Calculation Of Accidental and Dynamic Eccentricity

Question:

Please find attached files and let me know how to calculate the Accidental Eccentricity and the Dynamic Eccentricity  as reported in the STAAD Pro output. 

Explanation: 

 The Building Length (Along X) : 9.00 m

The Building Width (Along Z)  : 8.00 m

The Accidental eccentricity:

As per ASCE-07 code, where diaphragms are not flexible, the design
shall include the inherent torsional moment (Mt)
resulting from the location of the structure masses
plus the accidental torsional moments (Mta) caused by
assumed displacement of the center of mass each way
from its actual location by a distance equal to 5
percent of the dimension of the structure perpendicular to the direction of the applied forces.

Hence, the Multiplying factor for Accidental Torsion Moment is taken as 0.05.

Along X = (Length of the Structure perpendicular to direction of applied load along Z)* 5%

              = 9*.05 = 0.45

Along Z = (Length of the Structure perpendicular to direction of applied load along X)* 5%

              = 8*.05 = 0.40

The Dynamic Eccentricity:

The multiplying factor (DEC) for Natural Torsion Moment is taken as 1.5.

The Center of Mass for each floor diaphragm is reported in the output file

The C.M of the diaphragm 

X                Z

4.481     4.016

The Center of Rigidity of the same rigid floor is reported in the output file if  PRINT DIA CRcommand is invoked.

The C.R of the diaphragm 

X                            Z

4.33                4.133

The natural torsion is automatically included in the analysis for DEC <= 1.0 i.e. no additional inherent torsion is applied.

However, if DEC > 1.0, a twisting moment with modified eccentricity of (DEC-1) will act at CM.

For more information, please refer to the chapter 5.32.10.1.8 in the technical reference manual.

So, the Net Dynamic Eccentricity = Static Eccentricity*(DEC-1) -------------   Multiplying factor (DEC >1)

            Along X                        =  (C.M-C.R)*(1.5-1)

                                                 =  (4.481-4.33)*(.5)

                                                 =  0.074 = 0.07

            Along z                         =  (C.M-C.R)*(1.5-1)

                                                 =  (4.016-4.133)*(0.5)

                                                 = -0.058 = -0.06 

 Staad Output :