Seismic performance of moment resisting steel frame subjected to earthquake excitations

Abstract

This study presents static and dynamic assessments on the steel structures. Pushover analysis (POA) and incremental dynamic analysis (IDA) were run on moment resisting steel frames. The IDA study involves successive scaling and application of each accelerogram followed by assessment of the maximum response. Steel frames are subjected to nonlinear inelastic time history analysis for 14 different scaled ground motions, 7 near field and 7 far field. The results obtained from POA on the 3, 6 and 9 storey steel frames show consistent results for both uniform and triangular lateral loading. Uniform loading shows that the steel frames exhibits higher base shear than the triangular loading. The IDA results show that the far field ground motions has caused all steel frame design within the research to collapse while near field ground motion only caused some steel frames to collapse. The POA can be used to estimate the performance-based-seismic-design (PBSD) limit states of the steel frames with consistency while the IDA seems to be quite inconsistent. It is concluded that the POA can be consistently used to estimate the limit states of steel frames while limit state estimations from IDA requires carefully selected ground motions with considerations of important parameters.

Keywords

incremental dynamic analysis (IDA) / pushover analysis / performance-based seismic design

Introduction

Background

Most of the construction in Malaysia concentrates only on the use of reinforced concrete as the choice for the structural system. In the past few years the industry has been experiencing shortage of cement for concrete construction. With the incursion of inexperienced labor from neighboring countries has immobilized the pace in achieving the work of sound quality. With all these considerations, steel structures may provide a better choice for the construction industry present needs. However, in Malaysia, majority of the consultants and contractors are still not experienced in the design and construction of steel structures. Most of the steel structures used in Malaysia are intended for industrial purposes such as factories and warehouses. Medium and high rise structures with steel as the supporting structural elements are not common in Malaysia [1].

In recent times, there have been a number of earthquakes which occurred surrounding peninsular Malaysia whereby most of the population of Malaysia resides. Although Peninsular Malaysia is located on a stable part of the Eurasian Plate, buildings on soft soil are occasionally subjected to tremors due to far-field effects of earthquakes in Sumatra. In the last few years, tremors were felt several times in tell buildings in Singapore and Kuala Lumpur, the capital of Malaysia, due to large earthquakes in Sumatra [2].

There are a few advantages offered by the use of steel framing in a seismic event. One of it is that steel frame buildings are both very durable and light. This feature enables cost efficient construction of earthquake resistant buildings. Next, structural steel shows an unchanging reaction against repeated loads within the non-elastic boundary.

This study presents findings in the field of structural engineering in steel structures with considerations of seismic activity. Hence, seismic attention is now becoming an essential part in the design of buildings in Malaysia. In the current state that Malaysia is in, the structures that use steel as supporting member are mostly industrial buildings such as factories and warehouses which require long span for maximum utilization of the space available. This shows that the local contractors and consultant expertise and experience are limited to these types of structures.

With the advantages as stated in the introduction, steel structure can be a potential building to be used in Malaysia to resist any unforeseen earthquake activity that may affect the country. Steel structure construction speed is faster than concrete and steel exhibits high strength and ductility, which indicates that steel has strong toughness as well.

Although steel structure exhibits high strength and ductility, its damage measure would still have to be taken into account. Damage measure here is defined as measures of the damage potential of an earthquake based on parameters of a response spectra and displacement.

Objectives

The main objectives to be carried out in this analysis are:

1) To study the drift for Moment-Resisting-Steel-Frame (MRSF) subjected to earthquake excitation using SAP 2000.

2) To examine the drift for MRSF with the Performance-Based-Seismic-Design (PBSD) limit state.

Damage measure

In accessing the performance of the proposed structure performance against seismic activity loads, the measure on the damage such as cracks, displacements, and drifts will be observed for critical damages that will lead to structure collapse.

