Steel Frame Design Manual

Transcription

1 Steel rame Design Manual AIS# ASD-1989, AISC LRD-1993, & BS

2 Steel rame Design Manual AISC ASD-1989, AISC LRD-1993 and BS or ETABS 016 ISO ETA1815M7 Rev 0 Proudl developed in the United States o America Decemer 015

3 Copright Copright Computers & Structures, Inc., All rights reserved. The CSI Logo, SAP000, ETABS, and SAE are registered trademarks o Computers & Structures, Inc. Watch & Learn TM is a trademark o Computers & Structures, Inc. The computer programs SAP000 and ETABS and all associated documentation are proprietar and coprighted products. Worldwide rights o ownership rest with Computers & Structures, Inc. Unlicensed use o these programs or reproduction o documentation in an orm, without prior written authorization rom Computers & Structures, Inc., is explicitl prohiited. No part o this pulication ma e reproduced or distriuted in an orm or an means, or stored in a dataase or retrieval sstem, without the prior explicit written permission o the pulisher. urther inormation and copies o this documentation ma e otained rom: Computers & Structures, Inc. ino@csiamerica.com (or general inormation) support@csiamerica.com (or technical support)

4 DISCLAIMER CONSIDERABLE TIME, EORT AND EXPENSE HAVE GONE INTO THE DEVELOPMENT AND DOCUMENTATION O THIS SOTWARE. HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON THE ACCURACY OR THE RELIABILITY O THIS PRODUCT. THIS PRODUCT IS A PRACTICAL AND POWERUL TOOL OR STRUCTURAL DESIGN. HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC ASSUMPTIONS O THE SOTWARE MODELING, ANALYSIS, AND DESIGN ALGORITHMS AND COMPENSATE OR THE ASPECTS THAT ARE NOT ADDRESSED. THE INORMATION PRODUCED BY THE SOTWARE MUST BE CHECKED BY A QUALIIED AND EXPERIENCED ENGINEER. THE ENGINEER MUST INDEPENDENTLY VERIY THE RESULTS AND TAKE PROESSIONAL RESPONSIBILITY OR THE INORMATION THAT IS USED.

5 Ta le o Con tents CHAPTER I In tro duc tion 1 Over view Organization Recommended Reading CHAPTER II De sign Al go rithms 5 De sign Load Com i na tions De sign and Check Sta tions P- E ects El e ment Un sup ported Lengths Eective Length actor (K) Choice o In put Units CHAPTER III Check/De sign or AISC-ASD89 15 De sign Load ing Com i na tions Classiication o Sections Calculation o Stresses Calculation o Allowale Stresses Al low ale Stress in Ten sion Allowale Stress in Compression lexural Buckling lex ural-tor sional Buck ling Al low ale Stress in Bend ing I-sec tions Chan nel sec tions T-sec tions and Dou le an gles Box Sec tions and Rect an gu lar Tues Pipe Sec tions Round Bars i

6 CSI Steel Design Manual Rectangular and Square Bars Sin gle-an gle Sec tions General Sections Al low ale Stress in Shear Calculation o Stress Ratios Ax ial and Bend ing Stresses Shear Stresses CHAPTER IV Check/De sign or AISC-LRD93 45 De sign Load ing Com i na tions Classiication o Sections Calculation o actored orces Calculation o Nominal Strengths Com pres sion Ca pac it lexural Buckling lex ural-tor sional Buck ling Tor sional and lex ural-tor sional Buck ling Ten sion Ca pac it Nom i nal Strength in Bend ing Yielding Lateral-Torsional Buckling lange Lo cal Buck ling We Lo cal Buck ling Shear Capacities Calculation o Capacit Ratios Ax ial and Bend ing Stresses Shear Stresses CHAPTER V Check/De sign or BS De sign Load ing Com i na tions Classiication o Sections Calculation o actored orces Calculation o Section Capacities Com pres sion Re sis tance Ten sion Ca pac it Moment Capacit Plas tic and Com pact Sec tions Semi-compact Sections Lateral-Torsional Buckling Moment Capacit Shear Capacities Calculation o Capacit Ratios Local Capacit Check Un der Ax ial Ten sion Un der Ax ial Com pres sion ii

7 Tale o Contents Overall Buckling Check Shear Capacit Check CHAPTER VI De sign Out put 95 Over view Graph i cal Dis pla o De sign Out put Ta u lar Dis pla o De sign Out put Memer Speciic Inormation Reerences 101 In dex 103 iii

8 Chapter I Introduction Overview ETABS ea ture pow er ul and com pletel in te grated mod ules or de sign o oth steel and re in orced con crete struc tures. The pro gram pro vides the user with op - tions to cre ate, mod i, ana lze and de sign struc tural mod els, all rom within the same user in ter ace. The pro gram is ca pa le o per orm ing ini tial mem er siz ing and op ti mi za tion rom within the same in ter ace. The pro gram pro vides an in ter ac tive en vi ron ment in which the user can stud the stress con di tions, make ap pro pri ate changes, such as re vis ing mem er prop er ties, and re- examine the re sults with out the need to re- run the anal sis. A sin gle mouse click on an ele ment rings up de tailed de sign in or ma tion. Mem ers can e grouped to gether or de sign pur poses. The out put in oth graphi cal and tau lated or mats can e read il printed. The pro gram is struc tured to sup port a wide va ri et o the lat est na tional and in ter - na tional de sign codes or the auto mated de sign and check o con crete and steel rame mem ers. The steel de sign codes sup ported in pro gram can e ound in Desing > Steel rame De sign > Pre er ences menu. The de sign is ased upon a set o user- speciied load ing com i na tions. How ever, the pro gram pro vides a set o de ault load com i na tions or each de sign code sup - Overview 1

