PERFORM-3D Latest Version: V9.0.0

#### OVERVIEW

Traditionally, earthquake-resistant design has been strength-based, using linear elastic analysis. Since inelastic behavior is usually allowed for strong earthquakes, this is not entirely rational. Strength-based design considers inelastic behavior only implicitly. Displacement-based (or deformation-based) design considers inelastic behavior explicitly, using nonlinear inelastic analysis. Displacement-based design recognizes that in a strong earthquake, inelastic deformation (or ductility) can be more important than strength. PERFORM-3D allows you to use displacement-based design.

Procedures for displacement-based design using inelastic analysis are specified in ASCE 41, “Seismic Rehabilitation of Existing Buildings”. ASCE 41 applies to the retrofit of existing buildings, but the procedures can be applied to the design of new buildings. PERFORM-3D implements the procedures in ASCE 41. However, PERFORM-3D is a general tool for implementing displacement-based design. It is not limited to ASCE 41.

The response of a structure to earthquake ground motion, whether elastic or inelastic, is highly uncertain. Capacity design is a rational way to improve the response of a structure in a strong earthquake, by deliberately controlling its behavior. Capacity design controls the inelastic behavior of a structure, by allowing inelastic behavior only in locations chosen by the designer. In these locations the structural components are designed to be ductile. The rest of the structure remains essentially elastic, and can be less ductile. Controlling the behavior in this way improves reliability, reduces the amount of damage, and can reduce construction costs. PERFORM-3D allows you to apply capacity design principles.

PERFORM-3D has powerful capabilities for inelastic analysis, but it is not intended for general purpose nonlinear analysis. If you have no idea how your structure will behave when it becomes inelastic in a strong earthquake, PERFORM-3D can probably help you to identify the weak points, and hence can guide you in improving the design. However, PERFORM-3D is not intended for “design by analysis”, where the engineer expects the analysis to determine exactly how a structure will behave. PERFORM-3D is a powerful tool for implementing displacement-based design and capacity design. It will help you to produce better designs, but it will not do the engineering for you.

#### BUILT-IN STRUCTURAL COMPONENTS

#### Element Types:

- Frame element for beams, columns and braces.
- Wall element for shear walls.
- Slab element for floors.
- Bar elements (with only axial stiffness) of various types.
- Buckling restrained brace.
- Gap elements.
- Seismic isolators of rubber and friction pendulum type.
- Fluid damper, with nonlinear relationship between force and deformation rate.
- Connection panel zone, to model shear deformation in beam-to-column connections.
- Infill panel, with only shear strength and stiffness.
- Deformation “gages” of various types. These elements have no stiffness. They are used for calculating deformations, and hence deformation demand/capacity ratios.

#### Components:

In PERFORM-3D, most elements are made up of a number of components. For example, a beam element might consist of several components.

#### Component Properties:

All inelastic components have essentially the same force-deformation relationship. This is a basic tri-linear relationship, with optional strength loss that can be captured in PERFORM-3D.

#### Hysteresis Loops:

The hysteresis loop for an inelastic component can be varied to account for stiffness degradation. The loop can be plotted to check that it has the expected shape.

#### Demand/Capacity Ratios:

PERFORM-3D includes a large number of components, both inelastic and elastic. During an analysis, D/C ratios are calculated as follows:

- Deformation D/C ratios are calculated for inelastic components.
- Hence, components that are allowed to become inelastic can be checked to make sure they have sufficient ductility.
- Strength D/C ratios are calculated for elastic components.
- Hence, components that are required to remain essentially elastic can be checked to make sure they have sufficient strength.

#### Deformation Capacities:

Deformation capacities can be specified for inelastic components, for calculating deformation demand/capacity ratios. Deformation capacities can be specified for up to 5 performance levels.

The number of components with D/C ratios can be very large. To simplify decision making, components that have similar D/C measures can be grouped into Limit States. An example D/C measure is the concrete tension strain in a shear wall. Each limit state has a “usage ratio”, which is the maximum D/C ratio for any component in the limit state. For a structure to satisfy the performance requirements, the usage ratios for all limit states should not exceed 1.0.

