A COMPARATIVE STUDY OF A PIPING SYSTEM ......behavior between coupled and welded finite element models of piping systems, and it does not include work regarding the physical seismic

A COMPARATIVE STUDY OF A PIPING SYSTEM SUBJECTED TO EARTHQUAKE LOADS USING FINITE ELEMENT MODELING AND ANALYSIS

Gabriel E. Sánchez MartínezHome Institution: University of Puerto Rico, Mayagüez

Research Host Institution: Lehigh UniversityAdvisor: Ian C. Hodgson, P.E., S.E.

Network for Earthquake Engineering Simulation (NEES)13 September 2007

Abstract

This paper discusses the accuracy of a finite element model of a coupled piping system subjected to earthquake loads, as well as the differences in seismic behavior between coupled and welded piping system models. The test setup of a Victaulic coupled piping system tested at Lehigh University was modeled and analyzed with finite element methods. Two models were developed: (1) a welded pipe model, in which pipe connections were rigid, and (2) a coupled pipe model, in which couplings were modeled using the rotational stiffness characteristics of Victaulic couplings determined with static tests. The results of the coupled pipe model were compared to the laboratory data to determine the accuracy of the model in predicting real seismic behavior. Additionally, the results of the coupled and welded pipe models were compared to determine the differences in seismic behavior between the two systems. The introduction of this paper includes an overview of earthquake resistance in pipes, the Victaulic project, and basics of finite element analysis. This is followed by a discussion of the procedures carried out, including coupling tests and finite element modeling and analysis. Finally, this paper discusses the results and conclusions drawn and their significance.

1. Introduction

1.1 Importance of Earthquake Resistance of Pipes

Piping is a critical component of infrastructure, and it can be severely damaged by earthquakes, resulting in difficult, costly, and time consuming repairs. Damage to water pipes can be especially detrimental if it forces hospitals to close down following an earthquake, right when medical attention is needed to treat the people injured (Goodwin; Goodwin, Maragakis, & Itani). Moreover, fires usually start when earthquakes occur, because gas pipes and power lines break. The damage caused by fires can be greater than the damage caused by the seismic movements per se. Therefore, the piping of sprinkler systems and other fire suppression systems is important; if it breaks during an earthquake, subsequent fires may spread and cause additional building damage and deaths. For these reasons, piping with greater resistance to earthquakes is highly desirable.

1.2 Good Practices for Installing Pipe

When ground motions occur, differences in properties such as structural stiffness and resonant frequencies result in differences in the seismic behavior of buildings. Moreover, a structure's

Proceedings of the 2007 Earthquake Engineering Symposium for Young Researchers

paper 31 1 Seattle, Washington | August 8-12, 2007

response to an earthquake varies with height; movements at the base and roof of a building will not be the same. Because piping is especially susceptible to damage between two sites that move differently, special attention must be given to piping entering or exiting a building from the ground or a neighboring structure, and to piping across multiple stories within a building.

Two methods of reducing the susceptibility of piping to damage at these sites are through the use of a z-type offset configuration and through the use of a swing joint (Victaulic). A z-type offset configuration consists of relatively long lengths of pipe connected together using rotationally flexible joints, effectively creating displacement isolation between the two ends of the pipeline. A swing joint, on the other hand, consists of a number of pipe elbows connected with flexible pipe couplings. This allows movement with little resistance. Figure 1 shows an isometric view of a straight piece of pipe and the two connection methods mentioned.

Pipe can also suffer damage within a building if it is not braced properly. Braces hold the pipe to the roof and walls of a building, and restrain the piping from deforming laterally or hitting nearby objects. Excessive swaying can lead to failure during an earthquake. The National Fire Protection Association's Standard for the Installation of Sprinkler Systems offers criteria to follow for proper bracing in places where earthquakes are a concern.

1.3 The Victaulic Project

Victaulic is one of the world's leading manufacturers of mechanical pipe joining products. It competes against the welded pipe industry by offering a coupling alternative that is easier and faster to install than welding pipe together. Essentially, Victaulic couplings grip two pipe ends with a compressed rubber seal and by gripping grooves that have been cut or rolled into the pipe. Figure 2 shows a section view of a Victaulic coupling.

Figure 1: Isometric view of (a) a straight piece of pipe, (b) a z-type offset configuration, and (c) a swing joint, three ways of connecting pipe where relative displacements are expected during earthquakes. If one end of each pipe was fixed in place and the other was forced a certain distance, the leftmost piece, (a), would fail before the other two, (b) and (c). Figure 2: A Victaulic coupling joining two pipes with grooved ends. (Victaulic)

Victaulic offers both rigid and flexible couplings in order to increase the earthquake performance of piping. Flexible couplings are to be used where piping enters or exits a structure, and rigid couplings inside the structure.

Prior to the Victaulic project at Lehigh University's Advanced Technology for Large Structural Systems (ATLSS) laboratory, the company had performed bending and other ultimate strength



tests, as well as smaller-scale tests of their products' performance in actual earthquakes. However, these tests do not relate to earthquake performance directly, and only limited information has been obtained regarding Victaulic systems that have suffered real earthquakes. As a result, a full-scale test of a piping system was designed and carried out at Lehigh University's ATLSS Laboratory. The test setup involved suspending a rigid truss with hangers inside the laboratory. This truss simulated the roof of a building. Steel piping, joined with Victaulic couplings and welded at both ends to the laboratory strong wall, ran under the truss, suspended from it by standard piping hangers and braces. The piping assembly included a swing joint and a z-type offset configuration. Figure 3 is a photograph of the test setup.

