G-03 (Axial-Flexural Design of Concrete Columns) |
  
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G-03 (Axial-Flexural Design of Concrete Columns) |
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Objective
To verify the axial-flexural design of the rectangular and circular concrete columns
Problem Description
The following concrete columns [Ref 1, 2] are to be designed according to ACI 318-02 code.
Beam |
Dimension (in) |
fc (ksi) |
fys (ksi) |
Pu (kips) |
Mux (ft-kips) |
Muy (ft-kips) |
1 [Ref.1] |
Rectangular 16 x 16 |
3 |
60 |
249 (compression) |
55 |
110 |
2 [Ref. 2] |
Circular 26 |
4 |
60 |
1600 (compression) |
150 |
0 |
3 [Ref. 3] |
Rectangular 20 x 12 |
4 |
60 |
255 (compression) |
63.75 |
127 |
Finite Element Model
3 beam elements with appropriate material and design criteria assigned
Model type: 3D Frame
Results
The design results are compared with the [Ref 1] and [Ref 2] in the following table.
Beam |
ENERCALC 3D |
Reference |
|
Bars |
Unity Check |
Bars |
|
1 |
12#7 (4 on each side) |
0.976 |
12#7 (4 on each side) or 8#8 (3 on each side) |
2 |
13#10 |
0.982 |
12#10 |
3 |
8#9 (3 on each side) |
0.915 |
8#9 (3 on each side) |
Comments
The first column is biaxially loaded and therefore a 3D frame model is used. [Ref 1] gives 12#7 (4 on each side) bars or 8#8 (3 on each side) bars based on Equivalent Eccentricity Method and Bresler Reciprocal Load Method respectively. The program gives 12#7 bars (4#7 on each side) if trial bar size starts with #7 and bar layout uses ‘equal sides’ option. If 8#8 bars (3#8 on each side) are used, the program gives a unity check value of 1.024 (and therefore the design fails). Since the program always tries to find the first section that will pass the unity check (< 1.0), we need to limit the maximum reinforcement ratio (say 3% in this case) in order to see the unity check of the 8#8 bars (3#8 on each side) section. In addition, we also need to set the start and end bar sizes to be #8 and bar layout to be ‘equal sides’ in the column design criteria for comparison.
The second column is a circular spiral column. The program gives 13#10 bars while [Ref 2] gives 12#10. If 12#10 bars are used, the program gives a unity check value of 1.008 (and therefore the design fails). Practically speaking, 12#10 should be regarded as ok.
Each column is modeled with one 3D beam element with one support flag of 111100 (fixed in Dx, Dy, Dz and Dox) and the other support flag of 011100 (fixed in Dy, Dz and Dox). Nodal moments and forces are applied in respective directions. Since no slenderness is considered, very small effective length factors are used.
Reference
[1]. James G. MacGregor & James K. Wight, “Reinforced Concrete – Mechanics and Design”, 4th Edition, pp.529-532, Pearson Prentice Hall, 2005
[2]. James G. MacGregor & James K. Wight, “Reinforced Concrete – Mechanics and Design”, 4th Edition, pp.519, Pearson Prentice Hall, 2005
[3]. Arthur H. Nilson, David Darwin, Charles W. Dolan, “Design of Concrete Structures”, 13th Edition, pp. 278, McGraw-Hill Higher Education, 2004
