# Assessment of Response Modification Factor of Open Steel Platform Structures Subjected to Seismic Loads

## Abstract

Open frame steel platforms (hereinafter “OFS platforms”) are largely utilized in manufacturing and industrial facilities. OFS platforms are built around the refinery attached to the infrastructure to provide access for maintenance work. Nonlinear static pushover analysis and nonlinear dynamic time history analysis are conducted to study the inelastic behaviour of these frames. The analysis accounts for their unique detailing especially to elements that contribute to energy dissipation during major seismic events. Maximum inter-story drift and peak global roof drift were adopted as critical response parameters. The results show that the reserve strength of structure is less than that prescribed by the ASCE7-08 for ordinary concentric braced frame systems.

## 1 Introduction

Modal building codes such as ASCE/SEI 7-10, Minimum Design Loads for Buildings and Other Structures do not currently list a specific R factor for Open Frame Structure (OFS) platforms. This studies main objective is to determine the R factor for OFS platforms and introduce them into the building codes through numerical simulations to study the performance of these structures under major seismic events.

The main objective behind this study is to develop a more realistic value for the R factor that can be used by practicing engineers to design sturdier OFS platforms. The ultimate goal is to reduce the risk of damage of the OFS platforms or the infrastructures they are attached to during a major seismic event. Also, knowing the appropriate R factor specific of OFS platforms will help in designing such a structure that has enough capability to dissipate energy coming from outside forces (i.e. earthquake) without having excessive member sizes.

This paper will use nonlinear analysis to examine the unique detailing requirements of OFS platforms and to determine what limitations are appropriate for this type of platform by (1) utilizing nonlinear static analysis, to determine the ultimate lateral load resistance on the OFS platforms; and (2) utilizing nonlinear dynamic analysis to evaluate the structure’s energy dissipation capacity and characteristics during an earthquake. This study utilizes current data from the United States Geological Survey (hereinafter “USGS”) for earthquake ground accelerations and various model structures with varying levels in order to compare the calculated results with current R factors being utilized in current designs for OFS platforms. The results obtained from the analysis conducted will be used to develop an R factor for OFS platforms.

## 2 Open Frame Steel Structure

In these examples, “[T]he lateral resisting system for the open steel frames and the steel tower are formed of ordinary concentric brace frames. Lateral stability of the platforms is provided by horizontal braced members below the grating elevation. Due to constructability consideration, [it appears that] all steel connections are bolted at the field using bearing type connection (Salem).”

Currently, an R factor for OFS platforms has not been codified in a building code resource such as the ASCE/SEI 7-10, Minimum Design Loads for Buildings and Other Structures. The current practice is to estimate the seismic loads for these structures using parameters of similar building-type structures. Most commonly, for these OFS platforms, since they are made of steel and are braced frames with lateral force resisting systems, practicing engineers usually use the R factors of other systems mainly building frame system which is significantly different in terms of geometry and detailing from OFS where platforms have no floor or roof diaphragms with lumped masses. Therefore, building code design equations are not suitable to predict their performance during earthquakes. In this paper, the focus is on the direct comparison of ordinary concentric braced frame (OCBF) or special concentric braced frames (SCBF) R factors which are 3.25 and 6.0, respectively with the performance of the OFS.

## 3 Response Modification Factor

Structure configuration

Member | Steel section | End conditions | Length (ft) | |
---|---|---|---|---|

| Column | W10 × 33 | Continuous | 12.5 |

Exterior braces | W6 × 20 | Pinned - Pinned | 23.58 | |

Exterior beams | W12 × 60 | Pinned - Pinned | 40 | |

Inside beams | W12 × 35 | Pinned - Pinned | 40 and 10 | |

Horizontal bracing | WT5 × 16.5 | Pinned - Pinned | 14.14 | |

| Column | W10 × 33 | Continuous | 12.5 |

Exterior braces | W4 × 13 | Pinned - Pinned | 23.58 | |

Exterior beams | W12 × 60 | Pinned - Pinned | 40 | |

Inside beams | W12 × 35 | Pinned - Pinned | 40 and 10 | |

Horizontal bracing | WT5 × 16.5 | Pinned - Pinned | 14.14 |

An elastic design would assume the structure to have a linear force-deformation relationship, and thus be able to deform less and dissipate less energy. On the other hand, inelastic design acknowledges the ability to continuously deform and keep on dissipating energy. The use of right ductility and response modification factors can result in a safer and more cost effective structure than one designed using the elastic design force, which does not acknowledge the inelastic energy dissipating ability.

### 3.1 Ductility Factor, \( R\mu \)

This non-linear behavior can be captured from Pushover and Nonlinear Dynamic Analyses

### 3.2 Redundancy Factor

The Redundancy factor, Rr, measures the reliability of multiple vertical lines to transfer seismic-induced inertial force to the foundation (ATC-19). The following limitations apply to open frame structures may qualify for a reduction factor of 1.0 if there are four or more columns and three or more bays at each level. Otherwise, a factor of 1.3 shall apply.