Figure 3: Photograph of the Victaulic test setup at Lehigh University's ATLSS laboratory. A rigid truss, representing the roof of a building, hangs inside the laboratory. The piping comes from the strong wall and enters the simulated building, runs inside it braced appropriately, exits the truss, and goes back into the strong wall. The z-type offset configuration near the center of the truss and the swing joint at the back are designed to be flexible connections for the piping between the strong wall and the truss. Two of the three hydraulic actuators used to generate the earthquake movement (transverse direction) can be seen connected to the truss.

Three separate tests were performed, using pipe 4 inches, 8 inches, and 16 inches in diameter, all filled with water and pressurized at 200 psi. The National Fire Protection Association's Standard for the Installation of Sprinkler Systems was used as a guide for the bracing requirements and piping installation.

In order to simulate seismic movement, three hydraulic actuators were attached to the truss: two in the transverse direction and one in the longitudinal direction. The movement that the system was subjected to followed the International Code Council Evaluation Service's Acceptance Criteria For Seismic Qualification By Shake-Table Testing Of Nonstructural Components And Systems (AC156, June 2004). This criteria specifies that the motion should have a response spectra with minimum target spectral accelerations at frequencies from 1.3 Hz to 33.3 Hz. The following equations are used to calculate the required accelerations for the frequencies between



1.3 Hz and 8.3 Hz, AFLX, and for 33.3 Hz, ARIG:

AFLX=S DS12 zh ARIG=0.4S DS12 z

h (1)

where SDS is a ground specific spectral acceleration factor that varies with geographic location and soil condition, z is the height of the structure at the point being studied, and h is the total height of the structure (height of roof). Between 8.3 Hz and 33.3 Hz, the acceleration varies from AFLX at 8.3 Hz to ARIG at 33.3 Hz. Worst-case conditions make SDS = 1.0 g, which is the value that was assumed for purposes of testing. In addition, since the truss of the test setup simulated the roof, then z/h = 1, giving the following results:

AFLX=3.0 g ARIG=1.2 g (2)

Also following the guidelines established by the acceptance criteria, the test was designed to last 30 seconds, with 5 seconds of ramp-up, 20 seconds of full strength motion, and 5 seconds of ramp-down. The transverse and longitudinal acceleration time histories were randomly generated using a software called SIMQKE, from which the displacement time histories, shown in Figure 4 below, were calculated through double integration.

Figure 4: Displacement time histories that served as input to the hydraulic actuators, which shook the truss to simulate strong seismic movements.

1.4 Basics of Finite Element Analysis

This project focuses on the accuracy of a finite element model of the Victaulic piping system that was tested at Lehigh University's ATLSS Laboratory, as well as on the differences in seismic behavior between coupled and welded finite element models of piping systems, and it does not include work regarding the physical seismic tests. Finite element analysis (FEA) is a method of analysis in which the object or system being studied is divided into smaller parts called elements, and points connecting those parts called nodes; this process is called meshing. Next, constraints



are applied to the model to define physical limits, such as fixed or pinned connections, and loads are applied to define the forces, displacements, accelerations, etc., that the structure is being subjected to. For a system of connected objects, restraints, or relative constraints between parts of the model, are also defined. During analysis, a computer takes constraints, loads, and material and section properties into consideration and solves the system element by element. FEA may be used to solve problems of statics, dynamics, thermodynamics, acoustics, fluid mechanics, etc. For purposes of this project, a computer software called FEMAP was used to construct the model and mesh it, and another called ABAQUS was used for static and dynamic analysis.

There are three different ways to model parts with FEA: solid meshing, surface meshing, and line meshing. In solid meshing, elements are volume-occupying shapes, with nodes at the corners. This method is suitable for modeling irregular and complex shapes, and for obtaining detailed stress information at different sites along the thickness of materials. With surface meshing, parts are modeled with planar elements having nodes at the corners. The thickness of the different surfaces are specified as element properties, and information can be obtained along the surface of the modeled parts, but complex variation in behavior through their thickness cannot be modeled. Finally, parts may be meshed with line elements, a method suitable when the model contains beams, piping, etc. In this case, elements are lines with nodes at both ends. The cross-section and shape of the elements modeled are specified as element properties, and analysis information can be obtained only along the length of the parts modeled. Line meshing was chosen for this project because all of the members were beams or piping, and because this method is the least computationally expensive.

2. Procedures

In the following sections, the general procedures carried out for the 4 inch and 8 inch diameter pipe models are described. The 16 inch diameter piping system was not modeled due to lack of time.

2.1 Preliminary FE Models

The combination of FEMAP and ABAQUS is a powerful analysis tool, but because it has many applications and because FEMAP isn't exclusively designed to work with ABAQUS, many complexities are introduced. In fact, the input file that FEMAP generated for ABAQUS in all cases analyzed had to be edited prior to running analysis. Therefore, in order to know that analysis was being conducted correctly, simple verifiable models of beams were considered: first a cantilevered beam for static analysis, and then a roller constrained, free end beam for natural frequency and dynamic analysis. The FEA results for these models were compared to results calculated manually or found tabulated in structural dynamics textbooks (Clough & Penzien). Simple beam models also served to roughly determine what element density was appropriate to obtain accurate results without making analysis unnecessarily computationally expensive.

