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A RCHITECTURAL S TRUCTURES : Concrete in Compression F ORM, B EHAVIOR, AND D ESIGN ARCH 331 • crushing D R. A NNE N ICHOLS • vertical cracking S PRING 2018 – tension lecture twenty six • diagonal cracking – shear f  • c http://www.bam.de concrete construction: columns & frames http://www.building.co.uk Concrete Columns 2 Foundations Structures F2008abn Concrete Columns 1 Architectural Structures F2009abn Lecture 26 ARCH 331 Lecture 26 ARCH 331 Slenderness Columns Reinforcement • effective length in monolithic with • columns require respect to stiffness of joint:  & k – ties or spiral reinforcement to “confine” concrete • not slender when (#3 bars minimum) kL  u 22 r *not braced – minimum amount of longitudinal steel (4 bars minimum) Concrete Columns 4 Foundations Structures F2008abn Concrete Columns 3 Architectural Structures F2008abn Lecture 26 ARCH 331 Lecture 26 ARCH 331 1

Effective Length (revisited) Column Behavior • relative rotation  EI l   c  EI l b Concrete Columns 5 Foundations Structures F2008abn Concrete Columns 6 Foundations Structures F2008abn Lecture 26 ARCH 331 Lecture 26 ARCH 331 Column Design Columns with Bending •  c = 0.65 for ties,  c = 0.70 for spirals • eccentric loads can cause moments • P o – no bending • moments can change shape and induce     P 0 . 85 f ( A A ) f A more deflection o c g st y st (P-  ) • P u   c P n P – ties: P n = 0.8P o – spiral: P n = 0.85P o • nominal axial capacity:  – presumes steel yields – concrete at ultimate stress Concrete Columns 7 Foundations Structures F2008abn Concrete Columns 8 Foundations Structures F2008abn Lecture 26 ARCH 331 Lecture 26 ARCH 331 2

Columns with Bending Columns with Bending • for ultimate strength behavior, ultimate • need to consider strains can ’ t be exceeded combined – concrete 0.003 stresses f • linear strain – steel y E • steel stress at or s below f y • P reduces • plot interaction with M diagram Concrete Columns 9 Foundations Structures F2008abn Concrete Columns 10 Foundations Structures F2009abn Lecture 26 ARCH 331 Lecture 26 ARCH 331 Design Methods Design Considerations • calculation intensive • bending at both ends – P-  maximum – handbook charts – • biaxial bending computer programs • walls – unit wide columns – “ deep ” beam shear • detailing – shorter development lengths – dowels to footings Concrete Columns 11 Foundations Structures F2008abn Concrete Columns 12 Foundations Structures F2008abn Lecture 26 ARCH 331 Lecture 26 ARCH 331 3

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