Steel Design
ARCH 331Note Set 18F2015abnSteel DesignNotation:name for width dimensionname for areaarea of a bolteffective net area found from theproduct of the net area An by theshear lag factor UAg gross area, equal to the total areaignoring any holesAgv gross area subjected to shear forblock shear ruptureAn net area, equal to the gross areasubtracting any holes, as is AnetAnt net area subjected to tension forblock shear ruptureAnv net area subjected to shear for blockshear ruptureAw area of the web of a wide flangesectionAISC American Institute of SteelConstructionASD allowable stress designb name for a (base) width total width of material at ahorizontal section name for height dimensionbf width of the flange of a steel beamcross sectionB1 factor for determining Mu forcombined bending and compressionc largest distance from the neutralaxis to the top or bottom edge of abeamc1 coefficient for shear stress for arectangular bar in torsionCb lateral torsional bucklingmodification factor for moment inASD & LRFD steel beam designCc column slenderness classificationconstant for steel column designCm modification factor accounting forcombined stress in steel designCv web shear coefficientd calculus symbol for differentiation depth of a wide flange section nominal bolt diameteraAAbAe nominal bolt diametershorthand for dead loadshorthand for dead loadeccentricityshorthand for earthquake loadmodulus of elasticityfcaxial compressive stressfbbending stressfpbearing stressfvshear stressfv-maxmaximum shear stressfyyield stressFshorthand for fluid loadFallow(able) allowable stress allowable axial (compressive) stressFaFb allowable bending stressFcr flexural buckling stressFe elastic critical buckling stressFEXX yield strength of weld material nominal strength in LRFDFn nominal tension or shear strength ofa boltFp allowable bearing stressFt allowable tensile stress ultimate stress prior to failureFuFv allowable shear stressFy yield strengthFyw yield strength of web materialF.S. factor of safetyg gage spacing of staggered boltholesG relative stiffness of columns tobeams in a rigid connection, as is Ψh name for a heighthc height of the web of a wide flangesteel sectionH shorthand for lateral pressure loadI moment of inertia with respect toneutral axis bendingItrial moment of inertia of trial sectionIreq’d moment of inertia required atlimiting deflection moment of inertia about the y axisIyJ polar moment of inertiadbDDLeE307
ARCH 331Note Set 18 distance from outer face of Wflange to the web toe of fillet shape factor for plastic design ofsteel beamsK effective length factor for columns,as is kl name for length length of beam in rigid joint b length of column in rigid joint cL name for length or span length shorthand for live loadLb unbraced length of a steel beamLc clear distance between the edge of ahole and edge of next hole or edgeof the connected steel plate in thedirection of the loadLe effective length that can buckle forcolumn design, as is eLr shorthand for live roof load maximum unbraced length of asteel beam in LRFD design forinelastic lateral-torsional bucklingLp maximum unbraced length of asteel beam in LRFD design for fullplastic flexural strengthL’ length of an angle in a connectorwith staggered holesLL shorthand for live loadLRFD load and resistance factor designM internal bending momentMa required bending moment (ASD)Mn nominal flexure strength with thefull section at the yield stress forLRFD beam designMmax maximum internal bending momentMmax-adj maximum bending momentadjusted to include self weightMp internal bending moment when allfibers in a cross section reach theyield stressMu maximum moment from factoredloads for LRFD beam designMy internal bending moment when theextreme fibers in a cross sectionreach the yield stressn number of boltsn.a. shorthand for neutral axisF2015abn bearing length on a wide flangesteel section bearing type connection withthreads included in shear planep bolt hole spacing (pitch)P name for load or axial force vectorPa allowable axial force required axial force (ASD)Pallowable allowable axial forcePc available axial strengthPe1 Euler buckling strengthPn nominal column load capacity inLRFD steel designPr required axial forcePu factored column load calculatedfrom load factors in LRFD steeldesignQ first moment area about a neutralaxis generic axial load quantity forLRFD designr radius of gyrationry radius of gyration with respect to ay-axisR generic load quantity (force, shear,moment, etc.) for LRFD design shorthand for rain or ice load radius of curvature of a deformedbeamRa required strength (ASD)Rn nominal value (capacity) to bemultiplied by φ in LRFD anddivided by the safety factor Ω inASDRu factored design value for LRFDdesigns longitudinal center-to-centerspacing of any two consecutiveholesS shorthand for snow load section modulus allowable strength per length of aweld for a given sizeSreq’d section modulus required atallowable stressSreq’d-adj section modulus required atallowable stress when moment isadjusted to include self weightSC slip critical bolted connectionkN308
