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Chapter 1: Buildings

B: AN INTRODUCTION TO STRUCTURAL CONCEPTS IN EARTHQUAKE MITIGATION DESIGN

PART 2: TECHNICAL COMMENTARY, Part 1

 

THE FOLLOWING IS A DESCRIPTION OF THE DIFFERENT ANALYTICAL PROCEDURES USED BY STRUCTURAL ENGINEERS IN EARTHQUAKE ENGINEERING 


FROM: FEMA 356: A Prestandard and Commentary for the Seismic Rehabilitation of Buildings (p-2-8)


This section is reproduced from FEMA 356 in order to provide an introduction to the types of analytical procedures used for seismic risk assessments for existing buildings, leading upgrade design.  It is provided here for the general public because a general knowledge of these procedures and terminology can better equip decision makers to be able to make an informed decision on how best to proceed through the design stage.  This information can be valuable because in certain situations involving complex multi-story buildings of different structural systems, the more more elaborate and costly analytical procedure can sometimes lead to much greater savings in construction costs.  The reason for this is that the simplified procedures are not only less precise, but also potentially over-conservative, and thus predictive of a poorer performance in earthquakes than is actually the case.  

NOTE that this is a "prestandard," and as such, the language is in the form of demands and requirements, so that it can be incorporated into a building code or City-wide ordinance.  It is not published here with the intention that it be treated as more than a source of information.  For code preparation, please refer to the published document in its entirety, as the materials below have been condensed and edited.

C2.4 Analysis Procedures: Introduction

[The FEMA 356 "Prestandard" specifies that] an analysis of the building, including rehabilitation measures, shall be conducted to determine the forces and deformations induced in components of the building by ground motion corresponding to the selected Earthquake Hazard Level, or by other seismic geologic site hazards specified in Section 4.2.2. The analysis procedure shall comply with one of the following, and comply with the applicable acceptance criteria selected in accordance with Section 2.4.4:

1. Linear analysis subject to limitations specified in Section 2.4.1, and complying with the Linear Static Procedure (LSP) in accordance with Section 3.3.1, or the Linear Dynamic Procedure (LDP) in accordance with Section 3.3.2.

2. Nonlinear analysis subject to limitations specified in Section 2.4.2, and complying with the Nonlinear Static Procedure (NSP) in accordance with Section 3.3.3, or the Nonlinear Dynamic Procedure (NDP) in accordance with Section 3.3.4.

3. Alternative rational analysis in accordance with Section 2.4.3.

NOTE: The linear analysis procedures maintain the traditional use of a linear stress-strain relationship, but incorporate adjustments to overall building deformations and material acceptance criteria to permit better consideration of the probable nonlinear characteristics of seismic response. The Nonlinear Static Procedure (NSP), often called "pushover analysis," uses simplified nonlinear techniques to estimate seismic structural deformations. The Nonlinear Dynamic Procedure (NDP), commonly known as nonlinear time history analysis, requires considerable judgment and experience to perform, and may be used only within the limitations described in Section 2.4.2.2 of this standard.


C2.4.1 Linear Procedures

The results of the linear procedures can be very inaccurate when applied to buildings with highly irregular structural systems, unless the building is capable of responding to the design earthquake(s) in a nearly elastic manner. The procedures of Section 2.4.1.1 are intended to evaluate whether the building is capable of nearly elastic response.

C2.4.1.1 Method to Determine Limitations on Use of Linear Procedures:   The magnitude and distribution of inelastic demands are indicated by demand-capacity ratios (DCRs). Note that these DCRs are not used to determine the acceptability of component behavior. The adequacy of structural components and elements must be evaluated using the procedures contained in Chapter 3 along with the acceptance criteria provided in Chapters 4 through 8.  DCRs are used only to determine a structure's regularity. It should be noted that for complex structures, such as buildings with perforated shear walls, it may be easier to use one of the nonlinear procedures than to ensure that the building has sufficient regularity to permit use of linear procedures. If all of the computed controlling DCRs for a component are less than or equal to 1.0, then the component is expected to respond elastically to the earthquake ground shaking being evaluated. If one or more of the computed DCRs for a component are greater than 1.0, then the component is expected to respond elastically to the earthquake ground shaking being evaluated.  If one or more of the computed DCRs for the component are greater than 1.0, then the component is expected to respond inelastically to the earthquake ground shaking.

2.4.1.2 Limitations on Use of the Linear Static Procedure:  The Linear Static Procedure shall not be used for a building with one or more of the following characteristics:

1. The fundamental period of the building, T, is greater than or equal to 3.5 times Ts.

2. The ratio of the horizontal dimension at any story to the corresponding dimension at an adjacent story exceeds 1.4 (excluding penthouses). see: Irregularities

3. The building has a severe torsional stiffness irregularity in any story. A severe torsional stiffness irregularity exists in a story if the diaphragm above the story under consideration is not flexible and the results of the analysis indicate that the drift along any side of the structure is more than 150% of the average story drift. see: Irregularities

4. The building has a severe vertical mass or stiffness irregularity. A severe vertical mass or stiffness irregularity exists when the average drift in any story (except penthouses) exceeds that of the story above or below by more than 150%. see: Irregularities

5. The building has a nonorthogonal lateral-force- resisting system. For buildings in which linear procedures are applicable, but the Linear Static Procedure is not permitted, use of the Linear Dynamic Procedure shall be permitted. 

