ARCH 631 Note Set 21.1 S2017abn. Steel Design

Transcription

1 Steel Desig Notatio: a = ame or width dimesio A = ame or area Ag = gross area, equal to the total area igorig a holes Areq d-adj = area required at allowable stress whe shear is adjusted to iclude Aw sel weight = area o the web o a wide lage sectio, as is Aweb AISC= America Istitute o Steel Costructio ASD = allowable stress desig b b B B1 c c1 Cb = ame or a (base) width = ame or height dimesio = width o the lage o a steel beam cross sectio = width o a colum base plate = actor or determiig u or combied bedig ad compressio = largest distace rom the eutral axis to the top or bottom edge o a beam. as is cmax = coeiciet or shear stress or a rectagular bar i torsio = lateral torsioal bucklig modiicatio actor or momet i ASD & LRFD steel beam desig Cm = modiicatio actor accoutig or combied stress i steel desig Cv = web shear coeiciet d = ame or depth = depth o a wide lage sectio D = shorthad or dead load DL = shorthad or dead load E = shorthad or earthquake load = modulus o elasticit a = axial stress b = bedig stress p = bearig stress v = shear stress v-max = maximum shear stress = ield stress F = shorthad or luid load Fa = allowable axial (compressive) stress Fb = allowable bedig stress = lexural bucklig stress Fcr 415 Fe = elastic critical bucklig stress Fp = allowable bearig stress Fu = ultimate stress prior to ailure F = ield stregth Fw = ield stregth o web material h = ame or a height hc = height o the web o a wide lage steel sectio H = shorthad or lateral pressure load I = momet o iertia with respect to eutral axis bedig I = momet o iertia about the axis J = polar momet o iertia k = distace rom outer ace o W lage to the web toe o illet = shape actor or plastic desig o steel beams K = eective legth actor or colums, as is k l = ame or legth, as is L = colum base plate desig variable L = ame or legth or spa legth, as is l = shorthad or live load Lb = ubraced legth o a steel beam i LRFD desig Le = eective legth that ca buckle or colum desig, as is Lr = shorthad or live roo load = maximum ubraced legth o a steel beam i LRFD desig or ielastic lateral-torsioal bucklig Lp = maximum ubraced legth o a steel beam i LRFD desig or ull plastic lexural stregth LL = shorthad or live load LRFD = load ad resistace actor desig m = edge distace or a colum base plate = iteral bedig momet a = required bedig momet (ASD) max = maximum iteral bedig momet max-adj = maximum bedig momet adjusted to iclude sel weight e

2 = omial lexure stregth with the ull sectio at the ield stress or LRFD beam desig p = iteral bedig momet whe all ibers i a cross sectio reach the ield stress u = maximum momet rom actored loads or LRFD beam desig = iteral bedig momet whe the extreme ibers i a cross sectio reach the ield stress = edge distace or a colum base plate = colum base plate desig value.a. N P Pa Pc Pe1 Pr P Pp Pu r R Ra R Ru S = shorthad or eutral axis = bearig legth o a wide lage steel sectio = depth o a colum base plate = ame or load or axial orce vector = required axial orce (ASD) = available axial stregth = Euler bucklig stregth = required axial orce = omial colum load capacit i LRFD steel desig = omial bearig capacit o cocrete uder base plate = actored colum load calculated rom load actors i LRFD steel desig = radius o gratio = geeric load quatit (orce, shear, momet, etc.) or LRFD desig = shorthad or rai or ice load = required stregth (ASD) = omial value (capacit) to be multiplied b i LRFD ad divided b the saet actor i ASD = actored desig value or LRFD desig = shorthad or sow load = sectio modulus Sreq d = sectio modulus required at allowable stress Sreq d-adj = sectio modulus required at allowable stress whe momet is adjusted to iclude sel weight t = thickess o lage o wide lage tmi = miimum thickess o colum base plate tw = thickess o web o wide lage T = torque (axial momet) = shorthad or thermal load V = iteral shear orce Va = required shear (ASD) Vmax = maximum iteral shear orce Vmax-adj = maximum iteral shear orce adjusted to iclude sel weight V = omial shear stregth capacit or LRFD beam desig Vu = maximum shear rom actored loads or LRFD beam desig wequivalet = the equivalet distributed load derived rom the maximum bedig momet wsel wt = ame or distributed load rom sel weight o member W = shorthad or wid load X = colum base plate desig value Z = plastic sectio modulus o a steel beam Zreq d = plastic sectio modulus required Zx = plastic sectio modulus o a steel beam with respect to the x axis actual = actual beam delectio allowable = allowable beam delectio limit = allowable beam delectio limit max = maximum beam delectio = ield strai (o uits) b c v = resistace actor = resistace actor or bedig or LRFD = resistace actor or compressio or LRFD = resistace actor or shear or LRFD = colum base plate desig value = load actor i LRFD desig = pi ( radias or 180) = radial distace = saet actor or ASD 416