ARCH 331Note Set 18 thickness of the connected material thickness of flange of wide flange thickness of web of wide flange torque (axial moment) shorthand for thermal load throat size of a weldU shear lag factor for steel tensionmember designUbs reduction coefficient for blockshear ruptureV internal shear forceVa required shear (ASD)Vmax maximum internal shear forceVmax-adj maximum internal shear forceadjusted to include self weightVn nominal shear strength capacity forLRFD beam designVu maximum shear from factored loadsfor LRFD beam designw name for distributed loadwadjusted adjusted distributed load forequivalent live load deflection limitwequivalent the equivalent distributed loadderived from the maximum bendingmomentwself wt name for distributed load from selfweight of memberW shorthand for wind loadx horizontal distanceX bearing type connection withthreads excluded from the shearplaneF2015abn vertical distance plastic section modulus of a steelbeamZreq’d plastic section modulus requiredZx plastic section modulus of a steelbeam with respect to the x axisα method factor for B1 equation actual actual beam deflection allowable allowable beam deflection limit allowable beam deflection limit max maximum beam deflection yield strain (no units)εyttftwTyZφγ resistance factor diameter symbol resistance factor for bending forLRFD resistance factor for compressionfor LRFD resistance factor for tension forLRFD resistance factor for shear forLRFD load factor in LRFD designπθρΩ Σ φbφcφtφvSteel DesignStructural design standards for steel are establishedby the Manual of Steel Construction published by theAmerican Institute of Steel Construction, and usesAllowable Stress Design and Load and FactorResistance Design. With the 13th edition, bothmethods are combined in one volume which providescommon requirements for analyses and design andrequires the application of the same set ofspecifications.309pi (3.1415 radians or 180 )slope of the beam deflection curveradial distancesafety factor for ASDsymbol for integrationsummation symbol
ARCH 331Note Set 18F2015abnMaterialsAmerican Society for Testing Materials (ASTM) is the organization responsible for material andother standards related to manufacturing. Materials meeting their standards are guaranteed tohave the published strength and material properties for a designation.A36 – carbon steel used for plates, anglesA572 – high strength low-alloy use for some beamsA992 – for building framing used for most beams(A572 Grade 50 has the same properties as A992)ASDRa RnFy 36 ksi, Fu 58 ksi, E 29,000 ksiFy 60 ksi, Fu 75 ksi, E 29,000 ksiFy 50 ksi, Fu 65 ksi, E 29,000 ksiΩwhereRa required strength (dead or live; force, moment or stress)Rn nominal strength specified for ASDΩ safety factorFactors of Safety are applied to the limit stresses for allowable stress values:bending (braced, Lb Lp)bending (unbraced, Lp Lb and Lb Lr)shear (beams)shear (bolts)shear (welds)-Ω 1.67Ω 1.67 (nominal moment reduces)Ω 1.5 or 1.67Ω 2.00 (tabular nominal strength)Ω 2.00Lb is the unbraced length between bracing points, laterallyLp is the limiting laterally unbraced length for the limit state of yieldingLr is the limiting laterally unbraced length for the limit state of inelastic lateral-torsionalbucklingLRFDwhere Ru Σγ i RiRu φRnwhereφ resistance factorγ load factor for the type of loadR load (dead or live; force, moment or stress)Ru factored load (moment or stress)Rn nominal load (ultimate capacity; force, moment or stress)Nominal strength is defined as thecapacity of a structure or component to resist the effects of loads, as determined bycomputations using specified material strengths (such as yield strength, Fy, or ultimatestrength, Fu) and dimensions and formulas derived from accepted principles of structuralmechanics or by field tests or laboratory tests of scaled models, allowing for modelingeffects and differences between laboratory and field conditions310