9 CSI Steel Design Manual ported in the program. I the de ault load com i na tions are ac cept ale, no dei ni tion o ad di tional load com i na tion is re quired. In the de sign pro cess the pro gram picks the least weight sec tion re quired or strength or each ele ment to e de signed, rom a set o user speci ied sec tions. Di - er ent sets o avail ale sec tions can e speci ied or di er ent groups o ele ments. Also sev eral ele ments can e grouped to e de signed to have the same sec tion. In the check pro cess the pro gram pro duces de mand/ca pac it ra tios or ax ial load and iaxial moment interactions and shear. The demand/capacit ratios are ased on ele ment stress and al low ale stress or al low ale stress de sign, and on ac tored loads (ac tions) and ac tored ca paci ties (re sis tances) or limit state de sign. The checks are made or each user speci ied (or pro gram de aulted) load com i na - tion and at sev eral user con trolled sta tions along the length o the ele ment. Maxi - mum de mand/ca pac it ra tios are then re ported and/or used or de sign op ti mi za tion. All al low ale stress val ues or de sign ca pac it val ues or ax ial, end ing and shear actions are calculated the program. Tedious calculations associated with evaluat ing e ec tive length ac tors or col umns in mo ment rame tpe struc tures are auto - mated in the al go rithms. The pres en ta tion o the out put is clear and con cise. The in or ma tion is in a orm that al lows the designer to take ap pro pri ate re me dial meas ures i there is mem er over - stress. Backup de sign in or ma tion pro duced the pro gram is also pro vided or con ven ient veri i ca tion o the re sults. When us ing AISC-LRD de sign codes, re quire ments or con ti nu it plates at the eam to col umn con nec tions are eval u ated. The pro gram per orms a joint shear anal sis to de ter mine i douler plates are re quired in an o the joint panel zones. Max i mum eam shears re quired or the eam shear con nec tion de sign are re ported. Also max i mum ax ial ten sion or com pres sion val ues that are gen er ated in the mem - er are re ported. Spe cial 1989AISC-ASD and 1993 AISC--LRD seis mic de sign pro vi sions are im - ple mented in the cur rent ver sion o the pro gram. The ra tio o the eam lex ural ca - pac i ties with re spect to the col umn re duced lex ural ca pac i ties (re duced or ax ial orce e ect) as so ci ated with the weak eam-strong col umn as pect o an eam/col - umn intersection, are reported or special moment resisting rames. Capacit re - quire ments as so ci ated with seis mic ram ing ss tems that re quire duc til it are checked. Eng lish as well as SI and MKS met ric units can e used to de ine the model ge ome - tr and to spec i de sign pa rame ters. Overview

10 Chapter I Introduction Organization This man ual is or gan ized in the ol low ing wa: Chap ter II out lines vari ous as pects o the steel de sign pro ce dures o the pro gram. This chap ter de scries the com mon ter mi nol og o steel de sign as im ple mented in the program. Each o eleven su se quent chap ters gives a de tailed de scrip tion o a spe ciic code o prac tice as in ter preted and im ple mented in the program. Each chap ter de - scries the de sign load ing com i na tions to e con sid ered; al low ale stress or ca - pac it cal cu la tions or ten sion, com pres sion, end ing, and shear; cal cu la tions o de mand/ca pac it ra tios; and other spe cial con sid era tions re quired the code. Chap ter III gives a de tailed de scrip tion o the AISC ASD steel code (AISC 1989) as im ple mented in the pro gram. Chap ter IV gives a de tailed de scrip tion o the AISC LRD steel code (AISC 1993) as im ple mented in the pro gram. Chap ter V gives a de tailed de scrip tion o the Brit ish code BS 5950 (BSI 000) as im ple mented in the pro gram. Chap ter VI out lines vari ous as pects o the tau lar and graphi cal out put rom the program re lated to steel de sign. Recommended Reading It is rec om mended that the user read Chap ter II De sign Al go rithms and one o eleven su se quent chap ters cor re spond ing to the code o in ter est to the user. i nall the user should read De sign Out put in Chap ter VI or un der stand ing and in ter - pret ing the program out put re lated to steel de sign. Organization 3

11 Chapter II Design Algorithms This chap ter out lines vari ous as pects o the steel check and de sign pro ce dures that are used the pro gram. The steel de sign and check ma e per ormed ac cord ing to one o the ol low ing codes o prac tice. Amer i can In sti tute o Steel Con struc tion s Al low ale Stress De sign and Plas - tic De sign Spec i i ca tion or Struc tural Steel Build ings, AISC-ASD (AISC 1989). Ameri can In sti tute o Steel Con struc tion s Load and Re sis tance ac tor De - sign Speci i ca tion or Struc tural Steel Build ings, AISC-LRD (AISC 1994). Brit ish Stan dards In sti tu tion s Struc tural Use o Steel work in Build ing, BS 5950 (BSI 000). De tails o the al go rithms as so ci ated with each o these codes as im ple mented and in ter preted in the pro gram are de scried in su se quent chap ters. How ever, this chap ter pro vides a ack ground which is com mon to all the de sign codes. It is as sumed that the user has an en gi neer ing ack ground in the gen eral area o struc tural steel de sign and a mili ar it with at least one o the aove men tioned de - sign codes. 5

12 CSI Steel Design Manual or re er ring to per ti nent sec tions o the cor re spond ing code, a unique pre ix is as - signed or each code. or ex am ple, all re er ences to the AISC-LRD code carr the pre ix o LRD. Sim i larl, Re er ences to the AISC-ASD code carr the pre ix o ASD Re er ences to the Brit ish code carr the pre ix o BS Design Load Cominations The de sign load com i na tions are used or de ter min ing the vari ous com i na tions o the load cases or which the struc ture needs to e de signed/checked. The load com - i na tion ac tors to e used var with the se lected de sign code. The load com i na - tion ac tors are ap plied to the orces and mo ments o tained rom the as so ci ated load cases and the re sults are then summed to o tain the ac tored de sign orces and mo ments or the load com i na tion. or multi- valued load com i na tions in volv ing re sponse spec trum, time his tor, mov ing loads and multi- valued com i na tions (o tpe en vel op ing, square- root o the sum o the squares or a so lute) where an cor re spon dence e tween in ter act ing quan ti ties is lost, the pro gram auto mati call pro duces mul ti ple su com i na tions us ing maxima/min ima per mu ta tions o in ter act ing quan ti ties. Sepa rate com i na - tions with nega tive ac tors or re sponse spec trum cases are not re quired e cause the pro gram auto mati call takes the min ima to e the nega tive o the maxima or re - sponse spec trum cases and the aove de scried per mu ta tions gen er ate the re quired su com i na tions. When a de sign com i na tion in volves onl a sin gle multi- valued case o time his - tor or mov ing load, ur ther op tions are avail ale. The pro gram has an op tion to re - quest that time his tor com i na tions pro duce su com i na tions or each time step o the time his tor. Also an op tion is avail ale to re quest that mov ing load com i - na tions pro duce su com i na tions us ing maxima and min ima o each de sign quan - tit ut with cor re spond ing val ues o in ter act ing quan ti ties. or nor mal load ing con di tions in volv ing static dead load, live load, wind load, and earth quake load, and/or d namic re sponse spec trum earth quake load, the pro gram has uilt- in de ault load ing com i na tions or each de sign code. These are ased on the code rec om men da tions and are docu mented or each code in the cor re spond ing chapters. or other load ing con di tions in volv ing mov ing load, time his tor, pat tern live loads, sepa rate con sid era tion o roo live load, snow load, etc., the user must de ine 6 Design Load Cominations

