Moment magnification is an approximate evaluation of slenderness of a column.
Substructure considers two types of slender columns: Unbraced and Braced.
Note: Substructure does not determine the type of column slenderness (braced or unbraced) automatically, you must specify the type according to the circumstance of your project and relevant specifications.
For unbraced columns, Substructure will calculate the effective length factor, k, as follows:
The calculation of M2b and M2s in Substructure is different from the AASHTO Specifications requirements. Substructure only considers the total moment (e.g., moments MX and MZ for bottom of the column) and does not distinguish the moments due to the gravity or lateral loads, as specified by AASHTO Specifications.
With this assumption, for braced columns, Substructure only calculates the moment magnification factor δb and multiples this factor with the total moment to obtain the magnified factored moment. For unbraced columns, it calculates δs and multiplies this factor with the total moment to obtain the magnified factored moment. In Substructure, EI is calculated by the following equation:
Note: The dead load moment includes the moment due to self-weight. If the moment is zero or less than the value due to minimum eccentricity when calculating bd,
Substructure will multiply the minimum eccentricity (0.6 + 0.03h) with the axial force to obtain the moment.
Substructure uses the smaller total end moment for M1b and larger total end moment for M2b. For a braced column with any transverse loads acting on the column, Cm = 1. In addition, for unbraced columns, Cm = 1. Same as the calculation of bd, if the moment is zero or less than the value due to minimum eccentricity, Substructure uses the minimum eccentricity to obtain the moment.
Single curvature is due to the different sign of M1b and M2b, and double curvature results are from the same sign of M1b and M2b. If both M1b and M2b are zero, Substructure will use the single curvature equation and moments due to the minimum eccentricity to calculate Cm.
Substructure also takes into consideration a column with a drilled shaft or checking point. The connection point between the drilled shaft and column is treated the same as the column with a checking point, with respect to the moment magnification. The moment magnification factor at the checking point is interpolated from the moment magnification factors at the top and bottom of the column.
Moment Magnification Calculations for Column with Checking Point
If there is an intermediate strut,
Substructure assumes the moment about global Z-direction is restrained due to the strut. As a result,
Substructure calculates the moment magnification factor for the columns above the strut and below the strut separately for the moment with respect to Z-direction. The moment magnification factor in X-direction at the connection between the strut and column is interpolated from the moment magnification factors at the top and bottom of the column. This is illustrated below, where (a) Pier with an intermediate strut, (b) column is separated when calculates moment magnification for the moment in Z-direction at the connection between the column and strut, and (c) moment magnification factor in X-direction is interpolated at the connection between the column and strut.
Moment Magnification Calculations for Column
