APPLIED ARCHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 2018 lecture twenty one steel construction http://nisee.berkeley.edu/godden and design Steel Construction 1
Steel cast iron wrought iron - steel cables columns beams trusses frames Steel Construction 2 http://nisee.berkeley.edu/godden
Steel Construction standard rolled shapes open web joists plate girders decking Steel Construction 3
Steel Construction welding bolts Steel Construction 4 AISC Education
Steel Construction fire proofing cementitious spray encasement in gypsum intumescent expands with heat sprinkler system Steel Construction 5
Steel Materials high strength to weight ratio ductile beam size often limited by deflection column size limited by slenderness Steel Construction 6
Steel Beams types manufactured shapes http://nisee.berkeley.edu/godden castellated Steel Construction 7
Steel Beams types wide flange Steel Construction 8
Steel Beams types open web joists (manufactured trusses) Steel Construction 9
Steel Beams types (more) plate girder decking Steel Construction 10
Steel Beams http://nisee.berkeley.edu/godden Steel Construction 11
Steel Beams lateral stability - bracing local buckling - stiffen Steel Construction 12
Local Buckling steel I beams flange buckle in direction of smaller radius of gyration web force crippling Steel Construction 13
Local Buckling flange web Steel Construction 14
Shear in Web panels in plate girders or webs with large shear buckling in compression direction add stiffeners Steel Construction 15
Steel Beams end conditions a) away from connection - full section effective b) high shear only web effective Steel Construction 16
Steel Beams end conditions c) bolt holes less material d) local web buckling Steel Construction 17
Steel Beams bearing provide adequate area prevent local yield of flange and web Steel Construction 18
Steel Beams connections welds bolts Steel Construction 19
Steel Design Open Web Joists SJI: www.steeljoist.com Vulcraft: www.vulcraft.com K Series (Standard) 8-30 deep, spans 8-50 ft LH Series (Long span) 18-48 deep, spans 25-96 ft DLH (Deep Long Spans) 52-72 deep, spans 89-144 ft SLH (Long spans with high strength steel) pitched top chord 80-120 deep, spans 111-240 ft Steel Construction 20
Steel Design Open Web Joists ASD load for live load deflection limit in RED total in BLACK Steel Construction 21
Steel Design Open Web Joists load for live load deflection limit (L/360) in RED total in BLACK Steel Construction 22
Steel Beam Design American Institute of Steel Construction 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 Construction 23
Steel Beam Design AISC: 14 th ed. combined ASD & LRFD in one volume in 2005 Steel Construction 24
Unified Steel Design ASD R a bending (braced) = 1.67 bending (unbraced * ) = 1.67 shear = 1.5 or 1.67 shear (bolts & welds) = 2.00 shear (welds) = 2.00 R n Ω * flanges in compression can buckle Steel Construction 25
Unified Steel Design braced vs. unbraced Steel Construction 26
LRFD Steel Beam Design limit state is yielding all across section outside elastic range load factors & resistance factors f y = 50ksi f 1 E y 0.001724 Steel Construction 27
Load Types D = dead load L = live load L r = live roof load W = wind load S = snow load E = earthquake load R = rainwater load or ice water load T = effect of material & temperature Steel Construction 28
LRFD Load Combinations 1.4D 1.2D + 1.6L + 0.5(L r or S or R) ASCE-7 (2010) 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 Construction 29
Pure Flexure R M M 0.9F 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 Construction 30
Internal Moments - at yield material hasn t failed I bh M f f c 6 y y y 2 2 2 b(2 c) 2bc f y 6 3 f y Steel Construction 31
Internal Moments - ALL at yield all parts reach yield plastic hinge forms ultimate moment A tension = A compression M bc 2 f 3 M p y 2 y y = 50ksi 1 E y = 0.001724 Steel Construction 32
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 na. Steel Construction 33
Plastic Hinge Development Steel Construction 34
Plastic Hinge Examples stability can be effected Steel Construction 35
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 Construction 36
LRFD Shear (compact shapes) R V V 1.0(0.6 F A ) i i u v n yw 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 Construction 37
Flexure Design limit states for beam failure 1. yielding L 2. lateral-torsional buckling* 3. flange local buckling 4. web local buckling minimum M n governs p 1.76r y F y E R M M i i u b n Steel Construction 38
Compact Sections plastic moment can form before any buckling criteria b f 2t f 0.38 E F y and h t c w 3.76 E F y Steel Construction 39
Lateral Torsional Buckling moment based on lateral buckling M C M n b p C Steel Construction 40 b max 12.5M 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 max 2.5M 2M 4M 3M A B C
Beam Design Charts Steel Construction 41
Deflection Limits based on service condition no impairment to serviceability avoid ponding L/360 due to live load for beams & girders supporting plaster (service) Steel Construction 42
Steel Arches and Frames solid sections or open web http://nisee.berkeley.edu/godden Steel Construction 43
Steel Shell and Cable Structures Steel Construction 44
Approximate Depths Steel Construction 45
Unified Column Design limit states for failure 0.90 P F A c n cr g P P n a P P u c n 1. yielding 2. buckling Kl E 4.71 or F e 0.44 F r F y Kl E 4.71 or F e 0.44 F r F y y y F e elastic buckling stress (Euler) Steel Construction 46
Unified Column Design P n = F cr A g for for Kl r Kl r where 4.71 E F F cr 0.658 y 4.71 E F 0.877F F cr F e y 2 E KL r 2 F F e y e F y Steel Construction 47
Procedure for Analysis 1. calculate KL/r biggest of KL/r with respect to x axes and y axis 2. find F cr from appropriate equation tables are available 3. compute P n = F cr A g or find f c = P a /A or P u /A 4. is P a P n / or P u P n? yes: ok no: insufficient capacity and no good Steel Construction 48
Procedure for Design 1. guess a size (pick a section) 2. calculate KL/r biggest of KL/r with respect to x axes and y axis 3. find F cr from appropriate equations or find a table 4. compute P n = F cr A g or find f c = P a /A or P u /A Steel Construction 49
Procedure for Design (cont d) 5. is P a P n / or P u P n? yes: ok no: pick a bigger section and go back to step 2. 6. check design efficiency percentage of stress = if between 90-100%: good Pr 100% P if < 90%: pick a smaller section and go back to step 2. c Steel Construction 50
Column Tables Steel Construction 51
Beam-Column Design moment magnification (P-) M B M u 1 max factored B 1 C m 1 ( P / P ) u e1 C m modification factor for end conditions = 0.6 0.4(M 1 /M 2 ) or 0.85 restrained, 1.00 unrestrained P e1 Euler buckling strength P 2 EA e1 2 Kl r Steel Construction 52
Beam-Column Design LRFD (Unified) Steel for for P r P c P r P c 0.2 : 0.2 : P 8 u M M ux uy 1.0 cpn 9 bm nx bm ny P u M M ux uy 1.0 2c P n bm nx bm ny P r is required, P c is capacity c - resistance factor for compression = 0.9 b - resistance factor for bending = 0.9 Steel Construction 53
Construction Supervision proper grade material high strength bolts quality welds proper bolted conditions (ex. sc) fabrication and erection of steel frame connection details www.architecture.uwaterloo.ca Steel Construction 54