PARTICIPATION OF GRAVITY FRAMING AND INTERACTIONS IN THE LATERAL SEISMIC RESPONSE OF STEEL BUILDINGS

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PARTICIPATION OF GRAVITY FRAMING AND INTERACTIONS IN THE LATERAL SEISMIC RESPONSE OF STEEL BUILDINGS

TABLE OF CONTENTS

List of Figures……………………………………………………………………………. ….. v

List of Tables……………………………………………………………………………. ……. viii

Chapter 1 Introduction ………………………………………………………………………………………………. 1

1.1Motivation ……………………………………………………………………………………………………. 71.2Problem Statement ………………………………………………………………………………………… 8

1.3Scope …………………………………………………………………………………………………………… 8

1.4Significance ………………………………………………………………………………………………….. 9

Chapter 2 Literature Review  ……………………………………………………………………………………… 11

2.1Column stiffness effects on drift concentrations………………………………………………… 12

2.2Moment Rotation Behavior of Composite Shear Connections …………………………….. 14

2.3Equivalent Lateral Force Procedure …………………………………………………………………. 18

2.3.1 Base Shear …………………………………………………………………………………………. 19

2.3.2 Vertical Distribution of Forces ……………………………………………………………… 20

2.3.3 Modern Building Code ELF Procedures ………………………………………………… 21

2.4Background Steel Plates Shear Walls ………………………………………………………………. 23

2.4.1 Unstiffened SPSW ………………………………………………………………………………. 24

2.4.2 Mechanics of SPSW’s …………………………………………………………………………. 26

2.4.3 Design of SPSW systems …………………………………………………………………….. 27

2.5. Nonstructural components’ influence on seismic response ……………………………….. 27

Chapter 3 Elastic Analysis …………………………………………………………………………………………. 29

3.1Introduction ………………………………………………………………………………………………….. 29

3.2Preliminary Analysis ……………………………………………………………………………………… 29

Chapter 4  Parametric Study ………………………………………………………………………………………. 38

4.1General ………………………………………………………………………………………………………… 384.2Base Model ………………………………………………………………………………………………….. 44

4.3Parametric Analysis ………………………………………………………………………………………. 48

4.3.1 Story Over-strength Ratio ……………………………………………………………………. 494.3.2 Effects of Shear Connection Strength ……………………………………………………. 53

4.3.3 Effects of Gravity Column Flexural Rigidity ………………………………………….. 57

4.4Results of the Parametric Study ………………………………………………………………………. 59

4.4.1 Over-Strength Simulation Results …………………………………………………………. 60

4.4.2 Partially Restrained Connection Strength Simulation Results …………………… 66

4.4.3 Gravity Column Flexural Rigidity Simulation Results …………………………….. 70

4.5Discussion of results ……………………………………………………………………………………… 74

Chapter 5Analysis of Multi-Story SPSWs ……………………………………………………………………. 77

5.1  Introduction ……………………………………………………………………………………………….. 77

5.2Frame Models ………………………………………………………………………………………………. 785.2Non-linear Response History Analysis …………………………………………………………….. 83

5.3Summary of Results ………………………………………………………………………………………. 91

Chapter 6 Discussion and Conclusions ………………………………………………………………………… 92

6.1General ………………………………………………………………………………………………………… 92

6.2Discussion ……………………………………………………………………………………………………. 936.3General Conclusions ……………………………………………………………………………………… 94

6.4Significance …………………………………………………………………………………………………. 95

6.5Recommendations for Future Research ……………………………………………………………. 95

References ……………………………………………………………………………………………………………….. 97

Appendix A Frame Proportions ………………………………………………………………………………….. 99

Appendix B Ground Motions……………………………………………………………………………………… 101

Appendix C Sample ELFP Calculations ………………………………………………………………………. 103

Appendix D Parametric Case Summary ………………………………………………………………………. 105

Appendix E Over-Strength Ratio Plots ………………………………………………………………………… 108

Chapter 1  Introduction 

All buildings must include structural lateral force resisting system(s) to withstand wind loads, earthquake loads, and to provide stability under gravity loading. A number of different lateral force resisting systems have been used to provide lateral load resistance including moment frames, braced frames, and shear walls, among others.

