Understanding the concepts on Degrees of Freedom
Challenge has been submitted in PDF form in 3pages attached here alongwith, Summary is prepared for a glance which here as follows:
| Various Parameter corr. to various Modal Frequency | f1 | f2 | f3 | f4 | f5 |
| Natural Period (Tn) in seconds | 2 | 0.6852 | 0.4346 | 0.3383 | 0.2966 |
| Pseudo Acceleration(An) (dimensionless i.e. Sa/g) | 0.25 | 1 | 1.1 | 1.1 | 1.1 |
| Modal Mass (Mn) | 3.8615m | 3.8615m | 3.8615m | 3.8615m | 3.8615m |
| Modal Property (Ln) | 4.121m | -1.297m | 0.895m | -0.381m | 0.175m |
| Modal Mass Participation Factor (τn) | 1.067 | -0.33588 | 0.23177 | -0.09866 | 0.04532 |
| Effective Modal Mass (M') | 4.3979m | 0.4356m | 0.2074m | 0.0376m | 0.0079m |
| Base Shear (Vbn) | 1.0995mg | 0.4356mg | 0.22814mg | 0.04136mg | 0.00869mg |
| % of Effective modal Mass(M'/5m) | 87.96 | 8.712 | 5.37 | 0.9737 | 0.204 |
| Cummalative % of Effective modal mass | 87.96 | 96.67 |
Ist two modes to be taken into account to get Modal mass participating factor greater than 90%
Base Shear Distribution in each of the five storey due to specific Modal Frequency has been shown here alongwith:-
| Distribution of Base Shear to Different storey (mg) | f1 | f2 | f3 | f4 | f5 |
| First Storey | 0.089mg | 0.3006mg | 0.299mg | 0.117mg | 0.0319mg |
| 2nd Storey | 0.171mg | 0.3939mg | 0.08515mg | -0.097mg | -0.05374mg |
| 3rd Storey | 0.2387mg | 0.2153mg | -0.2748mg | -0.03624mg | 0.05848mg |
| 4th Storey | 0.2875mg | -0.11218mg | -0.1634mg | 0.1273mg | -0.0446mg |
| 5th Storey | 0.3129mg | -0.362mg | 0.228mg | -0.069656mg | 0.01665mg |
| Summation of Base Shear from abovr 5 Floors | 1.0991mg | 0.4356mg | 0.1739mg | .04149mg | 0.00867mg |
Combined Base Shear from SRSS rule will be 1.20518mg
Combined Base Shear will be Square root of the sum of the squares of base shears of five different Modal Frequency annotated as Vb1, Vb2, Vb3,.....=√(Vb1^2 + Vb2^2 + Vb3^2 + Vb4^2 + Vb5^2)