What Is Performance-Based Design for Infrastructure?

Capacity curve for R/C building with characteristic performance levels. Building a) is ductile while b) is brittle.

Just as the Titanic taught us that we couldn’t build an unsinkable ship, history has proven that we cannot build indestructible buildings. As a result, current seismic building codes have an ultimate limit state (ULS) that focuses on collapse prevention, and a serviceability limit state (SLS) that focuses on displacement, drift limits, immediate occupancy and potential building repair.

“The main change is that, currently, all modern approaches combine the performance-based design with the displacement-based design and assessment,” said Gregory Penelis, civil engineer and managing director of Penelis Consulting Engineers S.A.

“So, in essence, when we refer to performance-based design we actually mean displacement-based design for seismic excitations,” Penelis explained. “Instead of defining a strength requirement for a structure, the displacement capacity of the structure is defined and specific performance levels are defined.”

Seismic excitation performance level matrix. Diagonal represents the basic objective post Vision 2.000 according to FEMA 2.73 – 274/1997.

The displacement capacity of the design is typically calculated using a capacity curve, aka pushover curve. Within this curve, the performance levels of the structure are defined as follows:

Level 1 - Fully operation: insignificant damage
Level 2 - Immediate occupancy: minimal damage, retains the majority stiffness and strength
Level 3 - Life safety: significant damage, substantial stiffness loss, margin of deformation before collapse
Level 4 - Collapse prevention: extreme damage, survivors within building at risk of collapse

Penelis explained that current codes must ensure that structures can withstand a seismic event with the likelihood of occurring once every 475 years to an ultimate limit state, ULS, and 72 years for a serviceability limit state, SLS. However, these limits are increased for sensitive buildings, such as hospitals and schools, or at the discretion of the structure’s owner.

Due to the size, complexity and cost of the buildings, physical testing can be inaccurate and impractical. Using simulation software like Scia Engineer, design teams are able to assess the survivability of their building designs.

However, assessing the performance of the building isn’t limited to earthquakes. Wind, snow, rain, floods and even sabotage/blasts have been assessed as load conditions in performance-based designs of infrastructure. Scia Engineer can assess many of these performances. However, Penelis noted that seismic activity is often the most extensive performance-based design analysis.

How Simulation Can Assess a Building’s Performance

Athens Opera House modeled in Scia Engineer with seismic isolation. Building designed by Renzo Piano.

The most common methods used to assess a building under seismic loads are:

Modal spectral elastic analysis, aka modal response spectrum analysis
Equivalent static elastic analysis, aka lateral force method of analysis
Equivalent static inelastic analysis, aka pushover (either point hinge or fibber analysis)
Time history (t-h) inelastic analysis

When dealing with linear analysis, “European codes use the modal response spectrum analysis while the American standards call for the use of the lateral force method of analysis,” noted Penelis. “This difference is significant as the two methods have very distinct advantages and disadvantages.”

Penelis explained that the modal response spectrum analysis can assess the dynamic behaviour of a building. The method locates the building’s modes of vibration and then inputs them into the lateral force calculation. This assessment will produce displacements, internal forces and stress. However, these results will be unsigned.

For the lateral force method, Penelis explained that fundamental modes are used to calculate the forces. The load and stress results from this method are signed.

“The sign makes the results more comprehensive and clear with regard to several aspects as the combination of dynamic and static load cases, the biaxial bending with axial load of columns, the integration of stresses of non-rectangular cross section walls and cores, etcetera,” said Penelis.

As for nonlinear analysis, Penelis notes the difference between the point hinge approach and the fiber model. The point hinge approach uses moment vs. slope diagrams (M-θ diagrams) and it is used in many different software offerings. However, the cores and shear walls cannot be modeled using 2D elements so this method requires the use of linear finite elements for 2D components. He noted that this can create unknowns with respect to connectivity and the M-θ diagrams.

“On the other hand, most structural engineers know that increased complexity in the FEA model is not always a benefit,” warned Penelis. “Often younger colleagues tend to exaggerate on the complexity, thus introducing unintentional errors or mistakes in the results.”

