Reinforced Concrete Design Lecture 14 Dr. Nader Okasha

Design of Short Axially Loaded Columns

Columns According to ACI Code, a structural element with a ratio of height-to least lateral dimension exceeding three used primarily to support compressive loads is defined as column. Columns are vertical compression members of a structural frame intended to support the load-carrying beams. They transmit loads from the upper floors to the lower levels and then to the soil through the foundations. b l P h Column Beam Loads Footing Soil Slab

Columns Usually columns carry bending moment as well, about one or both axes of the cross section, and the bending action may produce tensile forces over a part of the cross section The main reinforcement in columns is longitudinal, parallel to the direction of the load and consists of bars arranged in a square, rectangular, or circular shape

Length of the column in relation to its lateral dimensions Columns may be divided into two categories 1- Short Columns, for which the strength is governed by the strength of the materials and the geometry of the cross section 2- Slender columns, for which the strength may be significantly reduced by lateral deflections. 3- Position of the load on the cross-section Columns can be classified as 1-Concentrically loaded columns, are subjected to axial force only 2-Eccentrically loaded columns, are subjected to moment in addition to the axial force.

Column Load: Tributary area method

Column Load: Beam reaction method

Load Summation on Column Section for Design

Analysis and Design of Short Columns Column Types: Tied Spiral Composite

Behavior of Tied and Spirally-Reinforced Columns Axial loading tests have proven that tied and spirally reinforced columns having the same cross-sectional areas of concrete and steel reinforcement behave in the same manner up to the ultimate load. At that load tied columns fail suddenly due to excessive cracking in the concrete section followed by buckling of the longitudinal reinforcement between ties within the failure region. For spirally reinforced columns, once the ultimate load is reached, the concrete shell covering the spiral starts to peel off. Only then, the spiral comes to action by providing a confining force to the concrete core, thus enabling the column to sustain large deformations before final collapse occurs.

Behavior of Tied and Spirally-Reinforced Columns Failure of a tied column Failure of a spiral column Deformation

Nominal Capacity and Design under Concentric Axial loads Ag = gross area = b*h Ast = area of long steel fc = concrete compressive strength fy = steel yield strength

Nominal Capacity and Design under Concentric Axial loads Maximum Nominal Capacity for Design Pn r = Reduction factor to account for accidental eccentricity r = 0.80 ( tied ) r = 0.85 ( spiral ) ACI 10.3.6.3

Nominal Capacity and Design under Concentric Axial loads f = 0.65 for tied columns f = 0.75 for spiral columns (was 0.70 in ACI318-05) r = 0.80 ( tied ) r = 0.85 ( spiral )

Nominal Capacity and Design under Concentric Axial loads or

Nominal Capacity and Design under Concentric Axial loads * when rg is known or assumed:

Nominal Capacity and Design under Concentric Axial loads Reinforcement Requirements (Spiral) Spiral Reinforcement Ratio, rs

Nominal Capacity and Design under Concentric Axial loads Reinforcement Requirements (Spiral)

Reinforcement Requirements (Longitudinal Steel Ast) Design Considerations Reinforcement Requirements (Longitudinal Steel Ast) ACI Code 10.9.1 requires

Reinforcement Requirements (Longitudinal Steel Ast) Design Considerations Reinforcement Requirements (Longitudinal Steel Ast) - Minimum Number of Bars ACI Code 10.9.2 min. of 6 bars in spiral arrangement min. of 4 bars in rectangular or circular ties min. of 3 bars in triangular ties

Reinforcement Requirements (Lateral Ties) Design Considerations Reinforcement Requirements (Lateral Ties) ACI Code 7.10.5.1 size f 8 bar if longitudinal bar f30 bar f12 bar if longitudinal bar f 32 bar f12 bar if longitudinal bars are bundled

Reinforcement Requirements (Lateral Ties) Design Considerations Reinforcement Requirements (Lateral Ties) Vertical spacing: (ACI 7.10.5.2) 16 db ( db for longitudinal bars ) 48 dstirrup least lateral dimension of column s s s

Reinforcement Requirements (Lateral Ties) Design Considerations Reinforcement Requirements (Lateral Ties) Arrangement Vertical spacing: (ACI 7.10.5.3) 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 15cm clear on either side from “support” bar. 2.)