ARCH 331Note Set 18F2015abnFactored Load CombinationsThe design strength, φRn , of each structural element or structural assembly must equal or exceedthe design strength based on the ASCE-7 (2010) combinations of factored nominal loads:1.4D1.2D 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 0.2S0.9D 1.0W0.9D 1.0ECriteria for Design of BeamsAllowable normal stress or normal stress from LRFD should not beexceeded:McI( M a M n / Ω or M u φ b M n )F b or φ F n f b Knowing M and Fy, the minimum plastic section modulus fitting the limit is:Z req 'd Determining Maximum Bending Moment M S req' d Fb MaFy ΩDrawing V and M diagrams will show us the maximum values for design. Remember:V Σ( w)dxM Σ(V )dxdM VdxdV wdxDetermining Maximum Bending StressFor a prismatic member (constant cross section), the maximum normal stress will occur at themaximum moment.For a non-prismatic member, the stress varies with the cross section AND the moment.Deflections1 M ( x) REIIf the bending moment changes, M(x) across a beam of constant material and crosssection then the curvature will change:θ slope The slope of the n.a. of a beam, θ, will be tangent to the radius ofcurvature, R:The equation for deflection, y, along a beam is:311y 1M ( x)dxEI 11θdx EIEI M ( x)dx
ARCH 331Note Set 18F2015abnElastic curve equations can be found in handbooks, textbooks, design manuals, etc.Computerprograms can be used as well. Elastic curve equations can be superimposed ONLY if the stressesare in the elastic range.The deflected shape is roughly the same shape flipped as the bending moment diagram but isconstrained by supports and geometry.Allowable Deflection LimitsAll building codes and design codes limit deflection for beam types and damage that couldhappen based on service condition and severity.y max ( x) actual allowable LUseLL onlyRoof beams:Industrial (no ceiling) L/180Commercialplaster ceilingL/240no plasterL/360Floor beams:Ordinary UsageL/360Roof or floor (damageable elements)valueDL LL*L/120L/180L/240L/240L/480* IBC 2012 states that DL for steel elements shall be taken as zeroLateral BucklingWith compression stresses in the top of a beam, a sudden “popping” or buckling can happeneven at low stresses. In order to prevent it, we need to brace it along the top, or laterally brace it,or provide a bigger Iy.Local Buckling in Steel Wide-flange Beams– Web Crippling or Flange BucklingConcentrated forces on a steel beam can cause the web to buckle (called web crippling). Webstiffeners under the beam loads and bearing plates at the supports reduce that tendency. Webstiffeners also prevent the web from shearing in plate girders.312
ARCH 331Note Set 18F2015abnThe maximum support load and interior load can bedetermined from:Pn (max end) ( 2.5k N )Fyw t wPn (interior) ( 5k N )Fyw t wwheretw thickness of the webFyw yield strength of the webN bearing lengthk dimension to fillet found in beam section tablesφ 1.00 (LRFD)Ω 1.50 (ASD)Beam Loads & Load TracingIn order to determine the loads on a beam (or girder, joist, column, frame, foundation.) we canstart at the top of a structure and determine the tributary area that a load acts over and the beamneeds to support. Loads come from material weights, people, and the environment. This area isassumed to be from half the distance to the next beam over to halfway to the next beam.The reactions must be supported by the next lower structural element ad infinitum, to the ground.LRFD - Bending or FlexureFor determining the flexural design strength, φbMn , for resistance to pure bending (no axial load)in most flexural members where the following conditions exist, a single calculation will suffice:Σγ i R i M u φ b M n 0 . 9 F y ZwhereMu maximum moment from factored loadsφb resistance factor for bending 0.9Mn nominal moment (ultimate capacity)Fy yield strength of the steelZ plastic section modulusfPlastic Section Modulusfy 50ksiPlastic behavior is characterized by a yield point and anincrease in strain with no increase in stress.E1εy 0.001724313ε