As an alternative, Penelis remarked that the fiber model method will create a more accurate solution for element plasticity. He said, “The method is also able to use more complex wall sections and cores as their plasticity is inherently inserted into the model of the element. This accuracy requires deep knowledge of material properties and their interface. Therefore, such a modelling approach can be extremely risky for practicing engineers not familiar with nonlinear analysis unless specific software is used to deals with these issues such as Scia Engineer.”

Scia Engineer, and many other software options, will also be able to perform both static linear and nonlinear analysis of the building design. In static nonlinear, the seismic activity is input into the simulation as increasing displacement steps. Both the fiber model and point hinge methods can solve this problem. However, the results will not be able to pin down the lateral load application points vertically and horizontally, or transform the force displacement curve into single degree of freedom (SDOF) capacity curves, which require additional mathematical manipulations.

The future might then be the dynamic t-h nonlinear analysis. Penelis noted that this analysis “is considered the most accurate and sophisticated analysis approach available, especially when the fiber approach is utilised.”

“It produces results which have taken into account the torsional effects and the seismic load distribution along the height inherently. And these displacement results do not require a transformation to an equivalent SDOF oscillator. However, this analysis is very sensitive to the selection of accellerograms (earthquake data), the concrete/rebar hysteresis, the distribution of masses, and the interpretation of the results on an element level,” said Penelis.

Modeling Building Performance in Scia Engineer

Athens National Library modeled in Scia Engineer with seismic isolation. Building designed by Renzo Piano.

It should be noted that almost any structural CAE software is able to perform an elastic analysis using either the lateral force method of analysis or the modal response spectrum analysis. This is also true of Scia Engineer.

Current practices, however, are based on plastic nonlinear analysis. To accommodate this, “most commercial software packages started to adopt the point hinge method,” noted Penelis.

“However, Scia Engineer decided to use the fiber element approach” he said. “By missing the point hinge analysis trend, Scia was able to get ahead of the curve with the fiber element approach. So in essence now Scia Engineer has a SeismoStruct engine that performs pushover analysis on the Scia Engineer Model and in the future will also perform t-h nonlinear analysis.”

“SeismoStruct,” Penelis added, “is one of the most reputable nonlinear structural analysis software used for academic purposes.”

Penelis also pointed out that this isn’t the first time that Scia Engineer has been ahead of the game. He said, “The user interface of Scia Engineer is very intuitive and based on modern CAD approaches. It uses a tree type menu for all the design parameters, and in such way it has been copied recently by the competition. The results are also accessed via a tree menu and are reported dynamically to a graphical environment and the engineering report.”

Unlike other industries that are bringing analysis forward into design, performance-based analysis is typically done after a building is designed according to code. However, Penelis noted that, thanks to the code, engineers rarely need to make a change to the design. Nonetheless, Scia Engineer allows users to create a 3D model from elastic designs and use all the seismic data and codes needed to assess the design. In fact, the program will automatically produce a pushover curve in two directions for various profiles. He noted that this makes the program easy to use to define the performance and determine the loading.

For more on Scia Engineer, follow this link.

Nemetschek Scia has sponsored this post. They have no editorial input to this post. All opinions are mine. —Shawn Wasserman

Dr.Gregory G. Penelis, MSc, DIC, Phd is the co-author of Concrete Buildings in Seismic Regions, by Taylor and Francis (CRC Press). He is the CEO of Penelis Consulting Engineers S.A., and has been involved in the design/review of more than 100 buildings throughout Europe and Middle East and software validations for Walter P Moore, Houston and HLW, New York. He has been involved in many research projects regarding the seismic assessment of listed and monumental buildings as well as urban nucleus. His team has developed the concrete and seismic design modules of Scia Engineer for the IBC.

He has been twice awarded the gold medal by the Patriarch of Alexandria and All Africa for his volunteer work. In addition to promoting BIM at the American Concrete Institute conference, he recently presented the innovative design approaches adopted for the largest ferrocement structure in the world, the Renzo Piano designed 330ftx330ft canopy of the new Athens Opera House, at the 2015 SEAOC Convention in Seattle.