SS - Seismic Design

A Good Example of How Material Ductility Impacts Lateral Structural Performance

How do buildings survive strong earthquakes without collapse?  That is a question that has puzzled expert structural designers and analysts for ages.  To begin to understand, however, the rigors involved with earthquakes... well, that is a simpler puzzle.  Let's elucidate that a little bit:

Above is the visual depiction of structural ductility. Ductility is the ability of a structure (or element of a structure) to withstand large inelastic deformations without significant loss of strength. It is equal to the inelastic deformation capacity of a structural member.

For a simple, elastic - perfectly plastic structure subject to monotonic loading, ductility can be quantified using the ductility factor, μ. In the definition of μ, Δyield is the displacement when the structure yields (i.e. when the structure has reached its plastic lateral capacity), and Δfailure is the displacement at which the structures begins to lose lateral load carrying capacity.

A basic concept of seismic-resistant design is the trade-off between strength and ductility. This concept is illustrated (in a highly simplified manner) by this slide.

The plot shows the relationship between lateral force and lateral displacement for a simple single-degree-of-freedom structure, with an elastic-perfectly plastic response. The plot can be viewed as the force-displacement response of the structure for a half-cycle of loading during an earthquake.

The solid line represents the response of a structure that remains elastic during the earthquake. The maximum lateral force experienced by the elastic structure is Helastic and the maximum displacement experienced by the structure is Δmax. Thus, if we wanted the structure to remain elastic during the earthquake, we would need to design our structure to remain elastic under a lateral load equal to Helastic.

Say we designed the structure to have a lateral strength of only 3/4*Helastic. If the structure sees the same earthquake as above (which will generate a force of Helastic in an elastic structure), the structure will yield when the lateral force reaches 3/4*Helastic. At this point, the lateral force on the structure can no longer increase. Rather, the effect of the earthquake on the structure beyond this point will be to impose inelastic displacement. That is, the earthquake will demand ductility of the structure rather than strength. The earthquake will continue to deform the structure in the inelastic range until the total displacement is about the same as for the elastic structure. Thus, a structure with a lateral strength less than Helastic can still survive the earthquake, as long as the structure can supply the needed inelastic deformation. i.e., can supply the needed ductility.

Similarly, we can design our structure with even lower levels of lateral strength, say 1/2 or 1/4 of the lateral force that an elastic structure would see. In each case, when the lateral strength of the structure ( 1/2*Helastic or 1/4*Helastic ) is reached, the structure will be incapable of resisting any additional lateral force. As before, the effect of the earthquake beyond this point will be to impose additional displacement upon the structure, rather than additional force. In each case, the maximum displacement will be about same as for the structure that remains elastic. That is, regardless of the structure's lateral strength, Δmax will be approximately the same.

Remnants of the San Francisco Earthquake in 1906

Some observations on seismic response......
• A structure can be designed with a lateral strength significantly less than that which will be seen by an elastic structure in an earthquake. However, to survive the earthquake without collapse, the structure must supply ductility. In the plot, ductility (inelastic deformation capacity) is represented by the horizontal dotted lines).
• As illustrated by the plot, the lower the lateral strength of the structure, the greater will be the required ductility. Thus, in seismic design, we can trade strength for ductility. We can give our structure a high lateral strength, in which case we need to provide little ductility. Alternatively, we can give our structure very low lateral strength (by designing for very low lateral forces), but then we must detail our structure to supply high levels of ductility. Building codes permit us (within a limited extent) to make this trade off between strength and ductility.
• Ductility means damage. That is, when we use ductility to survive an earthquake, we have to expect damage. For a structure that is designed to yield in an earthquake (the usual case), the maximum lateral force that the structure will see during the earthquake is defined by the structure's own lateral strength. In building codes, the Amplified Seismic Load is intended to provide a rough estimate of a structure's lateral strength, and therefore is intended to provide an estimate of the maximum lateral force that can be experienced by a structure in an earthquake. (The Amplified Seismic Load will be discussed in more detail later).
• Code specified seismic lateral forces are generally much smaller than would be required for the structure to remain elastic. That is, they are usually much less than Helastic. Thus, a typical code based design uses ductility to survive an earthquake. In this sense, the code specified seismic lateral forces do not represent the actual lateral force that an earthquake would generate in an elastic structure. Thus, in cases where code specified wind forces are greater than code specified earthquake forces, it is still necessary to provide ductility. Even though the lateral strength of the structure will be larger as a result of the fact that "wind controls," the resulting lateral strength of the structure is still likely well below Helastic, and therefore ductility will be needed. Thus, even when code specified wind forces are larger than code specified earthquake forces, ductile detailing requirements in building codes must still be satisfied.