ARCH 331Note Set 18F2015abnInternal Moments and Plastic HingesPlastic hinges can develop when all of the material in a crosssection sees the yield stress. Because all the material at that sectioncan strain without any additional load, the member segments oneither side of the hinge can rotate, possibly causing instability.For a rectangular section:Elastic to fy:I2bc 2bh 2b(2c )M y fy fy fy fyc663Fully Plastic:M ult or M p bc 2 f y 3 M y22For a non-rectangular section and internal equilibrium at σy, then.a. will not necessarily be at the centroid. The n.a. occurs wherethe Atension Acompression. The reactions occur at the centroids of thetension and compression areas.Instability from Plastic HingesAtension AcompressionShape Factor:The ratio of the plastic moment to the elastic moment at yield:Mk pk 3/2 for a rectangleMyk 1.1 for an I beamPlastic Section ModulusMpZ andfyk ZS314
ARCH 331Note Set 18F2015abnDesign for ShearVa Vn / Ω or Vu φvVnThe nominal shear strength is dependent on the cross section shape. Case 1: With a thick or stiffweb, the shear stress is resisted by the web of a wide flange shape (with the exception of ahandful of W’s). Case 2: When the web is not stiff for doubly symmetric shapes, singlysymmetric shapes (like channels) (excluding round high strength steel shapes), inelastic webbuckling occurs. When the web is very slender, elastic web buckling occurs, reducing thecapacity even more:Case 1) For h tw 2.24EFyVn 0.6Fyw Awφv 1.00 (LRFD)Ω 1.50 (ASD)where h equals the clear distance between flanges less the fillet or cornerradius for rolled shapesVn nominal shear strengthFyw yield strength of the steel in the webAw twd area of the webCase 2) For h tw 2.24EFyVn 0.6Fyw AwCvφv 0.9 (LRFD)Ω 1.67 (ASD)where Cv is a reduction factor (1.0 or less by equation)Design for FlexureMa Mn / Ω or Mu φb Mnφb 0.90 (LRFD)Ω 1.67 (ASD)The nominal flexural strength Mn is the lowest value obtained according to the limit states of1. yielding, limited at length Lp 1.76ryE, where ry is the radius of gyration in yFy2. lateral-torsional buckling limited at length Lr3. flange local buckling4. web local bucklingBeam design charts show available moment, Mn/Ω and φb Mn , for unbraced length, Lb, of thecompression flange in one-foot increments from 1 to 50 ft. for values of the bending coefficientCb 1. For values of 1 Cb 2.3, the required flexural strength Mu can be reduced by dividing itby Cb. (Cb 1 when the bending moment at any point within an unbraced length is larger thanthat at both ends of the length. Cb of 1 is conservative and permitted to be used in any case.When the free end is unbraced in a cantilever or overhang, Cb 1. The full formula is providedbelow.)NOTE: the self weight is not included in determination of Mn/Ω and φb Mn315
ARCH 331Note Set 18F2015abnCompact SectionsFor a laterally braced compact section (one for which the plastic moment can be reached beforelocal buckling) only the limit state of yielding is applicable. For unbraced compact beams andnon-compact tees and double angles, only the limit states of yielding and lateral-torsionalbuckling are applicable.bfhEECompact sections meet the following criteria:and c 3.76 0.382t fFytwFywhere:bf flange width in inchestf flange thickness in inchesE modulus of elasticity in ksiFy minimum yield stress in ksihc height of the web in inchestw web thickness in inchesWith lateral-torsional buckling the nominal flexural strength is M n C b M p ( M p 0 .7 F y S x Lb L p Mp) L L p rwhere Mp Mn FyZxand Cb is a modification factor for non-uniform moment diagrams where, when both ends ofthe beam segment are braced:12.5M maxCb 2.5M max 3M A 4 M B 3M CMmax absolute value of the maximum moment in the unbraced beam segmentMA absolute value of the moment at the quarter point of the unbraced beam segmentMB absolute value of the moment at the center point of the unbraced beam segmentMC absolute value of the moment at the three quarter point of the unbraced beamsegment length.Available Flexural Strength PlotsPlots of the available moment for the unbraced length for wide flange sections are useful to findsections to satisfy the design criteria of M a M n / Ω or M u φb M n . The maximum moment thatcan be applied on a beam (taking self weight into account), Ma or Mu, can be plotted against theunbraced length, Lb. The limiting length, Lp (fully plastic), is indicated by a solid dot ( ), whilethe limiting length, Lr (for lateral torsional buckling), is indicated by an open dot ( ). Solid linesindicate the most economical, while dashed lines indicate there is a lighter section that could beused. Cb, which is a lateral torsional buckling modification factor for non-zero moments at theends, is 1 for simply supported beams (0 moments at the ends). (see figure)316