Figure 1 Typical schematic of: (A) Braced Frame (B) Moment Resisting Frame and (C) Shear Wall

Figure 1 presents schematics for three common lateral force resisting systems. A braced frame, Figure 1A, resists lateral forces with diagonal bracing members. A moment resisting frame, Figure 1B, provides lateral force resistance with fully restrained beam-column connections. Shear walls, Figure 1C, resist lateral loads with infill material in the bays of a frame, that for steel plate shear walls (SPSW) are thin infill plates that buckle in shear then develop tension field action (Thorburn 1983). Shear wall can be composed of materials ranging from; reinforced concrete, reinforced masonry, to thin steel plates.

 

 

For the purpose of economy the lateral force resisting systems are typically connected to gravity systems and constitute only a small portion of the entire structural system of a building. Gravity systems utilize simple shear tab connections to connect the web of the beam to the column flange as illustrated in Figure 2a. The simple shear connection is assumed to transfer only shear forces and to have no resistance to rotation, although experimental testing of simple shear connections suggests the rotational stiffness and rotational strength of these connections can be a significant percentage of equivalent connections with restrained flanges as illustrated in Figure 2b (Liu and Astaneh-Asi 2004). The use of simple shear connections is more cost effective and easier to construct by comparison to restrained connections. For this reason, the majority of the building structural system is composed of gravity framing whereas lateral force resisting systems are included primarily to meet lateral load and drift requirements set forth by contemporary structural design standards (ASCE 7-10).

Figure 2 Illustration of steel connections: (A) simple shear connection; (B) moment resisting connection

Figure 2 illustrates typical simple shear and moment resisting connections. For the simple shear connection, the beam is connected to the column with a shear tab that is typically an angle section that is bolted to the beam web and/ or welded to the column flange (or web depending on the strong-axis orientation of the gravity column). For the analysis and design of the building structural system, this shear connection is typically idealized as a simple pin connection that is assumed not to possess any rotational stiffness or rotational strength. The moment resisting connection, illustrated in Figure 2B, in which the flanges of the beam are connected, either through angled section or full penetration grove welds, to the column flange provides both rotational stiffness and rotational strength that when part of the lateral force resisting system is detailed to develop the full plastic moment strength of the beam. The additional material and detailing required for moment resisting connections increase the cost and therefore limits their use to lateral force resisting framing.

Compatibility of deformations between the gravity framing and lateral force resisting system are imposed by concrete floor slabs in building structures acting as a rigid diaphragm. The gravity system will deform and therefore participate in the response of a structure under lateral loading. Conventional design practices have not required the inclusion of gravity columns in the analysis of lateral force resisting systems therefore their participation is not considered.  Past experimental tests (Liu and Astaneh-Asi 2004) have demonstrated that simple shear tab connections possess considerable rotational stiffness and strength in contrast to the behavior assumed by the pin idealization. Further evidence of the rotational stiffness and strength of these simple shear connections was observed following the 1994 Northridge earthquake in California. A Structural Engineers Association of California (SAC 1995) report credited these connections with the ability to “provide a large structural strength reserve capacity, as the survival of many heavily damaged moment frames during the Northridge earthquakes attests. Widespread utilization of partial restrained and composite bolted connections should be encouraged in the context of back up structural systems since they provide great redundancy and toughness.” Others (Hines and Fahnestock 2010) have begun to consider the use of gravity systems as secondary, or back-up, systems for the purpose of design; however that is not the goal of this study.