13 Chapter II Design Algorithms de sign load ing com i na tions ei ther in lieu o or in ad di tion to the de ault de sign load ing com i na tions. The de ault load com i na tions as sume all static load cases de clared as dead load to e ad di tive. Simi larl, all cases de clared as live load are as sumed ad di tive. How - ever, each static load case de clared as wind or earth quake, or re sponse spec trum cases, is as sumed to e non ad di tive with each other and pro duces mul ti ple lat eral load com i na tions. Also wind and static earth quake cases pro duce sepa rate load ing com i na tions with the sense (posi tive or nega tive) re versed. I these con di tions are not cor rect, the user must pro vide the ap pro pri ate de sign com i na tions. The de ault load com i na tions are in cluded in de sign i the user re quests them to e in cluded or i no other user de ined com i na tion is avail ale or con crete de sign. I an de ault com i na tion is in cluded in de sign, then all de ault com i na tions will auto mati call e up dated the pro gram an time the user changes to a di er ent de sign code or i static or re sponse spec trum load cases are modi ied. Live load re duc tion ac tors can e ap plied to the mem er orces o the live load case on an element- - element a sis to re duce the con tri u tion o the live load to the ac tored load ing. The user is cau tioned that i mov ing load or time his tor re sults are not re quested to e re cov ered in the anal sis or some or all the rame mem ers, then the e ects o these loads will e as sumed to e zero in an com i na tion that in cludes them. Design and Check Stations or each load com i na tion, each el e ment is de signed or checked at a num er o lo - ca tions along the length o the el e ment. The lo ca tions are ased on equall spaced seg ments along the clear length o the el e ment. The num er o seg ments in an el e - ment is re quested the user e ore the anal sis is made. The user can re ine the de sign along the length o an el e ment re quest ing more seg ments. The ax ial-lexure interaction ra tios as well as shear stress ra tios are cal cu lated or each sta tion along the length o the mem er or each load com i na tion. The ac tual memer stress components and corresponding allowale stresses are calculated. Then, the stress ra tios are evalu ated ac cord ing to the code. The con trol ling com - pres sion and/or ten sion stress ra tio is then o tained, along with the cor re spond ing iden ti i ca tion o the sta tion, load com i na tion, and code- equation. A stress ra tio greater than 1.0 in di cates an over stress or ex ceed ing a limit state. Design and Check Stations 7

14 CSI Steel Design Manual P- Eects The program de sign al go rithms re quire that the anal sis re sults in clude the P- e - ects. The P- e ects are con sid ered di er entl or raced or non swa and un raced or swa com po nents o mo ments in rames. or the raced mo ments in rames, the e ect o P- is lim ited to in di vid ual mem er sta il it. or un - raced com po nents, lat eral drit e ects should e con sid ered in ad di tion to in di - vid ual mem er sta il it e ect. In the program, it is as sumed that raced or non - swa mo ments are con tri uted rom the dead or live loads. Whereas, un - raced or swa mo ments are con tri uted rom all other tpes o loads. or the in di vid ual mem er sta il it e ects, the mo ments are mag ni ied with mo - ment mag ni i ca tion ac tors as in the AISC-LRD code is con sid ered di rectl in the de sign equa tions as in the Ca na dian, Brit ish, and Eu ro pean codes. No mo ment mag ni i ca tion is ap plied to the AISC-ASD code. or lat eral drit e ects o un raced or swa rames, the program as sumes that the am pli i ca tion is al read in cluded in the re sults e cause P- e ects are con sid ered or all ut AISC- ASD code. The us ers o the pro gram should e aware that the de ault anal sis op tion in the program is turned O or P- e ect. The de ault numer o it era tions or P- anal sis is 1. The user should turn the P- anal sis ON and set the maxi mum numer o it era tions or the anal sis. No P- anal sis is re quired or the AISC- ASD code. or ur ther re er ence, the user is re erred to CSI Anal sis Re er ence Man ual (CSI 005). Element Unsupported Lengths To ac count or col umn slen der ness e ects, the col umn un sup ported lengths are re - quired. The two un sup ported lengths are l 33 and l. See igure II-1. These are the lengths e tween sup port points o the ele ment in the cor re spond ing di rec tions. The length l 33 cor re sponds to in sta il it aout the 3-3 axis (ma jor axis), and l cor re - sponds to in sta il it aout the - axis (mi nor axis). The length l is also used or lateral- torsional uck ling caused ma jor di rec tion end ing (i.e., aout the 3-3 axis). See igure II- or cor re spon dence e tween the program axes and the axes in the de sign codes. Normall, the un sup ported el e ment length is equal to the length o the el e ment, i.e., the dis tance e tween END-I and END-J o the el e ment. See igure II-1. The pro - gram, how ever, al lows us ers to as sign sev eral el e ments to e treated as a sin gle mem er or de sign. This can e done di er entl or ma jor and mi nor end ing. 8 P- Eects

15 Chapter II Design Algorithms There ore, ex tra ne ous joints, as shown in igure II-3, that a ect the un sup ported length o an el e ment are au to mat i call taken into con sid er ation. Axis l 33 Axis 1 End j l End I Axis 3 igure II-1 Major and Minor Axes o Bending In de ter min ing the val ues or l and l 33 o the el e ments, the pro gram rec og nizes var i ous as pects o the struc ture that have an e ect on these lengths, such as mem er con nec tiv it, di a phragm con straints and sup port points. The pro gram au to mat i - call lo cates the el e ment sup port points and eval u ates the cor re spond ing un sup - ported el e ment length. There ore, the un sup ported length o a col umn ma ac tu all e eval u ated as e ing greater than the cor re spond ing el e ment length. I the eam rames into onl one di - rec tion o the col umn, the eam is as sumed to give lat eral sup port onl in that di rec - tion. The user has op tions to spec i the un sup ported lengths o the el e ments on an element--element asis. Element Unsupported Lengths 9

