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Limit States Flexure Elastic Plastic Stability (buckling) Shear Deflection Fatigue Supports

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Flexure Elastic Plastic Stability (buckling) LRFDASD

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Flexure - Elastic S=I/c : Section Modulus (Tabulated Value)

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Flexure - Plastic

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Z=(0.5A)a : Plastic Section Modulus (Tabulated Value) M p = A c f y = A t f y = f y (0.5A) a = M p =Zf y M p/ M y =Z/S For shapes that are symmetrical about the axis of bending the plastic and elastic neutral axes are the same C=T A c f y =A t f y A c =A t

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Flexure - Stability M p is reached and section becomes fully plastic Or Flange Local Buckling (FLB) Elastically or Inelastically Web Local Buckling (WLB) Elastically or Inelastically Lateral Torsional Buckling (LTB) Elastically or Inelastically A beam has failed when:

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Flexure - Stability Slenderness Parameter FLB =b f /2t f WLB =h/t w LTB = L b /r y tftf bfbf twtw h LbLb

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Flexure - Stability FLB and WLB (Section B5 Table B4.1) Evaluate Moment Capacity for Different FLB =b f /2t f WLB =h/t w Compact Non Compact Slender MpMp MrMr p r

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Slenderness Parameter - Limiting Values AISC B5 Table B4.1 pp 16.1-16

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Slenderness Parameter - Limiting Values AISC B5 Table B4.1 pp 16.1-17

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Slenderness Parameter - Limiting Values AISC B5 Table B4.1 pp 16.1-18

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Flexure - Stability FLB and WLB (Section B5 Table B4.1) FLB =b f /2t f WLB =h/t w Compact Non Compact Slender MpMp MrMr p r

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Bending Strength of Compact Shapes Lateral Torsional Buckling

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Bending Strength of Compact Shapes

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Laterally Supported Compact Beams

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Bending Strength of Compact Shapes

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Elastic Buckling

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C b = factor to account for non-uniform bending within the unbraced length L/4 ABC M max See AISC table 3-1 p 3.10

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Elastic Buckling

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C b = factor to account for non-uniform bending within the unbraced length R m =1 for doubly symmetric cross sections and singly symmetric subject to single curvature

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Elastic Buckling C b = factor to account for non-uniform bending within the unbraced length

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Elastic Buckling C b = factor to account for non-uniform bending within the unbraced length h o = distance between flange centroids = d-t f

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Bending Strength of Compact Shapes

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Inelastic Buckling Linear variation between M p and M r

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Nominal Flexural Strength – Compact Shapes

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Nominal Flexural Strength – NON-Compact Shapes Most W- M- S- and C- shapes are compact A few are NON-compact NONE is slender Webs of ALL hot rolled shapes in the manual are compact FLB and LTB Built-Up welded shapes can have non-compact or slender webs FLB, WLB, LTB (AISC F4 and F5)

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Nominal Flexural Strength – NON-Compact Shapes WLB

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Design of Beams - Limit States Flexure Elastic Plastic Stability (buckling) ShearShear DeflectionDeflection

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Design for Shear Large concentrated loads placed near beam supports Rigid connection of beams and columns with webs on the same plane Notched or coped beams Heavily loaded short beams Thin webs in girders

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Design for Shear V: Vertical shear at the section under consideration Q: First moment about of neutral axis of area of the cross section between point of interest and top or bottom of section (depends on y) I: Moment of inertia of section b: width of section at point of interest

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Design for Shear Web fails before flanges d/b=2Error ~3% d/b=1Error ~12% d/b=1/4Error 100% Small width b Nominal Strength if no buckling: Average Shear Stress

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Design for Shear Yielding Inelastic Buckling Elastic Buckling Failure of Web due to Shear: h/t w h/t w >260 Stiffeners are required Appendix F2

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Design for Shear AISC Specs G pp 16.1-64 Shear Strength must be sufficient to satisfy resistance factor for shear=0.9 nominal shear strength depends on failure mode maximum shear based on the controlling combination for factored loads LRFD Safety factor maximum shear based on the controlling combination for service loads ASD

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AISC Spec requirements for Shear C v depends on whether the limit state is web yielding, web inelastic buckling or web elastic buckling

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AISC Spec requirements for Shear Special Case for Hot Rolled I shapes with Most W shapes with

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AISC Spec requirements for Shear Chapter G All other doubly and singly symmetric shapes except round HSS

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DEFLECTIONS AISC Specs Chapter L Serviceability Limit State Use deflection formulas in AISC Part 3 Or standard analytical or numerical methods Calculate due to UNFACTORED (service) loads Governing Building Code, IBC etc Deflections due to Service Loads Limiting Value <

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Design Shear is rarely a problem in rolled steel beams usual practice Design for Flexure and Check for Shear and Deflections Or Design for Deflections and Check for Flexure and Shear

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Design Compute Required Moment Strength M u or M a –Weight of Beam can be assumed and verified or ignored and checked after member is selected Select shape that satisfies strength requirements A)Assume shape, compute strength, compare with required, revise if necessary or B)Use beam design aids in Part 3 of the Manual Check Shear and deflections

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