NOTE: For buildings that have irregular distributions of mass or stiffness, irregular geometries, or nonorthogonal lateral-force-resisting systems, the distribution of demands predicted by an LDP analysis will be more accurate than those predicted by the LSP. Either the response spectrum method or time history method may be used for evaluation of such structures.

2.4.2 Nonlinear Procedures

Nonlinear procedures shall be permitted for any of the rehabilitation strategies contained in Section 2.5. Nonlinear procedures shall be used for analysis of buildings when linear procedures are not permitted. Data collection for use with nonlinear procedures shall be in accordance with Section 2.2.6.

2.4.2.1 Nonlinear Static Procedure

The NSP shall be permitted for structures in which higher mode effects are not significant, as defined in this section. To determine if higher modes are significant, a modal response spectrum analysis shall be performed for the structure using sufficient modes to capture 90% mass participation. A second response spectrum analysis shall also be performed, considering only the first mode participation. Higher mode effects shall be considered significant if the shear in any story resulting from the modal analysis considering modes required to obtain 90% mass participation exceeds 130% of the corresponding story shear considering only the first mode response.

If higher mode effects are significant, the NSP shall be permitted if an LDP analysis is also performed to supplement the NSP. Buildings with significant higher mode effects must meet the acceptance criteria of this standard for both analysis procedures, except that an increase by a factor of 1.33 shall be permitted in the LDP acceptance criteria for deformation-controlled actions (m-factors) provided in Chapters 5 through 9. A building analyzed using the NSP, with or without a supplementary LDP evaluation, shall meet the acceptance criteria for nonlinear procedures specified in Section 3.4.3.

NOTE: The NSP is generally a more reliable approach to characterizing the performance of a structure than are linear procedures. However, it is not exact, and cannot accurately account for changes in dynamic response as the structure degrades in stiffness or account for higher mode effects. When the NSP is utilized on a structure that has significant higher mode response, the LDP is also employed to verify the adequacy of the design. When this approach is taken, less restrictive criteria are permitted for the LDP, recognizing the significantly improved knowledge that is obtained by performing both analysis procedures. 

2.4.2.2 Nonlinear Dynamic Procedure 

The NDP shall be permitted for all structures. An analysis performed using the NDP shall be reviewed and approved by an independent third-party engineer with experience in seismic design and nonlinear procedures. 

2.4.3 Alternative Rational Analysis 

Nothing in this standard shall be interpreted as preventing the use of any approved alternative analysis procedure that is rational and based on fundamental principles of engineering mechanics and dynamics. Such alternative analyses shall not adopt the acceptance criteria contained in this standard without first determining their applicability. All projects using alternative rational analysis procedures shall be reviewed and approved by an independent third-party engineer with experience in seismic design.

2.4.4 Acceptance Criteria

2.4.4.1 General

The acceptability of force and deformation actions shall be evaluated for each component in accordance with the requirements of Section 3.4. Prior to selecting component acceptance criteria for use in Section 3.4, each component shall be classified as primary or secondary in accordance with Section 2.4.4.2, and each action shall be classified as deformation-controlled (ductile) or force-controlled (nonductile) in accordance with Section 2.4.4.3. Component strengths, material properties, and component capacities shall be determined in accordance with Sections 2.4.4.4, 2.4.4.5, and 2.4.4.6, respectively. Component acceptance criteria not presented in this standard shall be determined by qualification testing in accordance with Section 2.8.

The rehabilitated building shall be provided with at least one continuous load path to transfer seismic forces, induced by ground motion in any direction, from the point of application to the final point of resistance. All primary and secondary components shall be capable of resisting force and deformation actions within the applicable acceptance criteria of the selected performance level.

C2.4.4.2 Primary and Secondary Elements and Components

In a typical building, nearly all elements, including many nonstructural components, will contribute to the building's overall stiffness, mass, and damping, and consequently its response to earthquake ground motion. However, not all of these elements are critical to the ability of the structure to resist collapse when subjected to strong ground shaking. The secondary designation typically will be used when a component or element does not contribute significantly or reliably in resisting earthquake effects because of low lateral stiffness, strength, or deformation capacity.

For example, exterior cladding and interior partitions can add substantial initial stiffness to a structure, yet this stiffness is not typically considered in the design of new buildings because the lateral strength of these elements is often small. Similarly, the interaction of floor framing systems and columns in shear wall buildings can add some stiffness, although designers typically neglect such stiffness when proportioning the building's shear walls.

The concept of primary and secondary elements permits the engineer to differentiate between the performance required of elements that are critical to the building's ability to resist collapse and of those that are not. For a given performance level, acceptance criteria for primary elements and components will typically be more restrictive than those for secondary elements and components.

Use of the secondary classification will allow certain components to experience greater damage and larger displacements than would otherwise be permitted for primary elements, as explained below. 

1. Although damage to the primary elements and some degradation of their stiffness may be permitted to occur, the overall function of these elements in resisting structural collapse should not be compromised.

2. For some structural performance levels, substantial degradation of the lateral-force-resisting stiffness and strength of secondary elements and components is permissible. However, the ability of these secondary elements and components to support gravity loads under the maximum induced deformations must be preserved.


Proceed to TECHNICAL COMMENTARY, PART 2

 

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