16 CSI Steel Design Manual 3 3 SAP000 z x x x x x x z ASD89, LRD95 & AASHTO CISC95 BS5950 EUROCODE 3 igure II- Correspondence etween the program Axes and Code Axes Eective Length actor (K) The col umn K-a ctor al go rithm has een de vel oped or uilding- tpe struc tures, where the col umns are ver ti cal and the eams are hori zon tal, and the e hav ior is a - si call that o a moment- resisting na ture or which the K-actor calculation is rela - tivel com plex. or the pur pose o cal cu lat ing K-a ctors, the ele ments are iden ti - ied as col umns, eams and races. All ele ments par al lel to the Z- axis are clas si ied as col umns. All ele ments par al lel to the X-Y plane are clas si ied as eams. The rest are races. 10 Eective Length actor (K)

17 Chapter II Design Algorithms igure II-3 Unsupported Lengths are Aected Intermediate Nodal Points The eams and races are as signed K-ac tors o unit. In the cal cu la tion o the K-ac tors or a col umn el e ment, the pro gram irst makes the ol low ing our sti - ness sum ma tions or each joint in the struc tural model: Ec I c S cx = L c x S x = Ec I c S c = L c S = EI L EI L where the x and su scripts cor re spond to the gloal X and Y di rec tions and the c and su scripts re er to col umn and eam. The lo cal - and 3-3 terms EI l and EI 33 l33 are ro tated to give com po nents along the gloal X and Y di rec tions to orm the ( EI / l) x and ( EI / l) val ues. Then or each col umn, the joint sum ma tions at END-I and the END-J o the mem er are trans ormed ack to the col umn lo cal 1--3 co or di nate ss tem and the G-val ues or END-I and the END-J o the mem er are cal cu lated aout the - and 3-3 di rec tions as ol lows: x Eective Length actor (K) 11

18 CSI Steel Design Manual I G = S S I G = S 33 S I c I I c 33 I 33 J G = S S J G = S 33 S J c J J c 33 J 33 I a ro ta tional re lease ex ists at a par tic u lar end (and di rec tion) o an el e ment, the cor re spond ing value is set to I all de grees o ree dom or a par tic u lar joint are deleted, the G-val ues or all mem ers con nect ing to that joint will e set to 1.0 or the end o the mem er con nect ing to that joint. inall, i G I and G J are known or a par tic u lar di rec tion, the col umn K-ac tor or the cor re spond ing di rec tion is cal cu - lated solv ing the ol low ing re la tion ship or : I J G G 36 = I J 6( G + G ) tan rom which K = /. This re la tion ship is the mathe mati cal ormulation or the evalua tion o K ac tors or moment- resisting rames as sum ing sideswa to e un in - hii ted. or other struc tures, such as raced rame struc tures, trusses, space rames, trans mis sion tow ers, etc., the K-a ctors or all mem ers are usu all unit and should e set so the user. The ol low ing are some im por tant as pects as so ci ated with the col umn K-a ctor al go rithm: An ele ment that has a pin at the joint un der con sid era tion will not en ter the sti - ness sum ma tions cal cu lated aove. An ele ment that has a pin at the ar end rom the joint un der con sid era tion will con tri ute onl 50% o the cal cu lated EI value. Also, eam ele ments that have no col umn mem er at the ar end rom the joint un der con sid era tion, such as can ti le vers, will not en ter the sti ness sum ma tion. I there are no eams ram ing into a par ticu lar di rec tion o a col umn ele ment, the associated G-value will e in in it. I the G-value at an one end o a col - umn or a par ticu lar di rec tion is in in it, the K-a ctor cor re spond ing to that di - rec tion is set equal to unit. I ro ta tional re leases ex ist at oth ends o an ele ment or a par ticu lar di rec tion, the cor re spond ing K-a ctor is set to unit. The auto mated K-actor calculation procedure can occasionall generate artiiciall high K-a ctors, spe cii call un der cir cum stances in volv ing skewed eams, ixed sup port con di tions, and un der other con di tions where the pro - gram ma have di i cult rec og niz ing that the mem ers are lat er all sup ported and K-a ctors o unit are to e used. 1 Eective Length actor (K)

19 Chapter II Design Algorithms All K-a ctors pro duced the pro gram can e over writ ten the user. These val ues should e re viewed and an un ac cept ale val ues should e re placed. Choice o Input Units Eng lish as well as SI and MKS met ric units can e used or in put. But the codes are ased on a spe ciic ss tem o units. All equa tions and de scrip tions pre sented in the su se quent chap ters cor re spond to that spe ciic ss tem o units un less oth er wise noted. or ex am ple, AISC- ASD code is pu lished in kip-inch- second units. B de - ault, all equa tions and de scrip tions pre sented in the chap ter Check/De sign or AIS C-ASD89 cor re spond to kip- inch- second units. How ever, an ss tem o units can e used to de ine and de sign the struc ture in the program. Choice o Input Units 13

20 Chapter III Check/Design or AISC-ASD89 This chap ter de scries the de tails o the struc tural steel de sign and stress check al - go rithms that are used the pro gram when the user se lects the AISC- ASD89 de - sign code (AISC 1989). Vari ous no ta tions used in this chap ter are de scried in Tale V-1. or re er ring to per ti nent sec tions and equa tions o the origi nal ASD code, a unique pre ix ASD is as signed. However, all re er ences to the Speci i ca tions or Al - low ale Stress De sign o Single- Angle Mem ers carr the pre ix o ASD SAM. The de sign is ased on user- speciied load ing com i na tions. But the pro gram pro - vides a set o de ault load com i na tions that should sat is re quire ments or the de - sign o most uild ing tpe struc tures. In the evalua tion o the ax ial orce/i ax ial mo ment ca pac it ra tios at a sta tion along the length o the mem er, irst the ac tual mem er orce/mo ment com po nents and the cor re spond ing ca paci ties are cal cu lated or each load com i na tion. Then the ca - pac it ra tios are evalu ated at each sta tion un der the in lu ence o all load com i na - tions us ing the cor re spond ing equa tions that are de ined in this chapter. The con - trol ling ca pac it ra tio is then o tained. A ca pac it ra tio greater than 1.0 in di cates over stress. Simi larl, a shear ca pac it ra tio is also cal cu lated sepa ratel. 15

