of λ and b LT c LT d LT e LT ψ facor facor facor facor C m,0 facor C m,0 facor a LT I T I raio of end momens (- axis) facor λ S. Venan orsional consan second momen of area abou - axis i, (x) maximum firs order momen δ x maximum member displacemen along he member Annex B α s α h C m facor facor Annex AB γ G G k γ Q Q k equivalen uniform momen facor parial facor for permanen loads characerisic value of permanen loads parial facor for variable loads characerisic value of variable loads 18
Annex BB λ eff,v effecive slenderness raio for buckling abou v-v axis λ eff, effecive slenderness raio for buckling abou - axis λ eff, effecive slenderness raio for buckling abou - axis L L cr S I w C ϑ,k K υ K ϑ ssem lengh buckling lengh shear siffness provided b sheeing warping consan roaional siffness provided b sabiliing coninuum and connecions facor for considering he pe of analsis facor for considering he momen disribuion and he pe of resrain E 1993-1-1: 005 (E) C ϑr,k roaional siffness provided b he sabiliing coninuum o he beam assuming a siff connecion o he member C ϑc,k roaional siffness of he connecion beween he beam and he sabiliing coninuum C ϑd,k roaional siffness deduced from an analsis of he disorsional deformaions of he beam cross secions L m L k L s C 1 C m C n a B 0 B 1 B η i s β R 1 R R 3 R 4 R 5 sable lengh beween adjacen laeral resrains sable lengh beween adjacen orsional resrains sable lengh beween a plasic hinge locaion and an adjacen orsional resrain modificaion facor for momen disribuion modificaion facor for linear momen gradien modificaion facor for non-linear momen gradien disance beween he cenroid of he member wih he plasic hinge and he cenroid of he resrain members facor facor facor raio of criical values of axial forces radius of graion relaed o cenroid of resraining member raio of he algebraicall smaller end momen o he larger end momen momen a a specific locaion of a member momen a a specific locaion of a member momen a a specific locaion of a member momen a a specific locaion of a member momen a a specific locaion of a member R E maximum of R 1 or R 5 R s c h h maximum value of bending momen anwhere in he lengh L aper facor addiional deph of he haunch or aper h max maximum deph of cross-secion wihin he lengh L h min minimum deph of cross-secion wihin he lengh L 19
E 1993-1-1: 005 (E) h s L h L verical deph of he un-haunched secion lengh of haunch wihin he lengh L lengh beween resrains 1.7 Convenions for member axes (1) The convenion for member axes is: x-x - - - along he member - axis of he cross-secion - axis of he cross-secion () For seel members, he convenions used for cross-secion axes are: generall: - - - cross-secion axis parallel o he flanges - cross-secion axis perpendicular o he flanges for angle secions: - - - axis parallel o he smaller leg - axis perpendicular o he smaller leg where necessar: u-u v-v - major principal axis (where his does no coincide wih he axis) - minor principal axis (where his does no coincide wih he axis) (3) The smbols used for dimensions and axes of rolled seel secions are indicaed in Figure 1.1. (4) The convenion used for subscrips ha indicae axes for momens is: "Use he axis abou which he momen acs." OTE All rules in his Eurocode relae o principal axis properies, which are generall defined b he axes - and - bu for secions such as angles are defined b he axes u-u and v-v. 0
E 1993-1-1: 005 (E) Figure 1.1: Dimensions and axes of secions 1
E 1993-1-1: 005 (E) Basis of design.1 Requiremens.1.1 Basic requiremens (1)P The design of seel srucures shall be in accordance wih he general rules given in E 1990. () The supplemenar provisions for seel srucures given in his secion should also be applied. (3) The basic requiremens of E 1990 secion should be deemed be saisfied where limi sae design is used in conjuncion wih he parial facor mehod and he load combinaions given in E 1990 ogeher wih he acions given in E 1991. (4) The rules for resisances, serviceabili and durabili given in he various pars of E 1993 should be applied..1. Reliabili managemen (1) Where differen levels of reliabili are required, hese levels should preferabl be achieved b an appropriae choice of quali managemen in design and execuion, according o E 1990 Annex C and E 1090..1.3 Design working life, durabili and robusness.1.3.1 General (1) Depending upon he pe of acion affecing durabili and he design working life (see E 1990) seel srucures should be designed agains corrosion b means of suiable surface proecion (see E ISO 1944) he use of weahering seel he use of sainless seel (see E 1993-1-4) deailed for sufficien faigue life (see E 1993-1-9) designed for wearing designed for accidenal acions (see E 1991-1-7) inspeced and mainained..1.3. Design working life for buildings (1)B The design working life should be aken as he period for which a building srucure is expeced o be used for is inended purpose. ()B For he specificaion of he inended design working life of a permanen building see Table.1 of E 1990. (3)B For srucural elemens ha canno be designed for he oal design life of he building, see.1.3.3(3)b..1.3.3 Durabili for buildings (1)B To ensure durabili, buildings and heir componens should eiher be designed for environmenal acions and faigue if relevan or else proeced from hem.