As building heights increase, the forces of nature begin to dominate the structural system and take on importance in the overall building system. The analysis and design of tall building are affected by lateral loads, particularly drift or sway caused by such loads. Drift or sway is the magnitude of the lateral displacement at the top of the building relative to its base [3].

Several terms are used to describe displacements with different meaning. The following definitions will clarify their use here. Global displacements, u represents the displacement relative to the base of an equivalent Single Degree of Freedom system representing the structure. Roof displacement refers to the lateral displacements of the roof of the building with respect to the base. The term u_{roof} has been used to describe it. Interstorey drift is the relative horizontal displacement between two adjacent floors bounding the storey. The term{\mathrm{\Delta }}_i is used here to describe its value at storey i. Drift ratio corresponds to the interstorey drift divided by the storey height {\mathrm{\Delta }}_i/h_i, with h_i being the vertical distance between the floors. Average drift refers to the roof displacement divided by the total height of the building is shown in Fig. 1 [4].

(1){\mathrm{\Delta }}_{ave}={\displaystyle \frac{u_{roof}}{h_{roof}}}

Nonlinear analysis

The static pushover analysis (POA) is a partial and relatively simple intermediate solution to the complex problem of predicting force and deformation demands imposed on structures and their elements by severe ground motion. The important terms are static and analysis. Static implies that a static method is being employed to represent a dynamic phenomenon; a representation that may be adequate in many cases but is doomed to failure sometimes. Analysis implies that a system solution has been created already and the POA is employed to evaluate the solution and modify it as needed. The POA does not create good solutions, it only evaluates solutions. If an engineer starts with a poor lateral system, the POA may render the system acceptable through system modifications, or prove it to be unacceptable, but it will not provide a safe path to a good structural system [5].

The nonlinear dynamic analysis that will be used is Incremental Dynamic Analysis (IDA). IDA is a parametric analysis method that estimates more thoroughly structural performance under seismic loads.

Under the Nonlinear Dynamic Procedure (NDP), design seismic forces, their distribution over the height of the building, and the corresponding internal forces and system displacements are determined using an inelastic response history dynamic analysis. The basis, modeling approaches, and acceptance criteria of the NDP are similar to those for the Nonlinear Static Procedure (NSP). The main exception is that the response calculations are carried out using Time-History Analysis. With the NDP, the design displacements are not established using a target displacement, but instead are determined directly through dynamic analysis using ground motion histories. Calculated response can be highly sensitive to characteristics of individual ground motions; therefore, it is recommended to carry out the analysis with more than one ground motion record. Because the numerical model accounts directly for effects of material inelastic response, the calculated internal forces will be reasonable approximations of those expected during the design earthquake (FEMA273) [6].

Performance-based-seismic-design (PBSD)

The promise of Performance-Based-Seismic-Design (PBSD) is to produce structures with predictable seismic performance. A comprehensive and well-coordinated effort by professionals from several disciplines is required. Performance based engineering is not new. Automobiles, airplanes, and turbines have been designed and manufactured using this approach for many decades. Generally in such applications one or more full-scale prototypes of the structure are built and subjected to extensive testing. The design and manufacturing process is then revised to incorporate the lessons learned from the experimental evaluations. Once the cycle of design, prototype manufacturing, testing and redesign is successfully completed, the product is manufactured in a massive scale. In the automotive industry, for example, millions of automobiles which are virtually identical in their mechanical characteristics are produced following each performance-based design exercise [7]. To utilize PBSD effectively and intelligently, one need to be aware of the uncertainties involved in both structural performance and seismic hazard estimations.

In this study, the permissible drift were used are based on the suggested drift percentage suggested by FEMA-356 [8]. Which are divided into four main categories, (a) 0.5% for fully operational; (b) 0.7% for operational; (c) less 2.5% for life safety and (d) higher 2.5% for near collapse.