21 CSI Steel Design Manual A = Cross- sectional area, in A e = Eective cross- sectional area or slen der sections, in A = Area o lange, in A g = Gross cross- sectional area, in Av, Av3 = Ma jor and mi nor shear ar eas, in A w = We shear area, dt w, in C = Bend ing Co e i cient C m = Moment Coeicient C w = Warp ing con stant, in 6 D = Out side di ame ter o pipes, in E = Modulus o elasticit, ksi a = Allowale axial stress, ksi = Al low ale ending stress, ksi 33, = Al low ale ma jor and mi nor end ing stresses, ksi cr = Critical compressive stress, ksi e33 e = = E ( K l r ) E ( K l r ) v = Al low ale shear stress, ksi = Yield stress o ma te rial, ksi K = E ec tive length ac tor K 33, K = Eective length K- actors in the ma jor and mi nor directions M 33, M = Major and mi nor end ing mo ments in mem er, kip- in M o = Lateral- torsional mo ment or an gle sections, kip- in P = Axial orce in mem er, kips P e = Euler uck ling load, kips Q = Re duc tion ac tor or slen der sec tion, = Q a Q s Q a = Reduction actor or stiened slender elements Q s = Re duc tion ac tor or unsti ened slen der elements S = Sec tion modu lus, in 3 S, S = Ma jor and mi nor sec tion moduli, in 3 33 Tale III-1 AISC-ASD Notations 16

22 Chapter III Check/Design or AISC-ASD89 S e, 33, S e, = E ec tive major and mi nor sec tion moduli or slen der sections, in 3 S c = Sec tion modu lus or com pres sion in an an gle section, in 3 V, V3 = Shear orces in major and mi nor directions, kips = Nomi nal di men sion o plate in a sec tion, in longer leg o an gle sections, t w or welded and 3 t w or rolled ox sec tions, etc. e = E ec tive width o lange, in = lange width, in d = Over all depth o mem er, in a = Axial stress ei ther in com pres sion or in tension, ksi = Nor mal stress in end ing, ksi 33, = Nor mal stress in ma jor and minor di rec tion ending, ksi v = Shear stress, ksi v, v3 = Shear stress in ma jor and minor di rec tion ending, ksi h = Clear dis tance e tween langes or I shaped sec tions ( d t ), in h e = E ec tive dis tance e tween langes less il lets, in k = Dis tance rom outer ace o lange to we toe o il let, in k c = Parameter used or classiication o sections, 4.05 i h t 0.46 w > 70, [ h t w ] 1 i h t w 70. l33, l = Ma jor and mi nor di rec tion un raced mem er lengths, in l c = Criti cal length, in r = Ra dius o g ra tion, in r33, r = Ra dii o g ra tion in the ma jor and mi nor di rec tions, in r z = Mini mum Ra dius o g ra tion or an gles, in t = Thick ness o a plate in I, ox, chan nel, an gle, and T sections, in t = lange thick ness, in t w = We thick ness, in w = Spe cial sec tion prop ert or an gles, in Tale III-1 AISC-ASD Notations (cont.) 17

23 CSI Steel Design Manual Eng lish as well as SI and MKS met ric units can e used or in put. But the code is ased on Kip- Inch- Second units. or sim plic it, all equa tions and de scrip tions pre - sented in this chap ter cor re spond to Kip- Inch- Second units un less oth er wise noted. Design Loading Cominations The de sign load com i na tions are the vari ous com i na tions o the load cases or which the struc ture needs to e checked. or the AISC- ASD89 code, i a struc ture is su jected to dead load (DL), live load (LL), wind load (WL), and earth quake in - duced load (EL), and con sid er ing that wind and earth quake orces are re versi le, then the ol low ing load com i na tions ma have to e de ined (ASD A4): DL DL + LL DL ± WL DL + LL ± WL DL ± EL DL + LL ± EL (ASD A4.1) (ASD A4.1) (ASD A4.1) (ASD A4.1) (ASD A4.1) (ASD A4.1) These are also the de ault de sign load com i na tions in the pro gram when ever the AISC-ASD89 code is used. The user should use other ap pro pri ate load ing com i - na tions i roo live load is sepa ratel treated, i other tpes o loads are pres ent, or i pat tern live loads are to e con sid ered. When de sign ing or com i na tions in volv ing earth quake and wind loads, al low ale stresses are in creased a ac tor o 4/3 o the regu lar al low ale value (ASD A5.). Live load re duc tion ac tors can e ap plied to the mem er orces o the live load case on an element- - element a sis to re duce the con tri u tion o the live load to the ac tored load ing. Classiication o Sections The al low ale stresses or ax ial com pres sion and lex ure are de pend ent upon the clas si i ca tion o sec tions as ei ther Com pact, Non compact, Slen der, or Too Slen der. The pro gram clas si ies the in di vid ual mem ers ac cord ing to the lim it ing width/thick ness ra tios given in Tale III- (ASD B5.1, 3.1, 5, G1, A-B5-). The dei ni tion o the sec tion prop er ties re quired in this ta le is given in igure III-1 and Tale III Design Loading Cominations

24 Chapter III Check/Design or AISC-ASD89 igure III-1 AISC-ASD Deinition o Geometric Properties Classiication o Sections 19

25 CSI Steel Design Manual Section Description Ratio Checked Compact Section Noncompact Section Slender Section t ( rolled) No limit t (welded) / k c No limit I-SHAPE d t w or a a ( 3.74 ), or a / > /. No limit No limit h t w No limit I compression onl, 53 otherwise ( ) t No limit BOX d t w As or I-shapes No limit No limit h t w No limit As or I-shapes As or I-shapes Other t t, d 6 None None w w t As or I-shapes As or I-shapes No limit d t w As or I-shapes No limit No limit CHANNEL h t w No limit As or I-shapes As or I-shapes Other No limit No limit I welded dw 0.5, t t w 3.0 I rolled dw 0.5, t t.0 w Tale III- Limiting Width-Thickness Ratios or Classiication o Sections Based on AISC-ASD 0 Classiication o Sections

26 Chapter III Check/Design or AISC-ASD89 Section Description Ratio Checked Compact Section Noncompact Section Slender Section t No limit d t w Not applicale 17 No limit T-SHAPE Other No limit No limit I welded dw 0.5, t t w 1.5 I rolled dw 0.5, t t 1.10 w DOUBLE ANGLES t Not applicale 76 No limit ANGLE t Not applicale 76 No limit PIPE D t 3, 300 3, ,000 (Compression onl) No limit or lexure ROUND BAR Assumed Compact RECTANGLE Assumed Noncompact GENERAL Assumed Noncompact Tale III- Limiting Width-Thickness Ratios or Classiication o Sections Based on AISC-ASD (Cont.) I the sec tion di men sions sat is the lim its shown in the ta le, the sec tion is clas si - ied as ei ther Com pact, Non com pact, or Slen der. I the sec tion sat is ies the cri te ria or Com pact sec tions, then the sec tion is clas si ied as Com pact sec tion. I the sec - tion does not sat is the cri te ria or Com pact sec tions ut sat is ies the cri te ria or Non com pact sec tions, the sec tion is clas si ied as Noncom pact sec tion. I the sec - tion does not satis the cri te ria or Com pact and Non com pact sec tions ut sat is ies Classiication o Sections 1

