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## Lecture Chp-9&10 – Columns

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**Lecture Goals**• Definitions for short columns • Columns**Analysis and Design of “Short” Columns**General Information Column: Vertical Structural members Transmits axial compressive loads with or without moment transmit loads from the floor & roof to the foundation**Analysis and Design of “Short” Columns**General Information • Column Types: • Tied • Spiral • Composite • Combination • Steel pipe**Analysis and Design of “Short” Columns**Tied Columns - 95% of all columns in buildings are tied Tie spacing h (except for seismic) tie support long bars (reduce buckling) ties provide negligible restraint to lateral expose of core**Analysis and Design of “Short” Columns**Spiral Columns Pitch = 1.375 in. to 3.375 in. spiral restrains lateral (Poisson’s effect) axial load delays failure (ductile)**Analysis and Design of “Short” Columns**Elastic Behavior An elastic analysis using the transformed section method would be: For concentrated load, P uniform stress over section n = Es / Ec Ac = concrete area As = steel area**Analysis and Design of “Short” Columns**Elastic Behavior The change in concrete strain with respect to time will effect the concrete and steel stresses as follows: Concrete stress Steel stress**Analysis and Design of “Short” Columns**Elastic Behavior An elastic analysis does notwork, because creep and shrinkage affect the acting concrete compression strain as follows:**Analysis and Design of “Short” Columns**Elastic Behavior Concrete creeps and shrinks, therefore we can not calculate the stresses in the steel and concrete due to “acting” loads using an elastic analysis.**Analysis and Design of “Short” Columns**Elastic Behavior Therefore, we are not able to calculate the real stresses in the reinforced concrete column under acting loads over time. As a result, an “allowable stress” design procedure using an elastic analysis was found to be unacceptable. Reinforced concrete columns have been designed by a “strength” method since the 1940’s. Creep and shrinkage do not affect the strength of the member. Note:**Behavior, Nominal Capacity and Design under Concentric Axial**loads 1. Initial Behavior up to Nominal Load - Tied and spiral columns.**Behavior, Nominal Capacity and Design under Concentric Axial**loads**Behavior, Nominal Capacity and Design under Concentric Axial**loads Let Ag = Gross Area = b*h Ast = area of long steel fc = concrete compressive strength fy = steel yield strength Factor due to less than ideal consolidation and curing conditions for column as compared to a cylinder. It is not related to Whitney’sstress block.**Behavior, Nominal Capacity and Design under Concentric Axial**loads 2. Maximum Nominal Capacity for Design Pn (max) r = Reduction factor to account for accidents/bending r = 0.80 ( tied ) r = 0.85 ( spiral ) ACI 10.3.6.3**Behavior, Nominal Capacity and Design under Concentric Axial**loads 3. Reinforcement Requirements (Longitudinal Steel Ast) Let - ACI Code 10.9.1 requires**Behavior, Nominal Capacity and Design under Concentric Axial**loads 3. Reinforcement Requirements (Longitudinal Steel Ast) - Minimum # of Bars ACI Code 10.9.2 min. of 6 bars in circular arrangement w/min. spiral reinforcement. min. of 4 bars in rectangular arrangement min. of 3 bars in triangular ties**Behavior, Nominal Capacity and Design under Concentric Axial**loads 3. Reinforcement Requirements (Lateral Ties) ACI Code 7.10.5.1 size # 3 bar if longitudinal bar # 10 bar # 4 bar if longitudinal bar # 11 bar # 4 bar if longitudinal bars are bundled**s s s**16 db ( db for longitudinal bars ) 48 db ( db for tie bar ) least lateral dimension of column Behavior, Nominal Capacity and Design under Concentric Axial loads 3. Reinforcement Requirements (Lateral Ties) Vertical spacing: (ACI 7.10.5.2)**3.**Reinforcement Requirements (Lateral Ties) 1.) At least every other longitudinal bar shall have lateral support from the corner of a tie with an included angle 135o. No longitudinal bar shall be more than 6 in. clear on either side from “support” bar. 2.) Behavior, Nominal Capacity and Design under Concentric Axial loads Arrangement Vertical spacing: (ACI 7.10.5.3)**Behavior, Nominal Capacity and Design under Concentric Axial**loads Examples of lateral ties.**Behavior, Nominal Capacity and Design under Concentric Axial**loads Reinforcement Requirements (Spirals ) ACI Code 7.10.4 size 3/8 “ dia.(3/8” f smooth bar, #3 bar dll or wll wire) clear spacing between spirals 1 in. 3 in. ACI 7.10.4.3**Behavior, Nominal Capacity and Design under Concentric Axial**loads Reinforcement Requirements (Spiral) Spiral Reinforcement Ratio, rs**Behavior, Nominal Capacity and Design under Concentric Axial**loads Reinforcement Requirements (Spiral) ACI Eqn. 10-5 where**Behavior, Nominal Capacity and Design under Concentric Axial**loads 4. Design for Concentric Axial Loads (a) Load Combination Gravity: Gravity + Wind: and Check for tension etc.**Behavior, Nominal Capacity and Design under Concentric Axial**loads 4. Design for Concentric Axial Loads (b) General Strength Requirement where, f = 0.65 for tied columns f = 0.7 for spiral columns**Behavior, Nominal Capacity and Design under Concentric Axial**loads 4. Design for Concentric Axial Loads (c) Expression for Design defined:**Behavior, Nominal Capacity and Design under Concentric Axial**loads or**Behavior, Nominal Capacity and Design under Concentric Axial**loads * when rg is known or assumed: * when Ag is known or assumed:**Example: Design Tied Column for Concentric Axial Load**Design tied column for concentric axial load Pdl = 150 k; Pll = 300 k; Pw = 50 k fc = 4500 psi fy = 60 ksi Design a square column aim for rg = 0.03. Select longitudinal transverse reinforcement.**Example: Design Tied Column for Concentric Axial Load**Determine the loading Check the compression or tension in the column**Example: Design Tied Column for Concentric Axial Load**For a square column r = 0.80 and f = 0.65 and r = 0.03**Example: Design Tied Column for Concentric Axial Load**For a square column, As=rAg= 0.03(15.2 in.)2 =6.93 in2 Use 8 #8 bars Ast = 8(0.79 in2) = 6.32 in2**Example: Design Tied Column for Concentric Axial Load**Check P0**Example: Design Tied Column for Concentric Axial Load**Use #3 ties compute the spacing < 6 in. No cross-ties needed**Example: Design Tied Column for Concentric Axial Load**Stirrup design Use #3 stirrups with 16 in. spacing in the column**Behavior under Combined Bending and Axial Loads**Usually moment is represented by axial load times eccentricity, i.e.**Behavior under Combined Bending and Axial Loads**Interaction Diagram Between Axial Load and Moment ( Failure Envelope ) Concrete crushes before steel yields Steel yields before concrete crushes Any combination of P and M outside the envelope will cause failure. Note: