eighteen combined in 2005 steel construction: materials & - PowerPoint PPT Presentation

A RCHITECTURAL S TRUCTURES : Steel Beam Design F ORM, B EHAVIOR, AND D ESIGN ARCH 331 • American Institute of Steel Construction D R. A NNE N ICHOLS – Manual of Steel Construction S PRING 2018 – ASD & LRFD lecture eighteen – combined in 2005 steel construction: materials & beams Steel Beams 1 Architectural Structures F2009abn Lecture 18 ARCH 331 Steel Beams 2 Foundations Structures F2008abn Lecture 18 ARCH 331 Steel Materials Steel Materials • smelt iron ore • cast into billets • add alloying elements • hot rolled • heat treatments • cold formed Hot Rolled • iron, carbon • residual stress • microstructure • corrosion-resistant “ weathering ” steels • stainless Cold Formed AISC AISC A36 steel, JOM 1998 Steel Beams 3 Foundations Structures F2008abn Steel Beams 4 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 1

Steel Materials Steel Properties • steel grades • high strength to weight ratio • elastic limit – yield (F y ) – ASTM A36 – carbon • inelastic – plastic • plates, angles • F y = 36 ksi & F u = 58 ksi • ultimate strength (F u ) – ASTM A572 – high strength low-alloy • ductile strain hardening • some beams • strength sensitive • F y = 60 ksi & F u = 75 ksi to temperature – ASTM A992 – for building framing • can corrode • most beams • fatigue • F y = 50 ksi & F u = 65 ksi Winnepeg DOT Steel Beams 5 Foundations Structures F2008abn Steel Beams 6 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 Structural Steel Steel Construction • standard rolled shapes (W, C, L, T) • welding • open web joists • bolts • plate girders • decking http://courses.civil.ualberta.ca Steel Beams 7 Foundations Structures F2008abn Steel Beams 8 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 2

Steel Construction Unified Steel Design • ASD • fire proofing R a ≤ R n  – cementicious spray – encasement in gypsum  = 1.67 – bending (braced) – intumescent – expands  = 1.67 – bending (unbraced * ) with heat  = 1.5 or 1.67 – shear – sprinkler system – shear (bolts & welds)  = 2.00  = 2.00 – shear (welds) * flanges in compression can buckle Steel Beams 10 Foundations Structures F2008abn Steel Beams 9 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 Unified Steel Design LRFD • braced vs. • loads on structures are unbraced – not constant – can be more influential on failure – happen more or less often – UNCERTAINTY       R R R R u D D L L n  - resistance factor  - load factor for (D)ead & (L)ive load Steel Beams 12 Foundations Structures F2008abn Steel Beams 11 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 3

ASCE-7 LRFD Steel Beam Design LRFD Load Combinations (2005) • 1.4(D + F) • limit state is yielding all across section • 1.2(D + F + T)+ 1.6(L + H)+ • outside elastic range 0.5(L r or S or R) • load factors & resistance factors • 1.2D + 1.6(L r or S or R) + (L or 0.8W) f • 1.2D + 1.6W + L + 0.5(L r or S or R) f y = 50ksi • 1.2D + 1.0E + L + 0.2S E 1  • 0.9D + 1.6W + 1.6H  y = 0.001724 • 0.9D + 1.0E + 1.6H Steel Beams 14 Foundations Structures F2008abn Steel Beams 13 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 Beam Design Criteria (revisited) Steel Beams • strength design • lateral stability - bracing – bending stresses predominate • local buckling – stiffen, or bigger I y – shear stresses occur • serviceability – limit deflection + + – stability • superpositioning – use of beam charts = = – elastic range only! – “ add ” moment diagrams – “ add ” deflection CURVES (not maximums) Steel Beams 16 Foundations Structures F2008abn Steel Beams 15 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 4

Local Buckling Local Buckling • steel I beams • web • flange • flange – buckle in direction of smaller radius of gyration • web – force – “ crippling ” Steel Beams 17 Foundations Structures F2008abn Steel Beams 18 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 Shear in Web Shear in Web • panels in plate girders or webs with large shear • plate girders and stiffeners • buckling in compression direction • add stiffeners http:// nisee.berkeley.edu/godden Steel Beams 19 Foundations Structures F2008abn Steel Beams 20 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 5

