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**Limit States Flexure Shear Deflection Fatigue Supports Elastic Plastic**

Stability (buckling) Shear Deflection Fatigue Supports

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Flexure LRFD ASD Elastic Plastic Stability (buckling)

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

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Flexure - Plastic

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**Mp = Acfy = Atfy = fy (0.5A) a = Mp=Zfy**

Flexure - Plastic C=T Acfy=Atfy Ac=At Mp = Acfy = Atfy = fy (0.5A) a = Mp=Zfy Mp/ My =Z/S For shapes that are symmetrical about the axis of bending the plastic and elastic neutral axes are the same Z=(0.5A)a : Plastic Section Modulus (Tabulated Value)

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**Flange Local Buckling (FLB) Elastically or Inelastically **

Flexure - Stability A beam has failed when: Mp 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

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**Lb Flexure - Stability Slenderness Parameter FLB l=bf/2tf WLB l=h/tw**

LTB l= Lb /ry tf bf tw h Lb

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**FLB and WLB (Section B5 Table B4.1) **

Flexure - Stability FLB and WLB (Section B5 Table B4.1) Evaluate Moment Capacity for Different l Compact Non Slender Mp Mr lp lr FLB l=bf/2tf WLB l=h/tw

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**Slenderness Parameter - Limiting Values**

AISC B5 Table B4.1 pp

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**Slenderness Parameter - Limiting Values**

AISC B5 Table B4.1 pp

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**Slenderness Parameter - Limiting Values**

AISC B5 Table B4.1 pp

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**FLB and WLB (Section B5 Table B4.1)**

Flexure - Stability FLB and WLB (Section B5 Table B4.1) Compact Non Slender Mp Mr lp lr FLB l=bf/2tf WLB l=h/tw

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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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**Bending Strength of Compact Shapes**

Laterally Supported Compact Beams

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**Bending Strength of Compact Shapes**

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**Bending Strength of Compact Shapes**

Elastic Buckling

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Elastic Buckling Cb = factor to account for non-uniform bending within the unbraced length See AISC table 3-1 p 3.10 Mmax A B C L/4 L/4 L/4 L/4

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Elastic Buckling

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Elastic Buckling

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Elastic Buckling Cb = factor to account for non-uniform bending within the unbraced length Rm= 1 for doubly symmetric cross sections and singly symmetric subject to single curvature

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

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Elastic Buckling Cb = factor to account for non-uniform bending within the unbraced length ho = distance between flange centroids = d-tf

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**Bending Strength of Compact Shapes**

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**Bending Strength of Compact Shapes**

Inelastic Buckling Linear variation between Mp and Mr

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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) Shear Deflection

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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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**Web fails before flanges**

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

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**Design for Shear h/tw Failure of Web due to Shear: Yielding**

Inelastic Buckling Elastic Buckling h/tw>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 LRFD resistance factor for shear=0.9 maximum shear based on the controlling combination for factored loads nominal shear strength depends on failure mode ASD maximum shear based on the controlling combination for service loads Safety factor

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**AISC Spec requirements for Shear**

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

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**Shear is rarely a problem in rolled steel beams usual practice**

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 Mu or Ma**

Weight of Beam can be assumed and verified or ignored and checked after member is selected Select shape that satisfies strength requirements Assume shape, compute strength, compare with required, revise if necessary or Use beam design aids in Part 3 of the Manual Check Shear and deflections

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