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 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 Beams Plate Girders

Structural Steel - Sections Built Up members I Shapes H Shapes Box Shapes

Beams Depending on the use they are referred to as: Joists 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 Purlins Support Roof Surface Roof Beams Support Purlins Spandrel Beams Support outside edges of a floor deck and outside walls of buildings Depending on the use they are referred to as:

Structural Steel - Characteristics Buckling:Instability due to slenderness

Elastic Buckling

Limit States

Flexure Elastic Plastic Stability (buckling) Shear Deflection Fatigue Supports

Flexure Elastic Plastic Stability (buckling) LRFDASD

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

Example Compute M y

Flexure - Plastic

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

Example Compute M p

Example

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:

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

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

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

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

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 Flange Compact Web Compactness Web Compact

Example Shape is compact and continuously supported => Plastic Hinge Forms Nominal Flexural Strength Moment Demand

Example LRFD OK ASD OK