E 1993-1-1: 005 (E) ()B The effecs of deerioraion of maerial, corrosion or faigue where relevan should be aken ino accoun b appropriae choice of maerial, see E 1993-1-4 and E 1993-1-10, and deails, see E 1993-1-9, or b srucural redundanc and b he choice of an appropriae corrosion proecion ssem. (3)B If a building includes componens ha need o be replaceable (e.g. bearings in ones of soil selemen), he possibili of heir safe replacemen should be verified as a ransien design siuaion.. Principles of limi sae design (1) The resisance of cross-secions and members specified in his Eurocode 3 for he ulimae limi saes as defined in E 1990, 3.3 are based on ess in which he maerial exhibied sufficien ducili o appl simplified design models. () The resisances specified in his Eurocode Par ma herefore be used where he condiions for maerials in secion 3 are me..3 Basic variables.3.1 Acions and environmenal influences (1) Acions for he design of seel srucures should be aken from E 1991. For he combinaion of acions and parial facors of acions see Annex A o E 1990. OTE 1 The aional Annex ma define acions for paricular regional or climaic or accidenal siuaions. OTE B For proporional loading for incremenal approach, see Annex AB.1. OTE 3B For simplified load arrangemen, see Annex AB.. () The acions o be considered in he erecion sage should be obained from E 1991-1-6. (3) Where he effecs of prediced absolue and differenial selemens need o be considered, bes esimaes of imposed deformaions should be used. (4) The effecs of uneven selemens or imposed deformaions or oher forms of presressing imposed during erecion should be aken ino accoun b heir nominal value P k as permanen acions and grouped wih oher permanen acions G k from a single acion (G k + P k ). (5) Faigue acions no defined in E 1991 should be deermined according o Annex A of E 1993-1-9..3. aerial and produc properies (1) aerial properies for seels and oher consrucion producs and he geomerical daa o be used for design should be hose specified in he relevan Es, ETAGs or ETAs unless oherwise indicaed in his sandard..4 Verificaion b he parial facor mehod.4.1 Design values of maerial properies (1) For he design of seel srucures characerisic values X K or nominal values X n of maerial properies should be used as indicaed in his Eurocode..4. Design values of geomerical daa (1) Geomerical daa for cross-secions and ssems ma be aken from produc sandards he or drawings for he execuion o E 1090 and reaed as nominal values. 3
E 1993-1-1: 005 (E) () Design values of geomerical imperfecions specified in his sandard are equivalen geomeric imperfecions ha ake ino accoun he effecs of: geomerical imperfecions of members as governed b geomerical olerances in produc sandards or he execuion sandard; srucural imperfecions due o fabricaion and erecion; residual sresses; variaion of he ield srengh..4.3 Design resisances (1) For seel srucures equaion (6.6c) or equaion (6.6d) of E 1990 applies: R R 1 k d = = R k ( η1x k1; ηix ki; a d ) (.1) γ γ where R k is he characerisic value of he paricular resisance deermined wih characerisic or nominal values for he maerial properies and dimensions γ is he global parial facor for he paricular resisance OTE For he definiions of η 1, η i, X k1, X ki and a d see E 1990..4.4 Verificaion of saic equilibrium (EQU) (1) The reliabili forma for he verificaion of saic equilibrium in Table 1. (A) in Annex A of E 1990 also applies o design siuaions equivalen o (EQU), e.g. for he design of holding down anchors or he verificaion of uplif of bearings of coninuous beams..5 Design assised b esing (1) The resisances R k in his sandard have been deermined using Annex D of E 1990. () In recommending classes of consan