3 Steel Desig Structural desig stadards or steel are established b the aual o Steel Costructio published b the America Istitute o Steel Costructio, ad uses Allowable Stress Desig ad Load ad Factor Resistace Desig. With the 13 th editio, both methods are combied i oe volume which provides commo requiremets or aalses ad desig ad requires the applicatio o the same set o speciicatios. aterials America Societ or Testig aterials (AST) is the orgaizatio resposible or material ad other stadards related to mauacturig. aterials meetig their stadards are guarateed to have the published stregth ad material properties or a desigatio. A36 carbo steel used or plates, agles A572 high stregth low-allo used or some beams A992 or buildig ramig used or most beams (A572 Grade 60 has the same properties as A992) F = 36 ksi, F u = 58 ksi, E = 29,000 ksi F = 60 ksi, F u = 75 ksi, E = 29,000 ksi F = 50 ksi, F u = 65 ksi, E = 29,000 ksi ASD R a R where R a = required stregth (dead or live; orce, momet or stress) R = omial stregth speciied or ASD = saet actor Factors o Saet are applied to the limit stresses or allowable stress values: bedig (braced, Lb < Lp) = 1.67 bedig (ubraced, Lp < Lb ad Lb > Lr) = 1.67 (omial momet reduces) shear (beams) = 1.5 or 1.67 shear (bolts) = 2.00 (tabular omial stregth) shear (welds) = 2.00 Lb is the ubraced legth betwee bracig poits, laterall Lp is the limitig laterall ubraced legth or the limit state o ieldig Lr is the limitig laterall ubraced legth or the limit state o ielastic lateral-torsioal bucklig 417

4 LRFD R u R where where R u R i i = resistace actor = load actor or the tpe o load R = load (dead or live; orce, momet or stress) R u = actored load (momet or stress) R = omial load (ultimate capacit; orce, momet or stress) Nomial stregth is deied as the capacit o a structure or compoet to resist the eects o loads, as determied b computatios usig speciied material stregths (such as ield stregth, F, or ultimate stregth, F u) ad dimesios ad ormulas derived rom accepted priciples o structural mechaics or b ield tests or laborator tests o scaled models, allowig or modelig eects ad diereces betwee laborator ad ield coditios Factored Load Combiatios R The desig stregth,, o each structural elemet or structural assembl must equal or exceed the desig stregth based o the ASCE-7 combiatios o actored omial loads: 1.4D 1.2D + 1.6L + 0.5(Lr or S or R) 1.2D + 1.6(Lr or S or R) + (L or 0.5W) 1.2D + 1.0W + L + 0.5(Lr or S or R) 1.2D + 1.0E + L + 0.2S 0.9D + 1.0W 0.9D + 1.0E Criteria or Desig o Beams Allowable ormal stress or ormal stress rom LRFD should ot be exceeded: F b or F c I ( a / or u b ) b Kowig ad F, the miimum plastic sectio modulus ittig the limit is: Z req'd a F S req'd F b Besides stregth, we also eed to be cocered about serviceabilit. This ivolves thigs like limitig delectios & crackig, cotrollig oise ad vibratios, prevetig excessive settlemets o oudatios ad durabilit. Whe we kow about a beam sectio ad its material, we ca determie beam deormatios. 418

