ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2016 lecture fifteen steel construction: materials & beams Steel Beams 1
Steel Beam Design American Institute of Steel Construction Manual of Steel Construction ASD & LRFD combined in 2005 Steel Beams 2
Steel Materials smelt iron ore add alloying elements heat treatments iron, carbon microstructure AISC Steel Beams 3 A36 steel, JOM 1998
Steel Materials cast into billets hot rolled cold formed residual stress corrosion-resistant weathering steels stainless Hot Rolled Cold Formed AISC Steel Beams 4
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 F y = 50 ksi & F u = 65 ksi Steel Beams 5
Steel Properties high strength to weight ratio elastic limit yield (F y ) inelastic plastic ultimate strength (F u ) ductile strength sensitive to temperature can corrode fatigue strain hardening Steel Beams 6 Winnepeg DOT
Structural Steel standard rolled shapes (W, C, L, T) open web joists plate girders decking Steel Beams 7
Steel Construction welding bolts Steel Beams 8 http://courses.civil.ualberta.ca
Steel Construction fire proofing cementicious spray encasement in gypsum intumescent expands with heat sprinkler system Steel Beams 9
Unified Steel Design ASD R a R n bending (braced) = 1.67 bending (unbraced * ) = 1.67 shear = 1.5 or 1.67 shear (bolts & welds) = 2.00 shear (welds) = 2.00 * flanges in compression can buckle Steel Beams 10
Unified Steel Design braced vs. unbraced Steel Beams 11
LRFD loads on structures are not constant can be more influential on failure happen more or less often UNCERTAINTY R u D R D L R L R n - resistance factor - load factor for (D)ead & (L)ive load Steel Beams 12
LRFD Steel Beam Design limit state is yielding all across section outside elastic range load factors & resistance factors f f y = 50ksi 1 E y = 0.001724 Steel Beams 13
LRFD Load Combinations 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 ASCE-7 (2010) H adds with 1.6 and resists with 0.9 (permanent) Steel Beams 14
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 15
Steel Beams lateral stability - bracing local buckling stiffen, or bigger I y Steel Beams 16
Local Buckling steel I beams flange buckle in direction of smaller radius of gyration web force crippling Steel Beams 17
Local Buckling flange web Steel Beams 18
Shear in Web panels in plate girders or webs with large shear buckling in compression direction add stiffeners Steel Beams 19
Shear in Web plate girders and stiffeners Steel Beams 20 http:// nisee.berkeley.edu/godden
Steel Beams bearing provide adequate area prevent local yield of flange and web Steel Beams 21
LRFD - Flexure R M M 0. 9 i i u b n F y Z 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 22
Internal Moments - at yield material hasn t failed I bh 2 M y c f y 6 f y b( 2c ) 2 2bc 2 6 f y f y 3 Steel Beams 23
Internal Moments - ALL at yield all parts reach yield plastic hinge forms ultimate moment A tension = A compression M p bc 2 f y 3 2 M y y = 50ksi E 1 y = 0.001724 Steel Beams 24
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 p f y 1 A d f y n.a A i d i Steel Beams 25
Plastic Hinge Development Steel Beams 26
Plastic Hinge Examples stability can be effected Steel Beams 27
Plastic Section Modulus shape factor, k = 3/2 for a rectangle k M p M y 1.1 for an I k Z S plastic modulus, Z Z M f y p Steel Beams 28
LRFD Shear (compact shapes) R V V 1. 0( 0. 6F i i u v n 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 29
LRFD - Flexure Design limit states for beam failure 1. yielding 2. lateral-torsional buckling* 3. flange local buckling 4. web local buckling minimum M n governs L 1. 76r p y F y E R i i M u M b n Steel Beams 30
Compact Sections plastic moment can form before any buckling criteria b f 2t f 0. 38 E F y and h c 3. 76 E t w F y Steel Beams 31
Lateral Torsional Buckling M n C moment based on lateral buckling M b p Steel Beams 32 C b 2. 5M max 12. 5M 2M 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 A max 4M B 3M C
Beam Design Charts Steel Beams 33
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 34
Design Procedure (revisited) 1. Know unbraced length, material, design method (, ) 2. Draw V & M, finding M max 3. Calculate Z req d (M a M n /) ( M M ) u b n 4. Choose (economical) section from section or beam capacity charts Steel Beams 35
Beam Charts by S x (Appendix) Steel Beams 36
Beam Charts by Z x (Appendix) Steel Beams 37 Lecture 18
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 38
Beam Design (revisited) 6. Evaluate shear - horizontal or (V a V n /) ( V V u v n ) rectangles and W s f v max 3V 2 A A V w eb V n = 0.6 F yw A w general f v max VQ Ib Steel Beams 39
Beam Design (revisited) 7. Provide adequate bearing area at supports (P a P n /) (P u P n ) Steel Beams 40
Beam Design (revisited) 8. Evaluate torsion f F v v circular cross section f v T J rectangular f v T c 1 ab 2 Steel Beams 41
Beam Design (revisited) 9. Evaluate deflections NO LOAD FACTORS y ( x ) max actual allowable Steel Beams 42
Load Tables & Equivalent Load uniformly distributed loads equivalent w M max w eq u iva len t 8 L 2 load for live load deflection limit in RED, total in BLACK Steel Beams 43
Sloped Beams stairs & roofs projected live load dead load over length perpendicular load to beam: equivalent distributed load: Steel Beams 44 w w adj. w cos w cos
Steel Arches and Frames solid sections or open web http:// nisee.berkeley.edu/godden Steel Beams 45
Steel Shell and Cable Structures Steel Beams 46
Approximate Depths Steel Beams 47