2.2 Coupling Stiffness Tests

Two finite element models were created and analyzed for each piping size: (1) a welded pipe model, in which connections between lengths of pipe were as stiff as the pipes themselves, and



(2) a coupled pipe model, in which couplings joining the pipes were modeled to behave like Victaulic couplings, which were less rotationally stiff than the pipe itself. However, before modeling the coupled piping system, the rotational stiffness properties of the Victaulic couplings had to be determined. This was done through a series of static tests conducted in the laboratory for the 4 inch flexible and rigid couplings, from which moment resistance with respect to the relative angle between the pipes was obtained. Figure 5 below is a schematic of the test.

Figure 5: Profile of the coupling test setup for 4 inch diameter pipe.

Figure 6: Moment-angle relationship of the 4 inch diameter pipe couplings. Linear piecewise regressions were used to define the connections between pipe lengths in the FE model.

The flexible and rigid couplings were tested each with the bolts aligned laterally and vertically (four tests in total). Two 4 foot long pieces of pipe with end caps were coupled together, filled with water, and pressurized at 200 psi in order to match the conditions of the earthquake test.



One of the pipes was fixed level, while the other was pulled upward at its end, making the coupling resist with a certain moment. This created an angle difference between the two lengths, which was measured with a digital level. The test began with the pipes level and ended when the moment load on the coupling was approximately its UL proof load, 3645 ft. lbs. (Hudson & Owens). Angular and load measurements were taken every 0.1º. From this data, illustrated in Figure 6, linear piecewise approximations of coupling stiffness were made, and connections with these stiffnesses were defined wherever rigid or flexible couplings were located.

Because of time constraints, the coupling test was not carried out for the 8 inch diameter couplings. However, the coupled finite element model of 8 inch diameter piping system was created and analyzed for comparison with the laboratory test and with the welded model. In order to define the rotational stiffness properties of the 8 inch couplings, a multiplier factor was applied to the 4 inch coupling stiffnesses, based on the UL proof loads of the 4 inch and 8 inch couplings:

M 8 inch=UL Proof Load 8inch

UL Proof Load 4 inchM 4 inch= 11 304 ft. lbs.3645 ft. lbs. M 4 inch=3.10M 4 inch (3)

2.3 Generation of Victaulic Test Setup FE Model

Three-dimensional models of the 4 inch and 8 inch diameter Victaulic piping systems were created with line elements using FEMAP, and a welded pipe version of each of these models was also created, for a total of 4 models. For each of these models, the mesh element densities were specified, lowest for the laboratory beams and columns to shorten computation time, and highest for the bracing and piping, since these elements contained the sites of interest for data recovery. Next, the material used for all of the elements was defined as steel with a 29,000,000 psi modulus of elasticity. Following that, the properties were defined, which contained section geometry, orientation, moment of inertia, and stress recovery point location information for the test setup beams and columns, the beams in the truss representing the roof of the building, the piping, the truss hangers, and the bracing that fastened the piping to the truss.

Next, the models were meshed, one property at a time. This process created redundant or coincident nodes wherever two lines met; that is, where two beams were joined, where the bracing was attached to the truss and to the pipe, where hangers linked to the overhead beams and the truss, and where two lengths of pipe were joined. Coincident nodes were merged in most of these cases, which created a rigid connection between members. An exception was made for all four models where hanger ends coincided with the overhead beams or the test truss, because a pin connection was necessary instead of a rigid one. Multi-point constraints (MPCs), a kind of restraint, were defined as dimensionless elements connecting the two nodes together at each of the eight sites where this happened. These MPCs restricted relative displacements between the coincident node pairs, as well as torque rotation, but allowed independent moment rotations, so that the truss was hanging and free to swing as in the laboratory. Another very important exception was made for the 4 inch and 8 inch coupled piping system models, at sites where pipe lengths met. Instead of joining the coincident nodes, dimensionless connector elements with the corresponding stiffness properties were defined. These connectors prevented relative displacement between the connected nodes, as well as torque rotation, but allowed moment rotations with moment resistances characteristic of the Victaulic couplings found at each



connection along the pipeline.

Next, constraints were defined to fix the laboratory test columns to the floor, and a test beam and the two ends of the pipe to the strong wall. (The test floor and wall were drawn only for purposes of visualization, but the constraints prevented any kind of motion at the nodes specified.) At this point, the model was ready for analysis. Figure 7 below shows the FE model of the 8 inch diameter pipe test setup.

Figure 7: Finite element model of the 8 inch Victaulic test setup. The geometry has been meshed, and the constraints and restraints have been defined. The support frame is colored maroon, the truss hangers dark gray, the rigid truss meant to represent the roof of a building light gray, and the pipe orange. The strong wall is behind in light gray and the strong floor below in dark gray.