5 Determiig aximum Bedig omet Drawig V ad diagrams will show us the maximum values or desig. Computer applicatios are ver helpul. Determiig aximum Bedig Stress For a prismatic member (costat cross sectio), the maximum ormal stress will occur at the maximum momet. For a o-prismatic member, the stress varies with the cross sectio AND the momet. Delectios Elastic curve equatios ca be oud i hadbooks, textbooks, desig mauals, etc...computer programs ca be used as well. Elastic curve equatios ca be superpositioed ONLY i the stresses are i the elastic rage. The delected shape is roughl the same shape lipped as the bedig momet diagram but is costraied b supports ad geometr. Allowable Delectio Limits All buildig codes ad desig codes limit delectio or beam tpes ad damage that could happe based o service coditio ad severit. L actual allowable value Use LL ol DL+LL* Roo beams: Idustrial (o ceilig) L/180 L/120 Commercial plaster ceilig L/240 L/180 o plaster L/360 L/240 Floor beams: Ordiar Usage L/360 L/240 Roo or loor (damageable elemets) L/480 * IBC 2012 states that DL or steel elemets shall be take as zero Lateral Bucklig With compressio stresses i the top o a beam, a sudde poppig or bucklig ca happe eve at low stresses. I order to prevet it, we eed to brace it alog the top, or laterall brace it, or provide a bigger I. 419

6 Local Bucklig i Steel I Beams Web Cripplig or Flage Bucklig Cocetrated orces o a steel beam ca cause the web to buckle (called web cripplig). Web stieers uder the beam loads ad bearig plates at the supports reduce that tedec. Web stieers also prevet the web rom shearig i plate girders. The maximum support load ad iterior load ca be determied rom: P P (max ed) 5 (iterior) ( 2. k N )F ( 5k N )F where w = 1.00 (LRFD) t w w t w t w = thickess o the web N = bearig legth k = dimesio to illet oud i beam sectio tables = 1.50 (ASD) Beam Loads & Load Tracig I order to determie the loads o a beam (or girder, joist, colum, rame, oudatio...) we ca start at the top o a structure ad determie the tributar area that a load acts over ad the beam eeds to support. Loads come rom material weights, people, ad the eviromet. This area is assumed to be rom hal the distace to the ext beam over to halwa to the ext beam. The reactios must be supported b the ext lower structural elemet ad iiitum, to the groud. LRFD Bedig or Flexure For determiig the lexural desig stregth, b, or resistace to pure bedig (o axial load) i most lexural members where the ollowig coditios exist, a sigle calculatio will suice: iri u b 0. 9FZ 420

7 where u = maximum momet rom actored loads b = resistace actor or bedig = 0.9 = omial momet (ultimate capacit) F = ield stregth o the steel Z = plastic sectio modulus Plastic Sectio odulus Plastic behavior is characterized b a ield poit ad a icrease i strai with o icrease i stress. Iteral omets ad Plastic Higes = 50ksi 1 E = Plastic higes ca develop whe all o the material i a cross sectio sees the ield stress. Because all the material at that sectio ca strai without a additioal load, the member segmets o either side o the hige ca rotate, possibl causig istabilit. For a rectagular sectio: Elastic to : I c bh 6 2 b 2c 6 2 2bc 3 2 Full Plastic: ult or p bc For a o-rectagular sectio ad iteral equilibrium at, the.a. will ot ecessaril be at the cetroid. The.a. occurs where the Atesio = Acompressio. The reactios occur at the cetroids o the tesio ad compressio areas. Atesio = Acompressio 421