Methodology

In this study, the methodology used for this research will be explained; the details and parameters of the steel structure design used for analysis will be discussed. The methodology starts with the steel structure design based on Eurocode 3 (EC3) [9], then, the analysis will begin with the usage of the SAP2000 software in nonlinear static and nonlinear dynamic analysis. The nonlinear static analysis will be in the form of uniform distribution and triangular distribution while the nonlinear dynamic analysis will utilize Incremental Dynamic Analysis (IDA) curve. The results from both of the static and dynamic analysis will then be compared and then used to estimate the limit state using Performance-Based-Seismic-Design (PBSD).

Moment-resisting steel frame (MRSF) structure

MRSFs are designed such that plastic hinges occur predominantly in beams rather than in columns (weak beam/strong column design) as shown in Fig. 2. This provides favorable performance, compared to strong beam/weak column behavior through which significant deformation and second order effects may arise in addition to the likelihood of premature storey collapse mechanisms. The only exception to this requirement is at the base of the ground floor columns, where plastic hinges may form.

Due to the spread of plasticity through flexural plastic hinges, MRSFs usually possess high ductility as reflected in the high reference q assigned in Eurocode 8 (EC8) [10]. Nevertheless, due to their inherent low stiffness, lateral deformation effects need careful considerations [11].

In this research, the parameters of the steel structure will be as follows:

Ground type A as stated in the Table 1 is rock or other rock-like geological formation, including at most 5 m of weaker material at the surface as given in EC8. Furthermore, the frame were designed based on the rigid connection. For the steel properties, bi-linear steel material types is used as for the analysis.

Frame design

The frame design was done using EC3 and EC8 standards, whereby the earthquake load and the gravity load was both calculated in the design. The total moment affecting the building was calculated using EC8 from the earthquake load and gravity load. The fundamental period of vibration of the structure, T_{\mathrm{1}} was considered using EC8 to calculate the horizontal storey seismic actions which contributes to the maximum bending moment for a sway load. The total maximum bending moment was the sum of moments calculated from gravity load and earthquake load.

Then, the beam and column design was proceeded when the bending moment was computed. The beam design was based on minimum plastic modulus with checks on shear resistance and deflection. The minimum was selected to create plastic hinges in order for analysis results to be displayed. There were two types of lateral loading done on the structure which is a uniform loading and a triangle loading. Since triangle loading is higher as it increases as it goes above the structure, therefore, the beam design for uniform loading was made to be the same as the triangle loading. This was done so that the POA for the uniform and triangle lateral loading could be used for comparison.

These goes the same for the column design whereby the loading applied to column under triangle lateral loading would certainly be larger in magnitude. Therefore, the column design under uniform lateral loading would be the same as the triangle loading. The designed dimension of the beam and column for the 3, 6 and 9 storey are listed in Table 2.

POA procedure

The analysis of the stated heights of the structures requires definition of several aspects such as materials information, frame sections dimensions, load patterns, load cases, frame hinges properties and joint constraints. Then, when these defining procedures are done they then assigned to their respective fields such joint constraints to joints, frame sections to their respective members (that is the right beam and column dimension to the right frame sections), hinge properties to its respective beams and columns and then finally the dead and imposed loads. Then when all defining and assigning has been done, the analysis was run to obtain the results.

IDA procedure

The IDA is done with the same steel frame designs used from the POA. 14 ground motions as shown in Table 3 and a Joyner-Boore Distance

Table 4 were selected to obtain the IDA curve for the nonlinear dynamic analysis. All the ground motion data can be downloaded free on the Pacific of Earthquake Engineering Research (PEER) website. The ground motion records were selected based on the near-field (<20 km) and far-field (>20 km) records with a magnitude in range of 6- 7. Then, these ground motions were scaled to elastic response spectra as given from EC8 according to the steel frames respective natural period. Each ground motion was scaled to intensities that range from S_a(T₁,5%) = 0.5 to 3.0 g by 0.5 g increments.

