Unified Straight and Curved Steel Girder Design Specifications Introduction Unified Steel Specifications Straight Curved One Spec! Unified Steel Girder Design Specification 2-1
Unified Steel Girder Design � Fundamentals � Design Checks � Examples Fundamentals � Primary-Strength Flexural & Shear Effects � Lateral Flange Effects � Differential Deflection Effects � Torsion Effects � Lateral Force Effects � Second-Order Effects � Cross Frame Forces Unified Steel Girder Design Specification 2-2
6.10.8 Flexural Resistance - Composite I FLB and LTB Sections in Negative Flexure & B a s i c Fo r m o f A l l F L B & L T B E q s Noncomposite I Sections - (cont’d) − F L L = − − y r b p ≤ F C 1 1 R R F R R F nc b − b h y c b h y c R F L L F n o r M n A n c h o r p o i n t 1 h y c r p F = R R F λ − λ F F m a x o r nc b h yc yr = − − f pf F 1 1 R R F M m a x M m a x nc λ − λ b h yc M m a x R F yc rf pf h A n c h o r p o i n t 2 M r M r F r o r M r = ≤ F F R R F π 2 nc cr b h yc C R E c o m p a c t c o m p a c t n o n c o m p a c t n o n c o m p a c t b b 2 ( i n e l a s t i c b u c k l i n g ) ( i n e l a s t i c b u c k l i n g ) L b r n o n s l e n d e r n o n s l e n d e r s l e n d e r s l e n d e r t ( e l a s t i c b u c k l i n g ) ( e l a s t i c b u c k l i n g ) λ p λ p λ r λ r L p o r λ p f L r o r λ rf L b o r b fc / 2 t fc Post Web Buckling Strength f ⇒ ≤ φ ≤ φ bu f R R F F f yf bu f b h yf R R b h Buckled Web Sheds Stress to the Compression Flange Reducing D c Flange Yielding Moment Tension Moment First Yield with Buckled Web Flange = ≤ R 1 . 0 = b M F S y y a 2 D = − −λ ≤ wc c R 1 1.0 + b rw 1200 300 a t wc w Unified Steel Girder Design Specification 2-3
Fundamentals � Primary Flexural & Shear Effects � Lateral Flange Effects � Differential Deflection Effects � Torsion Effects � Lateral Force Effects � Second-Order Effects � Cross Frame Forces Fundamentals � Primary Flexural & Shear Effects � Lateral Flange Effects � Differential Deflection Effects � Torsion Effects � Lateral Force Effects � Second-Order Effects � Cross Frame Forces Unified Steel Girder Design Specification 2-4
Differential Load/Deflection Effects • Outside girder carries OUTSIDE L1 L2 GIRDER more load • Vertical Deflection is not equal between adjacent PIER girders ABUT ABUT => Torsional Effects on INSIDE PLAN VIEW GIRDER Girders, Lateral Flange Bending, and Affects fit- up during construction Fundamentals � Primary Flexural & Shear Effects � Lateral Flange Effects � Differential Deflection Effects � Torsion Effects � Lateral Force Effects � Second-Order Effects � Cross Frame Forces Unified Steel Girder Design Specification 2-5
Torsion Effects � Deformations � Stresses Torsion Deformations � Twisting � Warping => Affect fit-up during construction Unified Steel Girder Design Specification 2-6
6.7.2 Dead Load Camber � Contract documents should state: • Intended erected position: • Webs vertical or plumb, or • Webs out-of-plumb 6.7.2 Dead Load Camber, cont’d � Contract documents should state: • Condition for intended position: • No-load, • Steel dead load, or • Full dead load Unified Steel Girder Design Specification 2-7
Torsion Stresses • St. Venant • Warping g n i d n e B e g n a l F l a r e t a L X X Normal Stresses Shear Stresses Fundamentals � Primary Flexural & Shear Effects � Lateral Flange Effects � Differential Deflection Effects � Torsion Effects � Lateral Force Effects � Second-Order Effects � Cross Frame Forces Unified Steel Girder Design Specification 2-8
Lateral Force Effects ± ≤ f f ? f F bu l bu r Bending stress due to vertical loads f l flange lateral bending stress due to wind, skew, or curvature “One-Third” Rule 1.2 1 F yf – f l / 3 (Hall and Yoo 1998) 0.856F yf – f l / 3 0.8 f bu / F yf Flange Plastic Strength 0.6 0.4 0.7F yf – f l / 3 0.2 AISC/AASHTO Beam- Column Interaction Curves 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 f l / F yf Unified Steel Girder Design Specification 2-9