8 Istabilit rom Plastic Higes: Shape Factor: The ratio o the plastic momet to the elastic momet at ield: k p k = 3/2 or a rectagle k 1.1 or a I beam Plastic Sectio odulus Z p ad k Z S Desig or Shear Va V / or Vu vv The omial shear stregth is depedet o the cross sectio shape. Case 1: With a thick or sti web, the shear stress is resisted b the web o a wide lage shape (with the exceptio o a hadul o W s). Case 2: Whe the web is ot sti or doubl smmetric shapes, sigl smmetric shapes (like chaels) (excludig roud high stregth steel shapes), ielastic web bucklig occurs. Whe the web is ver sleder, elastic web bucklig occurs, reducig the capacit eve more: Case 1) For h t Case 2) For h t E w V 0. 6Fw Aw F w v = 1.00 (LRFD) = 1.50 (ASD) where h equals the clear distace betwee lages less the illet or corer radius or rolled shapes V = omial shear stregth F w = ield stregth o the steel i the web A w = t w d = area o the web E F V 0. 6Fw AwCv v = 0.9 (LRFD) = 1.67 (ASD) where C v is a reductio actor (1.0 or less b equatio) 422

9 Desig or Flexure a / or u b b = 0.90 (LRFD) = 1.67 (ASD) The omial lexural stregth is the lowest value obtaied accordig to the limit states o 1. ieldig, limited at legth L 1. 76r p E F 2. lateral-torsioal bucklig limited at legth L r 3. lage local bucklig 4. web local bucklig, where r is the radius o gratio i b Beam desig charts show available momet, / ad, or ubraced legth, Lb, o the compressio lage i oe-oot icremets rom 1 to 50 t. or values o the bedig coeiciet Cb = 1. For values o 1<Cb2.3, the required lexural stregth u ca be reduced b dividig it b Cb. (Cb = 1 whe the bedig momet at a poit withi a ubraced legth is larger tha that at both eds o the legth. Cb o 1 is coservative ad permitted to be used i a case. Whe the ree ed is ubraced i a catilever or overhag, Cb = 1. The ull ormula is provided below.) NOTE: the sel weight is ot icluded i determiatio o b Compact Sectios For a laterall braced compact sectio (oe or which the plastic momet ca be reached beore local bucklig) ol the limit state o ieldig is applicable. For ubraced compact beams ad o-compact tees ad double agles, ol the limit states o ieldig ad lateral-torsioal bucklig are applicable. Compact sectios meet the ollowig criteria: where: b = lage width i iches t = lage thickess i iches E = modulus o elasticit i ksi F = miimum ield stress i ksi hc = height o the web i iches tw = web thickess i iches b 2t E ad F h t c w E F With lateral-torsioal bucklig the omial lexural stregth is L Cb ( 0.7F S ) p p x L where p = = F Z x b r L L p p p 423

10 ad C b is a modiicatio actor or o-uiorm momet diagrams where, whe both eds o the beam segmet are braced: max Cb max A max = absolute value o the maximum momet i the ubraced beam segmet A = absolute value o the momet at the quarter poit o the ubraced beam segmet B = absolute value o the momet at the ceter poit o the ubraced beam segmet C = absolute value o the momet at the three quarter poit o the ubraced beam segmet legth. B C Available Flexural Stregth Plots Plots o the available momet or the ubraced legth or wide lage sectios are useul to id sectios to satis the desig criteria o a / or u b. The maximum momet that ca be applied o a beam (takig sel weight ito accout), a or u, ca be plotted agaist the ubraced legth, Lb. The limit Lp is idicated b a solid dot (), while Lr is idicated b a ope dot ( ). Solid lies idicate the most ecoomical, while dashed lies idicate there is a lighter sectio that could be used. Cb, which is a lateral torsioal bucklig modiicatio actor or o-zero momets at the eds, is 1 or simpl supported beams (0 momets at the eds). (see igure) 424

