The structures shown in Figure below was used to illustrate various capabilities of the Dynamic Response program. Seven separate response analyses are illustrated: 1. The dynamic response of the structure due to ground motion was determined using the response spectrum approach. The responses of each mode were added using the Complete Quadratic Combination (CQC) method.
2. The response of the structure due to ground motion was determined using the Time History approach.
3. This problem is an engine vibration problem where the motion of the deck due to excitation from reciprocating machinery was analyzed. 4. The dynamic response due to a step load defined using a force time history was analyzed.
5. The structural response due to extreme wind gusts from four directions was determined. 6. Fatigue damage due to wind fatigue was performed using the spectral wind capabilities. 7. Fatigue damage due to vibration caused by ice floes was calculated by the program.
The following is an example of a response analysis for a base driven system using the Response Spectrum approach.
The structure in Figure 1 stands in 82.02 feet of water. It is located in a seismic zone with rock type soil where the ratio of effective ground acceleration to gravitational acceleration is 0.20.
The response spectrum was applied equally along both principal orthogonal horizontal axes along with an acceleration spectrum equal to one-half of that applied in the vertical direction. All three spectra were applied simultaneously and the responses were combined using the complete quadratic combination (CQC) method. Five percent critical damping was assumed.
The static analysis included gravity and buoyancy loads. The stresses induced by earthquake loads were combined with the static stresses for the purpose of member strength check. For tubular joint check, the seismic stresses were doubled then combined with the static stresses. In either case, the allowable stresses were increased by 70 percent.
Note: For any dynamic analysis, a foundation super element, dummy pile or equivalent pile stub used to simulate the soil/pile interaction must be developed using the PSI or PILE program.
For this sample problem, Load Case 1 containing the gravity and buoyancy of the structure was generated by Seastate then solved. Dynpac was used to generate the dynamic characteristics of the structure. The mass of the structure includes the mass associated with gravity, enclosed fluid and added mass.
The Dynamic Response program was used to predict the response of the structure due to the ground motion caused by an earthquake. The structure was analyzed using the response spectrum approach with an effective horizontal ground acceleration of 0.20*G.
The following is the Dynamic Response input file used in conjunction with the generalized mass file and solution file from Dynpac.
A. The DROPT line specifies analysis options, namely:
a. A base driven spectral earthquake analysis is to performed (‘SPEC’ in columns 7-10). b. A mudline elevation of -82.02 is specified in columns 19-24.
B. The SDAMP line specifies that the overall structural damping is 5.0 percent.
C. The STCMB line is used to have seismic and static results combined automatically. The STCMB line designates the following: a. Seismic loading is to be factored by 1.0 when combined with static loading for element check load cases.
b. Seismic loading is to be factored by 2.0 when combined with static loading for joint check load cases as designated by 2.0 in columns 13-17. c. Load case 1 from the static solution file is to be combined with the seismic load cases.
D. The LOAD line specifies that loading data is to follow.
E. The SPLAPI line defines the spectral analysis parameters as follows:
a. The API RP2A spectrum for soil type ‘A’ is to be used for each direction as specified by ‘A’ in columns 22, 29 and 36. b. Modal responses will be combined using the CQC method as designated in columns 38-41.
c. A response or ground acceleration factor of 0.20 * G is specified in columns 11-15.
d. The percent of the ground acceleration factor to be applied in each of the global directions is 100.0, 100.0 and 50.0 for the X, Y and Z global directions respectively as specified by 1.0, 1.0 and 0.50 in columns 16-21, 23-28 and 30-35, respectively.
F. The response function for the global X, Y and Z directions for joint 405 is requested on the RSFUNC line. The response function and power spectral density for 5 percent damping plotted verse time will be generated (PG1WO in columns 70-74).
Note: This file created by the Dynamic Response program, contains the responses for each of the three directions. The modal responses are combined using the CQC method as specified to obtain directional responses which are then combined using the RMS or SRSS method. The combine steps are executed automatically as part of the Dynamic Response analysis.
When using the STCMB line, the program creates four seismic+static load combinations, two for element check and two for joint can check, for each seismic load case as follows:
LC Combine Type Description
1 PRST Element code check case, seismic axial tension
2 PRSC Element code check case, seismic axial compression
3 PRST Joint can check case, seismic axial tension
4 PRSC Joint can check case, seismic axial compression
When using the STCMB feature, the Combine program is executed automatically to combine the seismic results and the static results. Two load cases for each member check and joint check will be created to account for the cyclic nature of the seismic loading.
Note: The STCMB feature requires that the static solution file exist prior to executing the earthquake analysis. If the STCMB feature is note used, the user must create the Combine input file and execute Combine as a separate analysis step.
Note: Only load cases 1 and 2 are selected in the Post input file, while only load cases 3 and 4 are selected in the Joint Can input file. Notice also that the ‘JO’ option which designates that stresses are to be checked only at the member ends is specified in the Post input file.