01. Design Data

Design Data

Code

Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19)

References

• Reinforced Concrete Design, 9^th Edition, 2021, Pincheira J. et. al., Oxford University Press, Example 10.18.1

• spColumn Engineering Software Program Manual v10.00, STRUCTUREPOINT, 2021

• “Interaction Diagram - Tied Reinforced Concrete Column Design Strength (ACI 318-19)” Design Example, STRUCTUREPOINT, 2022

• “Interaction Diagram - Tied Reinforced Concrete Column with High-Strength Reinforcing Bars (ACI 318-19)” Design Example, STRUCTUREPOINT, 2022

• “Interaction Diagram - Barbell Concrete Shear Wall Unsymmetrical Boundary Elements (ACI 318-19)” Design Example, STRUCTUREPOINT, 2022

• “Interaction Diagram - Building Elevator Reinforced Concrete Core Wall Design Strength (ACI 318-19)” Design Example, STRUCTUREPOINT, 2022

Design Data

f_c’ = 5000 psi

f_y = 60,000 psi

Cover = 1.5 in.

Column Diameter = 20 in.

Stirrups, longitudinal reinforcement and reinforcement locations are shown in Figure 1 and Table 1.

Table 1 - Reinforcement Configuration
Layer, i	d_i, in	n_i	A_si, in²	nA_si, in²
1	2.64	1	1.27	1.27
2	4.79	2	1.27	2.54
3	10.00	2	1.27	2.54
4	15.21	2	1.27	2.54
5	17.37	1	1.27	1.27
			A_st = Σ n_iA_s_i	10.16

Solution

Use the traditional hand calculations approach to generate the interaction diagram for the concrete column section shown above by determining the following seven control points:

Point 1: Maximum compression

Point 2: Bar stress near tension face equal to zero, (f_s = 0)

Point 3: Bar stress near tension face equal to 0.5 f_y (f_s = 0.5 f_y)

Point 4: Bar stress near tension face equal to f_y (f_s = f_y)

Point 5: Bar strain near tension face equal to ɛ_y + 0.003

Point 6: Pure bending

Point 7: Maximum tension

Several terms are used to facilitate the following calculations:

A_comp	= concrete area in compression, in².
	= geometric centroid location along the y-axis, in.
P_o	= nominal axial compressive strength, kip
ϕP_o	= factored axial compressive strength, kip
ϕP_n,max	= maximum (allowable) factored axial compressive strength, kip
c	= distance from the fiber of maximum compressive strain to the neutral axis, in.
a	= depth of equivalent rectangular stress block, in.
C_c	= compression force in equivalent rectangular stress block, kip
ɛ_s,i	= strain value in reinforcement layer, in./in.
C_s	= compression force in reinforcement, kip
T_s	= tension force in reinforcement, kip

04 Control Points

Figure 2- Circular Column Section Interaction Diagram Control Points