27 CSI Steel Design Manual the cri te ria or Slen der sec tions, the sec tion is clas si ied as Slender sec tion. I the lim its or Slen der sec tions are not met, the sec tion is clas si ied as Too Slen der. Stress check o Too Slen der sec tions is e ond the scope o SAP000. In clas si ing we slen der ness o I-shapes, Box, and Chan nel sec tions, it is as - sumed that there are no in ter me di ate sti en ers (ASD 5, G1). Dou le an gles are conservativel assumed to e separated. Calculation o Stresses The stresses are cal cu lated at each o the pre vi ousl de ined sta tions. The mem er stresses or non- slender sec tions that are cal cu lated or each load com i na tion are, in gen eral, ased on the gross cross- sectional prop er ties.: = P/A a = M /S = M /S = V /A v v = V /A v 3 3 v 3 I the sec tion is slen der with slen der sti ened ele ments, like slen der we in I, Chan - nel, and Box sec tions or slen der langes in Box, e ec tive sec tion moduli ased on re duced we and re duced lange di men sions are used in cal cu lat ing stresses. a = P/A (ASD A-B5.d) 33 = M 33 /Se, 33 (ASD A-B5.d) = M /Se, (ASD A-B5.d) v = V /Av (ASD A-B5.d) v 3 = V 3 /Av 3 (ASD A-B5.d) The lexural stresses are cal cu lated ased on the prop er ties aout the principal axes. or I, Box, Chan nel, T, Dou le-an gle, Pipe, Cir cu lar and Rec tan gu lar sec tions, the prin ci pal axes co in cide with the geo met ric axes. or Single- angle sec tions, the de - sign con sid ers the prin ci pal properties. or gen eral sec tions it is as sumed that all sec tion prop er ties are given in terms o the prin ci pal di rec tions. or Single- angle sec tions, the shear stresses are cal cu lated or di rec tions along the geo met ric axes. or all other sec tions the shear stresses are cal cu lated along the geo met ric and prin ci ple axes. Calculation o Stresses

28 Chapter III Check/Design or AISC-ASD89 Calculation o Allowale Stresses The al low ale stresses in com pres sion, ten sion, end ing, and shear are com puted or Com pact, Non com pact, and Slen der sec tions ac cord ing to the ol low ing su - sec tions. The al low ale lexural stresses or all shapes o sec tions are cal cu lated ased on their prin ci pal axes o end ing. or the I, Box, Chan nel, Cir cu lar, Pipe, T, Dou le-an gle and Rec tan gu lar sec tions, the prin ci pal axes co in cide with their geo - met ric axes. or the An gle sec tions, the prin ci pal axes are de ter mined and all com - pu ta tions re lated to lex ural stresses are ased on that. I the user speci ies nonz ero al low ale stresses or one or more ele ments in the pro - gram Overwrites Ele ment De sign Data orm, these val ues will over ride the aove men tioned cal cu lated val ues or those ele ments as de ined in the ol low ing su sec tions. The speci ied al low ale stresses should e ased on the prin ci pal axes o end ing. Allowale Stress in Tension The al low ale ax ial ten sile stress value a is as sumed to e = 0.6 (ASD D1, ASD SAM ) a It should e noted that net sec tion checks are not made. or mem ers in ten sion, i l r is greater than 300, a mes sage to that e ect is printed (ASD B7, ASD SAM ). or sin gle an gles, the mini mum radius o g ra tion, r z, is used in stead o r and r 33 in com put ing l r. Allowale Stress in Compression The al low ale ax ial com pres sive stress is the minimum value o tained rom lex - ural uck ling and lexural- torsional uck ling. The al low ale com pres sive stresses are de ter mined ac cord ing to the ol low ing su sec tions. or mem ers in com pres sion, i Kl r is greater than 00, a warn ing mes sage is printed (ASD B7, ASD SAM 4). or sin gle an gles, the mini mum radius o g ra - tion, r z, is used in stead o r and r 33 in com put ing Kl r. lexural Buckling The allowale axial compressive stress value, a, de pends on the slen der ness ra tio Kl r ased on gross sec tion prop er ties and a cor re spond ing criti cal value, C c, where Calculation o Allowale Stresses 3

29 CSI Steel Design Manual Kl r = C c = K 33 l33 K l max, r33 r, and E. (ASD E, ASD SAM 4) or sin gle an gles, the mini mum radius o g ra tion, r z, is used in stead o r and r 33 in com put ing Kl r. or Com pact or Non com pact sec tions a is evalu ated as ol lows: = a 5 3 ( Kl/r) 1.0 C c 3( Kl/r) ( Kl/r) C 8 c C c 3, i Kl r C c, (ASD E-1, SAM 4-1) = a 1 E 3( Kl r), i Kl r > C c. (ASD E-, SAM 4-) I Kl r is greater than 00, then the cal cu lated value o a is taken not to ex ceed the value o a cal cu lated us ing the equa tion ASD E- or Com pact and Non com - pact sec tions (ASD E1, B7). or Slender sec tions, ex cept slen der Pipe sec tions, a is evalu ated as ol lows: = Q a ( Kl/r) 1.0 C c 3 ( Kl/r) 8 C c ( Kl/r) 8C 3 c 3, i Kl r C c, (ASD A-B5-11, SAM 4-1) = a 1 E 3( Kl r), i Kl r > C c. (ASD A-B5-1, SAM 4-) where, C c = E Q. (ASD A-B5.c, ASD SAM 4) 4 Calculation o Allowale Stresses

