sixteen steel construction: materials & beams Steel Beam Design Steel Properties Steel Materials American Institute of Steel Construction steel grades

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1 ELEENTS OF ARCHITECTURAL STRUCTURES: FOR, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 015 lecture sixteen Steel Beam Design American Institute o Steel Construction anual o Steel Construction ASD & LRFD combined in 005 steel construction: materials & beams Steel Beams 1 S009abn Steel Beams Steel aterials steel grades Steel Beams 3 AST A36 carbon plates, angles F 36 ksi & F u 58 ksi AST A57 high strength low-allo some beams F 60 ksi & F u 75 ksi AST A99 or building raming most beams F 50 ksi & F u 65 ksi Steel Properties high strength to weight ratio elastic limit ield (F ) inelastic plastic ultimate strength (F u ) ductile strength sensitive to temperature can corrode atigue Steel Beams 4 strain hardening Winnepeg DOT 1

2 Structural Steel standard rolled shapes (W, C, L, T) open web joists plate girders decking Steel Construction welding bolts Steel Beams 5 Steel Beams 6 Uniied Steel Design ASD R a R n Ω bending (braced) Ω 1.67 bending (unbraced * ) Ω 1.67 shear Ω 1.5 or 1.67 shear (bolts & welds) Ω.00 shear (welds) Ω.00 Uniied Steel Design braced vs. unbraced * langes in compression can buckle Steel Beams 7 S01abn Steel Beams 8 S01abn

3 LRFD loads on structures are not constant can be more inluential on ailure happen more or less oten UNCERTAINTY LRFD Steel Beam Design limit state is ielding all across section outside elastic range load actors & resistance actors 50ksi R u γ D R D φ - resistance actor + γ R L L φr n 1 E ε ε γ - load actor or (D)ead & (L)ive load Steel Beams 9 Steel Beams 10 LRFD Load Combinations 1.4D 1.D + 1.6L + 0.5(L r or S or R) Steel Beams 11 ASCE-7 (010) 1.D + 1.6(L r or S or R) + (L or 0.5W) 1.D + 1.0W + L + 0.5(L r or S or R) 1.D + 1.0E + L + 0.S 0.9D + 1.0W 0.9D + 1.0E F has same actor as D in 1-5 and 7 H adds with 1.6 and resists with 0.9 (permanent) Beam Design Criteria (revisited) strength design bending stresses predominate shear stresses occur serviceabilit limit delection stabilit superpositioning use o beam charts elastic range onl! add moment diagrams add delection CURVES (not maximums) Steel Beams 1 + 3

4 Steel Beams lateral stabilit - bracing local buckling stien, or bigger I Local Buckling steel I beams lange buckle in direction o smaller radius o gration web orce crippling Steel Beams 13 Steel Beams 14 Local Buckling lange web Shear in Web panels in plate girders or webs with large shear buckling in compression direction add stieners Steel Beams 15 Steel Beams 16 4

5 Shear in Web plate girders and stieners Steel Beams bearing provide adequate area prevent local ield o lange and web Steel Beams 17 nisee.berkele.edu/godden S010abn Steel Beams 18 S010abn LRFD - Flexure Σγ iri u φb n 0. 9F u - maximum moment φ b - resistance actor or bending 0.9 n - nominal moment (ultimate capacit) F - ield strength o the steel Z - plastic section modulus* Z Internal oments - at ield material hasn t ailed I c b ( c) 6 bh 6 bc 3 Steel Beams 18 Steel Beams 19 5

6 Internal oments - ALL at ield all parts reach ield plastic hinge orms ultimate moment A tension A compression p bc 3 σ 50ksi σ 1 E ε ε n.a. o Section at Plastic Hinge cannot guarantee at centroid A 1 A moment ound rom ield stress times moment area p A d 1 Σ n. a A d i i Steel Beams 0 Steel Beams 1 Plastic Hinge Development Plastic Hinge Examples stabilit can be eected Steel Beams Steel Beams 3 6

7 Plastic Section odulus shape actor, k 3/ or a rectangle 1.1 or an I plastic modulus, Z k p k Z S Z p LRFD - Shear Σγ iri Vu φvvn 1. 0( 0. 6F V u - maximum shear φ v - resistance actor or shear 0.9 V n - nominal shear F w - ield strength o the steel in the web A w - area o the web t w d w A w ) Steel Beams 4 Steel Beams 5 LRFD - Flexure Design limit states or beam ailure 1. ielding. lateral-torsional buckling* 3. lange local buckling 4. web local buckling minimum n governs Σγ R i i u Lp 1. 76r φ b n F E Compact Sections plastic moment can orm beore an buckling criteria and b t h t c w E F E F Steel Beams 6 Steel Beams 8 S01abn 7

8 Lateral Torsional Buckling Beam Design Charts n b[ ] p moment based on C lateral buckling Steel Beams 8 C b.5 max 1.5 max C b modiication actor max - max moment, unbraced segment A - moment, 1/4 point B moment, center point C moment, 3/4 point A B + 3 C Steel Beams 30 S01abn Charts & Delections beam charts solid line is most economical dashed indicates there is another more economical section sel weight is NOT included in n delections no actors are applied to the loads oten governs the design Design Procedure (revisited) 1. Know unbraced length, material, design method (Ω, φ). Draw V &, inding max 3. Calculate Z req d ( b F b ) ( u φ b n 4. Choose (economical) section rom section or beam capacit charts ) Steel Beams 30 Steel Beams 31 S009abn 8

9 Beam Charts b Z x (pg. 50) Beam Design (revisited) 4*. Include sel weight or max and repeat 3 & 4 i necessar 5. Consider lateral stabilit Unbraced roo trusses were blown down in 1999 at this project in oscow, Idaho. Photo: Ken Carper Steel Beams 33 S010abn Steel Beams 3 S009abn Beam Design (revisited) 6. Evaluate shear stresses - horizontal ( or v F v ) ( Vu φvvn ) 3V V W and rectangles v max A A web Beam Design (revisited) 7. Provide adequate bearing area at supports P A p F p thin walled sections VQ v max Ib Steel Beams 33 Steel Beams 34 9

10 Beam Design (revisited) 8. Evaluate torsion ( v F v ) Beam Design (revisited) 9. Evaluate delections NO LOAD FACTORS circular cross section v Tρ J rectangular v T c 1 ab max ( x) actual allowable Steel Beams 35 Steel Beams 36 Load Tables & Equivalent Load uniorml distributed loads equivalent w max w equivalent 8 L Steel Arches and Frames solid sections or open web load or live load delection limit in RED, total in BLACK nisee.berkele.edu/godden Steel Beams 37 TOPIC 38 S009abn 10

11 Steel Shell and Cable Structures Approximate Depths TOPIC 39 S009abn TOPIC 40 S009abn 11