## 4 Numerical Simulations

### 4.1 Design of Model Structure

The structures were modeled to be 40 ft × 40 ft and had a combination of internal beams as well as horizontal bracing to account for the members that will hold up the grating that shall support personnel as they are completing their maintenance on the refineries. The elevation view illustrated in Fig. 3 shows the story height of every model structure which is fixed at 12.5 ft and has chevron bracing. The columns are considered as hinged to the foundation. The design criterion, dead load of 0.1 kip per linear foot, was provided by Process Industry Practices, PIP STC01015, on the internal longitudinal beams and 0.05 kip per linear foot on the exterior longitudinal beams due to tributary area. A99 (Fy = 50 ksi) steel was utilized for every steel member of these OFS platforms. The chevron braces designed on these platforms are to account for the lateral seismic loads that the structure may experience.

### 4.2 Nonlinear Static Analysis (Push over Analysis)

Nonlinear static push-over analysis is conducted to determine the ultimate lateral load resistance as well as the sequence of yielding/buckling events. Eigen value analysis was conducted first to determine the elastic natural periods and mode shapes of the structure. Then pushover analysis were carried out to evaluate the global yield limit state and the structural capacity by progressively increasing the lateral story forces proportional to the fundamental mode shape.

### 4.3 Nonlinear Dynamic Time – History Analysis

Fast Nonlinear Dynamic Analysis, herein FNA, was used to conduct the Non-Linear Dynamic Analysis portion. The FNA method utilizes hinges as described in previous section in order to capture nonlinear material behaviour. With nonlinear behaviour placed in as hinges, it applies ground motions as modal applications. Modal application of acceleration time history ensures the runtime is short compared to other nonlinear dynamic analysis methods. The modal application is defined as Load-Dependent Ritz vector application in SAP2000. For each ground motion, the maximum displacement and base shear is obtained. The combination of all of the 22 ground motion results is called Incremental Dynamic Analysis. The Incremental Dynamic Analysis (IDA) results show a more realistic performance compared to the Pushover due to the dynamic application of real ground motions.

### 4.4 Ground Motions

## 5 Results and Discussions

Result of pushover analysis for model structure

6 story | 12 story | 18 story | ||||
---|---|---|---|---|---|---|

Case I | Case II | Case I | Case II | Case I | Case II | |

V | 96.392 | 29.666 | 95.394 | 28.19 | 94.948 | 26.778 |

Vy | 146.049 | 44.9491 | 144.537 | 42.712 | 143.86 | 40.573 |

Ve | 162.507 | 70.802 | 155.559 | 68.724 | 150.852 | 66.691 |

Ru | 1.11269 | 1.575 | 1.076 | 1.609 | 1.049 | 1.644 |

Ro | 1.515 | 1.515 | 1.515 | 1.515 | 1.515 | 1.515 |

Rr | 1 | 1 | 1 | 1 | 1 | 1 |

R | 1.686 | 2.387 | 1.631 | 2.438 | 1.589 | 2.49 |

24 story | 27 story | 30 story | ||||
---|---|---|---|---|---|---|

V | 98.954 | 28.145 | 94.505 | 25.058 | 92.103 | 27.921 |

Vy | 149.93 | 42.6441 | 143.189 | 37.9661 | 139.55 | 42.3051 |

Ve | 141.529 | 63.873 | 131.892 | 62.147 | 119.109 | 60.874 |

Ru | 0.944 | 1.498 | 0.916 | 1.637 | 0.854 | 1.4389 |

Ro | 1.515 | 1.515 | 1.515 | 1.515 | 1.515 | 1.515 |

Rr | 1 | 1 | 1 | 1 | 1 | 1 |

R | 1.43 | 2.269 | 1.388 | 2.48 | 1.293 | 2.18 |

The inelastic time-history analyses were conducted for both Case I and Case II of the OFS platforms which aided in the development of the structure’s response curve. This curve was developed for each case study by plotting the maximum base shear and maximum top story drift for earthquake response. Figure 10 below, provides one example of the dynamic analysis results compared to the static pushover results for the 30 story OFS platform in Case I. The results indicate that the dynamic envelopes form below the yield point from the static nonlinear analysis; which will result in an even lower R factor for these structures.

The nonlinear static analysis was also compared with the dynamic performance curve and the results illustrated that for the 30 story case study, yielding was reached at an earlier time and the response modification factor was decreased. However, both performance curves resulted in the same conclusion that the R factor used in the industry for OFS platforms, typically the R value for OCBFs of 3.25, over estimates the structure’s energy dissipating capabilities. Lastly, the studies conducted illustrated that for both Case I and Case II, the story drifts of all structures taller than six stories were beyond the allowable drift limit set forth by ASCE 7-10.

## 6 Conclusions

From the analysis conducted, the R factor of the case studies decreased as the number of stories increased. Based on the results of this study, the current practice in designing these unique structures underestimates the value of the R factor for OFS platforms when they use the R factor of 3.25 for the ordinary concentric braced frames, especially when they are using stiffer sections. Underestimating a structures capability of dissipating energy may result in failures of structures and can risk public safety. It is recommended to continue to researching these structures by changing the parametric of the structure, span size, conducting a risk analysis, testing prototypes, and running numerical analysis to obtain a more accurate values of R factors for these structures.

## Notes

### Acknowledgments

The authors would like to acknowledge the support provided by the department of Civil Engineering at Cal Poly Pomona in offering the computer recourses that was necessary to conduct this study

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