=> Lateral Force Effects & “One-Third” Rule 1 + ≤ φ f f F l bu f nc 3 1 + ≤ φ f f F f l bu f yt bu 3 Bending stress due to vertical loads f l flange lateral bending stress due to wind, skew, or curvature Implementation of “One-Third” Rule 1 + ≤ f f F Strength Limit State, Constructibility-Compression l bu r Discretely Braced Flanges 3 1 + ≤ Strength Limit State – Compact Straight M f S M l u x r 3 1 ⇒ + ≤ f f F Constructibility Yielding 1 l bu r 3 1 ⇒ 1 1 + ≤ f f F Service Limit State l bu r 2 3 2 Braced Flanges Continuously ≤ = f F ALL L.S., Continuously Braced Flanges, f 0 l bu r Unified Steel Girder Design Specification 2-10
Implementation of “One-Third” Rule 1 + ≤ Strength Limit State, Constructibility-Compression f f F l bu r Discretely Braced Flanges 3 1 + ≤ Strength Limit State – Compact Straight M f S M u l x r 3 1 ⇒ + ≤ f f F Constructibility Yielding 1 l bu r 3 1 ⇒ 1 1 + ≤ f f F Service Limit State l bu r 2 3 2 Braced Flanges Continuously ≤ = f F f 0 ALL L.S., Continuously Braced Flanges, l bu r Implementation of “One-Third” Rule 1 + ≤ f f F Strength Limit State, Constructibility-Compression l bu r Discretely Braced Flanges 3 1 + ≤ Strength Limit State – Compact Straight M f S M l u x r 3 1 ⇒ + ≤ f f F Constructibility Yielding 1 l bu r 3 1 ⇒ 1 1 + ≤ f f F Service Limit State l bu r 2 3 2 Braced Flanges Continuously ≤ = f F ALL L.S., Continuously Braced Flanges, f 0 l bu r Unified Steel Girder Design Specification 2-11
Implementation of “One-Third” Rule 1 + ≤ Strength Limit State, Constructibility-Compression f f F l bu r Discretely Braced Flanges 3 1 + ≤ Strength Limit State – Compact Straight M f S M u l x r 3 1 ⇒ + ≤ f f F Constructibility Yielding 1 l bu r 3 1 ⇒ 1 1 + ≤ f f F Service Limit State l bu r 2 3 2 Braced Flanges Continuously ≤ = f F f 0 ALL L.S., Continuously Braced Flanges, l bu r Implementation of “One-Third” Rule 1 + ≤ f f F Strength Limit State, Constructibility-Compression l bu r Discretely Braced Flanges 3 1 + ≤ Strength Limit State – Compact Straight M f S M l u x r 3 1 ⇒ + ≤ f f F Constructibility Yielding 1 l bu r 3 1 ⇒ 1 1 + ≤ f f F Service Limit State l bu r 2 3 2 Braced Flanges Continuously ≤ = f F ALL L.S., Continuously Braced Flanges, f 0 l bu r Unified Steel Girder Design Specification 2-12
Fundamentals � Primary Flexural & Shear Effects � Lateral Flange Effects � Differential Deflection Effects � Torsion Effects � Lateral Force Effects � Second-Order Effects � Cross Frame Forces (Primary Members) Second-Order Effects (Art. 6.10.1.6) C R > b b L 1 . 2 L � If b p f F bu yc Second-order compression-flange lateral bending stresses may be approximated by amplifying first-order value: π 2 0 . 85 C R E = ≥ = b b f f f F l l l cr 1 1 f 2 − bu L 1 b F cr r t Unified Steel Girder Design Specification 2-13
Fundamentals � Primary Flexural & Shear Effects � Lateral Flange Effects � Differential Deflection Effects � Torsion Effects � Lateral Force Effects � Second-Order Effects � Cross Frame Forces ( Primary Members ) Unified Curved Steel Girder Design � Fundamentals � Design Checks � Examples Unified Steel Girder Design Specification 2-14
Design Checks � Constructibility � Service Limit State � Fatigue Limit State � Strength Limit State 6.10.3.2 Constructibility - Flexure � Discretely braced compression flanges 1 + ≤ φ = f f F ( FLB or LTB , max R F ) l bu f nc h yc 3 + ≤ φ f f R F l bu f h yc 9 0 . 9 Ek = = ≤ φ ⇒ = k ( R 1 . 0 ) f F F ( ) 2 bu f crw b crw 2 D D D c t � Discretely braced tension flanges w + ≤ φ f f R F l bu f h yt � Continuously braced flanges ≤ φ f R F bu f h yf Unified Steel Girder Design Specification 2-15
Design Checks � Constructibility � Service Limit State � Fatigue Limit State � Strength Limit State 6.10.4.2 Service Limit State Permanent Deformations � Composite: ≤ f 0 . 95 R F f h yf ( ) − ≤ f F M only c crw f + 2 ≤ l f 0 . 95 R F f h yf � Noncomposite: f + 2 ≤ l f 0 . 80 R F f h yf f ≤ F c crw f + 2 ≤ l f 0 . 80 R F f h yf Unified Steel Girder Design Specification 2-16
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