30 Chapter III Check/Design or AISC-ASD89 or slen der sec tions, i Kl r is greater than 00, then the cal cu lated value o a is taken not to ex ceed its value cal cu lated us ing the equa tion ASD A-B5-1 (ASD B7, E1). or slen der Pipe sec tions a is evalu ated as ol lows: 66 a = (ASD A- B5-9) D t The re duc tion ac tor, Q, or all com pact and non com pact sec tions is taken as 1. or slender sections, Q is com puted as ol lows: Q = Q Q, where (ASD A-B5..c, SAM 4) s a Q s = re duc tion ac tor or un sti ened slen der ele ments, and (ASD A-B5..a) Q a = re duc tion ac tor or sti ened slen der ele ments. (ASD A-B5..c) The Q s ac tors or slen der sec tions are cal cu lated as de scried in Tale III-3 (ASD A-B5.a, ASD SAM 4). The Q a ac tors or slen der sec tions are cal cu lated as the ra tio o e ec tive cross- sectional area and the gross cross- sectional area. Q a Ae = (ASD A- B5-10) A g The e ec tive cross- sectional area is com puted ased on e ec tive width as ol lows: ( ) A = A t e g e e or un sti ened el e ments is taken equal to, and e or sti ened el e ments is taken equal to or less than as given in Tale III-4 (ASD A-B5.). or wes in I, ox, and Chan nel sec tions, h e is used as e and h is used as in the aove equa tion. lexural-torsional Buckling The allowale axial compressive stress value, a, de ter mined the limit states o tor sional and lexural- torsional uck ling is de ter mined as ol lows (ASD E3, C-E3): = Q a ( Kl/r) 8 C ( Kl/r) c C e e c ( Kl/r) 8C e 3 c 3, i ( ) Kl/r C, (E-1, A- B5-11) e c Calculation o Allowale Stresses 5

31 CSI Steel Design Manual Section Tpe Reduction actor or Unstiened Slender Elements (Q s ) Equation Reerence 1.0 i t 95 k c, t k i 95 k < t < 195 k, I-SHAPE Qs = [ ] [ ] { } c c c 6,00 k t i t 195 k. c c ASD A-B5-3, ASD A-B5-4 BOX Q s =1 ASD A-B5.c CHANNEL As or I-shapes with t replaced t. ASD A-B5-3, ASD A-B5-4 T-SHAPE DOUBLE- ANGLE or langes, as or langes in I-shapes. or we see elow. 1.0, i d tw 17, Qs [ d tw], i 17 < d tw < 176, {[ ] } 0,000 d tw, i d tw 176. Q s 1.0, i t 76, = [ t], i 76 < t < 155, 15,500 {[ t] }, i t 155. ASD A-B5-3, ASD A-B5-4, ASD A-B5-5, ASD A-B5-6 ASD A-B5-1, ASD A-B5-, SAM 4-3 ANGLE Qs = [ ] [ ] 1.0, i t 76, t, i 76 < t < 155, { } 15,500 t, i t 155. ASD A-B5-1, ASD A-B5-, SAM 4-3 PIPE Q s =1 ASD A-B5.c ROUND BAR RECTAN- GULAR Q s =1 ASD A-B5.c Q s =1 ASD A-B5.c GENERAL Q s =1 ASD A-B5.c Tale III-3 Re duc tion ac tor or Un sti ened Slen der Ele ments, Q s 6 Calculation o Allowale Stresses

32 Chapter III Check/Design or AISC-ASD89 Section Tpe Eective Width or Stiened Sections Equation Reerence I-SHAPE h e h h, i, tw = t 53 w 44.3 h , i >. ( h t t w ) w P (compression onl, = ) ASD A-B5-8 A g BOX h e e h h, i, tw = t 53 w 44.3 h , i >. ( h t t w ) w , i, t = 53 t , i >. ( h t t ) P (compression onl, = ) (compr., lexure, A g = 0.6 ) ASD A-B5-8 ASD A-B5-7 CHANNEL h e h h, i, tw = t 53 w 44.3 h , i >. ( h t t w ) w P (compression onl, = ) ASD A-B5-8 A g T-SHAPE = e ASD A-B5.c DOUBLE- ANGLE e = ASD A-B5.c ANGLE = e ASD A-B5.c PIPE Q a = 1, (However, special expression or allowale axial stress is given.) ASD A-B5-9 ROUND BAR RECTAN- GULAR Not applicale e = ASD A-B5.c GENERAL Not applicale Tale III-4 Eective Width or Stiened Sections Calculation o Allowale Stresses 7

33 CSI Steel Design Manual = a where, 1 3 E ( Kl/r) e, i ( ) Kl/r > C. (E-, A- B5-1) e c C c = E Q, and (ASD E, A-B5.c, SAM 4) ( Kl/r) e = E. (ASD C- E-, SAM 4-4) e ASD Com men tar (ASD C-E3) re ers to the 1986 ver sion o the AISC-LRD code or the cal cu la tion o e. The 1993 ver sion o the AISC-LRD code is the same as the 1986 ver sion in this respect. e is cal cu lated in the pro gram as ol lows: or Rec tan gu lar, I, Box, and Pipe sec tions: e EC w = + GJ 1 ( K l ) I + I z z 33 (LRD A- E3-5) or T-sections and Dou le-angles: e = + H 4 H 1 1 ( e + ez ) e ez e ez (LRD A- E3-6) or Channels: e = + H 4 H 1 1 ( e33 + ez ) e33 ez e33 ez (LRD A- E3-6) or Sin gle-angle sec tions with equal legs: e = + H 4 H 1 1 ( e33 + ez ) e33 ez e33 ez (ASD SAM C- C4-1) or Single- angle sec tions with une qual legs, e is cal cu lated as the mini mum real root o the ol low ing cu ic equa tion (ASD SAM C- C4-, LRD A- E3-7): 8 Calculation o Allowale Stresses

34 Chapter III Check/Design or AISC-ASD89 x 0 ( e e33 )( e e )( e ez ) e ( e e ) 0 e ( e e33 ) = 0, r r where, x 0, 0 are the co or di nates o the shear cen ter with re spect to the cen troid, x 0 = 0 or doule- angle and T- shaped mem ers (-axis o sm me - tr), 0 0 I r = x I 33 0 A g = po lar ra dius o g ra tion aout the shear center, x H = 1 r, (LRD A- E3-9) 0 e33 e = = E ( K 33l33 r33) E ( K l r), (LRD A- E3-10), (LRD A- E3-11) ez EC w = + GJ 1 ( K l ) Ar, (LRD A- E3-1) z z 0 K, K are e ec tive length ac tors in mi nor and ma jor di rec tions, 33 K z is the e ec tive length ac tor or tor sional uck ling, and it is taken equal to K in the pro gram, l, l are e ec tive lengths in the mi nor and ma jor di rec tions, 33 l z is the e ec tive length or tor sional uck ling, and it is taken equal to l. or an gle sec tions, the prin ci pal mo ment o in er tia and ra dii o g ra tion are used or com put ing e (ASD SAM 4). Also, the maxi mum value o Kl, i.e, max( Kl, K33l33 ), is used in place o K l or K l in cal cu lat ing and e e33 in this case. Calculation o Allowale Stresses 9

