CIENE4226_L8_Plate_Girders2_2020.pdf - CIEN E4226 Advanced...

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L8-1CIEN E4226Advanced Design of Steel StructuresSpring 2020; Thursday 7.00 – 9.30pm, 227 MUDD Amr Aly, Virginia Mosquera[email protected]; 332.204.7965[email protected]; 212-367-2918TA: Lampros Svolos: [email protected]
L8-2COURSE OUTLINE – Plate Girders, Lecture 8 II. Plate GirdersLecture 8 – March 26th, 2020Plate GirdersPlate Girder ConstructionDifferential Equilibrium EquationBuckling Stress of PlatesPost Buckling Behavior of PlatesRules of Thumb for the Design of Plate GirdersFlexural Limit StatesFlange Buckling Limit state Bend-buckling of the Web Nominal Moment Strength Nominal Shear StrengthNominal Shear Strength – including Tension FieldIntermediate Stiffeners Bearing Stiffeners Design Example
L. F. Geschwindner - Unified Design of Steel Structures. 2ndEd. Wiley, 2012 G. Salmon, J.E. Johnson – Steel Structures. 4th Ed., Harper Collins, 1996. (lib)A. Williams – Structural Steel Design LRFD. Kaplan AEC Engineering. 2001. (lib) L. F. Geschwindner - Unified Design of Steel Structures. 2ndEd. Wiley, 2012 T.V. Galambos – Guide to Stability Design Criteria for Metal Structures. 5th Ed. John Wiley & Sons, NY. 1998. (lib)G. Ballio, F.M. Mazzolani – Theory and Design of Steel Structures. Taylor and Francis.1984.D.A. Nethercot – Limit States Design of Structural Steelwork. Chapman & Hall, 2nd Ed. 1996. A.C. Ugural, S.K. Fenster – Advanced Strength and Applied Elasticity. 3rd Ed. Prentice Hall. 1995. (lib) AISC Steel Construction Manual. 13th, 14th& 15thEds. (lib)J. McCormac, Stephen Csernak – Structural Steel Design, 5thEd. Prentice Hall. 2012Timoshenko S.P. and Gere J.M. – ‘Theory of Elastic Stability’, McGraw Hill Book Company, New York, 1961.. Dowling P.J, Knowles P. and Owens G.W – ’Structural Steel Design’, The Steel Construction Institute, 1988. Gaylord E. H. et al – ‘Design of Steel Structures’, McGraw Hill, 1992. Bulson P. S. – ‘Theory of Flat Plates’, Chatto and Windus, London, 1970. Bleich H. – ‘Buckling Strength of Metal Structures’, McGraw Hill, 1952. L8-3PLATE GIRDERS – REFFERENCES
L8-4PLATE GIRDERS: Nominal Shear StrengthIn I-shaped plate girders, the web carries most of the shearTypically, plate girders have thin web 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠ℎ 𝑡𝑡𝑤𝑤>970𝐹𝐹𝑦𝑦Web stability is a major concernElastic Bucking: Stress of any plate is given as:𝐹𝐹𝑐𝑐𝑐𝑐=𝑘𝑘𝜋𝜋2𝐸𝐸121− 𝜇𝜇2𝑏𝑏𝑡𝑡2For pure shear the buckling stress iswritten as𝜏𝜏𝑐𝑐𝑐𝑐=𝑘𝑘𝑣𝑣𝜋𝜋2𝐸𝐸121−𝜇𝜇2𝑡𝑡2(59)For simply supported edges (displ. is prevented, but rotation about edges unrestrained)with 𝑘𝑘𝑣𝑣= 4.0 + 5.34/𝑎𝑎 ℎ2for 𝑎𝑎 ℎ ≤1.0and 𝑘𝑘𝑣𝑣=4.0𝑎𝑎 ℎ2+ 5.34for 𝑎𝑎 ℎ ≥1.0The theoretical expressions for 𝑘𝑘𝑣𝑣are expressed in AISC-G2.1b as𝑘𝑘𝑣𝑣= 5for unstiffened webs having 𝑡𝑡𝑤𝑤< 260𝑘𝑘𝑣𝑣= 5 +5(𝑎𝑎)2for stiffened webs𝑘𝑘𝑣𝑣= 5for stiffened webs with 𝑎𝑎> 3.0or 𝑎𝑎>260ℎ 𝑡𝑡𝑤𝑤2
L8-5PLATE GIRDERS: Nominal Shear StrengthFor use in design, equation (59) is expressed in a non-dimensional form, defining the ratio of shear stress at buckling 𝜏𝜏𝑐𝑐𝑐𝑐to the shear stress at yield 𝜏𝜏𝑦𝑦as:web shear coeff.𝐶𝐶𝑣𝑣=𝜏𝜏𝑐𝑐𝑐𝑐𝜏𝜏𝑦𝑦=𝜋𝜋2𝐸𝐸𝑘𝑘𝑣𝑣𝜏𝜏𝑦𝑦121−𝜇𝜇2ℎ 𝑡𝑡2(60)Substituting 𝐸𝐸=

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