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Beams BEAMS A structural member loaded in the transverse direction to the longitudinal axis. Internal Forces: Bending Moments and Shear Beam Shapes Section Properties AISC Section I Beams h 970 tw fy Plate Girders h 970 tw fy • W- (eg W44x335) Most commonly Used/Wide Flange I, pp 1-10:1-27 • S- (eg S24x121) pp. 1-30:1-31 • M- (eg M12x11.8) pp. 1-28:1-29 • Channels (eg C15x50) pp. 1-34:1-39 Structural Steel - Sections Built Up members I Shapes H Shapes Box Shapes Fillet Welding Welding Fillet of Web Web to to of Flange Plates Plates Flange Beams E 29,0 0 0.38 9.15 6.2 p 0.38 0 5 F Depending on the use they are referred to as: Joists y Support Floor Deck Floor Beams Beams that support joists Girders: Support most load in a floor system Lintels Over Windows and Door Openings Support portion of wall above opening Beams Depending on the use they are referred to as: Purlins Support Roof Surface Roof Beams Support Purlins Spandrel Beams Support outside edges of a floor deck and outside walls of buildings Structural Steel - Characteristics Buckling: Instability due to slenderness Elastic Buckling Limit States Load Deflection 500 450 Load (kips) 400 350 300 250 200 150 100 50 0 0 4 8 12 Deflection (in) 16 20 FEM 24 Test Limit States Limit States Limit States Limit States • Flexure •Elastic •Plastic •Stability (buckling) • • • • Shear Deflection Fatigue Supports Flexure LRFD bM n M u b 0.90 ASD Mn Ma b b 1.67 Elastic Plastic Stability (buckling) Flexure - Elastic My f I f max M max M max c I S S=I/c : Section Modulus (Tabulated Value) Example Compute My Flexure - Plastic 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) Example Compute Mp Example 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 Flexure - Stability FLB Slenderness Parameter WLB LTB =bf/2tf =h/tw = Lb /ry bf tf h tw Lb Flexure - Stability FLB and WLB (Section B5 Table B4.1) Evaluate Moment Capacity for Different Mp Mr Non Compact Compact Slender p r FLB WLB =bf/2tf =h/tw 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) Mp Mr Non Compact Compact Slender p r FLB WLB =bf/2tf =h/tw Example The beam shown is a W16X31 of A992 steel. It supports a reinforced concrete slab that provides continuous lateral support of the compression flange. Service dead load is 450 lb/ft (does not include weight of beam). Service live load is 550 lb/ft. Does the beam have adequate moment strength? Example Determine Nominal Flexural Strength Flange Compactness bf 6.28 2t f p 0.38 E 29,000 0.38 9.15 6.28 Fy 50 Flange Compact Web Compactness h 15.7 62.8 tw 0.25 p 3.76 29,000 90.55 62.8 50 Web Compact Example Shape is compact and continuously supported => Plastic Hinge Forms Nominal Flexural Strength Mn M p Fy Z x 5054.0 2,700in - kips 225ft.kips Moment Demand wD 450 31 481lb/ft 0.48130 MD 54.11 ft - kips 8 2 wL2 M max @ mid - span 8 wL 550lb/ft 0.5530 ML 61.88 ft - kips 8 2 Example LRFD M u 1.2M D 1.6M L 164 ft - kips b M n 0.9225.0 203ft - kips M u 164 OK ASD M a M D M L 54 61.88 116.0 ft - kips M n 225 135ft - kips M a 116 b 1.67 OK