35 CSI Steel Design Manual Allowale Stress in Bending The al low ale end ing stress de pends on the ol low ing cri te ria: the geo met ric shape o the cross- section, the axis o end ing, the com pact ness o the sec tion, and a length pa rame ter. I-sections or I- sections the length pa rame ter is taken as the lat er all un raced length, l, which is com pared to a criti cal length, l c. The criti cal length is de ined as l c 76 0, 000 A = min, d, where (ASD 1-) A is the area o com pres sion lange, Major Axis o Bending I l is less than l c, the ma jor al low ale end ing stress or Com pact and Noncom pact sec tions is taken de pend ing on whether the sec tion is welded or rolled and whether is greater than 65 ksi or not. or Com pact sec tions: 33 = 0.66 i 65 ksi, (ASD 1-1) 33 = 0.60 i > 65 ksi, (ASD 1-5) or Non com pact sec tions: 33 = t, i rolled and 65 ksi, (ASD 1-3) 33= t k c, i welded and 65 ksi, (ASD1-4) 33 = 0.60 i > 65 ksi.. (ASD 1-5) I the un raced length l is greater than l c, then or oth Com pact and Non - com pact I- sections the al low ale end ing stress de pends on the l r T ra tio. 30 Calculation o Allowale Stresses

36 Chapter III Check/Design or AISC-ASD89 or l 10, 000 C r T, 33 = 0.60, (ASD 1-6) or 10, 000 C l 510, 000 C <, r T 33 ( l / rt ) = C 0.60, and (ASD 1-6) , 000 or l 510, 000 > r T C, C = 0, l r 0.6, (ASD 1-7) ( / T ) and 33 is taken not to e less than that given the ol low ing or mula: 33 1, 000 C = 0.6 (ASD 1-8) l d A ( / ) where, r T is the ra dius o g ra tion o a sec tion com pris ing the com pres sion lange and 1 3 the com pres sion we taken aout an axis in the plane o the we, M a C = + M + M M a.3, where (ASD 1.3) M a and M are the end mo ments o an un raced seg ment o the mem er and M a is nu mer i call less than M ; M a M e ing pos i tive or dou le cur va ture end ing and neg a tive or sin gle cur va ture end ing. Also, i an mo ment within the seg ment is greater than M, C is taken as 1.0. Also, C is taken as 1.0 or can ti le vers and rames raced against joint trans la tion (ASD 1.3). The pro - gram de aults C to 1.0 i the un raced length, l, o the mem er is re de ined the user (i.e. it is not equal to the length o the mem er). The user can over - write the value o C or an mem er spec i ing it. Calculation o Allowale Stresses 31

37 CSI Steel Design Manual The al low ale end ing stress or Slen der sec tions ent aout their ma jor axis is de ter mined in the same wa as or a Non com pact sec tion. Then the ol low ing ad di tional con sid era tions are taken into ac count. I the we is slen der, then the pre vi ousl com puted al low ale end ing stress is re duced as ol lows: = R R, where (ASD G-1) R R 33 PG e 33 PG e = A w h 760 = , (ASD G) A t 33 3 ( 3 ) 1 + A 1 + A w A A w 1.0, (h rid gird ers) (ASD G) R e =1.0, (non- hrid gird ers) (ASD G) A w = Area o we, in, A = Area o com pres sion lange, in, 0.6 = (ASD G) 33 = Al low ale end ing stress as sum ing the sec tion is non- compact, and 33 = Al low ale end ing stress a ter con sid er ing we slenderness. In the aove ex pres sions, R e is taken as 1, e cause cur rentl the pro gram deals with onl non-h rid gird ers. I the lange is slen der, then the pre vi ousl com puted al low ale end ing stress is taken to e lim ited as ollows. ( ) Q 0.6, where (ASD A-B5.a, A-B5.d) 33 s Q s is de ined ear lier. 3 Calculation o Allowale Stresses

38 Chapter III Check/Design or AISC-ASD89 Minor Axis o Bending The mi nor di rec tion al low ale end ing stress is taken as ol lows: or Com pact sec tions: = 0.75 i 65 ksi, (ASD -1) = 0.60 i > 65 ksi, (ASD -) or Non com pact and Slen der sec tions: = t, i 65 ksi, (ASD -3) = 0.60 i > 65 ksi.. (ASD -) Channel sections or Chan nel sec tions the length pa rame ter is taken as the lat er all un raced length, l, which is com pared to a criti cal length, l c. The criti cal length is de - ined as l c 76 0, 000 A = min, d, where (ASD 1-) A is the area o com pres sion lange, Major Axis o Bending I l is less than l c, the ma jor al low ale end ing stress or Com pact and Noncom pact sec tions is taken de pend ing on whether the sec tion is welded or rolled and whether is greater than 65 ksi or not. or Com pact sec tions: 33 = 0.66 i 65 ksi, (ASD 1-1) 33 = 0.60 i > 65 ksi, (ASD 1-5) or Non com pact sec tions: = t, i rolled and 65 ksi, (ASD 1-3) Calculation o Allowale Stresses 33

39 CSI Steel Design Manual = t k c, i welded and 65 ksi, (ASD 1-4) 33 = 0.60 i > 65 ksi.. (ASD 1-5) I the un raced length l is greater than l c, then or oth Com pact and Noncom pact Chan nel sections the al low ale end ing stress is taken as ollows: 33 1, 000 C = 0.6 (ASD 1-8) l d A ( / ) The al low ale end ing stress or Slen der sec tions ent aout their ma jor axis is de ter mined in the same wa as or a Non com pact sec tion. Then the ol low ing ad di tional con sid era tions are taken into ac count. I the we is slen der, then the pre vi ousl com puted al low ale end ing stress is re duced as ol lows: = R R (ASD G-1) 33 e PG 33 I the lange is slen der, the pre vi ousl com puted al low ale end ing stress is taken to e lim ited as ollows: ( ) Q 0.6 (ASD A-B5.a, A-B5.d) 33 s The dei ni tion or r T, C, A, A w, R e, R PG, Q s, 33, and 33 Minor Axis o Bending are given ear lier. The mi nor di rec tion al low ale end ing stress is taken as ol lows: = 0.60 (ASD -) T-sections and Doule angles or T sec tions and Dou le an gles, the al low ale end ing stress or oth ma jor and mi nor axes ending is taken as, = 0.60 Q. s 34 Calculation o Allowale Stresses