ARCH 331Note Set 18F2015abnDesign ProcedureThe intent is to find the most light weight member (which is economical) satisfying the sectionmodulus size.1. Determine the unbraced length to choose the limit state (yielding, lateral torsional bucklingor more extreme) and the factor of safety and limiting moments. Determine the material.2. Draw V & M, finding Vmax and Mmax.for unfactored loads (ASD, Va & Ma) or from factoredloads (LRFD, Vu & Mu)3. Calculate Zreq’d when yielding is the limit state. This step is equivalent to determining ifM max M maxMuM max and Z req 'd to meet the design criteria thatfb F b , Z req' d FyFbφ b FySΩMa Mn / Ω or Mu φb MnIf the limit state is something other than yielding,determine the nominal moment, Mn, or use plots ofavailable moment to unbraced length, Lb.4. For steel: use the section charts to find a trial Z andremember that the beam self weight (the second numberin the section designation) will increase Zreq’d. Thedesign charts show the lightest section within a groupingof similar Z’s.**** Determine the “updated” Vmax and Mmax including thebeam self weight, and verify that the updated Zreq’d has been met.******317
ARCH 331Note Set 18F2015abn5. Consider lateral stability.6. Evaluate horizontal shear using Vmax. This step is equivalent to determining if f v Fv issatisfied to meet the design criteria that Va Vn / Ω or Vu φvVn3VVV 2 A Aweb t w dVQ IbFor I beams:f v max Others:f v maxVn 0.6 Fyw Awor V n 0.6 F yw Aw C v7. Provide adequate bearing area at supports. This step is equivalent to determining ifis satisfied to meet t
ARCH 331 Note Set 18 F2015abn 307 Steel Design Notation: a name for width dimension A name for area Ab area of a bolt Ae effective net area found from the product of the net area An by the shear lag factor U Ag gross area, equal to the total area ignoring any holes Agv gross area subjected to shear for block shear rupture
EN 1993-1-4 Design of steel structures: General rules: Supplementary rules for stainless steels EN 1993-1-5 Design of steel structures: Plated structural elements EN 1993-1-8 Design of steel structures: Design of joints EN 1993-1-9 Design of steel structures: Fatigue EN 1993-1-10 Design of steel structures: Material toughness and through .
steel, weathering steel, fire-resistant steel, high-toughness steel, low-yield-point steel, memory alloy steel, additive manufacturing steel and other types/grades of steel used in construction different from low grade carbon steel. Currently, the council focuses on the structures made of HPS and their joints using bolted and welded connections.
on behalf of sumitomo metal industries limited. american boiler manufacturers association and american boiler manufacturers association, bhp steel pty ltd. bhp new zealand steel limited bhp steel americas inc. and nippon steel corp., kawasaki steel corp., katakura steel. nkk corp., kobe special steel ltd.
1.2.1 Steel Deck Institute (SDI) A. SDI C-2011, Standard for Composite Steel Floor Deck-Slabs B. SDI NC-2010, Standard for Noncomposite Steel Floor Deck C. SDI RD-2010, Standard for Steel Roof Deck 1.3 Definitions Accessories: Cold-formed steel components of the steel deck system other than the steel deck, which
EN 1993-1-3 Design of steel structures: General rules: Supplementary rules for cold-formed members and sheeting EN 1993-1-4 Design of steel structures: General rules: Supplementary rules for stainless steels EN 1993-1-5 Design of steel structures: Plated structural elements EN 1993-1-8 Design of steel structures: Design of joints EN 1993-1-9 .
1. Introduction, history of steel structures, the applications and some representative structures, production of steel 2. Steel products, material properties and testing, steel grades 3. Manufacturing of steel structures, welding, mechanical fasteners 4. Safety of structures, limit state design, codes and specifications for the design 5.
used in steel bridges and their tensile, chemical, and impact energy requirements. A timeline of major design changes, such as welding and bolting, composite design, and fatigue design, is presented. 17. Key Words . Steel bridges, bridge design, welding, bolting, steel properties, AASHTO, AASHO, ASTM, historic steel . 18. Distribution Statement
anddistribution systems using welded steel pipe. Publication Number D631-0807-e Published by AMERICAN IRON AND STEEL INSTITUTE In cooperation with, and editorial collaboration by, STI/SPFA (Steel Tank Institute/Steel Plate Fabricators Association).