11 Desig Procedure The itet is to id the most light weight member (which is ecoomical) satisig the sectio modulus size. 1. Determie the ubraced legth to choose the limit state (ieldig, lateral torsioal bucklig or more extreme) ad the actor o saet ad limitig momets. Determie the material. 2. Draw V &, idig Vmax ad max.or uactored loads (ASD, Va & a) or rom actored loads (LRFD, Vu & u) 3. Calculate Zreq d whe ieldig is the limit state. This step is equivalet to determiig i max max max u b Fb, Zreq 'd ad Z req d to meet the desig criteria that ' S F F b bf / a or u b I the limit state is somethig other tha ieldig, determie the omial momet,, or use plots o available momet to ubraced legth, Lb. 4. For steel: use the sectio charts to id a trial Z ad remember that the beam sel weight (the secod umber i the sectio desigatio) will icrease Zreq d The desig charts show the lightest sectio withi a groupig o similar Z s. ****Determie the updated Vmax ad max icludig the beam sel weight, ad veri that the updated Zreq d has bee met.****** 5. Evaluate horizotal shear usig Vmax. This step is equivalet to determiig i v Fv is satisied to meet the desig criteria that V V / V V For I beams: Others: vmax vmax 3V 2A VQ Ib V A a or u v 6. Provide adequate bearig area at supports. This step is equivalet to determiig i is satisied to meet the desig criteria that Pa P / or Pu P T T 7. Evaluate shear due to torsio v or F 2 v J c ab web V t d 1 (circular sectio or rectagular) 8. Evaluate the delectio to determie i max LL LLallowed ad/or max Total Tota lallowed w V 0. 6F w A w or V 0. 6F w A w C P A v p F p **** ote: whe calculated > limit, Irequired ca be oud with: ad Sreq d will be satisied or similar sel weight ***** FOR ANY EVALUATION: 425 too big I req ' d I limit trial

12 Redesig (with a ew sectio) at a poit that a stress or serviceabilit criteria is NOT satisied ad re-evaluate each coditio util it is satisactor. Load Tables or Uiorml Loaded Joists & Beams Tables exist or the commo loadig situatio o uiorml distributed load. The tables either provide the sae distributed load based o bedig ad delectio limits, the give the allowable spa or speciic live ad dead loads icludig live load delectio limits. 2 w L I the load is ot uiorm, a equivalet uiorm load ca be calculated equivalet max rom the maximum momet equatio: 8 I the delectio limit is less, the desig live load to check agaist allowable must be icreased, ex. Criteria or Desig o Colums I we kow the loads, we ca select a sectio that is adequate or stregth & bucklig. I we kow the legth, we ca id the limitig load satisig stregth & bucklig. w adjusted w llhave L / 360 L / 400 table limit wated Desig or Compressio America Istitute o Steel Costructio (AISC) aual 14 th ed: Pa P / or Pu cp where P P u i i is a load actor P is a load tpe is a resistace actor P is the omial load capacit (stregth) = 0.90 (LRFD) = 1.67 (ASD) For compressio where : P F cr A g Ag is the cross sectio area ad Fcr is the lexural bucklig stress 426

13 The lexural bucklig stress, Fcr, is determied as ollows: whe KL r E or ( Fe 0. 44F ): F whe KL r F cr F F F e F E or ( Fe 0. 44F ): F cr F e where Fe is the elastic critical bucklig stress: F e 2 E KL 2 r Desig Aids Tables exist or the value o the lexural bucklig stress based o slederess ratio. I additio, tables are provided i the AISC aual or Available Stregth i Axial Compressio based o the eective legth with respect to least radius o gratio, r. I the critical eective legth is about the largest radius o gratio, rx, it ca be tured ito a eective legth about the axis b dividig b the ractio rx/r. Sample AISC Table or Available Stregth i Axial 427