#### Frame Structures:

Simple frame structures consist of beam and column elements. Beam and column elements can be made up of a variety of components, and may be elastic or inelastic. P-delta effects can be considered or ignored.

#### Shear Wall Structures:

Shear walls are modeled using plane wall elements. Complex shear cores are made up of plane elements. Wall elements can have inelastic behavior in bending and shear. Coupling beams are usually modeled using beam elements, with inelastic behavior in either bending or shear.

#### ANALYSIS

#### Types:

PERFORM-3D can run the following analysis types:

- Mode shapes, periods, and effective mass factors.
- Gravity load.
- Static push-over.

- Response history for earthquake ground motion.
- Response history for dynamic forces.
- Response spectrum analysis (with limitations).

The nonlinear analysis strategies are very reliable, even when inelastic components have negative stiffness, and when P-delta effects cause the structure to become unstable.

#### Sequences:

The most common analysis sequence is:

- Apply gravity loads.
- Run one or more static push-over analyses, with constant gravity load.
- Run one or more earthquake response history analyses, with constant gravity load.
- This is a “standard” sequence. A “general” sequence can also be applied, for example cyclic push-over as follows:
- Apply gravity loads.
- Add push-over loads to a specified drift in the positive direction.
- Add push-over loads to a specified drift in the negative direction.
- Etc., progressively increasing the specified drift in each direction.

#### Series:

An “analysis series” is a series of analyses, with a standard or general analysis sequence. For each analysis series, the following structure properties can be changed:

- The mass distribution and magnitude. This can affect static push-over analysis as well as dynamic response history analysis.
- The amount and type of damping for dynamic response history analysis.
- The strengths and stiffnesses of the structural components (within certain limits).

This allows you to change the structural properties without setting up a new analysis model.

#### BEHAVIOUR CHECK TOOLS

PERFORM-3D includes a number of tools for processing the analysis results. One set of tools allows you to study the behavior of a structure, and to check that the analysis look reasonable. These tools are as follows:

- Deflected shapes. These can be animated, for both static push-over and dynamic response history analysis.
- Time histories of many response quantities, including node displacements, velocities and accelerations; element and component forces and deformations; and forces on “structure sections” that cut through all or parts of the structure.
- Hysteresis loops for inelastic components.
- Moment and shear diagrams for beams, columns, and shear walls. These can be animated.
- Energy balance, showing strain energy, kinetic energy, inelastic work, and damping energy. This includes a comparison of external and internal work, which provides a good indication of the numerical accuracy of the analysis.

These tools are not directly useful for making design decisions. For this, see the next section, Performance Assessment.

#### PERFORMANCE ASSESSMENT TOOLS

#### Performance Assessment Tools:

The results of an analysis are useful only if they are presented in a way that supports decision making for design. PERFORM-3D includes powerful tools that assess the performance of a structure, and hence support design. These tools are as follows:

- Target displacement calculation for push-over analysis. A number of methods can be used, including those in ASCE 41 and FEMA 440.
- Usage ratio plots for single load cases. As the drift increases in a push-over analysis, or time increases in a response history analysis, the usage ratios for the limit states progressively increase. A usage ratio plot shows how the usage ratios vary for user-selected groups of limit states.
- Usage ratio envelopes for load combinations. It is common practice to run response history analyses for several earthquakes (often 7 or more), and to assess performance based the mean values of the usage ratios. The tool implements this procedure.
- Deflected shapes with color coding based on D/C ratio. These can be used to identify “hot spots” where the components are most heavily deformed.

#### Processing of Results:

- The PERFORM-3D analysis results are saved in a number of results files, each file containing results of a specific type (for example, node displacements).
- If the performance assessment tools in PERFORM-3D do not meet your needs, you can access the results files, and process the results in any way that you choose.
- You must, of course, write computer code to do the processing. You can use almost any programming language.

#### IMPORT AND EXPORT

Models can be imported to PERFORM-3D from SAP2000 or ETABS. These are partial models, consisting mainly of nodes, elements, and loads. Component properties are not included, because these properties are different in PERFORM-3D than in SAP2000 and ETABS.