1. Lecture - Design of Columns
CEN 347

3. Introduction

16. Types of Column

19. Types of Column

20. Types of Column

22. Strength of short or Slender Columns

23. Strength of short or Slender Columns

24. Strength of short or Slender Columns

51. 0.70
0.65

56. 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

57. Analysis and Design of “Short” Columns
General Information
Column:

58. Analysis and Design of “Short” Columns
Tie Columns % 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

59. Analysis and Design of “Short” Columns
Spiral Columns
Pitch = in. to in.
spiral restrains lateral (Poisson’s effect)
axial load delays failure (ductile)

60. 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.

61. 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

62. Analysis and Design of “Short” Columns
Elastic Behavior
An elastic analysis does not work because creep and shrinkage affect the acting concrete compression strain as follows:

63. 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

64. 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.
Note:
Creep and shrinkage do not affect the strength of the member.

65. Behavior, Nominal Capacity and Design under concentric Axial loads1.
Initial Behavior up to Nominal Load - Tied and spiral columns.

66. 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’s stress block.

67. Behavior, Nominal Capacity and Design under concentric Axial loads2.
Maximum Nominal Capacity for Design Pn (max)
r = Reduction factor to account for accidents/bending
r = ( tied )
r = ( spiral )

68. Behavior, Nominal Capacity and Design under concentric Axial loads3.
Reinforcement Requirements (Longitudinal Steel Ast)
Let
- ACI Code requires

69. Behavior, Nominal Capacity and Design under concentric Axial loads3.
Reinforcement Requirements (Longitudinal Steel Ast)
- Minimum # of Bars ACI Code
min. of 6 bars in circular arrangement w/min. spiral reinforcement.
min. of 4 bars in rectangular arrangement

70. Behavior, Nominal Capacity and Design under concentric Axial loads3.
Reinforcement Requirements (Lateral Ties)
ACI Code
size
# 3 bar if longitudinal bar # 10 bar # 4 bar if longitudinal bar # 11 bar # 4 bar if longitudinal bars are bundled

71. Behavior, Nominal Capacity and Design under concentric Axial loads3.
Reinforcement Requirements (Lateral Ties)
Vertical spacing:
s s s
16 db ( db for longitudinal bars ) db ( db for tie bar ) least lateral dimension of column

72. Behavior, Nominal Capacity and Design under concentric Axial loads3.
Reinforcement Requirements (Lateral Ties)
Vertical spacing: Arrangement,
1.)
At least every other longitudinal bar shall have lateral support from the corner of a tie with an included angle o.
No longitudinal bar shall be more than 6 in. clear on either side from “support” bar.
2.)

73. Behavior, Nominal Capacity and Design under concentric Axial loads
Examples of lateral ties.

74. Behavior, Nominal Capacity and Design under concentric Axial loads
Reinforcement Requirements (Spirals )
ACI Code
- size
3/8 “ f (3/8” f smooth bar, #3 bar dll or wll wire)
- clear spacing:
1 in. 3 in.

75. Behavior, Nominal Capacity and Design under concentric Axial loads
Reinforcement Requirements (Spiral)
Spiral Reinforcement Ratio, rs

76. Behavior, Nominal Capacity and Design under concentric Axial loads
Reinforcement Requirements (Spiral)
ACI Eqn. 10-6
where

77. Behavior, Nominal Capacity and Design under concentric Axial loads4.
Design for Concentric Axial Loads
(a) Load Combination
Gravity:
Gravity + Wind:
and
Etc.

78. Behavior, Nominal Capacity and Design under concentric Axial loads4.
Design for Concentric Axial Loads
(b) General Strength Requirement
where,
f = 0.7 for tied columns
f = 0.75 for spiral columns

79. Behavior, Nominal Capacity and Design under concentric Axial loads4.
Design for Concentric Axial Loads
(c) Expression for Design
defined:

80. Behavior, Nominal Capacity and Design under concentric Axial loads

81. Behavior, Nominal Capacity and Design under concentric Axial loads
* when rg is known or assumed:
* when Ag is known or assumed:

82. Example: 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 = Select longitudinal transverse reinforcement.

83. Behavior under Combined Bending and Axial Loads
Usually moment is represented by axial load times eccentricity, i.e.

86. Behavior under Combined Bending and Axial Loads
Resultant Forces action at Centroid
( h/2 in this case )
Moment about geometric center

90. 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
Note: Any combination of P and M outside the envelope will cause failure.

91. Behavior under Combined Bending and Axial Loads
Axial Load and Moment Interaction Diagram -General

92. Example: Axial Load vs. Moment Interaction Diagram