twenty two concrete construction: flat spanning systems, columns & frames ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

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1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture twenty two concrete construction: nisee.berkeley.edu/godden flat spanning systems, columns & frames Concrete Spans 1

2 Reinforced Concrete Design economical & common resist lateral loads Concrete Spans 2

3 Reinforced Concrete Design flat plate 5-10 thick simple formwork lower story heights flat slab same as plate 2 ¼ 8 drop panels Concrete Spans 3

4 Reinforced Concrete Design beam supported slab depth ~ L/ deep one-way joists 3 5 slab 8 20 stems 5-7 webs The Architect s Studio Companion Concrete Spans 4

5 Reinforced Concrete Design two-way joist waffle slab 3-5 slab 8-24 stems 6-8 webs beam supported slab 5-10 slabs taller story heights Concrete Spans 5

6 Reinforced Concrete Design simplified frame analysis strips, like continuous beams moments require flexural reinforcement top & bottom both directions of slab continuous, bent or discontinuous Concrete Spans 6

7 Reinforced Concrete Design one-way slabs (wide beam design) approximate analysis for moment & shear coefficients two or more spans ~ same lengths w u from combos uniform loads with L/D 3 n is clear span (+M) or average of adjacent clear spans (-M) Concrete Spans 7

8 Reinforced Concrete Design Concrete Spans 8

9 Reinforced Concrete Design two-way slabs - Direct Design Method 3 or more spans each way uniform loads with L/D 3 rectangular panels with long/short span 2 successive spans can t differ > longer/3 column offset no more than 10% span Concrete Spans 9

10 Reinforced Concrete Design Concrete Spans 10

11 Shear in Concrete at columns want to avoid stirrups can use shear studs or heads Concrete Spans 11

12 Shear in Concrete critical section at d/2 from column face, column capital or drop panel Concrete Spans 12

13 Shear in Concrete at columns with waffle slabs Concrete Spans 13 nisee.berkeley.edu/godden

14 Openings in Slabs careful placement of holes shear strength reduced bending & deflection can increase Concrete Spans 14

15 General Beam Design f c & f y needed usually size just b & h even inches typical (forms) similar joist to beam depth b:h of 1:1.5-1:2.5 b w & b f for T to fit reinforcement + stirrups slab design, t S 2 bh deflection control & shear 6 Concrete Spans 15

16 General Beam Design (cont d) custom design: longitudinal steel shear reinforcement detailing Concrete Spans 16

17 Space Frame Behavior handle uniformly distributed loads well bending moment tension & compression couple with depth member sizes can vary, but difficult Concrete Spans 17

18 Space Frame Behavior shear at columns support conditions still important point supports not optimal fabrication/construction can dominate design Concrete Spans 18

19 Folded Plates increased bending stiffness with folding lateral buckling avoided Concrete Spans 19

20 Folded Plates common for roofs edges need stiffening Concrete Spans 20 nisee.berkeley.edu/godden

21 Folded Plates State Farm Center (Assembly Hall), University of Illinois Harrison & Abramovitz 1963 Edge-supported dome spanning 400 feet wound with 614 miles of one-fifth inch steel wire Concrete Spans 21

22 Concrete in Compression crushing vertical cracking tension diagonal cracking shear c f Concrete Spans 22

23 Columns Reinforcement columns require ties or spiral reinforcement to confine concrete (#3 bars minimum) minimum amount of longitudinal steel (#5 bars minimum: 4 with ties, 5 with spiral) Concrete Spans 23

24 Slenderness effective length in monolithic with respect to stiffness of joint: & k not slender when kl u r 22 Concrete Spans 24

25 Effective Length (revisited) relative rotation EI EI l l c b Concrete Spans 25

26 Column Behavior Concrete Spans 26

27 Column Design c = 0.65 for ties, c = 0.75 for spirals P o no bending P o 0.85 f ( A A ) P u c P n ties: P n = 0.8P o spiral: P n = 0.85P o nominal axial capacity: presumes steel yields concrete at ultimate stress c g st f y A st Concrete Spans 27

28 Columns with Bending eccentric loads can cause moments moments can change shape and induce more deflection (P- ) P Concrete Spans 28

29 Columns with Bending for ultimate strength behavior, ultimate strains can t be exceeded concrete steel f E P reduces with M y s Concrete Spans 29

30 Columns with Bending need to consider combined stresses linear strain steel stress at or below f y plot interaction diagram Concrete Spans 30

31 Design Methods calculation intensive handbook charts computer programs Concrete Spans 31

32 Design Considerations bending at both ends P- maximum biaxial bending walls unit wide columns deep beam shear detailing shorter development lengths dowels to footings Concrete Spans 32