sixteen steel construction: materials & beams Steel Beams 1 - PowerPoint PPT Presentation

E LEMENTS OF A RCHITECTURAL S TRUCTURES : Steel Beam Design F ORM, B EHAVIOR, AND D ESIGN ARCH 614 • American Institute of Steel Construction D R. A NNE N ICHOLS – Manual of Steel Construction S PRING 2019 – ASD & LRFD lecture – combined in 2005 sixteen steel construction: materials & beams Steel Beams 1 Elements of Architectural Structures S2009abn Steel Beams 2 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 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 -- ASTM A913 • fatigue • • F y = 50 ksi & F u = 65 ksi some columns • Grade 65 and 70 Winnepeg DOT Steel Beams 4 Elements of Architectural Structures S2007abn Steel Beams 3 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 1

Steel Construction Structural Steel • welding • standard rolled shapes (W, C, L, T) • bolts • open web joists • plate girders • decking http://courses.civil.ualberta.ca Steel Beams 6 Elements of Architectural Structures S2007abn Steel Beams 5 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 Unified Steel Design Unified Steel Design • ASD • braced vs. R a ≤ R n  unbraced  = 1.67 – bending (braced)  = 1.67 – bending (unbraced * )  = 1.5 or 1.67 – shear – shear (bolts & welds)  = 2.00  = 2.00 – shear (welds) * flanges in compression can buckle Steel Beams 7 Elements of Architectural Structures S2012abn Steel Beams 8 Elements of Architectural Structures S2012abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 2

LRFD LRFD Steel Beam Design • loads on structures are • limit state is yielding all across section – not constant • outside elastic range – can be more influential on failure • load factors & resistance factors – happen more or less often f – UNCERTAINTY f y = 50ksi       R R R R E u D D L L n 1   y = 0.001724  - resistance factor  - load factor for (D)ead & (L)ive load Steel Beams 9 Elements of Architectural Structures S2007abn Steel Beams 10 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 ASCE-7 LRFD Load Combinations Beam Design Criteria (revisited) (2010) • strength design • 1.4D – bending stresses predominate • 1.2D + 1.6L + 0.5(L r or S or R) – shear stresses occur • 1.2D + 1.6(L r or S or R) + (L or 0.5W) • serviceability – limit deflection • 1.2D + 1.0W + L + 0.5(L r or S or R) + + – stability • 1.2D + 1.0E + L + 0.2S • superpositioning • 0.9D + 1.0W – use of beam charts = = – elastic range only! • 0.9D + 1.0E – “ add ” moment diagrams • F has same factor as D in 1-5 and 7 – “ add ” deflection CURVES • H adds with 1.6 and resists with 0.9 (permanent) (not maximums) Steel Beams 12 Elements of Architectural Structures S2007abn Steel Beams 11 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 3

Steel Beams Local Buckling • lateral stability - bracing • steel I beams • local buckling – stiffen, or bigger I y • flange – buckle in direction of smaller radius of gyration • web – force – “ crippling ” Steel Beams 13 Elements of Architectural Structures S2007abn Steel Beams 14 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 Local Buckling Shear in Web • web • panels in plate girders or webs with large shear • flange • buckling in compression direction • add stiffeners Steel Beams 15 Elements of Architectural Structures S2007abn Steel Beams 16 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 4

Shear in Web Steel Beams • plate girders and stiffeners • bearing – provide adequate area – prevent local yield of flange and web http:// nisee.berkeley.edu/godden Steel Beams 17 Elements of Architectural Structures S2010abn Steel Beams 18 Elements of Architectural Structures S2010abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 LRFD - Flexure Internal Moments - at yield • material hasn ’ t failed       R M M 0 . 9 F Z i i u b n y 2 I bh   M u - maximum moment M f f y y y  b - resistance factor for bending = 0.9 c 6 M n - nominal moment (ultimate capacity)   F y - yield strength of the steel 2 2 2 2 b c bc   f f Z - plastic section modulus* y y 6 3 Steel Beams 18 Elements of Architectural Structures S2007abn Steel Beams 19 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 5

Internal Moments - ALL at yield n.a. of Section at Plastic Hinge • all parts reach yield • cannot guarantee at centroid • plastic hinge forms •  f y· A 1 =  f y· A 2 • ultimate moment • moment found from • A tension = A compression yield stress times moment area       3 2 M f A d f A d M bc f M  y = 50ksi 2 p y 1 y i i p y y n . a E 1   y = 0.001724 Steel Beams 20 Elements of Architectural Structures S2007abn Steel Beams 21 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 Plastic Hinge Development Plastic Hinge Examples • stability can be effected Steel Beams 22 Elements of Architectural Structures S2007abn Steel Beams 23 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 6

Plastic Section Modulus LRFD - Shear • shape factor, k M       k  R V V 1 . 0 ( 0 . 6 F A ) p i i u v n yw w M y = 3/2 for a rectangle V u - maximum shear k  Z  v - resistance factor for shear = 0.9  1.1 for an I S V n - nominal shear F yw - yield strength of the steel in the web M Z  p A w - area of the web = t w d • plastic modulus, Z f y Steel Beams 24 Elements of Architectural Structures S2007abn Steel Beams 25 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 LRFD - Flexure Design Compact Sections • • plastic moment can form before any limit states for beam failure F buckling  1. yielding y L 1 . 76 r p y • criteria E 2. lateral-torsional buckling* 3. flange local buckling b E  f 4. web local buckling 0.38 – 2 t F • minimum M n governs f y      h E  R M M c – and 3.76 i i u b n t F w y Steel Beams 28 Elements of Architectural Structures S2012abn Steel Beams 26 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 7

Lateral Torsional Buckling Beam Design Charts     moment based on M C M n b p lateral buckling 12 . 5 M  max C    b 2 . 5 M 2 M 4 M 3 M max A B C C b = modification factor M max - |max moment|, unbraced segment M A - |moment|, 1/4 point M B = |moment|, center point M C = |moment|, 3/4 point Steel Beams 28 Elements of Architectural Structures S2007abn Steel Beams 30 Elements of Architectural Structures S2012abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 Charts & Deflections Design Procedure (revisited) • beam charts 1. Know unbraced length, material, design method (  ,  ) – solid line is most economical – dashed indicates there is another more 2. Draw V & M, finding M max economical section   – self weight is NOT included in M n f  F 3. Calculate Z req’d • deflections b b   ( M M ) – no factors are applied to the loads u b n – often governs the design 4. Choose (economical) section from section or beam capacity charts Steel Beams 31 Elements of Architectural Structures S2009abn Steel Beams 30 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 8

Beam Charts by Z x (pg. 250) 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 32 Elements of Architectural Structures S2009abn Steel Beams 33 Elements of Architectural Structures S2010abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 Beam Design (revisited) Beam Design (revisited) 6. Evaluate shear - horizontal 7. Provide adequate bearing   P   f    • area at supports ( V V ) or F f F u v n v v p p A 3 V V   f • W and rectangles  v max 2 A A web VQ  f v • thin walled sections  max Ib Steel Beams 33 Elements of Architectural Structures S2007abn Steel Beams 34 Elements of Architectural Structures S2007abn Lecture 16 ARCH 614 Lecture 16 ARCH 614 9