2.4 FE Static Analysis

The first analysis carried out was a static analysis. In a static analysis, loads such as forced displacements or prescribed forces that do not vary in time are defined and the FEA program finds an equilibrium solution. For this project, static analysis was used to find the system equilibrium for gravity loading; that is, the solution of the system supporting its own weight. This was done by applying a distributed vertical acceleration load throughout the system. This step was useful for two reasons. First, it served to verify that all the regions in the model were connected correctly. If a region was let unconnected by mistake, which could happen if coincident nodes are not joined or if MPCs are not defined where they should be, free elements would deflect excessively. Second, it served to check agreement between the gravity definition and total mass of the system. The total mass times the acceleration due to gravity (keeping units

Support Frame

Truss Hangers

Rigid Truss Pipe

Strong Wall

Strong Floor



consistent) should be equal to the sum of the vertical components of force of all the constraints (i.e., supports). A disagreement between these quantities would suggest a faulty gravity or property definition. These checks were important to assure that results of further and more complex analysis were trustworthy.

2.5 FE Natural Frequency Analysis

After static analysis, natural frequency analysis, also known as modal analysis, was performed to determine the natural frequencies of vibration of the test setup. Natural frequencies are frequencies at which an object will naturally oscillate if it is hit, plucked, or otherwise excited. If an object is subjected to vibration at one of its natural frequencies, it oscillates with an increasingly larger amplitude. Damping, or energy loss in the form of heat, drag, sound, and deformations, causes the vibration to attenuate instead of allowing its amplitude to grow continuously large. If a part of the piping system during the earthquake test was excited at its natural frequency, it could shake violently, and perhaps even fail. Therefore, it was useful to predict what these frequencies were in order to keep a close watch on those parts during the laboratory testing.

Natural Frequency FEA also served to confirm that all of the regions in the model were connected properly; for example, if a piece of pipe was not attached to the bracing in the model, it would not move with the bracing when vibrating. Additionally, this analysis helped verify that the natural frequencies of the truss were out of the range of the frequency spectrum of the test earthquake wave, or above 33.3 Hz. The truss had been designed rigid so that it would not resonate during the test and affect the earthquake behavior of the piping or the sensors used to gather data.

2.6 FE Dynamic Analysis

Finally, implicit linear dynamic analysis was performed. In this kind of finite element analysis, time varying displacements or loads are introduced to the model, and the analysis program solves the system in steps of time, taking into account the materials and properties and using the solution of each time step as initial conditions for the next. To conduct this analysis, the displacement functions shown in Figure 4 were defined with respect to time for the longitudinal and transverse directions, and the loads associated to these functions were defined at the nodes where the actuators were attached to the truss in the laboratory setup. Next, dynamic analysis was set up to run for 30 seconds using time steps of 0.01 seconds (100 Hz, 3000 time steps, for both welded pipe models), 0.005 seconds (200 Hz, 6000 time steps, for 8 inch diameter coupled model), or 0.001 seconds (1000 Hz, 30000 time steps, for 4 inch diameter coupled model), depending on the magnitude of the deformations and the nonlinearity introduced to the analysis by the coupling definitions.

The input file for analysis in ABAQUS was edited to add damping. The method used to calculate damping is called Rayleigh damping, in which two parameters, α and β, are calculated based on two frequencies, ω1 and ω2, at which damping is assumed to be the same, this damping being specified as a percentage of the critical damping, ξ. Critical damping is the minimum damping necessary for an object or system to go back to its initial position without vibration if it



is excited. For this investigation, ξ was assumed to be 5% critical damping, and ω1 and ω2 were taken to be 1 Hz and 40 Hz, respectively. Using the formulas provided in Dynamics of Structures (Clough & Penzien), we have the following:

{}= 212

{12

1 }= 2×0.052×140{2×1×2×40

1 }={ 0.61300.000388} (4)

Another change done to the input file for analysis in ABAQUS was to add a gravity loading static analysis step prior to the dynamic analysis step. This was done so that the weight of objects in the model was taken into account during the earthquake motion. Also, the output instructions were specified, asking ABAQUS to write displacement information to the results file for all of the nodes at 10 Hz, and displacement, acceleration, and strain information for the nodes and elements where sensors were placed in the laboratory earthquake test at 100 Hz. This allowed an animation of all the seismic shaking to be observed after analysis and permitted comparison between FEM data and sensor data from the real seismic test.

2.7 Preparation of Laboratory Data

The data of the accelerometers, linear variable differential transformers (LVDTs, used to measure relative displacement), and strain gages from the 4 inch and 8 inch laboratory tests was taken at a frequency of 1024 Hz. This resulted in data files larger than necessary for comparison with the models, since FEM results were recorded at 100 Hz. Moreover, when graphs of laboratory sensor data were viewed, the signals seemed very busy and contained noise and a lot of high frequency spikes that were possibly caused by clanking of clamped bracing connections. This would make comparisons with the models tedious and largely inexact.

In order to solve these two problems, a selective down-sampling algorithm was designed. This algorithm worked by analyzing groups of data points around each 100 Hz time step (at 1024 Hz, approximately 10 points per time step). For each group, the quartiles were calculated, and any points 1.5 times the interquartile range (distance between first and third quartiles) above the third quartile or below the first quartile were considered outliers and removed. Then the remaining points were averaged and the result was written as the data point for the corresponding time step. The algorithm was coded in Perl and used to process the data files for both laboratory tests. This resulted in more manageable file sizes and cleaner laboratory data, which made graphical comparisons, particularly of behavior at lower frequencies, more practical and objective. As a point of comparison, a Fast Fourier Transform Low Pass Filter was applied to a sample of the original data using MATLAB, and the resulting graphs looked similar. However, the selective down-sampling method was chosen because it cleaned and down-sampled entire data files in one step. Figure 8 shows an example of laboratory data before and after the selective down-sampling algorithm was applied.