So to recap, structures must have adequate strength and ductility to resist earthquakes.  Strength is not the only important determinant of stability and impact resistance.  So the construction of heavier structures with redundancies (multiple ways of transferring load to a foundation) does not necessarily infer a wise and conservative decision by a structural designer.  And oftentimes, if these structures are swayed fiercely by lateral forces, it can quickly become a highly unwise or possibly even regretful decision.  So to all designers out there who value strength performance over stiffness: be wise.

Note above: The concept that Δmax remains the same, regardless of the lateral strength of the structure, and regardless of whether the structure responds elastically or inelastically, is a simplification. It is a useful simplification to understand the basic concept of trading strength for ductility in seismic design.

PPP Notes - Seismic Design

SEISMIC FOUNDATION ISSUES

 (These notes are compiled from AGS)

SEISMIC DESIGN

 

• According to the theory of plate tectonics, the Earth’s crust is divided into constantly moving plates.
• Earthquakes occur when, as a result of slowly accumulating pressure, the ground slips abruptly along a geological fault plane or on near a plate boundary.
• The resulting waves of vibration within the Earth create ground motions at the surface, which, in turn, induce movement within buildings.
• The frequency, magnitude, and duration of the ground motion; physical characteristics of the building; and geology of a site determine how these forces affect a building.

 

DESIGN JUDGMENT

 

• During a seismic event, buildings designed to the minimum levels required by model codes often sustain damage, even significant structural damage.
• Early discussions with an owner should explore the need to limit properly loss in an earthquake, and the desirability of attempting to ensure continued building operation immediately afterward.
• To achieve these results, it may be necessary to make design decisions that are more carefully tuned to the seismic conditions of a site than the code requires.
• The relationship between the period of ground motion and the period of building motion is of great importance to building design.
• Fundamental periods of motion in structures range from 0.1 seconds for a one-story building to 4.0 seconds or more for a high-rise building.
• Ground generally vibrates for a period of between 0.5 and 1.0 second.  If the period of ground motion and the natural period of motion in a building coincide, the building may resonate, and the loads will be increased.
• Theoretically, one part of the seismic design solution is to “tune” the building so that its own period of motion falls outside the estimated range of ground motion frequency.
• In practice, this tuning is very seldom carried out.
• Rather, design professionals rely on increased load effects required by the applicable code to take care of the problem.

 

SEISMIC CODES

 

• The building code adopted in most jurisdictions in the United States is International Building Code (IBC).
• There are some significant changes to the seismic forces determined by this code compared to seismic forces determined by previous building codes.
• The IBC 2006 code seismic provisions are designed around a level of earthquake that is expected to be exceeded only 2 percent of the time in the next 50 years.
• The level of seismic design for most structures, per the IBC, is based on a “collapse protection” strategy (commonly referred to as a “life safety” level), which assumes that there may be significant damage to the structure up to the point of collapse but that the structure does not collapse.
• The structural engineer will design a lateral force-resisting structural assembly to resist a design-level earthquake. 
• These designs are developed from detailed maps that indicate the ground spectral accelerations of buildings, which are based upon known past seismic events, in combination with probability studies.
• These maps typically include known fault locations, which help to determine the distance of the building from any known fault.
• The ground accelerations can typically be found down to the county level in the United States. 
• The geotechnical engineer works with the design team to develop the site coefficient, which is dependent on the local soil layers and depths.
• The following information is based on the requirements in the IBC 2006 Building Code, which in turn is based on the 2000 National Earthquake Hazards Reduction Program (NEHRP). 
• Detached one- and two-family dwellings are exempt from seismic regulations in areas other than those with high seismicity.