14 Procedure or Aalsis 1. Calculate KL/r or each axis (i ecessar). The largest will gover the bucklig load. 2. Fid Fcr as a uctio o KL/r rom the appropriate equatio (above) or table. 3. Compute P = FcrAg or alterativel compute c = Pa/A or Pu/A 4. Is the desig satisactor? Is Pa P/ or Pu cp? es, it is; o, it is o good or Is c Fcr/ or cfcr? es, it is; o, it is o good Procedure or Desig 1. Guess a size b pickig a sectio. 2. Calculate KL/r or each axis (i ecessar). The largest will gover the bucklig load. 3. Fid Fcr as a uctio o KL/r rom appropriate equatio (above) or table. 4. Compute P = FcrAg or alterativel compute c = Pa/A or Pu/A 5. Is the desig satisactor? Is P P/ or Pu cp? es, it is; o, pick a bigger sectio ad go back to step 2. Is c Fcr/ or cfcr? es, it is; o, pick a bigger sectio ad go back to step Check desig eiciec b calculatig percetage o stress used: Pa Pu 100% or 100% P c P I value is betwee %, it is eiciet. I values is less tha 90%, pick a smaller sectio ad go back to step 2. Colums with Bedig (Beam-Colums) I order to desig a adequate sectio or allowable stress, we have to start somewhere: 1. ake assumptios about the limitig stress rom: - bucklig - axial stress - combied stress 1. See i we ca id values or r or A or Z. 2. Pick a trial sectio based o i we thik r or A is goig to gover the sectio size. 428

15 3. Aalze the stresses ad compare to allowable usig the allowable stress method or iteractio ormula or eccetric colums. 4. Did the sectio pass the stress test? - I ot, do ou icrease r or A or Z? - I so, is the dierece reall big so that ou could decrease r or A or Z to make it more eiciet (ecoomical)? 5. Chage the sectio choice ad go back to step 4. Repeat util the sectio meets the stress criteria. Desig or Combied Compressio ad Flexure: The iteractio o compressio ad bedig are icluded i the orm or two coditios based o the size o the required axial orce to the available axial stregth. This is otated as Pr (either Pa rom ASD or Pu rom LRFD) or the axial orce beig supported, ad Pc (either P/ or ASD or cp or LRFD). The icreased bedig momet due to the P- eect must be determied ad used as the momet to resist. Pr For 0. 2 : P c Pq 8 x 10. P 9 x (ASD) Pr For 0. 2 Pa x : 10. P 2P c x (ASD) Pu P c (LRFD) Pu 2 P c 8 9 b (LRFD) b ux ux x x b u b u where: or compressio c = 0.90 (LRFD) = 1.67 (ASD) or bedig b = 0.90 (LRFD) = 1.67 (ASD) m For a braced coditio, the momet magiicatio actor B1 is determied b B ( P where Cm is a modiicatio actor accoutig or ed coditios u Whe ot subject to trasverse loadig betwee supports i plae o bedig: = (1/2) 1.0, where 1 ad 2 are the ed momets ad 1<2. 1/2 is positive whe the member is bet i reverse curvature (same directio), egative whe bet i sigle curvature. Whe there is trasverse loadig betwee the two eds o a member: = 0.85, members with restraied (ixed) eds = 1.00, members with urestraied eds = 1.00 (LRFD), 1.60 (ASD) Pe1 =Euler bucklig stregth P e 1 2 EA Kl 2 r C 1 0 ) 1 1 P. e1 429

16 Criteria or Desig o Coectios ad Tesio embers Reer to the speciic ote set. Criteria or Desig o Colum Base Plates Colum base plates are desiged or bearig o the cocrete (cocrete capacit) ad lexure because the colum puches dow the plate ad it could bed upward ear the edges o the colum (show as 0.8b ad 0.95d). The plate dimesios are B ad N ad are preerabl i ull iches with thickesses i multiples o 1/8 iches. LRFD miimum thickess: t mi l 2P 0. 9F where l is the larger o m, ad m = N 0.95d 2 db 4 = u BN B 0.8b 2 2 X 1 (1 1 X ) where X depeds o the cocrete bearig capacit o c Pp, with c = 0.65 ad Pp = 0.85 ca 4db X ( d b ) Pu P 4db ( d b Pu (0.85 ) BN 2 2 c p ) c c 430