Results and discussion

The comparison of the obtained 3 storey IDA curves and POAs curves are as shown in Fig. 3. It can be seen that the two POA curves exhibits higher base shears compared to the two IDA curves. The IDA curves seem to be quite consistent at the beginning but after the 1.5 g intensity the IDA curves seems to not so consistent compared to lower ground motion intensities. The POA curve is quite consistent throughout with the increase of roof drift. This shows that the selection of suitable ground motion for the IDA analysis has some influence in affecting the outcome of the analysis in terms of base shear and roof drift. In drifts of less than 1%, four of the curves show consistent increase in base shear.

Figure 4 shows four curves which are two IDA curve generated with far field and near field ground motions and the other two are POA curve of uniform loading and triangular loading for the 6 storey steel frame. In this analysis, the results show that four of curves are consistently increasing in base shear with the drift increase up to 2%. The IDA curves produced in the 6 storey frame seems to have higher base shear as compared to the POA curves. This may be due to higher flexibility of the 6 storey when it is subjected to the selected ground motions, hence higher base shears are recorded with the increment of ground motion intensity. As seen in Fig. 4, the POA curves records highest base shear of 4500 kN and 3900 kN due to uniform loading and triangular loading respectively. On the other hand, IDA curve due to far field ground motion can be seen only experience structure collapse state after it reaches 4700 kN. IDA curve due to near field ground motion shows that the 6 storey steel frame experienced collapse after base shear reaches 6500 kN.

Two IDA curves and 2 POA curves obtained from analysis run on the 9 storey steel frame was combined in Fig. 5. In drift of less than 2%, it can be seen that four of the curves increases consistently with the increase of drift. After 2% drift, the IDA curves seem to be remain constant throughout with the increase in drift until about 12 to 14%. However, the POA curves base shear increases slowly with the increase in drift until about 6% drift where the base shear is reached at maximum, consequently the base shear decreases as it shows that the structure has collapse when base shear reaches the maximum. POA curve due to uniform loading yields a maximum base shear of 4400 kN while POA curve due to triangular loading yields a maximum base shear of 3700 kN. From approximation, IDA curve due to near field ground motion cause the structure collapse after 3800 kN as consequently there is a sudden decrease in drift. While for IDA curve due to far field ground motion, the base shear reaches maximum at 5600 kN where subsequently the sudden decrease in drift occurred.

Conclusions

Pushover analysis (POA)

The damage measure used in this study is the roof drifts, and from the analysis results obtained it can be seen from the POA curves of the 3, 6 and 9 storey steel frames that the structure under uniform lateral loading exhibits higher base shear as compared to the triangular lateral loading.

This is due to lower loading magnitude of uniform lateral loading as compared to triangular lateral loading. The uniform lateral loading accentuates more demands on the lower storeys as compared to demands on the high storeys. It emphasizes the importance of storey shear force in contrast with overturning moments. While for triangular lateral loading, it focuses more of the higher storeys demands and overturning moments.

The observed lower base shear in triangular lateral loading may be also due to the fact that most of triangular lateral loading is focused on the top part of the steel frame, therefore the roof displacement will be higher and base shear will be lower as compared to the uniform lateral loading.

In uniform lateral loading, the base shear for 3 and 6 storey seems to have almost similar values as compared to the 9 storey steel frame which exhibits a high base shear. From this research, it can be seen that the higher the number of storeys, the base shear gets higher and also the initial stiffness.

In the triangular lateral loading, the results that the 9 storey also exhibits higher base shear than the 3 and 6 storey. Initially, the 3 and 6 storey shows similar stiffness whereby their base shear increases almost similarly with the increase of drift. However, the 6 storey base deviates earlier at 1% drift as compared to the 3 storey. Although the 3 storey POA curve increase similarly in base shear as 6 storey, but it intersects slightly with the 9 storey POA curve in the range of 1.2% to 1.6% drift. This shows that the 3 storey merely has higher initial stiffness when subjected to triangular lateral loading in that range.

Most of the hinges were formed in the beams and only in the base of the first storey columns. This shows that the steel frames are of weak beam/ strong column design, which provides favorable performances as compared to strong beam/ weak column design behavior.