Once all of the results were ready, time history graphs were created for the 4 inch and 8 inch diameter piping systems, one per sensor, showing laboratory, coupled pipe model, and welded pipe model data. This allowed visual comparison of laboratory sensor data with the corresponding coupled piping model results, as well as between coupled and welded piping model results.



Figure 8: Accelerometer laboratory data for one of the accelerometers used in the 8 inch diameter piping system test. The raw data is shown in red, and the blue on top is the cleaned and down-sampled data after being processed. Notice how vibrations at lower frequencies are revealed.

Figure 9: Plan view instrumentation diagram of the Victaulic test setup. 7 uniaxial accelerometers, 4 uniaxial truss-pipe relative displacement sensors, 6 pipe strain gages, and 8 bracing strain gages were used in the comparison. (Adapted from a drawing by Ian C. Hodgson, P.E., S.E.)

3. Results and Discussion

The following sections discuss two separate sets of comparisons of seismic test behavior: (1) the real laboratory seismic test and the coupled pipe finite element model, and (2) the coupled pipe



finite element model and the welded pipe finite element model. The goal of the former was to determine how accurate the finite element model of the coupled piping system was in predicting the seismic response of the Victaulic piping system tested at Lehigh University's ATLSS laboratory. The goal of the latter was to determine the differences in seismic response between a coupled and a welded piping system suspended from a structure. These comparisons were done for individual sensors that took measurements of uniaxial acceleration, truss-pipe relative displacement, pipe strain, and bracing strain during the 30 seconds of earthquake shaking at the laboratory. For each type of sensor, these comparisons are discussed for the 4 inch diameter and 8 inch diameter groups. Figure 9 is a plan view of the location of each sensor considered. Reference will be made to it during the discussion of the results.

3.1. Uniaxial Accelerations

3.1.1 Accelerations in the 4 inch Diameter Piping System

Figure 10 below shows the results for the A3 accelerometer, which measured transverse acceleration near the coupling joining the two lengths of pipe in the lower center of the truss.

Figure 10: An example of the graphs used for comparison, showing data for the A3 accelerometer in the 4 inch diameter case. Laboratory data is in blue, coupled FEM data in red, and welded FEM data in green.

With the exception of spikes, the coupled model exhibited stronger accelerations at lower frequencies than the actual laboratory setup, and the laboratory setup responded with a comparatively more uniform distribution of frequencies. The corresponding acceleration in the welded model was lower than that in the coupled model, and at a slightly higher frequency. This behavior was expected, since the welded piping system was stiffer. Movement in the transverse direction at the location of the A3 sensor for welded pipe had to do with that whole length of pipe arching back and forth, with the maximum arching near A3. For coupled pipe, the connection at the middle was less rotationally stiff, so it was free to sway more, forming an angle between the two lengths of pipe connected. Figure 11 illustrates these two kinds of swaying. The models predicted peak accelerations of 6 g's for the coupled piping and 4 g's for the welded piping.



Figure 11: Swaying of welded piping (a) involved comparatively large deformations, while swaying of coupled piping (b) involved an angle between the two lengths of pipe joined by the coupling.

In the case of sensor A4, which measured acceleration at the same place but in the longitudinal direction, the coupled model accurately predicted the general frequencies and amplitudes of acceleration observed in the laboratory (2.5 – 3.0 g's). The welded model was close to this range, with peak accelerations of 3.5 g's. This was expected because the coupling does not add axial flexibility.

Looking at accelerations corresponding to A5, located close to bracing at the swing joint side of the pipeline and in the transverse direction, the coupled FEM predicted peak accelerations around 1.5 g's, falling short of the laboratory results, which were between 2 and 4 g's. This discrepancy could be related to the connection details for braces. The braces were modeled as welded, but this was not exactly the case, since beam clamps were used in some cases. However, the results for the coupled and welded models were very similar. This is reasonable, considering that the site is close to braces that restrain the pipe from swaying, regardless of connection stiffnesses. Accelerations corresponding to A6, located at the same place but in the longitudinal direction, were practically the same in the laboratory and both models.

The coupled FEM results for accelerometer A7, located at the base of the z-type configuration offset and oriented in the transverse direction, were very similar to the laboratory results in both frequency and amplitude, with peak accelerations of approximately 1g. On the other hand, the resulting accelerations for the welded pipe model were noticeably higher, at around 3 g's. This happened because the welded pipe was stiff and moved with the truss as it shook, but when flexible couplings were added, displacement isolation allowed the pipe at that location to sway in place. Figure 12 is the graph of the comparisons carried out for A7. At the same site but in the longitudinal direction, A8 accelerations were in the range of 2-3 g's for the laboratory and both models. This suggests that the flexible couplings did not significantly change the behavior of the z-type configuration offset in the longitudinal direction.

For the case of the longitudinal accelerations at the top of the z-type configuration offset, corresponding to A9, the coupled FEM exhibited accelerations of 2-3 times the magnitude of those in the laboratory (2-4 g's vs. 1.5 g's), although the frequencies were comparable. The welded FEM accelerations were even larger in amplitude, with peaks of up to 5 g's. In this case, the flexible couplings reduced the pull in the pipe by allowing bending at the elbows.



Figure 12: An example of good accuracy of the coupled FEM in predicting real laboratory seismic behavior.