parial facors γ i he characerisic values R k were obained from R k = R d γ i (.) where R d are design values according o Annex D of E 1990 γ i are recommended parial facors. OTE 1 The numerical values of he recommended parial facors γ i have been deermined such ha R k represens approximael he 5 %-fracile for an infinie number of ess. OTE For characerisic values of faigue srengh and parial facors γ f for faigue see E 1993-1-9. OTE 3 For characerisic values of oughness resisance and safe elemens for he oughness verificaion see E 1993-1-10. (3) Where resisances R k for prefabricaed producs should be deermined from ess, he procedure in () should be followed. 4
E 1993-1-1: 005 (E) 3 aerials 3.1 General (1) The nominal values of maerial properies given in his secion should be adoped as characerisic values in design calculaions. () This Par of E 1993 covers he design of seel srucures fabricaed from seel maerial conforming o he seel grades lised in Table 3.1. OTE For oher seel maerial and producs see aional Annex. 3. Srucural seel 3..1 aerial properies (1) The nominal values of he ield srengh f and he ulimae srengh f u for srucural seel should be obained a) eiher b adoping he values f = R eh and f u = R m direc from he produc sandard b) or b using he simplificaion given in Table 3.1 OTE The aional Annex ma give he choice. 3.. Ducili requiremens (1) For seels a minimum ducili is required ha should be expressed in erms of limis for: he raio f u / f of he specified minimum ulimae ensile srengh f u o he specified minimum ield srengh f ; he elongaion a failure on a gauge lengh of 5,65 A o (where A 0 is he original cross-secional area); he ulimae srain ε u, where ε u corresponds o he ulimae srengh f u. OTE The limiing values of he raio f u / f, he elongaion a failure and he ulimae srain ε u ma be defined in he aional Annex. The following values are recommended: f u / f 1,10; elongaion a failure no less han 15%; ε u 15ε, where ε is he ield srain (ε = f / E). () Seel conforming wih one of he seel grades lised in Table 3.1 should be acceped as saisfing hese requiremens. 3..3 Fracure oughness (1) The maerial should have sufficien fracure oughness o avoid brile fracure of ension elemens a he lowes service emperaure expeced o occur wihin he inended design life of he srucure. OTE The lowes service emperaure o be adoped in design ma be given in he aional Annex. () o furher check agains brile fracure need o be made if he condiions given in E 1993-1-10 are saisfied for he lowes emperaure. 5
E 1993-1-1: 005 (E) (3)B For building componens under compression a minimum oughness proper should be seleced. OTE B The aional Annex ma give informaion on he selecion of oughness properies for members in compression. The use of Table.1 of E 1993-1-10 for σ = 0,5 f () is recommended. (4) For selecing seels for members wih ho dip galvanied coaings see E 1461. Table 3.1: ominal values of ield srengh f and ulimae ensile srengh f u for ho rolled srucural seel Sandard and seel grade E 1005-40 mm ominal hickness of he elemen [mm] 40 mm < 80 mm f [/mm ] f u [/mm ] f [/mm ] f u [/mm ] S 35 35 360 15 360 S 75 75 430 55 410 S 355 355 510 335 470 S 450 440 550 410 550 E 1005-3 S 75 /L 75 390 55 370 S 355 /L 355 490 335 470 S 40 /L 40 50 390 50 S 460 /L 460 540 430 540 E 1005-4 S 75 /L 75 370 55 360 S 355 /L 355 470 335 450 S 40 /L 40 50 390 500 S 460 /L 460 540 430 530 E 1005-5 S 35 W 35 360 15 340 S 355 W 355 510 335 490 E 1005-6 S 460 Q/QL/QL1 460 570 440 550 6