The relationship of the base shear and the hinges formation depends on the arrangement of the steel frames. From the 3 bay steel frame designs of the research, during the critical steps, most of the collapse hinges are formed in the bottom storeys. The 3 and 6 storey have less percentage of collapse state hinges as compared to 9 storey steel frame. Given that the design it based on weak beam/ strong column philosophy, it can be said that the higher the base shear, the higher the percentage of collapse hinges formation.

Incremental dynamic analysis (IDA)

The results obtained from the IDA for the near field ground motion shows that the 3 storey steel frame did not collapse even though the ground motion intensity is at 3.0g. On the other hand, the 6 and 9 storey steel frame has experienced collapse when the ground motion has been increased to 3.0 g. For the far field ground motion, all three types of steel frames of 3, 6 and 9 storey steel frame has experienced collapse when the ground motion intensity reached 3.0 g.

In the opinion of the author, the near field ground motion should have caused all the steel frames to collapse while only the far field ground motion would only probably caused the 9 storey steel frame to collapse. However, the results show otherwise, the far field ground motion has caused all the steel frames to collapse and the near field ground motion has only caused the 6 and 9 storey to collapse with the 3 storey steel frame still standing. This may be attributed to the soil-structure interaction that caused this observation. The soil type may have some influence over the behavior of the structure when subjected to the far field ground motions.

It may also have been due to poor selection of far field ground. Some of the far field ground motion shows inconsistent movements, whereby several of the far field ground motions selected show sudden increase in spectral acceleration which was then followed by low values of spectral acceleration nearing the end of the respective ground motions. The results have shown that it may have been affected by these sudden rises in acceleration. Therefore, to perform a better and more accurate analysis, parameters such as peak ground acceleration (PGA) and peak ground velocity (PGV) shall be taken into account in the selection of ground motions to ensure the ground motion are of valid and usable picks.

Recommendations for future research

One of the recommendations for future research is on the selection of ground motion for the IDA curve generation from the time history analysis. The far field ground motion analysis results has shown that all steel frames have collapsed. This result may have been different if the process of ground motion selection is done with more meticulous preparation.

References

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[2] Balendra T, Li Z. Seismic Hazard of Singapore and Malaysia. EJSE Special Issue: Earthquake Engineering in the low and moderate seismic regions of Southeast Asia and Austrialia, 2008, 57-63

[3] Rahman A, Ahmed A A M, Mamun M R. Drift Analysis due to earthquake load on tall structures. Journal of Civil Engineering and Construction Technology, 2012, 4: 154-158

[4] FIB. Displacement-based Seismic Design of Reinforced Concrete Buildings: State-of-art Report. International Federation for Structural Concrete (FIB), 2003, 25: 192

[5] Krawinkler H. Pushover analysis: Why, how, when, and when not to use it. In: Proceedings of the 65th Annual Structural Engineers Association of California Convention. Maui, Hawaii, 1996

[6] FEMA-273. NEHRP Guidelines for Seismic Rehabilitation of Buildings.Washington DC: Building Seismic Safety Council, 1997

[7] Naeim F, Bhatia H, Lobo R M. Performance Based Seismic Engineering, in Seismic Design Handbook. 2001, 759-765

[8] FEMA-356. Prestandard and commentry for the seismic rehabilitation of buildings. Washington DC: Federal Emergency Management Agency, 2000

[9] BSI. Eurocode 3 (EC3): Design of Steel Structures in Part 1-1: General rules and rules for buildings. London, 2005

[10] BSI. Eurocode 8 (EC8): Design Provisions for Earthquake Resistance of Structures, in Part 1: General Rules, Seismic Actions and Rules for Building. London, 2004

[11] Elghazouli A Y, Castro J M. Design of Steel Structures, in Seismic Design of Buildings to Eurocode 8. Elghazouli AY, ed. Spon Press, 2009

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