Hello to everybody,

I am using the dynamic module of CAESAR II for a seismic analysis based on response spectra method.
I have three spectrum load cases corresponding to the three principal directions of the system, each one composed by the combination 100-40-40 of base spectra.
In order to check the compliance of acceleration experienced by valves present in the analysed system, I need to know the accelerations in the three directions corresponding to the analysed spectrum load cases, but in the program output it is not available the acceleration output report.

Can someone help me to figure out a solution of this problem?

Thanks in advance.

P72

1) First calculate the modal displacement at the node in question by multiplying the Mass Participation Factor for each mode of vibration by the mass normalized mode shape. The Mass Participation Factor (as displayed by CAESAR II) includes both the Mode Participation Factor and the Spectral Acceleration. Regardless of what units are in use, the MPF (as displayed by CAESAR II) always are calculated and displayed in “English” units – meaning, if the MPF is multiplied by the Mass Normalized Mode shapes, it will always give the resultant displacements in inches. In the example below you see 9 extracted modes of vibration, which experience Mass Participation Factors under the specified load of:
Freq Angular Freq Mass Part Factor
0.863 5.42 -4.48983
1.319 8.289 8.15185
1.541 9.683 -13.68175
1.549 9.736 5.81452
1.801 11.314 1.80595
3.37 21.176 3.55044
5.921 37.201 0.49518
8.333 52.359 -0.5056
9.014 56.639 -0.78774

Multiply each Mass Part Factor by its corresponding Mass Normalized Mode shape to determine the displacements of each mode. For example, for, say, node 20 using Mode 1, MPF = -4.48983; the Mode Shape Displacements are (X = -0.0048, Y = -0.0138, Z = -0.0003). This gives modal displacements of (X = 0.021551 inches, Y = 0.06196 inches, Z = 0.001347 inches).

2) Second, the acceleration of each mode, at each node, can be calculated from that mode’s displacement at that node. Since the node must travel through +/- that displacement each time it cycles, and it has to do it with an angular frequency of W (the frequency in Hz times 2pi), it’s acceleration is defined as Disp * W^2. So next, multiply that displacement by the square of the modal angular frequency. This gives you the modal accelerations at each node.

In the example, the angular frequency of mode 1 is 5.42, squared is 29.376, so the modal acceleration at node 20 is (X = 0.633 inches/sec^2, Y = 1.82 inches/sec^2, Z = 0.03957 inches/sec^2). These can be converted to Gs by dividing by 386.4 in/sec^2, so we get: (X = 0.1638G, Y = 0.00471G, Z = 0.000102G).

3) Last, combine the modal accelerations using whatever method has been selected for modal combinations (either SRSS, ABS, or GROUP). For this example SRSS is used (for simplicity’s sake) over the 9 modes extracted. So the resultant Y displacement at node 20 would be = SQRT(SQR(0.06196)+SQR(0.81437)+SQR(0.313312)+…+SQR(-0.10997)) = 1.467392, which can be confirmed in the CAESAR II dynamic output Displacement Report. Accelerations should be combined using the same method as was used to combine the displacements, Y-acceleration is = SQRT(SQR(0.00471) + SQR(0.144807)+SQR(0.076206)+…+SQR(-0..91298)) = 1.728G.

4) Finally, if you are looking for a resultant acceleration, the acceleration in all three directions should be combined spatially, using the SRSS method.

Excel really helps here.

Great, Dave!

Thanks a lot for your precise and clear indication.

I take the opportunity for asking You about another issue relevant to CII dynamic analysis: could you suggest a similar method to determine the mass participation factor of each vibration mode in the three directions?

Thanks in advance.

P72