17 Listig o W shapes i Descedig Order o Zx or Beam Desig Z x US (i. 3 ) I x US (i. 4 ) Sectio I x SI (10 6 mm. 4 ) Z x SI (10 3 mm.3) Z x US (i. 3 ) I x US (i. 4 ) Sectio I x SI (10 6 mm. 4 ) Z x SI (10 3 mm.3) W33X W24X W24X W14X W36X W30X W30X W24X W18X W21X W14X W27X W12X W12X W21X W18X W24X W14X W33X W24X W27X W21X W18X W27X W30X W12X W14X W14X W21X W18X W12X W24X W24X W21X W33X W12X W30X W14X W18X W18X W27X W24X W14X W16X W12X W21X W30X W14X W21X W18X W24X W12X W18X W24X W14X W16X W12X W14X W30X W21X W27X W12X W21X W18X W24X W21X W18X W14X W14X W24X W30X W16X W12X W12X W21X W10X W27X W18X W18X (cotiued) 431

18 Listig o W Shapes i Descedig order o Zx or Beam Desig (Cotiued) Z x US (i. 3 ) I x US (i. 4 ) Sectio I x SI (10 6 mm. 4 ) Z x SI (10 3 mm.3) Z x US (i. 3 ) I x US (i. 4 ) Sectio I x SI (10 6 mm. 4 ) Z x SI (10 3 mm.3) W21X W18X W14X W12X W24X W16X W18X W14X W12X W8X W16X W12X W10X W10X W21X W14X W21X W16X W14X W12X W18X W8X W12X W14X W14X W10X W10X W16X W18X W12X W21X W14X W12X W8X W21X W10X W16X W12X W14X W10X W18X W8X W10X W14X W12X W10X W21X W8X W16X W12X W18X W8X W14X W10X W12X W12X W10X W8X W16X W10X W18X W8X W14X W12x W12X W10X W10X W12X W16X W8X W12X W10X W8X W8X W14X W10X W10X W8X W8X

19 Available Critical Stress, cfcr, or Compressio embers, ksi (F = 36 ksi ad c = 0.90) KL/r c F cr KL/r c F cr KL/r c F cr KL/r c F cr KL/r c F cr

20 Available Critical Stress, cfcr, or Compressio embers, ksi (F = 50 ksi ad c = 0.90) KL/r c F cr KL/r c F cr KL/r c F cr KL/r c F cr KL/r c F cr

21 Beam Desig Flow Chart Collect data: L,,, limits; id beam charts or load cases ad actual equatios ASD Allowable Stress or LRFD Desig? LRFD Collect data: F, Fu, ad saet actors Fid Vmax & max rom costructig diagrams or usig beam chart ormulas Fid Zreq d ad pick a sectio rom a table with Zx greater or equal to Zreq d Determie sel wt (last umber i ame) or calculate sel wt. usig A oud. Fid max-adj & Vmax-adj. Collect data: load actors, F, Fu, ad equatios or shear capacit with V Fid Vu & u rom costructig diagrams or usig beam chart ormulas with the actored loads Pick a steel sectio rom a chart havig b u or the kow ubraced legth OR id Zreq d ad pick a sectio rom a table with Zx greater or equal to Zreq d No Calculate Zreq d-adj usig max-adj. Is Zx(picked) Zreq d-adj? Determie sel wt (last umber i ame) or calculate sel wt. usig A oud. Factor with D. Fid u-max-adj & Vu-max-adj. Yes Is Vmax-adj (0.6FwAw)/.? Yes No pick a ew sectio with a larger web area Calculate max (o load actors!) usig superpositioig ad beam chart equatios with the Ix or the sectio is max limits? This ma be both the limit or live load delectio ad total load delectio.) Is u b Is Vu v(0.6fwaw) Yes No No pick a sectio with a larger web area too big I req ' d I trial limit No pick a sectio with a larger Ix Yes (DONE) 435