Missing mass – How to Consider


  
 Applies To 
  
 Product(s):STAAD.Foundation Advanced
 Version(s):All
 Environment: N/A
 Area: Analysis Solutions
 Subarea: Response Spectrum Analysis
 Original Author:Jason Coleman
Bentley Technical Support Group
  

Missing mass – How to Consider Definitions

Missing mass mode
The fictitious mode which represents all the modes which are not calculated during eigensolution
Calculated modes
The individual modes which are calculated during eigensolution.

Required Input

Input required for instructing STAAD to include MISSING MASS when performing a response spectrum analysis.

  1. MIS f6

    The term MIS tells STAAD to consider missing mass. In other words, if the word MIS is omitted, the missing mass calculations are not performed.

    f6 is the spectral acceleration for the missing mass mode in units of length/sec2. This value is not multiplied by SCALE. If f6 is zero (0) or not entered, the spectral acceleration will be based on Item (2) described next.

  2. ZPA f7

    This input is required only if f6 as described in Item 1 is not provided or set to zero. f7 is not used if f6 is entered.

    f7 is the frequency at which the spectral acceleration for the missing mass mode is evaluated (if f6 is not entered) from the input period versus acceleration pairs. If f7 is not specified, or set to zero, STAAD will assume a value of 33 Hz.

  3. FF1 f8

    This term is required only if the ASCE modal combination method is used. It is the f1 term in equation 3.2-23 of the ASCE 4-98 standard. It represents a frequency and has units of Hz. Its default value is 2 Hz.

  4. FF2 f9

    This term also is required only if the ASCE modal combination method is used. It is the f2 term in equation 3.2-23 of the ASCE 4-98 standard. It too represents a frequency and has units of Hz. Its default value is 33 Hz. If f9 is assigned a value less than f8, f9 is reset to 33 Hz

Calculations

Procedure used by STAAD for combining the response from the missing mass mode with those from the calculated modes.

  1. The response from each of the calculated modes is combined using the specified modal combination method: CQC, SRSS, TEN, etc.
  2. The structural response associated with the missing mass mode is then combined with the value from step (a) using the SRSS method.

Examples

Example 1

SPECTRUM CQC X 1.0 ACC SCALE 9.81 CDAMP LOG MIS

Example 2

SPECTRUM ASCE Z 1 ACC SCALE 386.08 DAMP 0.04 MIS ZPA

FAQ

Question

How is the missing mass mode evaluated?

Answer

Using equation 3.2-8 of ASCE 4-98 :

{MissMassMode} = { {Ub} – SUM[PartFact(i) {Phi(i)} ] }. Sum over modes.

[K]{X0} = [ M ] {MissMassMode} * (Sa miss)

(Sa miss) = spectral acceleration (based on user input accel or input zpa frequency.

The missing mass mode is the difference between the static deformation due to a 1 g static load in a global direction and the sum of the responses of each mode extracted due to a 1g excitation. This is the amount of deformation that cannot be represented by the modes that were extracted.

The modes that were not extracted also have a dynamic component that the missing mass mode cannot represent (non-rigid response). It is assumed that if all of the modes up to the ZPA are included, then there will be very little non-rigid response. ASCE4-98 and other documents describe how to calculate the ZPA from the test data from the site.