design of bending members in steel. steel wide flange beams in an office building

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Design of Bending Members in Steel Slide 2 Steel wide flange beams in an office building Slide 3 Composite Steel-Concrete Girders Slide 4 German Historical Museum An example of curved steel beams Slide 5 Sea to sky highway, Squamish Steel Girders for Bridge Decks Slide 6 Cantilevered arms for steel pole Slide 7 What can go wrong ? STEEL BEAMS: Bending failure Lateral torsional buckling Shear failure Bearing failure (web crippling) Excessive deflections Slide 8 Bending Strength Linear elastic stresses M Design Equation: Where F b is the characteristic bending strength For steel this is F b = F y For timber it is F b = f b (K D K H K Sb K T ) y Slide 9 Plastic moment capacity of steel beams Yield moment MyMy FyFy Plastic moment MpMp FyFy C T a AcAc AtAt Which is the definition of the plastic section modulus Z Z can be found by halving the cross-sectional area and multiplying the distance between the centroids of the two areas with one of the areas This is also called the first moment of area So, when do we use the one or the other ?? Slide 10 Steel beam design equation For laterally supported beams (no lateral torsional buckling) M r = F y Z for class 1 and 2 sections M r = F y S for class 3 sections where = 0.9 Slide 11 Steel cross-section classes Class 4 Real thin plate sections Will buckle before reaching F y at extreme fibres M r < M y (Use Cold Formed Section Code S136) Class 3 Fairly thin (slender) flanges and web Will not buckle until reaching F y in extreme fibres M r = M y Class 2 Stocky plate sections Will not buckle until at least the plastic moment capacity is reached M r = M p Class 1 Very stockyplate sections Can be bent beyond M p and can therefore be used for plastic analysis M r = M p Slide 12 Load deflection curves for Class 1 to Class 4 sections Slide 13 Local buckling of the compression flange Slide 14 Local torsional buckling of the compression flange Slide 15 Local web buckling Slide 16 Lateral torsional buckling x x x y y y y xx yy LeLe Elastic buckling: M u = / L e (GJ EI y ) + (/L) 2 EI y EC w Moment gradient factor Torsional stiffness Lateral bending stiffness Warping stiffness Slide 17 Moment resistance of laterally unsupported steel beams LeLe M r / MuMu M max = M y for class 3 or M p for class 1 and 2 0.67M max M max 1.15 M max [1- (0.28M max /M u )] Slide 18 Shear stress in a beam max V/A w =V/wd b=w A N.A. y d y A b d max = V(0.5A)(d/4) (bd 3 /12)b =1.5 V/A Slide 19 Shear design of a steel I-beam d w h A w = d.w for rolled shapes and h.w for welded girders V r = A w 0.66 F y for h/w 1018/F y = 54.4 for 350W steel For welded plate girders when h/w 1018/F y the shear stress is reduced to account for buckling of the web (see clause This is the case for all rolled shapes Slide 20 Bearing failures in a steel beam k N N+4t N+10t w For end reactions For interior reactions Slide 21 Deflections A serviceability criterion Avoid damage to cladding etc. ( L/180) Avoid vibrations ( L/360) Aesthetics ( L/240) Use unfactored loads Typically not part of the code


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