Comparison of Effective Flexural Stiffness for Critical Buckling of Concrete Columns and Piers
A primary concern in calculating the critical axial buckling load Pc (Euler buckling load Pe in AASHTO) is the choice of the stiffness that reasonably approximates the variation in stiffness due to cracking, creep, and concrete nonlinearity. (EI)eff (or EI) is used in the process of determining the moment magnification at column ends and along the column length in sway and nonsway frames.
| ACI 318-19/14 (6.6.4.4.2) ACI 318-11 (10.10.6 (10-13)) |
| CSA A23.3-19/14/04 (10.15.3.1) |
AASHTO 9th Edition (4.5.3.2.2b-5) | |
| ACI 318-19/14 (6.6.4.5.2) ACI 318-11 (10.10.6 (10-12)) |
| CSA A23.3-19/14/04 (10.15.3.1) |
AASHTO 9th Edition (4.5.3.2.2b-3) | |
| ACI 318-19/14 (6.6.4.6.2b) ACI 318-11 (10.10.7.4 (10-21)) |
| CSA A23.3-19/14/04 (10.16.3.2) |
AASHTO 9th Edition (4.5.3.2.2b-4) | |
Design codes provide the following options to calculate (EI)eff as follows: | |
| ACI 318-19/14 (6.6.4.4.4) ACI 318-11 (10.10.6.1) |
| CSA A23.3-19/14/04 (10.15.3.1) |
| AASHTO 9th Edition (5.6.4.3) |
Where: | |
βdns – ACI definition | |
= ratio used to account for reduction of stiffness of columns due to sustained axial loads. Note that βdns is used for non-sway frames and sway frames when slenderness effects are calculated along column length. For sway frames where slenderness effects are calculated at column ends, βds (the ratio of maximum factored sustained shear within a story to the maximum factored shear in that story associated with the same load combination) is used instead of βdns. | |
βd – CSA definition | |
= (for non-sway frames and for strength and stability checks of sway frames) the ratio of the maximum factored sustained axial load to the maximum factored axial load associated with the same load combination. | |
= (for sway frames) the ratio of the maximum factored sustained shear within a storey to the maximum factored shear in that storey. | |
βd – AASHTO definition | |
= ratio of maximum factored permanent load moments to maximum factored total load moment (always positive). | |
For ACI, the moment of inertia of the column or wall section, I, in Eq. (6.6.4.4.4c) is calculated as follows: | |
| ACI 318-19/14 (Table 6.6.3.1.1(b)) ACI 318-11 (10.10.4.1 (10-8)) |
* CSA A23.3-14 and prior are using EI instead of (EI)eff.
** Where ϕm = 0.75 for CSA and ϕK = 0.75 for AASHTO.
† Utilized by spColumn.