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

E LEMENTS OF A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN ARCH 614 D R. A NNE N ICHOLS S PRING 2019 lecture sixteen steel construction: materials & beams Steel Beams 1 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Steel Beam Design • American Institute of Steel Construction – Manual of Steel Construction – ASD & LRFD – combined in 2005 Steel Beams 2 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Steel Materials • steel grades – ASTM A36 – carbon • plates, angles • F y = 36 ksi & F u = 58 ksi – ASTM A572 – high strength low-alloy • some beams • F y = 60 ksi & F u = 75 ksi – ASTM A992 – for building framing • most beams -- ASTM A913 • • F y = 50 ksi & F u = 65 ksi some columns • Grade 65 and 70 Steel Beams 3 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Steel Properties • high strength to weight ratio • elastic limit – yield (F y ) • inelastic – plastic • ultimate strength (F u ) • ductile strain hardening • strength sensitive to temperature • can corrode • fatigue Winnepeg DOT Steel Beams 4 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Structural Steel • standard rolled shapes (W, C, L, T) • open web joists • plate girders • decking Steel Beams 5 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Steel Construction • welding • bolts http://courses.civil.ualberta.ca Steel Beams 6 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Unified Steel Design • ASD R a  R n Ω  = 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 S2019abn Lecture 16 ARCH 614

Unified Steel Design • braced vs. unbraced Steel Beams 8 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

LRFD • loads on structures are – 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 9 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

LRFD Steel Beam Design • limit state is yielding all across section • outside elastic range • load factors & resistance factors f f y = 50ksi E 1   y = 0.001724 Steel Beams 10 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

ASCE-7 LRFD Load Combinations (2010) • 1.4D • 1.2D + 1.6L + 0.5(L r or S or R) • 1.2D + 1.6(L r or S or R) + (L or 0.5W) • 1.2D + 1.0W + L + 0.5(L r or S or R) • 1.2D + 1.0E + L + 0.2S • 0.9D + 1.0W • 0.9D + 1.0E • F has same factor as D in 1-5 and 7 • H adds with 1.6 and resists with 0.9 (permanent) Steel Beams 11 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Beam Design Criteria (revisited) • strength design – bending stresses predominate – 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 12 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Steel Beams • lateral stability - bracing • local buckling – stiffen, or bigger I y Steel Beams 13 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Local Buckling • steel I beams • flange – buckle in direction of smaller radius of gyration • web – force – “crippling” Steel Beams 14 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Local Buckling • web • flange Steel Beams 15 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Shear in Web • panels in plate girders or webs with large shear • buckling in compression direction • add stiffeners Steel Beams 16 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Shear in Web • plate girders and stiffeners http:// nisee.berkeley.edu/godden Steel Beams 17 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Steel Beams • bearing – provide adequate area – prevent local yield of flange and web Steel Beams 18 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

LRFD - Flexure       R M M 0 . 9 F Z i i u b n y M u - maximum moment  b - resistance factor for bending = 0.9 M n - nominal moment (ultimate capacity) F y - yield strength of the steel Z - plastic section modulus* Steel Beams 19 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Internal Moments - at yield • material hasn’t failed 2 I bh   M f f y y y 6 c   2 2 2 2 b c bc   f f y y 6 3 Steel Beams 20 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Internal Moments - ALL at yield • all parts reach yield • plastic hinge forms • ultimate moment • A tension = A compression    3 2  y = 50ksi M bc f M 2 p y y E 1   y = 0.001724 Steel Beams 21 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

n.a. of Section at Plastic Hinge • 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 22 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Plastic Hinge Development Steel Beams 23 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Plastic Hinge Examples • stability can be effected Steel Beams 24 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Plastic Section Modulus • 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 25 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

LRFD - Shear  i R i = V u ≤  v V n = 1.0(0.6 F yw A w ) V u - maximum shear  v - resistance factor for shear = 1.0 V n - nominal shear F yw - yield strength of the steel in the web A w - area of the web = t w d Steel Beams 26 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

LRFD - Flexure Design • limit states for beam failure F  y L 1 . 76 r 1. yielding p y E 2. lateral-torsional buckling* 3. flange local buckling 4. web local buckling • minimum M n governs      R M M i i u b n Steel Beams 27 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Compact Sections • plastic moment can form before any buckling • criteria b E  f 0 . 38 – 2 t F f y h E  c – and 3 76 . t F w y Steel Beams 28 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Lateral Torsional Buckling     moment based on M C M n b lateral buckling p 12 . 5 M  max C    b 2 . 5 M 3 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 29 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Beam Design Charts Steel Beams 30 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Charts & Deflections • 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 31 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Design Procedure (revisited) 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 32 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Beam Charts by Z x (pg. 250) Steel Beams 33 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

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 34 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Beam Design (revisited) 6. Evaluate shear - horizontal       • ( V V ) V V / or u v n a n 3 V V   f • W and rectangles  v max 2 A A web V n = 0.6 F yw A w VQ  • f v general  max Ib Steel Beams 35 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614

Beam Design (revisited) 7. Provide adequate bearing ( P a ≤ P n /  ) area at supports ( P u ≤  P n ) Steel Beams 36 Elements of Architectural Structures S2019abn Lecture 16 ARCH 614