# Seismic Assessment and Retrofit of Pre-Northridge High Rise Steel Moment Resisting Frame Buildings with Bilinear Oil Dampers

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Prototype Tall Building

_{y}= 248 MPa), and welded box columns. These were typically made of ASTM A36 and/or ASTM A572 Gr. 42 (i.e., nominal yield stress, F

_{y}= 290 MPa) steel. The modulus of elasticity of the steel material E was assumed to be 200 GPa in all cases. Material properties for steel components are obtained from Tables 9.1 and 9.3 (1961–1990, Group 1) of ASCE 41-17 [27]. Columns were spliced at every three stories. The column splices were placed at 1.2 m (4 ft) above the respective floor. Column splices featured partial joint penetration groove (PJP) welds to reflect the design practice of the time of construction [36]. Moreover, member design was based on allowable stress design [37]. The above design assumptions and fabrication detailing were found to be representative of tall building designs in the 1970s in North America [9,11,33].

_{c,G/}P

_{ye,c}(i.e., P

_{ye,c}is the expected yield strength of the columns) was 32% at the ninth story. The peak P

_{c,G/}P

_{ye,c}ratio is comparable with prior work on existing tall buildings [9].

## 3. Nonlinear Building Model

## 4. Seismic Performance Assessment of the Prototype Tall Building per ASCE-41

#### 4.1. Nonlinear Static Analysis

#### 4.2. Nonlinear Response History Analysis

#### 4.2.1. Ground Motion Selection

_{n}, of the building (i.e., T

_{n}= 5 s), the primary seismic hazard source is the San Andreas Fault. The selected ground motions are from 15 different seismic events. At most, six records are selected from the same seismic event. The selected ground motions are generated by earthquakes having moment magnitudes between 6.2 and 7.6. A median shear wave velocity of about 245 m/s represents the shear wave velocity interval of D-type soil. Only magnitude scaling is employed. The maximum scale factor to be applied for the BSE-2E level in all ground motions should be less than 5.0 for NRHA. Indicatively, the mean values of the scale factors to be used at BSE-2E and BSE-1E levels are 3.1 and 2.0, respectively. Ground motion records are scaled such that the mean spectral ordinate of the 5% damped response spectrum is not less than that of the 5% damped target spectrum over a period range from 0.2 T

_{n}to 1.5 T

_{n}. Figure 3 show the absolute acceleration response spectra of the selected and scaled ground motion records, including their mean spectra. In the same figures, the target spectra at BSE-2E level are superimposed for comparison purposes.

#### 4.2.2. Assessment of Global Engineering Demand Parameters

#### 4.2.3. Assessment of Local Engineering Demand Parameters

_{c,G+E}/P

_{ye,c}ratios) and tensile force demands (T

_{c,G+E}/T

_{ye,c}ratios) at BSE-2E. The simulation results suggest that the column axial force demands are significantly higher in the X-loading direction relative to those in the Y-loading direction due to the smaller number of bays. The exterior columns experience high axial load demands due to the dynamic overturning effects. From Figure 6b,c, higher force demands are typically observed in lower stories. The highest values are observed in the third-story exterior columns. Interestingly, the peak compressive axial load ratio reached the squash load (see Figure 6b), while the corresponding tensile force exceeded 0.5 T

_{ye,c}. (see Figure 6c).

_{ye,c}in compression to 0.3 T

_{ye,c}in tension. The compressive force in the interior columns is less than 0.5 P

_{ye,c}. The normalized axial force component of the gravity load for columns P

_{G}/P

_{ye}< 0.6; hence, the steel columns are not considered to be force-controlled as per ASCE 41-17 [27].

#### 4.3. Column Splice Demands

_{C}, prior to fracture. Material and geometric properties associated with the material toughness, the crack length, and the flange thickness of the upper and lower columns are imperative in this case. Figure 7b indicates the locations of column splices and their peak tensile stresses in MPa, σ

_{D}, recorded at the fiber extremity of the smallest of the two column cross-sections forming a column splice in the X-loading direction. Due to dynamic overturning effects, all exterior column splices at the lower half and the upper stories of the building exhibit tensile stresses (see Figure 7b). The σ

_{D}values correspond to median peak tensile stresses. The blue dots represent sections where no tensile stresses are observed. Sections with peak tensile stresses are highlighted with orange dots. The peak stresses that exceed the estimated stress capacity, σ

_{C}, [11,31,32] are highlighted in red. The simulation results suggest that about 35% of the column splices are potentially vulnerable to brittle fracture at a BSE-2E seismic intensity.

## 5. Retrofit Solutions

#### 5.1. Design Objectives for Retrofit

#### 5.2. Bilinear Oil Dampers

#### 5.3. Multi-Degree-of-Freedom Performance Curves

#### 5.4. Design of Bilinear Oil Dampers

_{d,i}is the number of dampers at story i; θ

_{i,j}the inclination angle of the dampers at bay j; ${K}_{b,i}$ and ${K}_{d,i}$ are the total lateral supporting brace and internal damper stiffness at each story computed in design, respectively.

