Beam_Design_Notes - DESIGN OF STEEL BEAMS[Reading Allen H.G...

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Beam_Design_Notes.doc p1 JWB September 2005 DESIGN OF STEEL BEAMS [Reading: Allen, H.G. and Bulson, P.S. Background to Buckling , McGraw-Hill, 1980; Trahair, N.S. and Bradford, M.A. Behaviour and Design of Steel Structures , 2 nd Ed., Taylor & Francis, 1994; CIVIL 211: Lecture Notes on Beam Behaviour, Plastic Analysis and Plate Buckling] I NTRODUCTION The strength limit state requirement for beam design was stated earlier as (see plastic analysis notes) n * M M φ (1) where M * denotes the maximum bending moment due to the application of factored loads, φ is the strength reduction factor (0.9), and M n is the nominal beam moment strength (M P or M RP ) 1.2G+1.5Q Factored Loads Analysis Design Actions (bending moments) (plastic or elastic) However, the assumption that the bending strength of the beam is φ M P is not always justified. Local or lateral buckling may occur before the full plastic moment capacity of the section is reached, and prevent it from being reached. L OCAL B UCKLING AND S ECTION M OMENT C APACITY , M S As discussed under plate buckling, parts of a beam cross-section may buckle locally before the fully plastic state is reached, or even before yield stress is reached, depending on their slenderness ratio. The high stresses in the compression flange tend to cause buckling as shown in the figure, limiting the section moment capacity, M s . The effects of local buckling are accounted for in the same way as used for column sections, using an effective section property that depends on the slenderness ratio of the web and flange. Plate element slenderness ratio, λ e : 250 t d or 250 T b y 1 y 1 e σ σ = λ (2) n * M M φ b 1 d 1 t T
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Beam_Design_Notes.doc p2 JWB September 2005 Plate element yield and plasticity limits, λ ey and λ ep : λ ey and λ ep are limiting values of slenderness ratio that determine the way a section will fail (for the origins of λ ey see pages 9 and 10 of Plate Buckling Notes). The values are specified in Table 5.2 of the Steel Design Standard, NZS3404. Selected values are shown in Table 1 below. Section slenderness ratio, λ s : ey e e s largest with element plate of λ λ λ = λ (3) Section description: Hot-rolled UB, UC Heavily welded BOX Cold-formed CHS Cold-formed RHS Plate element widths: b 1 d 1 b 1 b 2 b 1 d 1 d 0 b 2 d 1 λ ep 9 8 Flange outstand b 1 λ ey 16 14 λ ep 30 30 Flange b 2 supported along both edges λ ey 35 40 λ ep 82 82 45 Web d 1 supported along both edges λ ey 180 130 60 λ ep 50 Diameter d 0 λ ey 120 Table 1 Plasticity and yield slenderness limits (selected cases from Table 5.2, NZS3404). Section moment capacity M s and effective section modulus Z eff y eff s Z M σ = (4) Beams are divided into three categories depending on how the section slenderness compares with the plastic and yield slenderness limits, as shown in Table 2.
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Beam_Design_Notes.doc p3 JWB September 2005 Slenderness range Behaviour Effective Section Modulus Classification ep s λ < λ Section able to reach and sustain fully plastic moment M P , without local buckling p eff Z Z = COMPACT ey s ep λ < λ < λ Local buckling starts after yielding, but before fully plastic moment is achieved.
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