twenty two concrete construction: flat spanning systems, columns & frames Reinforced Concrete Design Reinforced Concrete Design

Size: px
Start display at page:

Download "twenty two concrete construction: flat spanning systems, columns & frames Reinforced Concrete Design Reinforced Concrete Design"

Transcription

1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2013 lecture twenty two economical & common resist lateral loads concrete construction: flat spanning systems, columns & frames Concrete Spans 1 Lecture 22 Architectural Structures nisee.berkeley.edu/godden F2009abn Concrete Spans 2 flat plate 5-10 thick simple formwork lower story heights flat slab same as plate 2 ¼ 8 drop panels 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 3 Concrete Spans 4 1

2 two-way joist waffle slab 3-5 slab 8-24 stems 6-8 webs beam supported slab 5-10 slabs taller story heights simplified frame analysis strips, like continuous beams moments require flexural reinforcement top & bottom both directions of slab continuous, bent or discontinuous Concrete Spans 5 Concrete Spans 6 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 Concrete Spans 8 2

3 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 Concrete Spans 10 Shear in Concrete at columns want to avoid stirrups can use shear studs or heads Shear in Concrete critical section at d/2 from column face, column capital or drop panel Concrete Spans 11 Concrete Spans 12 3

4 Shear in Concrete at columns with waffle slabs Openings in Slabs careful placement of holes shear strength reduced bending & deflection can increase Concrete Spans 13 nisee.berkeley.edu/godden Concrete Spans 14 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 2 bh slab design, t S 6 deflection control & shear General Beam Design (cont d) custom design: longitudinal steel shear reinforcement detailing Concrete Spans 15 Concrete Spans 16 4

5 Space Frame Behavior handle uniformly distributed loads well bending moment tension & compression couple with depth member sizes can vary, but difficult Space Frame Behavior shear at columns support conditions still important point supports not optimal fabrication/construction can dominate design Concrete Spans 17 Concrete Spans 18 Folded Plates increased bending stiffness with folding lateral buckling avoided Folded Plates common for roofs edges need stiffening nisee.berkeley.edu/godden Concrete Spans 19 Concrete Spans 20 5

6 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 in Compression crushing vertical cracking tension diagonal cracking shear f c Concrete Spans 21 Architectural Structures Concrete Columns 2 Columns Reinforcement columns require ties or spiral reinforcement to confine concrete (#3 bars minimum) Slenderness effective length in monolithic with respect to stiffness of joint: & k not slender when kl u 22 r minimum amount of longitudinal steel (#5 bars minimum: 4 with ties, 5 with spiral) Concrete Columns 3 Concrete Columns 4 6

7 Effective Length (revisited) relative rotation Column Behavior EI l EI l c b Concrete Columns 5 Concrete Columns 6 Column Design c = 0.65 for ties, c = 0.75 for spirals P o no bending P 0.85 f ( A A ) f A o 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 y st Columns with Bending eccentric loads can cause moments moments can change shape and induce more deflection (P- ) P Concrete Columns 7 Concrete Columns 8 7

8 Columns with Bending for ultimate strength behavior, ultimate strains can t be exceeded concrete f y steel E P reduces with M s Columns with Bending need to consider combined stresses linear strain steel stress at or below f y plot interaction diagram Concrete Columns 9 Concrete Columns 10 F2009abn Design Methods calculation intensive handbook charts computer programs 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 Columns 11 Concrete Columns 12 8