3.1.2 Accelerations in the 8 inch Diameter Piping System

The 8 inch diameter coupled FEM was accurate in predicting the frequency and amplitude of the accelerations corresponding to A3 in the 8 inch diameter piping system, with the exception of spikes in the laboratory signal. In both cases, the peaks were of about 2.5 g's. The welded model predicted slightly weaker accelerations (1.5 g's). For the longitudinal A4 accelerations in the same part of the pipeline, the coupled model predicted slightly lower accelerations than the ones measured in the laboratory (with peaks of 2 g's vs. 3 g's). The welded model predicted slightly lower accelerations, with a difference of less than 0.5 g's. The differences in accelerations for 8 inch diameter pipe were not as dramatic as the ones seen for the 4 inch diameter pipe because bracing support was added near the A3 and A4 accelerometers.

Comparing the A5 and A6 accelerations, both the laboratory signal and the coupled model peaks were around 2 g's, which is indicative of a good prediction, while the welded peak accelerations were moderately lower, probably because the welded system was stiffer. With 4 inch diameter pipe, no significant difference was observed between the coupled system and the welded system. The situation changed a little in this case because of the added mass; inertial accelerations made the braces relatively more flexible.

In the case of accelerometer A7, laboratory signal peaks were around 1.5 g's and 3 g's, coupled FEM peaks around 1.5 g's, and welded FEM peaks in the range of 4-5 g's. The coupled model predicted acceleration magnitudes well for the greater portion of the duration of the test. Since flexible couplings were absent in the welded model, no relative bending could take place at the elbows of the z-type configuration offset, and stronger accelerations took place. As in the case of the 4 inch diameter pipe, the longitudinal accelerations at the same site, A8, were in the same range for the laboratory signal and both models, in this case 2-4 g's. Looking at the



measurements corresponding to A9, peak accelerations were between 1g and 2 g's for all three cases, the coupled FEM predictions of amplitude being roughly accurate and the welded and coupled model predictions being alike.

3.2. Truss-Pipe Relative Displacements (LVDTs)

There was a problem with the LVDT laboratory signals during testing for the 4 inch diameter piping system, so no relative displacement data could be recovered. Though the problem was solved for the 8 inch diameter piping system test, the resulting relative displacements looked suspicious. Because the bracing beam clamps caused excessive swaying during testing, the laboratory relative displacement data was not considered in the comparative study. Instead, comparisons were made only between the coupled and welded piping finite element models.

3.2.1 Relative Displacements in the 4 inch Diameter Piping System

LVDT1 measured relative displacements between the truss and the pipe in the longitudinal direction near the swing joint. The coupled and welded models' relative displacements at this site were at the same frequency and in phase, but the coupled model exhibited larger relative displacements for most of the 30 seconds of shaking (peaks of roughly 1.8 in vs. 0.6 in.). This behavior is counterintuitive, because the swing joint with flexible couplings is supposed to isolate relative displacements along the pipeline and minimize relative displacements between the truss and the pipe. In fact, the added swaying came from the middle of the pipe in the long horizontal run (where A3 was positioned). As illustrated in Figure 13, the coupling added flexibility at that location and allowed a lot of transverse swaying during the simulated earthquake, which caused the elbow to the right to sway in the longitudinal direction. Since the pipe was rigidly held by the bracing in the swing joint side of the truss, the elbow swaying caused the pipe to pivot about the braced point of the pipe, which in turn caused the piping at the other end of the bracing (where LVDT1 was located) to sway longitudinally as well.

Figure 13: Coupled piping swaying and pivoting about the braced point, causing relative displacements under the truss. The figure is not drawn to scale and is exaggerated for clarity. The coupling is colored orange.

This complex cause-effect pivoting behavior did not occur with welded pipe, because swaying in the middle was reduced and the elbow was stiffer. To prevent this from happening, bracing should have been installed to reduce swaying in the middle of the truss, as was done for the 8 inch diameter test.

Regarding relative displacements at the same place but in the transverse direction (LVDT2), the coupled model predicted negligible relative displacements, while the welded model predicted



relative displacements above 0.3 inches. It is reasonable to expect flexible couplings to make the swing joint more effective in comparison to a welded swing joint.

At the other side of the truss, relative longitudinal displacements corresponding to LVDT3 varied from 0.5 in to 2 in for the coupled model, and from 0.25 in to 0.5 in for the welded model. This behavior occurred for the same reason discussed for LVDT1. As for LVDT4, in the transverse direction, negligible relative displacements were observed for both the coupled and the welded models, which suggests that a z-type offset configuration is effective even without the added flexibility of couplings.

3.2.2 Relative Displacements in the 8 inch Diameter Piping System

Going back to the swing joint side of the truss, the longitudinal truss-pipe relative displacements (LVDT1) for the 8 inch diameter pipe differed in waveform between the coupled and welded FEMs, but the peak relative displacements, albeit occurring at different times, were in both cases around 0.4 inches. Since bracing prevented swaying near the middle of the truss, the pivot bending phenomenon did not take place. In the transverse direction (LVDT2), relative displacements were significantly lower in the coupled model, due to the flexibility added by couplings to the swing joint. This confirms that the swing joint with flexible couplings was very effective in isolating disjoint motions, while the welded version of the swing joint acted like a stiffer spring and transferred some load to the pipe entering the region under the truss. This is illustrated in Figure 14.

