fifteen steel construction: materials & beams ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2016 lecture

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1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2016 lecture fifteen steel construction: materials & beams Steel Beams 1

2 Steel Beam Design American Institute of Steel Construction Manual of Steel Construction ASD & LRFD combined in 2005 Steel Beams 2

3 Steel Materials smelt iron ore add alloying elements heat treatments iron, carbon microstructure AISC Steel Beams 3 A36 steel, JOM 1998

4 Steel Materials cast into billets hot rolled cold formed residual stress corrosion-resistant weathering steels stainless Hot Rolled Cold Formed AISC Steel Beams 4

5 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

6 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

7 Structural Steel standard rolled shapes (W, C, L, T) open web joists plate girders decking Steel Beams 7

8 Steel Construction welding bolts Steel Beams 8

9 Steel Construction fire proofing cementicious spray encasement in gypsum intumescent expands with heat sprinkler system Steel Beams 9

10 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

11 Unified Steel Design braced vs. unbraced Steel Beams 11

12 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

13 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 = Steel Beams 13

14 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

15 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

16 Steel Beams lateral stability - bracing local buckling stiffen, or bigger I y Steel Beams 16

17 Local Buckling steel I beams flange buckle in direction of smaller radius of gyration web force crippling Steel Beams 17

18 Local Buckling flange web Steel Beams 18

19 Shear in Web panels in plate girders or webs with large shear buckling in compression direction add stiffeners Steel Beams 19

20 Shear in Web plate girders and stiffeners Steel Beams 20 nisee.berkeley.edu/godden

21 Steel Beams bearing provide adequate area prevent local yield of flange and web Steel Beams 21

22 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

23 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

24 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 = Steel Beams 24

25 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

26 Plastic Hinge Development Steel Beams 26

27 Plastic Hinge Examples stability can be effected Steel Beams 27

28 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

29 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

30 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

31 Compact Sections plastic moment can form before any buckling criteria b f 2t f E F y and h c E t w F y Steel Beams 31

32 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

33 Beam Design Charts Steel Beams 33

34 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

35 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

36 Beam Charts by S x (Appendix) Steel Beams 36

37 Beam Charts by Z x (Appendix) Steel Beams 37 Lecture 18

38 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

39 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

40 Beam Design (revisited) 7. Provide adequate bearing area at supports (P a P n /) (P u P n ) Steel Beams 40

41 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

42 Beam Design (revisited) 9. Evaluate deflections NO LOAD FACTORS y ( x ) max actual allowable Steel Beams 42

43 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

44 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

45 Steel Arches and Frames solid sections or open web nisee.berkeley.edu/godden Steel Beams 45

46 Steel Shell and Cable Structures Steel Beams 46

47 Approximate Depths Steel Beams 47