Seismic Analysis of Pressure Vessels
Depending on where your pressure vessel will be installed, a seismic analysis may be required. While design standards for storage tanks such as API 650 provide details on how to calculate and evaluate for seismic loads, the ASME Boiler & Pressure Vessel Code does not. Luckily, there are more than a few standards that provide details on how to evaluate pressure vessels for seismic loads. While the details between these standards may differ, the methods and procedures for calculating and evaluating seismic loads are largely the same. The most commonly specified standard for determining seismic loads in the United States is ASCE 7 (“Minimum Design Loads for Buildings and Other Structures”).
Calculation of the Magnitude of the Seismic Loads
In ASCE 7 the magnitude of the seismic loads used in design of pressure vessels are based on a number of factors. These include:
Geographical location of the pressure vessel
Type of soil the pressure vessel’s support structure is on
Fundamental period of the pressure vessel (and its contents)
The importance of the pressure vessel with respect to health and safety
Height of the base of the pressure vessel with respect to its support structure (if the pressure vessel is not on the ground)
Ductility of the pressure vessel
Geographical Location of the Pressure Vessel
Seismic ground accelerations used in determining the design seismic forces are based on the geographical location of the pressure vessel and its proximity to seismically active faults capable of producing large earthquakes. ASCE 7 provides maps of the U.S. with seismic ground accelerations. Alternately, the U.S. Geological Survey (USGS) website (www.usgs.gov) can be used to acquire this information.
Soil
The seismic ground accelerations are then scaled by factors dependent on the type of soil the pressure vessel’s support structure is on. There are six classifications of soil used by ASCE 7, which are referred to as the Site Class. The different Site Classes are: A (hard rock), B (rock), C (very dense soil and soft rock), D (stiff soil), E (soft clay soil), and F (soils vulnerable to potential failure or collapse under seismic loading such as liquefiable soils).
Fundamental Period of the Pressure Vessel
The fundamental period of the pressure vessel can also affect the magnitude of the design seismic loads. While pressure vessels can usually be considered to act as a rigid body when subjected to seismic loads, sometimes their construction is such that this is not the case. Additionally, if the pressure vessel is filled with liquid, consideration must be given to the effects of the movement of the contents when subjected to seismic loads. With pressure vessels containing liquid, a portion of the liquid will move as a rigid mass (referred to as the impulsive mass), while the remainder will slosh back and forth (referred to as the convective mass). This behavior will affect the magnitude of the seismic loads on the pressure vessel.
Importance Factor
The magnitude of the design seismic loads will also be affected by what is called an Importance Factor. The Importance Factor is a scaling factor that accounts for the degree of risk to human life, health, and welfare associated with damage or loss of use of the pressure vessel. If the failure of the pressure vessel could pose a substantial risk to human life or is required in maintaining the operation of an essential facility (e.g. hospital, emergency services, etc.), the design seismic loads will be scaled accordingly.
Location of the Base of the Pressure Vessel
Another factor affecting the magnitude of the design seismic loads is the location of the base of the pressure vessel with respect to its support structure. If the pressure vessel is supported by another structure, such as located on the third floor of a building or platform, the seismic loads at the pressure vessel will be greater than those at ground level.
Pressure Vessel Ductility
Lastly, the magnitude of the design seismic loads are adjusted by what is referred to as a Response Modification Coefficient. This factor is used to account for the ductility of the structure.
Static Analysis Method - Equivalent Lateral Force Analysis Procedure
Most of the time pressure vessels can be evaluated for seismic loads using hand calculations. Specifically, this method is referred to as the Equivalent Lateral Force Analysis Procedure. The Equivalent Lateral Force Analysis Procedure is appropriate for pressure vessels that respond to seismic loads as a rigid mass; which is typically the case. With the Equivalent Lateral Force Analysis Procedure, seismic forces on the pressure vessel are calculated using equations provided in ASCE 7 (or similar Standard). Most of the pressure vessel design software available have the capability of evaluating seismic loads using the Equivalent Lateral Force Analysis Procedure. While hand calculations are generally used to evaluate the pressure vessel for the seismic loads, there may be times when finite element analysis is desirable. An example of this would be when finite element analysis has been used to evaluate other loads which are to be combined with the seismic loads.
Dynamic Analysis Methods
While the Equivalent Lateral Force Analysis Procedure is often appropriate for evaluating pressure vessels for seismic loads, there will be circumstances where using a dynamic analysis is required. This typically happens when the pressure vessel or its support structure is such that it does not respond as a rigid mass to seismic loads, when the site soil for the pressure vessel is Site Class F, when failure of the pressure vessel could pose a substantial risk to human life, or if the operation of the pressure vessel after a seismic event is essential. ASCE 7 provides details on how to determine if a dynamic analysis is required. If a dynamic analysis is required, there are two types to choose from: the Modal Response Spectrum Analysis Procedure, and the Seismic Response History Procedure. Both of these methods typically require the use of finite element analysis.
Dynamic Analysis Method - Seismic Response History Procedure
The Seismic Response History Procedure defines the seismic loads as a function of time. When this procedure is required by a customer, they will provide the seismic loads from a known (recorded) past seismic event. The design load will pretty much be what you would see from a seismograph, a rapidly changing load. Seismic response history analyses using finite element analysis require calculating solutions at very small time intervals in order to accurately capture the rapidly varying load and the response of the pressure vessel to that load. The computer run times for seismic response history analyses are typically long such that seismic response history analyses of pressure vessels are uncommon.
Dynamic Analysis Method - Modal Response Spectrum Analysis Procedure
The other, more common, dynamic analysis procedure is a Modal Response Spectrum Analysis. Unlike the Seismic Response History Procedure, Modal Response Spectrum Analyses use seismic loads that are defined with respect to period (or frequency). The magnitude of the loads for modal response spectrum analyses can be calculated using ASCE 7 or are sometimes provided by the customer. Performing a modal response spectrum analysis usually requires the use of finite element analysis. In a modal response spectrum analysis, the response of a pressure vessel at its natural frequencies are obtained from a modal analysis, scaled by seismic accelerations corresponding to the respective natural frequencies, and then combined using one of several methods such as the square root of the sum of the squares (SRSS).
Evaluation of Results
Whether the Equivalent Lateral Force Analysis Procedure or one of the dynamic analysis procedures is used, the goal is to calculate stresses in the pressure vessel and its supports to compare to allowable stress limits from the ASME Code. While this is often the primary focus of the seismic analysis, there are other things that must be considered. These include: the direction of seismic loads and whether they can be evaluated independently or should be combined, displacements of the pressure vessel, supports, and attachments, and flexibility of attached piping. ASCE 7 provides details on how to address and evaluate these topics.
In conclusion, there are a number of factors that go into determining the magnitude of the seismic loads to be used in the design of pressure vessels. Most pressure vessels can be evaluated for seismic loads using the Equivalent Lateral Force Analysis Procedure and hand calculations. While pressure vessel design software often includes the capability of evaluating for seismic loads, the engineer should be conversant with the appropriate Code or standard to correctly define the input parameters used in the Equivalent Lateral Force Analysis Procedure. For those circumstances where the Equivalent Lateral Force Analysis Procedure is not permitted, a Modal Response Spectrum Analysis or Seismic Response History Analysis should be performed by an engineer experienced with these types of analyses and FEA.