Figure 14: Victaulic flexible couplings made the swing joint more effective in reducing pipe swaying at the entrance of the pipeline to the truss, in comparison to a welded swing joint.



Counterintuitive seismic behavior was observed again, this time in the longitudinal relative pipe displacements (LVDT3): the coupled FEM exhibited peaks in the range of 0.7-1 in, while the welded one in the range of 0.2-0.3 in. In other words, the welded version of the z-type offset configuration was more effective than the one with flexible couplings, perhaps because the added flexibility allowed more sway, which, in combination with the mass of the long lengths of pipe, resulted in a higher kinetic energy that had to be overcome with each change of direction. To minimize this effect, rigid couplings could have been used for the offset configuration in place of flexible ones. The transverse relative displacements corresponding to LVDT4 were similar and small in magnitude for both models.

3.3 Pipe Strain

3.3.1 Pipe Strain in the 4 inch Diameter Piping System

The laboratory measurements of strain in the front left side of the piping system (PSG1 and PSG2) had peaks of 150μ-200μ, while the equivalent in the coupled piping FEM had peaks of 50μ-70μ, and in the welded piping FEM of 300μ-450μ. By comparing PSG1 with PSG2, it was determined that most of the strain was due to flexural bending. Although the coupled FEM did not offer a good prediction of what happened in the laboratory, the laboratory result was bounded by both FEM models. Regarding differences in performance between welded pipe and coupled pipe, it is reasonable that pipe strains were lower for the coupled piping model because the coupling allowed swaying through changes in the angle between the lengths of pipe connected, without the pipe having to bend as much. Figure 11 illustrates the difference. Exactly the same pattern was observed in the right side (PSG5 and PSG6), with laboratory peaks in the range of 150μ-250μ, coupled model peaks of 100μ-125μ, and welded model peaks of about 500μ.

Laboratory pipe strains in the middle (PSG3 and PSG4) were also due to flexural bending, and varied widely during the duration of motion, with peaks of 100μ-1000μ. The coupled model predicted strains with peaks around 325μ, and the welded model predicted strains with peaks around 225μ. Neither of the models' results were close to the laboratory results for a significant part of the 30 seconds of shaking. Contrary to what happened in the sides, pipe strain in the center was higher in the coupled model. This suggests that the coupling localized bending stress close to itself, while the welded pipe distributed the stress along the length of the pipe.

3.3.2 Pipe Strain in the 8 inch Diameter Piping System

For the 8 inch diameter piping, the pipe strains corresponding to PSG1 and PSG2 during the real testing peaked at around 325μ with spikes of over 2000μ, while the respective bending strains in the coupled and welded models had peaks of approximately 25μ and 200μ. Therefore, the strain in both models was below the laboratory strain, and the coupled pipe underwent less strain than the welded pipe because of the flexibility provided by the coupling. In the right side (PSG5 and PSG6), the laboratory strain data contained peaks of about 150μ with spikes over 2000μ. The pipe strains in the coupled model were very low in comparison, while those in the welded model sustained peaks of about 500μ. Once again, strain was not accurately predicted by any of the models, and the strain in the welded pipe was larger than that in the coupled pipe.



When comparing pipe strains corresponding to PSG3 and PSG4 in the middle, the laboratory strains contained peaks between 250μ and 500μ, with spikes of over 2000μ, while the coupled pipe model strains were of very low amplitude (under 25μ) and the welded pipe strains were between 200μ and 400μ. Curiously, the welded model's strain at this location was more or less in phase with the laboratory data and roughly accurate in terms of magnitude. Braces near PSG3 and PSG4 minimized shaking, and with the added flexibility of a coupling, the finite element model showed that the pipe suffered virtually no stress. In the case of the welded pipe, some bending occurred to accommodate for the movement of the length of pipe to the right.

3.4 Bracing Strain

Comparisons between the laboratory test and finite element models revealed generalized poor agreement between model and laboratory bracing strain data. Several factors could have affected the accuracy of the models, most notably that vertical support for the z-type offset configuration and the swing joint were not included in the models but existed in the real test, so the braces in the model were supporting more weight than the braces in the laboratory. Hence, only the comparison between the coupled piping system FE model and the welded piping system FE model were considered in detail.

3.4.1 Bracing Strain in the 4 inch Diameter Piping System

The bracing strain histories in the transverse left brace (SG1 and SG2) contained peaks of 950μ for coupled pipe and 400μ for welded pipe. Since SG1 and SG2 were out of phase, the strain in this brace was predominantly caused by bending. The strain in the brace holding the coupled pipe was higher because of the pivoting phenomenon described in Section 3.2.1. SG3 and SG4 measured strain in the longitudinal left brace. Peaks between 400μ and 750μ for the coupled model and between 300μ and 400μ for the welded model were observed. Most of the strain in this brace was due to axial loading, which also agrees with the pivoting behavior.

Bracing strain corresponding to the sensors SG5 and SG6 had peaks of 1000μ for the coupled model and 1200μ for the welded model. The coupled model exhibited primarily bending-related strains, which concurs with the idea of the pivoting phenomenon. In contrast, the welded model exhibited primarily axial strains, a consequence of the stiffer welded swing joint acting as a spring. The longitudinal strain history corresponding to SG7 and SG8 had peaks of 600μ for the coupled pipe, the double of the strain peaks observed for the welded pipe. Loading on this brace was mostly axial in both cases.

