twenty two concrete construction: http:// nisee.berkeley.edu/godden - PowerPoint PPT Presentation

A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN A RCH 331 D R. A NNE N ICHOLS S UMMER 2018 lecture twenty two concrete construction: http:// nisee.berkeley.edu/godden flat spanning systems, columns & frames Concrete Spans 1 Architectural Structures Su2018abn Lecture 22 ARCH 331

Reinforced Concrete Design • economical & common • resist lateral loads Concrete Spans 2 Architectural Structures Su2018abn Lecture 22 ARCH 331

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 Architectural Structures Su2018abn Lecture 22 ARCH 331

Reinforced Concrete Design • beam supported – slab depth ~ L/20 – 8”–60” deep • one-way joists The Architect’s Studio Companion – 3”–5” slab – 8”–20” stems – 5” - 7” webs Concrete Spans 4 Architectural Structures Su2018abn Lecture 22 ARCH 331

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 Architectural Structures Su2018abn Lecture 22 ARCH 331

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 Architectural Structures Su2018abn Lecture 22 ARCH 331

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 Architectural Structures Su2018abn Lecture 22 ARCH 331

Reinforced Concrete Design Concrete Spans 8 Architectural Structures Su2018abn Lecture 22 ARCH 331

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 Architectural Structures Su2018abn Lecture 22 ARCH 331

Reinforced Concrete Design Concrete Spans 10 Architectural Structures Su2018abn Lecture 22 ARCH 331

Shear in Concrete • at columns • want to avoid stirrups • can use shear studs or heads Concrete Spans 11 Architectural Structures Su2018abn Lecture 22 ARCH 331

Shear in Concrete • critical section at d/2 from – column face, column capital or drop panel Concrete Spans 12 Architectural Structures Su2018abn Lecture 22 ARCH 331

Shear in Concrete • at columns with waffle slabs http:// nisee.berkeley.edu/godden Concrete Spans 13 Architectural Structures Su2018abn Lecture 22 ARCH 331

Openings in Slabs • careful placement of holes • shear strength reduced • bending & deflection can increase Concrete Spans 14 Architectural Structures Su2018abn Lecture 22 ARCH 331

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 S  • slab design, t 6 – deflection control & shear Concrete Spans 15 Architectural Structures Su2018abn Lecture 22 ARCH 331

General Beam Design (cont’d) • custom design: – longitudinal steel – shear reinforcement – detailing Concrete Spans 16 Architectural Structures Su2018abn Lecture 22 ARCH 331

Space “Frame” Behavior • handle uniformly distributed loads well • bending moment – tension & compression “couple” with depth – member sizes can vary, but difficult Concrete Spans 17 Architectural Structures Su2018abn Lecture 22 ARCH 331

Space “Frame” Behavior • shear at columns • support conditions still important – point supports not optimal • fabrication/construction can dominate design Concrete Spans 18 Architectural Structures Su2018abn Lecture 22 ARCH 331

Folded Plates • increased bending stiffness with folding • lateral buckling avoided Concrete Spans 19 Architectural Structures Su2018abn Lecture 22 ARCH 331

Folded Plates • common for roofs • edges need stiffening http:// nisee.berkeley.edu/godden Concrete Spans 20 Architectural Structures Su2018abn Lecture 22 ARCH 331

Folded Plates www.library.illinois.edu – 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 Architectural Structures Su2018abn Lecture 22 ARCH 331

Concrete in Compression • crushing • vertical cracking – tension • diagonal cracking – shear f  f  • c c http://www.bam.de Concrete Spans 22 Architectural Structures Su2018abn Lecture 22 ARCH 331

Columns Reinforcement • columns require – ties or spiral reinforcement to “confine” concrete (#3 bars minimum) – minimum amount of longitudinal steel (4 bars minimum) Concrete Spans 23 Architectural Structures Su2018abn Lecture 22 ARCH 331

Slenderness • effective length in monolithic with respect to stiffness of joint:  & k • not slender when kL  u 22 r *not braced Concrete Spans 24 Architectural Structures Su2018abn Lecture 22 ARCH 331

Effective Length (revisited) • relative rotation  EI l   c  EI l b Concrete Spans 25 Architectural Structures Su2018abn Lecture 22 ARCH 331

Column Behavior Concrete Spans 26 Architectural Structures Su2018abn Lecture 22 ARCH 331

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 c g st y st • 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 Concrete Spans 27 Architectural Structures Su2018abn Lecture 22 ARCH 331

Columns with Bending • eccentric loads can cause moments • moments can change shape and induce more deflection (P-  ) P  Concrete Spans 28 Architectural Structures Su2018abn Lecture 22 ARCH 331

Columns with Bending • for ultimate strength behavior, ultimate strains can’t be exceeded – concrete 0.003 f y – steel E s • P reduces with M Concrete Spans 29 Architectural Structures Su2018abn Lecture 22 ARCH 331

Columns with Bending • need to consider combined stresses • linear strain • steel stress at or below f y • plot interaction diagram Concrete Spans 30 Architectural Structures Su2018abn Lecture 22 ARCH 331

Design Methods • calculation intensive – handbook charts – computer programs Concrete Spans 31 Architectural Structures Su2018abn Lecture 22 ARCH 331

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 Architectural Structures Su2018abn Lecture 22 ARCH 331