Examples of lateral ties Design Considerations Examples of lateral ties

Reinforcement Requirements (Spirals ) Design Considerations Reinforcement Requirements (Spirals ) ACI Code 7.10.4.2 size 10 mm diameter ACI 7.10.4.3 clear spacing between spirals 2.5cm 7.5cm

Design Considerations Clear Distance between Reinforcing Bars ACI Code specify that for tied or spirally reinforced columns, clear distance between bars, shown in Figure, is not to be less than the larger of 1.50 times bar diameter or 4 cm. This is done to ensure free flow of concrete among reinforcing bars.

Design Considerations Concrete Protection Cover ACI Code specifies that for reinforced columns, the clear concrete cover is not to be taken less than 4 cm for columns not exposed to weather or in contact with ground. It is essential for protecting the reinforcement from corrosion or fire hazards. Minimum Cross Sectional Dimensions The ACI Code does not specify minimum cross sectional dimensions for columns. Column cross sections 20 × 25 cm are considered as the smallest practicable sections. For practical considerations, column dimensions are taken as multiples of 5 cm. Lateral Reinforcement Ties are effective in restraining the longitudinal bars from buckling out through the surface of the column, holding the reinforcement cage together during the construction process, confining the concrete core and when columns are subjected to horizontal forces, they serve as shear reinforcement.

Design Considerations Factored Loads For gravity loads only, Pu = 1.2 PD+1.6 PL For dead, live and wind loads, Pu = 1.2 PD+1.0 PL+1.6 PW For dead and wind loads, Pu = 0.9 PD + 1.3 PW or Pu = 1.2 PD + 0.8 PW For dead, live and earthquake loads, Pu = 1.2 PD+1.0 PL+1.0 PE For dead and earthquake loads, Pu = 0.9 PD + 1.0 PE

Design Procedure for Short Axially Loaded Columns Evaluate the factored axial load Pu acting on the column. Decide on a reinforcement ratio ρg that satisfies ACI Code limits. Usually a 1 % ratio is chosen for economic considerations. Determine the gross sectional area Ag of the concrete section. Choose the dimensions of the cross section based on its shape. Readjust the reinforcement ratio by substituting the actual cross sectional area in the respective equation. This ratio has to fall within the specified code limits. Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions.

Design Procedure for Short Axially Loaded Columns From reinforcement tables, choose the number and diameters of needed reinforcing bars. For rectangular sections, a minimum of four bars is needed, while a minimum of six bars is used for circular columns. Design the lateral reinforcement according to the type of column, either ties or spirals. Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements. Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement.

Example 1 The cross section of a short axially loaded tied column is shown in Figure. It is reinforced with 6 16mm bars. Calculate the design load capacity of the cross section. Use fc′=280 kg/cm2 and fy = 4200 kg/cm2. Solution: Clear distance between bars Sc Only, one ties is required for the cross section Figure [1] 6Φ16 25 40 Ties Φ8@25cm Sc=12.8 cm 6Φ16 25 40

Example 1 The spacing between ties is not exceed the smallest of 16 db =16(1.6) = 25.4 cm 48 ds = 48(0.8) = 38.4 cm 25 cm Thus, ACI requirements regarding reinforcement ratio, clear distance between bars and tie spacing are all satisfied. The design load capacity ΦPn Φ 8mm ties spaced @ 25 cm

Example 2 Design a short tied column to support a factored concentric load of 1000 kN, with one side of the cross section equals to 25 cm. Solution

Check spacing

Stirrup design

Example 3 Design a short, spirally reinforced column to support a service dead load of 800 kN and a service live load of 400 kN. Solution

Check spacing between longitudinal bars Solution Check spacing between longitudinal bars D’ =35-2(4)-2(0.8)-1.4=24cm

Design the needed spiral, try f 8