Limit States Flexure Elastic Plastic Stability (buckling) Shear Deflection Fatigue Supports Flexure u n bM M > Elastic Plastic Stability (buckling) abnMM>OLRFDASD 90 . 0 =b 67 . 1 = ObFlexure - Elastic IMyf =S=I/c : Section Modulus (Tabulated Value) SMIcM fmaxmax max= =Flexure - Plastic Flexure - Plastic Z=(0.5A)a : Plastic Section Modulus (Tabulated Value) 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 C=T Acfy=Atfy Ac=At Flexure - Stability 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 A beam has failed when: Flexure - Stability Slenderness Parameter FLB =bf/2tf WLB =h/tw LTB = Lb /ry tf bf tw h Lb Flexure - Stability FLB and WLB (Section B5 Table B4.1) Evaluate Moment Capacity for Different FLB =bf/2tf WLB =h/tw Compact Non Compact Slender Mp Mr p r Slenderness Parameter - Limiting Values AISC B5 Table B4.1 pp 16.1-16 Slenderness Parameter - Limiting Values AISC B5 Table B4.1 pp 16.1-17 Slenderness Parameter - Limiting Values AISC B5 Table B4.1 pp 16.1-18 Flexure - Stability FLB and WLB (Section B5 Table B4.1) FLB =bf/2tf WLB =h/tw Compact Non Compact Slender Mp Mr p r Bending Strength of Compact Shapes Lateral Torsional Buckling Bending Strength of Compact Shapes yy pFEr L 76 . 1 =Bending Strength of Compact Shapes Laterally Supported Compact Beams x y p nZ F M M = =yy p bFEr L L 76 . 1 = EJch S Fh SJcFEr L Lo x yo x yts r b( )222078 . 0 1||.|

\|+ =tsbo x ts bbcrrLh SJcr LE CFtx y rS F M 7 . 0 =Elastic Buckling Cb = factor to account for non-uniform bending within the unbraced length L/4L/4L/4L/4 ABC Mmax 0 . 33 4 3 5 . 25 . 12maxmaxs+ + +=mC B AbRM M M MMCSee AISC table 3-1 p 3.10 Elastic Buckling Elastic Buckling Elastic Buckling Cb = factor to account for non-uniform bending within the unbraced length 0 . 33 4 3 5 . 25 . 12maxmaxs+ + +=mC B AbRM M M MMCRm=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 ( )222078 . 0 1||.|

\|+ =tsbo x ts bbcrrLh SJcr LE CFtElastic Buckling Cb = factor to account for non-uniform bending within the unbraced length xw ytsSC Ir =2=channels for2shapes I symmetric doublyfor 1wyoCIhcho = distance between flange centroids = d-tf Bending Strength of Compact Shapes Bending Strength of Compact Shapes Inelastic Buckling ( )pp rp br p p b nML LL LM M M C M s(((

=r b pL L L