Applies To
Product(s):	AutoPIPE
Version(s):	ALL;
Area:	Load case
Date Logged & Current Version	Dec 2025 25.00.00.299

Problem:

Why different Response Spectra produce the same results in AutoPIPE Response Spectrum Analysis?

Solution:

The model consists of a 2‑inch NPS vertical riser rigidly anchored at the base, with no internal fluid mass (SG = 0). The pipe extends 5 ft above the anchor point and supports a 200‑lb axial gravitational load applied at the top node. Two independent lateral response‑spectrum inputs are applied to the system for dynamic evaluation.

Spectrum file #1:

Spectrum file #2:

The only variation between Spectrum #1 and Spectrum #2 occurs at Line 2 of the input data: Spectrum #1 defines a period of 10 sec with a corresponding acceleration of 193 in/s², whereas Spectrum #2 specifies a period of 2 sec with an acceleration of 772 in/s². Beyond this single point, both spectra are identical.

Given this isolated difference in the spectrum definition, should the dynamic analysis results for the two spectra be expected to differ or remain the same?

In reflection, I would expect the values of the 2 spectrums to be fairly close or the same. Here is why:

1. AutoPIPE uses Newton’s law for a vibrating structure: Mass × Acceleration + Damping × Velocity + Stiffness × Displacement = Earthquake force.

2. From AutoPIPE help> Response Spectrum Theory:

For a particular ground excitation, the response spectrum is constructed by computing the maximum response of a series of single DOF oscillators to the excitation. Using the response spectrum, the maximum response in each direction for each mode is calculated. Modal responses in each direction are combined using the specified combination method. The final response is calculated by combining the response from three directions using Square Root of the Sum of the Squares (SRSS) method. The methods described in the following subsections are available in AutoPIPE to combine the response of individual modes.

3. Given the Frequency report:

4. Notice the frequency for the first 5 modes, <1 sec. Also, the first 5 modes capture almost 96 % in all 3 axis directions.

5. The response spectrum starts at 1 sec, but from the frequency report, all modes have T < 1 sec. Therefore, the smallest given acceleration applied would always assume to be (a = 3.864 in /s/s).

6. Next the force per mode is calculated and finally all the combined modes are combined using SRSS.

7. By the time the results are calculated by SRSS the results for both R1 and R2 could be virtually identical.

In Conclusion:

The difference between Spectrum #1 and Spectrum #2 does not matter because your structure does not have any modes with a period above 1 sec. Therefore, the computed forces for both spectra are the same. If your structure had a mode with a period of 10 sec or 20 sec, then the results would be very different because the acceleration at those periods is much higher.

02l. Why different Response Spectra produce the same results in AutoPIPE Response Spectrum Analysis

Problem:

Solution:

See Also