A response spectrum analysis is run by using linear interpolation for the following site spectrum period and acceleration in the Earthquake tab under Vessel Properties>Load Conditions :
Seismic code used in ASCE 7-2010.
The analysis is run, the 5 modes and period are calculated as follows. The natural frequency is calculated by finite element beam stiffness matrix.
The T=0.116 corresponding to which the spectral acceleration obtained from the site spectrum data is 0.238g which is obtained as follows:
See the site spectrum table:
Cs = Sa (since this is a response spectrum analysis) = 0.1 + 0.016 (0.28-0.23)/(0.2-0.1) = 0.238 g (by linear interpolation from the above table using period = 0.116) which is reported in the calculation report below:
Once Cs is obtained, further calculations performed as follows:
W=3,769.94 daN.(vessel weight for the design case)
The base shear V=Cs x W = 0.238 g x 3769.94/g = 897 daN.
Cvx obtained as shown in the report below, where wx is the weight of the section and hx is the distance from the datum:
Fx = Cvx * V = eg. for section 12 , Fx = 0.00099 x 897 = 0.88803 = 0.9 as stated in the report.
Fv = 0.2 x SDS x wx = 0.2 * (0.9g) x wx as in report, explanation as follows: (refer ASCE 7-10 par. 184.108.40.206)
The vertical seismic load effect is a combination of Weight:
so the Vertical Load Fv at each level is equal to 0.2SDS*wx (wx = weight at each level).
Eg. for section 12: Fv=0.2 x .9 x 19.7 = 3.546 = 3.6 as in the report.