3.4.2 Bracing Strain in the 8 inch Diameter Piping System

For the 8 inch diameter piping system, the strain history corresponding to strain gages SG1 and SG2 included peaks of 600μ for the coupled model and 400μ for the welded model. Additionally, comparison of strains SG3 and SG4 revealed peaks of 400μ for the coupled model and 250μ for the welded model, both being predominantly caused by axial loading. This result relates to the larger truss-pipe relative displacements observed in the coupled model at the z-type offset configuration for LVDT3. At the other side of the pipeline, near the swing joint, the coupled model showed peak strains of approximately 300μ for both the transverse brace (SG5



and SG6), and the longitudinal brace (SG7 and SG8), while welded model showed strains up to 10 times as large. Both braces were acting primarily in their respective axial directions. This great difference was probably a consequence of the stiffness of the welded swing joint in comparison to the flexibility of the swing joint with flexible couplings.

4. Conclusions

There is no substitute for a real-scale earthquake test of a piping system to study its behavior under seismic loading. The ABAQUS finite element models of the 4 inch diameter and 8 inch diameter Victaulic coupled piping systems were not consistently accurate in predicting the results of the seismic shake test at Lehigh University's ATLSS laboratory. Approximately 70% of the uniaxial acceleration measurements were predicted accurately or approximately. However, the pipe and bracing strains given by finite element analysis were generally not in the range of the strains measured in the laboratory. Unfortunately, laboratory truss-pipe relative displacement data could not be used to better determine the accuracy of the model. Improvements need to be made to the model if greater accuracy is desired.

The finite element models provided a good comparison of seismic behavior between a piping system composed of pipe joined by Victaulic couplings and the same system composed of welded pipe. Couplings added localized flexibility to the system, modifying the stiffness properties and seismic response of the system as a whole. In general, the model with couplings behaved better under earthquake loads than the welded model. For example, the swing joint with Victaulic flexible couplings performed much better than the welded version. Even so, the added flexibility also introduced unwanted motions into the modeled system; namely, excessive swaying in one location caused pivoting of the pipeline about a braced point in the 4 inch diameter piping system. The finite element model made it possible to identify the problem and its origin, and it was subsequently determined that additional bracing would have controlled the unwanted motion, as seen in the 8 inch diameter piping system model. Since seismic response is dramatically affected by several factors, it is difficult to predict what will happen to a suspended piping system during an earthquake. Thus, finite element analysis is a useful tool to compare different scenarios when a large-scale or real-scale shake test is not feasible.

5. Possible Future Work

This investigation can be furthered in a number of ways. Vertical supports for the z-type offset configuration and swing joint could be added to the model, with the goal of making bracing strain gage results more comparable to the laboratory bracing strains. Bracing connections could be modeled more accurately and nonlinear analysis could be used to include factors such as plastic deformation and failure of members. The investigation can also be expanded to include other pipe sizes, earthquake records, and test configurations, including modeling and analysis of a multistory piping system.



6. Acknowledgments

This work would not have been made possible without the support of the following people and organizations. To them, my sincere expression of gratitude.

● Network for Earthquake Engineering Simulation (NEES), for providing the Research Experience for Undergraduates opportunity and organizing meetings and activities that complemented my investigation with rewarding experiences

● National Science Foundation, for the financial support given to NEES● Ian C. Hodgson, P.E., S.E., for the introduction into the project and guidance throughout

the summer investigation● Lehigh University's ATLSS Laboratory and personnel, for providing testing equipment

and expert help with laboratory testing● Victaulic, for providing the materials and equipment necessary for the coupling tests, and

for providing information necessary to create the finite element models● Gary Novak, for coordinating the program's activities at Lehigh University● Tommy Marullo, for his help with laboratory data recovery● Peter Bryan, for his help with technical matters● Civil Engineering Department of the University of Puerto Rico, Mayagüez, for providing

access to the ABAQUS software in order to finish finite element analysis after the end of the summer program

7. References

American Institute of Steel Construction. (1973). Manual of Steel Construction (7th ed.).

Clough, R. W., & Penzien, J. (1993). Dynamics of Structures (2nd ed.). New York: McGraw-Hill.

FoF. Review of the Seismic Adequacy of the Victaulic Grooved Pipe Joining System.

Goodwin, E. Seismic Behavior of Welded Hospital Piping Systems. Reno, Nevada: University of Nevada, Reno.

Goodwin, E., Maragakis, E., & Itani, A. Experimental Comparison of the Seismic Response of Welded and Threaded Hospital Piping Systems. Reno, Nevada: University of Nevada, Reno.

Hudson, D. & Owens, S. (June 2007). UL Proof Loads of Victaulic Couplings [Telephone conversation]. Victaulic.

ICC Evaluation Service. (2004). Acceptance Criteria for Seismic Qualification by Shake-Table Testing of Nonstructural Components and Systems (AC 156).

National Fire Protection Association. (1991). Standard for the Installation of Sprinkler Systems (NFPA 13, 1991 ed.)

Victaulic. (2000). Design Data for Seismic Applications of Victaulic Grooved System. Victaulic.



Documents

A COMPARATIVE STUDY OF A PIPING SYSTEM ......behavior between coupled and welded finite element models of piping systems, and it does not include work regarding the physical seismic