_{b}is the modulus of elasticity of the supporting steel brace (205 GPa); A

_{b,i,j}and L

_{b,i,j}are the cross-sectional area and the length of the supporting brace, respectively; L

_{tot,i,j}is the total diagonal length between working points; L

_{d,i,j}is length of the damper portion; L

_{rigid,i,j}is the rigid zone length, which is approximately 1000 mm in this case. The supporting length of the brace, L

_{b,i,j}, refers to the damper assembly length excluding the damper portion and the rigid zone length. It is also assumed that A

_{b,i,j}is valid for the entire L

_{b,i,j}. Thus, the mechanical model shown in Figure 8c is deemed representative. Details on the damper’s properties can be found in Akcelyan [39].

#### 5.5. Effect of Vertical Damping Distribution

#### Balanced Vertical Damping Distribution

## 6. Proposed Retrofit Solution

#### 6.1. Seismic Assessment of the Retrofitted Building

#### 6.2. Local Engineering Demand Parameters

#### 6.2.1. Beam Plastic Rotational Demands

#### 6.2.2. Column Axial Load Demands

_{ye,c}of the columns. From Figure 14c, higher tensile forces are observed in only a few ground motions. In particular, the tensile forces exceed 0.6 T

_{ye,c}. Figure 15a indicates the median column normalized peak compressive forces for the retrofitted building in 1–1 frame columns. Figure 7a and Figure 15a depict the effect of damper placement on the column forces. In this case, the increase in median column normalized peak compressive forces in B- and D-axis columns is larger compared to the non-retrofitted building. This is more evident in the 1–1 frame, where dampers are densely installed. For instance, as shown in Figure 7a at story 30 of the non-retrofitted building, the exterior columns exhibit about 0.3 P

_{ye,c,}compressive force, while this value in the B- and D-axis columns is about 0.2 P

_{ye,c}. For the retrofitted building, although the compressive force in exterior columns remains the same, the B- and D-axis columns experience relatively higher increase in compressive force, exceeding that of the exterior columns. This increase is due to the additional forces that the framing members experience due to the damper placement.

_{ye,c}to 0.16 P

_{ye,c}in the retrofitted configuration.

#### 6.2.3. Column Splice Demands

#### 6.2.4. Damper Stroke, Post-Relief Velocity Ratios and Forces

## 7. Summary and Conclusions

- Existing tall buildings are likely to have a high collapse risk based on the regional seismic hazard due to lack of capacity design principles as well as inadequate structural detailing at the time of construction. The 40-story building examined as part of the present study had a probability of collapse of 72% at the BSE-2E level;
- Bottom story exterior columns are likely to experience high compressive and tensile force demands due to dynamic overturning effects. Particularly, the compressive force demands may reach up to the expected column yield strength. For the examined 40-story building, the axial load demands ranged, on average, from 0.8 P
_{ye,c}in compression to 0.3 T_{ye,c}in tension. Conversely, interior columns within the same stories experience compressive axial forces up to 0.5 P_{ye,c}; - The simulation results suggest that there is no significant difference in column axial loads between the BSE-1E and BSE-2E seismic intensities. Unless the reduction in SDRs is considerable, depending on the employed retrofit solution, the column axial load demands are likely to remain high at the BSE-2E;
- Up to about 35% of the column splices were likely to experience brittle fractures at the BSE-2E seismic intensity. On the other hand, a considerable number of interior column splices are not susceptible to fracture;
- Oil dampers with relief valves were employed for the seismic retrofit of the examined building. The damper design was carried out by using the MDF performance curves method. Multiple retrofit solutions were exploited. A damping distribution method was proposed, and a detailed seismic performance assessment of the retrofitted building was carried out via NRHA. The main findings are summarized as follows:
- For retrofits where the steel MRF still exhibits inelastic behavior, the effective shear force proportional damping distribution is the most inefficient retrofit solution that causes damage concentration at stories where dampers are not provided, particularly at low and medium damping levels;
- For the retrofitted 40-story building, the proposed balanced shear force proportional damping distribution method provided the most uniform peak SDR distribution, while at the medium damping level the probability of collapse reduced from 72% to 10% at the BSE-2E hazard level. The peak SDRs were mostly concentrated in the bottom stories;
- At the BSE-2E hazard level, high axial force demands in the upper story columns of the non-retrofitted building were minimized after the implementation of the seismic retrofit solution. Conversely, compressive and tensile forces in the bottom exterior columns were not reduced. Furthermore, the damper installation led to an increase in the interior column forces. However, the difference in forces at mid-interior columns was minimal due to the inverted-V damper configuration;
- On average, about 27% of column splices were found to be vulnerable at the BSE-2E hazard level. Tensile stresses at upper story column splices were reduced. The opposite was observed in the bottom story exterior columns. It is recommended to strengthen the exterior column splices at the lower half of the building as well as the first story columns;
- At the BSE-E hazard level, the median peak damper displacements were less than 50% of the damper stroke limits. Although the median values of the peak post-relief velocity ratio were between 2.3 to 9.8, the corresponding damper forces were not large. This underscores the main advantage of utilizing bilinear oil dampers for seismic retrofit applications;