Shear From Partially Restrained Connections           Shear From P-Delta Effects             Shear in Gravity System

P                                                                                   P

Figure 3 Free body diagram of gravity column

To illustrate how the strength of the partially restrained shear tab connections translates into participation of the gravity frame, Figure 3 presents a free body diagram of a gravity column in its deformed state. Moment develops in these partially restrained shear tab connections as the building drifts due to lateral loading. Applying the strength of these partially restrained connections, Mpbeam, to the gravity column and taking moment equilibrium about point B, top of column (see Figure 3) yields an expression for the shear at the base of the gravity column due to the partially restrained shear connection, VShearConneciton:

VShearConnection M pbeam                                                  (1)

L

where Mpbeam is the moment strength of the partially restrained shear connections at each story expressed as a coefficient times the plastic moment capacity of the beam, Mpbeam, and L is the total height of the structure. However, being a gravity column it carries gravity loads, therefore to maintain equilibrium a shear, VP-delta, must be present at the base of the gravity column due to the P-delta effects but acting in opposite direction of VShearConneciton as illustrated in Figure 3. The component of base shear due to the P-delta effects can be expressed as:

VP Delta Pdeltai                                                       (2)

L

where P is the gravity load applied to the column at each story, and deltai is the drift at story i. It is clear from the free-body diagrams show in Figure 3, that the shear tab connection results in a component of shear at the base of the gravity column and hence the participation of the gravity framing in the lateral force response. However, the magnitude of the contribution and its impact and the resulting participation of the gravity frame in the lateral force resistance of the building structural system has not been well established.

More recently, research on the seismic performance of concentrically braced frames (CBF) (MaCrae et al. 2004; Fahnestock et al. 2010) determined the gravity columns in the CBFs, typically assumed to not participate in the lateral force resistance, contribute to the overall strength and stiffness of the lateral force resisting system beyond that provided by the braces

(MacRae et al. 2004). This research concluded that the flexural stiffness of gravity columns in

CBFs can significantly reduce non-uniform drifts along the height of the frame (MacRae et al. 2004). Similar reduction in drift concentrations were observed in research on buckling resistant braced frames (Ariyaratana and Fahnestock 2010).

There are likely two, interconnected, reasons for the participation of the gravity columns in the lateral response of the building system. First, among these reasons is the simple shear connections possess rotational stiffness and strength although it is assumed they are idealized pins as previously discussed and secondly, compatibility between the lateral force resisting system and the gravity columns requires that when non-uniform story drifts occur the gravity frame columns participate.

 

 

Uniform Story Drift                                                 Non-Unifrom Story Drift

 

Figure 4 Illustration of gravity column participation

Figure 4 presents two illustrations to demonstrate the potential participation of a continuous gravity column for a three-story frame archetype for both uniform story drift (left) and non-uniform story drift (right) assuming idealized pin beam-column connections for both cases. The illustration on the left of Figure 4 shows that when the story drifts are uniform, the gravity column simply rotates about its base, also assuming idealized pin connections. The frame shown on the right of Figure 4 has non-uniform drift demands and an inter-story drift concentration at the second story, where drift is defined as the difference in lateral displacement between the top and bottom of a story level. When drift is non-uniform, whereby drift is concentrated at a particular story level, as illustrated on the right of Figure 4, the gravity column must deform, i.e. bend/shear, due to compatibility with the lateral force resisting system. The compatibility occurs because of the presence of the floor diaphragm that connects the gravity columns to the lateral force resisting system. Shear forces that developed in the gravity columns are transferred though the rigid diaphragm to the lateral force resisting system. Previous research has shown that the forces developed in the gravity framing system by this compatibility of deformations helped to mitigate drift concentrations in CBFs (Ji et al. 2009).

As illustrated in Figure 4, the assumption that the gravity columns do not participate in the lateral response of the building structural system is valid only when the inter story drifts are uniform. However, this is rarely observed for the seismic response of buildings due to strength and stiffness discontinuities between adjacent floors due, in part, to limited material size and/or section sizes. Discontinuities in story stiffness and strength translate into non-uniform drift demands and thus engage the gravity columns through compatibility. Another factor contributing to non-uniform drifts in the lateral response is higher modes of vibration, meaning that the dynamic response is not always governed by the 1st mode response. High modes are more likely to participate as the structure’s height increases. It is reasonable to hypothesize the participation of the continuous gravity columns increases as the height of the buildings increases.

