5 Flexure - CE 4401 Steel and Concrete Design CE 4401 STEEL...

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CE 4401 Steel and Concrete Design Steel Flexural Members -1 CE 4401 STEEL FLEXURAL MEMBERS AISC Manual Part 5 and AISC Specification Chapters B, F, L Flexural members: subjected to bending moment AISC F Beams: primary flexural members Girders: large beams Joists: small trusses used as beams Geometry Rule of thumb: 10 < L / d < 24 typically (to achieve reasonable serviceability) Larger L/d Æ Bouncier Beam Material Composition 1. Homogeneous – all the same material 2. Composite– more than one material a. Composite = concrete + steel b. Hybrid – different steel in flanges and web L d F yf F yw F yf > F yw
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CE 4401 Steel and Concrete Design Steel Flexural Members -2 BEHAVIOR UNDER FLEXURAL LOAD In-Plane Flexure /Lateral Torsional Buckling In–plane (elevation) Out-of-plane (plan view) Local Buckling Flange local buckling (FLB) Web local buckling (WLB) Lateral Buckling (LTB) L b = unbraced length P P Δ Out-of-plane bracing
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CE 4401 Steel and Concrete Design Steel Flexural Members -3 Critical slenderness parameters, λ , for flexure member: = L b / r y for lateral-torsional buckling (LTB) = b f /(2 t f ) for flange local buckling (FLB) = h / t w for web local buckling (WLB) Consider in-plane flexure (first drawing on prior page). Response would be: We’ll define these terms later M p M λ = L b / r y , b f /(2 t f ), h / t w Compact Non-compact Slender M θ Slender Non-compact Compact Ideal M p
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CE 4401 Steel and Concrete Design Steel Flexural Members -4 Elastic Behavior of Beams Recall key features of elastic behavior of beams (from deformable body mechanics and linear structural analysis) 1. Stress-strain curve is as follows: 2. Small deflections (i.e. sin θ =tan θ = θ ) 2 2 dz v d = φ 3. Sections that are initially planar and perpendicular to neutral axis remain so Æ y φ = ε Æ y E E φ = ε = σ Æ φ = φ = φ = σ = x A A I E dA y E dA y E ydA M 2 2 OR x EI M = φ Æ x I My = σ AND ' ' v EI M x = σ ε E 1 z y v φ dz
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CE 4401 Steel and Concrete Design Steel Flexural Members -5 Inelastic Behavior of Beams Bent about Strong Axis AISC Section F2 For considering inelastic behavior of beams for design, the following are commonly assumed: 1. Stress-strain curve is as follows: 2. Small deflections 3. Sections that are initial planar and perpendicular to neutral axis remain so M y = σ y S x Yield Moment Limit Æ M p Plastic Moment F y σ ε E = 0 E 1 y y y y ε y ε y σ y σ y σ y σ y σ y σ y σ y σ y
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CE 4401 Steel and Concrete Design Steel Flexural Members -6 Yield moment: Moment at which first yield occurs in cross section (at extreme fiber of cross section)
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5 Flexure - CE 4401 Steel and Concrete Design CE 4401 STEEL...

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