E 1993-1-1: 005 (E) Table 3.1 (coninued): ominal values of ield srengh f and ulimae ensile srengh f u for srucural hollow secions Sandard and seel grade E 1010-1 40 mm ominal hickness of he elemen [mm] 40 mm < 80 mm f [/mm ] f u [/mm ] f [/mm ] f u [/mm ] S 35 H 35 360 15 340 S 75 H 75 430 55 410 S 355 H 355 510 335 490 S 75 H/LH 75 390 55 370 S 355 H/LH 355 490 335 470 S 40 H/HL 40 540 390 50 S 460 H/LH 460 560 430 550 E 1019-1 S 35 H 35 360 S 75 H 75 430 S 355 H 355 510 S 75 H/LH 75 370 S 355 H/LH 355 470 S 460 H/LH 460 550 S 75 H/LH 75 360 S 355 H/LH 355 470 S 40 H/LH 40 500 S 460 H/LH 460 530 3..4 Through-hickness properies (1) Where seel wih improved hrough-hickness properies is necessar according o E 1993-1-10, seel according o he required quali class in E 10164 should be used. OTE 1 Guidance on he choice of hrough-hickness properies is given in E 1993-1-10. OTE B Paricular care should be given o welded beam o column connecions and welded end plaes wih ension in he hrough-hickness direcion. OTE 3B The aional Annex ma give he relevan allocaion of arge values Z according o 3.() of E 1993-1-10 o he quali class in E 10164. The allocaion in Table 3. is recommended for buildings: Table 3.: Choice of quali class according o E 10164 Targe value of Z according o E 1993-1-10 Required value of Z Rd expressed in erms of design Z-values according o E 10164 Z 10 10 < Z 0 Z 15 0 < Z 30 Z 5 Z > 30 Z 35 7
E 1993-1-1: 005 (E) 3..5 Tolerances (1) The dimensional and mass olerances of rolled seel secions, srucural hollow secions and plaes should conform wih he relevan produc sandard, ETAG or ETA unless more severe olerances are specified. () For welded componens he olerances given in E 1090 should be applied. (3) For srucural analsis and design he nominal values of dimensions should be used. 3..6 Design values of maerial coefficiens (1) The maerial coefficiens o be adoped in calculaions for he srucural seels covered b his Eurocode Par should be aken as follows: modulus of elasici E = 10 000 / mm E shear modulus G = 81 000 / mm² (1 + ν) Poisson s raio in elasic sage ν = 0, 3 6 coefficien of linear hermal expansion α = 1 10 perk (for T 100 C) OTE For calculaing he srucural effecs of unequal emperaures in composie concree-seel 6 srucures o E 1994 he coefficien of linear hermal expansion is aken as α = 10 10 per K. 3.3 Connecing devices 3.3.1 Faseners (1) Requiremens for faseners are given in E 1993-1-8. 3.3. Welding consumables (1) Requiremens for welding consumables are given in E 1993-1-8. 3.4 Oher prefabricaed producs in buildings (1)B An semi-finished or finished srucural produc used in he srucural design of buildings should compl wih he relevan E Produc Sandard or ETAG or ETA. 4 Durabili (1) The basic requiremens for durabili are se ou in E 1990. () The means of execuing he proecive reamen underaken off-sie and on-sie should be in accordance wih E 1090. OTE E 1090 liss he facors affecing execuion ha need o be specified during design. (3) Pars suscepible o corrosion, mechanical wear or faigue should be designed such ha inspecion, mainenance and reconsrucion can be carried ou saisfacoril and access is available for in-service inspecion and mainenance. 8
(4)B For building srucures no faigue assessmen is normall required excep as follows: a) embers supporing lifing appliances or rolling loads b) embers subjec o repeaed sress ccles from vibraing machiner c) embers subjec o wind-induced vibraions d) embers subjec o crowd-induced oscillaions E 1993-1-1: 005 (E) (5) For elemens ha canno be inspeced an appropriae corrosion allowance should be included. (6)B Corrosion proecion does no need o be applied o inernal building srucures, if he inernal relaive humidi does no exceed 80%. 