       1.1       Motivation

Previous research and relatively simple demonstration of the equilibrium and compatibility of framing systems suggests that the gravity framing will participate in the lateral response of building structures through: (1) the stiffness and strength provided by the partial restrained simple shear tab connections; (2) the compatibility between the lateral framing and continuous gravity columns; and (3) participation of higher modes in the response of the frame to dynamic lateral loading. At this moment, contemporary structural design standards, i.e. ASCE 710, do not require the gravity framing to be explicitly considered in either the analysis or design of the building lateral force resisting system. However, it is clear from previous research and simple mechanics that the gravity framing system will participate in the lateral force resistance of the building structural system to some degree. Others (Hines and Fahnestock 2010) have advocated relying on the gravity system as a “back-up” or “secondary” system.

 

       1.2       Problem Statement

Gravity framing systems with simple shear connections will participate in the lateral response of the building structural system whether designed to or not.  Some (Hines and Fahnestock 2010) have advocated accounting for this “reserve capacity” for the design of the building system. Currently, this reserve strength is typically ignored in the analysis and design of lateral force resisting systems. While it is widely acknowledge that the gravity frame will participate in the lateral force resistance, there lacks a comprehensive study to understand systematically how the gravity framing affects demands throughout the building structural system. The objective of this study, therefore, is to fill this knowledge gap by systematically understanding the impact of each gravity framing factor, i.e. partially restrained connections, compatibility between the gravity and lateral force resisting system and higher mode effects.

       1.3       Scope

The scope of this research was to determine the influence of gravity framing on the seismic response of steel lateral force resisting systems. Three possible ways to which the gravity framing will contribute to the seismic response were considered.

  1. Continuous gravity columns
  2. Partially restrained behavior of shear tab connections
  3. Higher mode effects seen in structures of increasing height

The steel lateral force resisting systems considered for this study were steel plate shear walls (SPSWs) and moment resisting frames (MRFs). Lateral force resisting systems were designed for building archetypes of 3, 9, and 20 stories.

 

 

The response characteristics of interest that may be affected by the gravity framing system in the modeling are as follows.

  • Fundamental period
  • Distribution of base shear at story levels
  • Story drifts
  • Ductility demands (i.e. plastic deformations in the frame)

The seismic responses of these steel buildings were evaluated at 3 levels of seismic loading. Ground motion magnitudes were chosen based on contemporary seismic design philosophy. In seismic design, 3 levels of loading are typically evaluated with specific performance criteria at each level; (1) Moderate events; limited damage of non-structural components and no damage to structural systems; (2) Design events; non-structural component damage expected and structural members may sustain repairable damage; (3) Maximum considered event; structural systems sustain severe damage but the building should not collapse (ATC 1978).

       1.4       Significance

The effect of the gravity framing on the response of steel building structures subjected to seismic loading is not well understood. The redundancy and over-strength provided by gravity framing systems was credited with preventing the collapse of several moment frame structures during the Northridge earthquake of 1994 (SAC 1995). Knowledge gained from this study can be used to guide future decisions whether to use the gravity frame as a “secondary system” or whether gravity framing “must” be explicitly considered when analyzing and designing lateral force resisting systems. This study will also provide an indication of forces the gravity system sees in the seismic response that it is not designed for, particularly axial loads

(tension/compression forces) being transferred through simple shear connections in the gravity framing. It is of the utmost importance to maintain these connections in order to carry the gravity loading of a structure to prevent collapse. Moments developed in the gravity columns may also stress the members beyond their elastic range leading to the failure of these members under their

gravity loading.

PARTICIPATION OF GRAVITY FRAMING AND INTERACTIONS IN THE LATERAL SEISMIC RESPONSE OF STEEL BUILDINGS

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