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Comparison of pushover curves and story drift ratios for in the X-loading direction, (

**a**) pushover curves, (

**b**) story drift ratios for ductile case, (

**c**) story drift ratios for base case, (

**d**) story drift ratios for brittle case.

**Figure 3.**5% damped response spectra of selected and scaled ground motions in comparison with ASCE-41-13 target spectrum for two-dimensional analyses; BSE-2E level.

**Figure 4.**Engineering demand parameters in the X-loading direction (BSE-1E), (

**a**) peak SDR, (

**b**) peak normalized story shear force, (

**c**) peak absolute floor acceleration.

**Figure 5.**Engineering demand parameters in the X-loading direction (BSE-2E), (

**a**) peak SDR, (

**b**) peak normalized story shear force, (

**c**) peak absolute floor acceleration.

**Figure 6.**(

**a**) Peak beam plastic rotations, (

**b**) normalized peak compressive, and (

**c**) tensile column forces (BSE-2E).

**Figure 7.**(

**a**) Median column normalized peak compressive forces and median peak (%), (

**b**) tensile stresses at column splices as built (MPa) (BSE-2E).

**Figure 8.**(

**a**) MDF performance curves, (

**b**) flexural-shear beam model, and (

**c**) two-dimensional frame model.

**Figure 9.**Damper design based on nine different retrofit schemes, (

**a**) low damping and effective SFPDD, (

**b**) medium damping and effective SFPDD, (

**c**) high damping and effective SFPDD, (

**d**) low damping and direct SFPDD, (

**e**) medium damping and direct SFPDD, (

**f**) high damping and direct SFPDD, (

**g**) low damping and balanced SFPDD, (

**h**) medium damping and balanced SFPDD, (

**i**) high damping and balanced SFPDD.

**Figure 10.**Comparison of peak SDRs based on nine different retrofit schemes in the X-loading direction, (

**a**) low damping level, (

**b**) medium damping level, (

**c**) high damping level.

**Figure 12.**Engineering demand parameters of the retrofitted building (BSE-1E), (

**a**) peak SDR, (

**b**) peak normalized story shear force, (

**c**) peak absolute floor acceleration.

**Figure 13.**Engineering demand parameters of the retrofitted building (BSE-2E), (

**a**) peak SDR, (

**b**) peak normalized story shear force, (

**c**) peak absolute floor acceleration.

**Figure 14.**(

**a**) Peak beam plastic rotations and (

**b**) normalized peak compressive and (

**c**) normalized tensile column forces of the retrofitted building (BSE-2E).

**Figure 15.**(

**a**) Median column normalized peak compressive forces and median peak [%], (

**b**) tensile stresses at column splices of the retrofitted building [MPa] (BSE-2E).

**Figure 16.**(

**a**) Median peak damper displacements [mm], (

**b**) median response of peak damper post-relief velocity ratio, and (

**c**) median response of peak damper forces [KN] (BSE-2E).

**Table 1.**Effective SDF parameters obtained from performance curve for three damping levels in the X-loading direction.

Case | ${K}_{d}^{\u2033}/{K}_{fs}$ | ${K}_{b}/{K}_{fs}$ | ${\mu}_{d}$ | β_{eff}[%] |
---|---|---|---|---|

Bare frame | - | - | 1.5 | |

Low damping | 0.25 | 1.0 | 2.0 | 7.4 |

Medium damping | 0.5 | 2.0 | 1.5 | 13.3 |

High damping | 1.0 | 4.0 | 1.2 | 22.2 |

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## Share and Cite

**MDPI and ACS Style**

Akcelyan, S.; Lignos, D.G.
Seismic Assessment and Retrofit of Pre-Northridge High Rise Steel Moment Resisting Frame Buildings with Bilinear Oil Dampers. *Buildings* **2023**, *13*, 139.
https://doi.org/10.3390/buildings13010139

**AMA Style**

Akcelyan S, Lignos DG.
Seismic Assessment and Retrofit of Pre-Northridge High Rise Steel Moment Resisting Frame Buildings with Bilinear Oil Dampers. *Buildings*. 2023; 13(1):139.
https://doi.org/10.3390/buildings13010139

**Chicago/Turabian Style**

Akcelyan, Sarven, and Dimitrios G. Lignos.
2023. "Seismic Assessment and Retrofit of Pre-Northridge High Rise Steel Moment Resisting Frame Buildings with Bilinear Oil Dampers" *Buildings* 13, no. 1: 139.
https://doi.org/10.3390/buildings13010139