 

TERMS

 

• The seismic community has an extensive set of terms that describe common conditions in the field.
• Here is a short list of these terms and their definitions:
• Base Shear (static analysis): Calculated total shear force acting at the base of a structure, used in codes as a static representation of lateral earthquake forces.  Also referred to as equivalent lateral loads.
• Design Earthquake: Earthquake ground motion for which a building is designed.  This is typically about two-thirds of the maximum considered earthquake (MCE) when designing per the IBC codes.
• Drift and Story Drift: Lateral deflection of a building or structure.  Story drift is the relative movement between adjacent floors.
• Ductility: The ability of a structural frame to bend, but not break.  Ductility is a major factor in establishing the ability of a building to withstand large earthquakes.  Ductile materials (steel, in particular) fail only after permanent deformation has taken place.  Good ductility requires special detailing of the joints.
• Dynamic Analysis: A structural analysis based on the vibration motion of a building.  Dynamic analysis is time-consuming, and normally reserved for complex project.
• Forces, In-Plane: Forces exerted parallel to a wall or frame.
• Forces, Out-of-Plane: Forces exerted perpendicular to a wall or frame.
• Maximum Considered Earthquake (MCE): The greatest ground-shaking expected to occur during an earthquake at a site.  These values are somewhat higher than those of the design earthquake, particularly in areas where seismic events are very infrequent.  The code maps are based on earthquakes of this magnitude.
• Reentrant Corner: The inside building corner of an L-, H-, X-, or T-shaped building plan.

 

ESTABLISHING SEISMIC FORCES

 

• The equivalent lateral force procedure is the most common method used to determine seismic design forces.
• In the ELFP, the seismic load, V (base shear), is determined by multiplying the weight of the building by a factor of Cs (V=CsW). 
• The value of Cs depends on the size of the design earthquake, the type of soil, the period of the building, the importance of the building, and the response-modification factor (a variable that accounts for different levels of ductility for different types of later force-resisting systems used).
• This force is applied at the base of the structure then is distributed vertically throughout the building according to the stiffness of the lateral elements of the structure (for a “rigid” diaphragm), or according to tributary width of lateral elements of the structure (for a “flexible” diaphragm).

 

DESIGN AND RESISTING SEISMIC FORCES/FOUNDATIONS ISSUES

 

• A design that resists seismic forces for a structure makes use of the lateral system’' ductility.
• Ductile lateral systems are designed to deflect more under seismic loading than what would be expected from something such as wind loading.
• This allows for the use of smaller effective seismic design forces and more reasonably sized members.
• It’s important, however, that the overall design still be capable of handling the expected deflections.
• Story drifts that are too large can result in secondary forces and stresses for which the structure was not designed, as well as increase the damage to the interior and exterior building components, and hinder the means of egress from the building.
• Typical means of resisting these forces include the use of moment frames, shear walls, and braced frames.
• Each of these types of lateral systems can be made up of one of the main structural materials (such as steel or reinforced concrete moment frames; masonry, wood, or reinforced concrete shear walls; or steel or reinforced concrete-braced frames). 
• The building configuration and design parameters will have a major effect on which system to choose and, subsequently, the lateral system chosen will have a major impact on the foundations required to resist the loads.
• Moment frames typically are distributed more evenly over the building footprint and have little or no uplift.
• Moment frames also generally have large base moments that can be difficult to resist. 
• In addition, moment frames will tend to have greater lateral deflections than other stiffer systems (such as shear walls or braced frames).
• Concrete shear walls and steel-braced frames are more localized, not only concentrating lateral shear at the base but also having a high potential for net uplift forces to be resisted.
• These forces are difficult to resist with some foundation systems and should be reviewed extensively before selecting the lateral load-resisting system.
• Tall, narrow structures tend to have overturning issues before they will face sliding issues.
• Conversely, short structures face sliding problems rather than overturning problems.
• Seismic motion rocks the building, increasing overturning loads, and can act in any direction.
• Thus, resistance to overturning is best achieved at a building’s perimeter, rather than at its core.
• Building foundations must be designed to resist the lateral forces transmitted through the earth and the forces transmitted from the lateral load-resisting system to the earth.
• In general, softer soils amplify seismic motion.

 

FOUNDATION STRATEGIES FOR SEISMIC DESIGN

 

UPLIFT

 

• Braced buildings typically end up with high-tension loads at the foundations. 
• Shallow foundations are difficult to design with high-tension loads.
• Some strategies are available to resist these uplift forces:
• Increase the dead load by removing adjacent columns, increasing the tributary area.
• Deepen the footing, increasing the soil load.
• Increase the footing dimensions, to increase the soil and concrete loads.
• Decrease column spacing, to decrease the brace forces.
• Change the foundation type (typically, to a deep foundation that can resist the uplift more effectively).

 

SHEAR

 

• Braces and shear walls tend to collect the lateral forces and concentrate the loads in a few locations.
• Shallow and deep foundations have limited lateral load-resisting capability.
• By combining several foundations together, it is possible to effectively increase the lateral load resistance.
• The concrete tie beams are typically designed to distribute the lateral loads through tension or compression of the beam.