5 Srucural analsis 5.1 Srucural modelling for analsis 5.1.1 Srucural modelling and basic assumpions (1) Analsis should be based upon calculaion models of he srucure ha are appropriae for he limi sae under consideraion. () The calculaion model and basic assumpions for he calculaions should reflec he srucural behaviour a he relevan limi sae wih appropriae accurac and reflec he anicipaed pe of behaviour of he cross secions, members, joins and bearings. (3) The mehod used for he analsis should be consisen wih he design assumpions. (4)B For he srucural modelling and basic assumpions for componens of buildings see also E 1993-1-5 and E 1993-1-11. 5.1. Join modelling (1) The effecs of he behaviour of he joins on he disribuion of inernal forces and momens wihin a srucure, and on he overall deformaions of he srucure, ma generall be negleced, bu where such effecs are significan (such as in he case of semi-coninuous joins) he should be aken ino accoun, see E 1993-1-8. () To idenif wheher he effecs of join behaviour on he analsis need be aken ino accoun, a disincion ma be made beween hree join models as follows, see E 1993-1-8, 5.1.1: simple, in which he join ma be assumed no o ransmi bending momens; coninuous, in which he behaviour of he join ma be assumed o have no effec on he analsis; semi-coninuous, in which he behaviour of he join needs o be aken ino accoun in he analsis (3) The requiremens of he various pes of joins are given in E 1993-1-8. 5.1.3 Ground-srucure ineracion (1) Accoun should be aken of he deformaion characerisics of he suppors where significan. OTE E 1997 gives guidance for calculaion of soil-srucure ineracion. 9
E 1993-1-1: 005 (E) 5. Global analsis 5..1 Effecs of deformed geomer of he srucure (1) The inernal forces and momens ma generall be deermined using eiher: firs-order analsis, using he iniial geomer of he srucure or second-order analsis, aking ino accoun he influence of he deformaion of he srucure. () The effecs of he deformed geomer (second-order effecs) should be considered if he increase he acion effecs significanl or modif significanl he srucural behaviour. (3) Firs order analsis ma be used for he srucure, if he increase of he relevan inernal forces or momens or an oher change of srucural behaviour caused b deformaions can be negleced. This condiion ma be assumed o be fulfilled, if he following crierion is saisfied: α α cr cr where α cr F F cr F = F F = F cr cr 10 15 for elasic analsis for plasic analsis (5.1) is he facor b which he design loading would have o be increased o cause elasic insabili in a global mode is he design loading on he srucure is he elasic criical buckling load for global insabili mode based on iniial elasic siffnesses OTE A greaer limi for α cr for plasic analsis is given in equaion (5.1) because srucural behaviour ma be significanl influenced b non linear maerial properies in he ulimae limi sae (e.g. where a frame forms plasic hinges wih momen redisribuions or where significan non linear deformaions from semi-rigid joins occur). Where subsaniaed b more accurae approaches he aional Annex ma give a lower limi for α cr for cerain pes of frames. (4)B Poral frames wih shallow roof slopes and beam-and-column pe plane frames in buildings ma be checked for swa mode failure wih firs order analsis if he crierion (5.1) is saisfied for each sore. In hese srucures α cr ma be calculaed using he following approximaive formula, provided ha he axial compression in he beams or rafers is no significan: α cr where H V H = V h δ H, (5.) is he design value of he horional reacion a he boom of he sore o he horional loads and ficiious horional loads, see 5.3.(7) is he oal design verical load on he srucure on he boom of he sore δ H, is he horional displacemen a he op of he sore, relaive o he boom of he sore, when he frame is loaded wih horional loads (e.g. wind) and ficiious horional loads which are applied a each floor level h is he sore heigh 30