Steel Beams LRFD - Flexure • bearing       R M M 0 . 9 F Z – provide i i u b n y adequate area M u - maximum moment – prevent  b - resistance factor for bending = 0.9 local yield M n - nominal moment (ultimate capacity) of flange F y - yield strength of the steel and web Z - plastic section modulus* Steel Beams 21 Foundations Structures F2008abn Steel Beams 22 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 Internal Moments - at yield Internal Moments - ALL at yield • material hasn ’ t failed • all parts reach yield • plastic hinge forms • ultimate moment 2 I bh   M f f • A tension = A compression y y y c 6   2 2 2 2  b c bc   3   2 M bc f M  y = 50ksi f f 2 p y y y y 6 3 E 1   y = 0.001724 Steel Beams 23 Foundations Structures F2008abn Steel Beams 24 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 6

n.a. of Section at Plastic Hinge Plastic Hinge Development • cannot guarantee at centroid •  f y· A 1 =  f y· A 2 • moment found from yield stress times moment area    M f A d f A d p y 1 y i i n . a Steel Beams 25 Foundations Structures F2008abn Steel Beams 26 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 Plastic Hinge Examples Plastic Section Modulus • stability can be effected • shape factor, k M k  p M y = 3/2 for a rectangle k  Z  1.1 for an I S M Z  p • plastic modulus, Z f y Steel Beams 27 Foundations Structures F2008abn Steel Beams 28 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 7

LRFD – Shear (compact shapes) LRFD - Flexure Design • limit states for beam failure  i R i = V u ≤  v V n = 1.0(0.6 F yw A w ) 1. yielding 2. lateral-torsional buckling* V u - maximum shear 3. flange local buckling  v - resistance factor for shear = 1.0 4. web local buckling V n - nominal shear • minimum M n governs F yw - yield strength of the steel in the web      R M M A w - area of the web = t w d i i u b n Steel Beams 29 Foundations Structures F2008abn Steel Beams 30 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 Compact Sections Lateral Torsional Buckling   • plastic moment can form before any   moment based on M C M n b p buckling lateral buckling • criteria 12 . 5 M  max C b E    b 2 . 5 M 3 M 4 M 3 M  f 0.38 max A B C – C b = modification factor 2 t F f y M max - |max moment|, unbraced segment h E M A - |moment|, 1/4 point  – and c 3.76 M B = |moment|, center point t F w y M C = |moment|, 3/4 point Steel Beams 31 Foundations Structures F2008abn Steel Beams 32 Foundations Structures F2008abn Lecture 18 ARCH 331 Lecture 18 ARCH 331 8

Charts & Deflections Beam Design Charts • beam charts – solid line is most economical – dashed indicates there is another more economical section – self weight is NOT included in M n • deflections – no factors are applied to the loads – often governs the design Steel Beams 34 Foundations Structures F2008abn Steel Beams 33 Foundations Structures Su2011abn Lecture 18 ARCH 331 Lecture 15 ARCH 331 Design Procedure (revisited) Beam Charts by S x (Appendix) 1. Know unbraced length, material, design method (  ,  ) 2. Draw V & M, finding M max ( M a ≤ M n /  ) 3. Calculate Z req’d   ( M M ) u b n 4. Choose (economical) section from section or beam capacity charts Steel Beams 36 Foundations Structures F2008abn Steel Beams 35 Foundations Structures Su2011abn Lecture 18 ARCH 331 Lecture 15 ARCH 331 9

Beam Charts by Z x (Appendix) Beam Design (revisited) 4*. Include self weight for M max – it’s dead load – and repeat 3 & 4 if necessary 5. Consider lateral stability Unbraced roof trusses were blown down in 1999 at this project in Moscow, Idaho. Photo: Ken Carper Steel Beams 37 Foundations Structures F2011abn Steel Beams 37 Foundations Structures Su2011abn Lecture 18 ARCH 331 Lecture 15 ARCH 331 Beam Design (revisited) Beam Design (revisited) 7. Provide adequate bearing 6. Evaluate shear - horizontal ( P a ≤ P n /  )   a ≤ V n /  ) area at supports • ( V V ) ( V or ( P u ≤  P n ) u v n 3 V V   f • rectangles and W’s  v max 2 A A web V n = 0.6 F yw A w VQ  • f general  v max Ib Steel Beams 39 Foundations Structures F2008abn Steel Beams 38 Foundations Structures Su2011abn Lecture 18 ARCH 331 Lecture 15 ARCH 331 10