# Limit States Flexure Shear Deflection Fatigue Supports Elastic Plastic

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

Flexure LRFD ASD Elastic Plastic Stability (buckling)

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

Flexure - Plastic

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)

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

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

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

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

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

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

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

Bending Strength of Compact Shapes
Lateral Torsional Buckling

Bending Strength of Compact Shapes

Bending Strength of Compact Shapes
Laterally Supported Compact Beams

Bending Strength of Compact Shapes

Bending Strength of Compact Shapes
Elastic Buckling

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

Elastic Buckling

Elastic Buckling

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

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

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

Bending Strength of Compact Shapes

Bending Strength of Compact Shapes
Inelastic Buckling Linear variation between Mp and Mr

Nominal Flexural Strength – Compact Shapes

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)

Nominal Flexural Strength – NON-Compact Shapes
WLB

Design of Beams - Limit States
Flexure Elastic Plastic Stability (buckling) Shear Deflection

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

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

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:

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

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

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

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

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

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

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

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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