10NCEE
Tenth U.S. National Conference on Earthquake Engineering
Frontiers of Earthquake Engineering
July 21-25, 2014
Anchorage, Alaska
DEFINING RIGID VS. FLEXIBLE
NONSTRUCTURAL COMPONENTS
B. E. Kehoe1
ABSTRACT
Seismic design of nonstructural components using ASCE 7-10 considers the interaction between
the response of the nonstructural component and the response of the building by means of a
component amplification factor, ap, that accounts for the dynamic interaction between the
nonstructural component and the response of the building. ASCE 7-10 provides tables of
architectural, mechanical, and electrical components that specify values for ap. The values in the
tables are either 1.0 or 2.5 for components considered rigid or flexible, respectively. ASCE 7-10
provides a definition for determining whether a component is rigid based on the component's
period of vibration.
The tabulated values of nonstructural amplification factors may not adequately characterize the
actual seismic behavior of some nonstructural components since the values do not consider the
actual properties of the nonstructural components and the effect of actual support and bracing.
While ASCE 7-10 provides a formula for determining the actual period of mechanical and
electrical components, this formula is seldom used in actual practice. Determining the period of
vibration of a nonstructural component does not provide all of the information needed to assess
how a nonstructural component will respond during an earthquake since it does not consider the
predominant periods of vibration of the building.
The vibrational periods for some common nonstructural components are tabulated based on
considerations of material properties and dimensions. Data from component testing are also
summarized and compared to calculated values. The influence of support conditions are also
described. Recommendations for changes to building code requirements are presented.
1
Associate Principal, Wiss, Janney, Elstner Associates, Inc., Emeryville, CA 94608
Kehoe BE. Defining Rigid vs. Flexible Nonstructural Components. Proceedings of the 10th National Conference in
Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.
Defining Rigid vs. Flexible Nonstructural Components
B. E. Kehoe1
ABSTRACT
Seismic design of nonstructural components using ASCE 7-10 considers the interaction between
the response of the nonstructural component and the response of the building by means of a
component amplification factor, ap, that accounts for the dynamic interaction between the
nonstructural component and the response of the building. ASCE 7-10 provides tables of
architectural, mechanical, and electrical components that specify values for ap. The values in the
tables are either 1.0 or 2.5 for components considered rigid or flexible, respectively. ASCE 7-10
provides a definition for determining whether a component is rigid based on the component's
period of vibration.
The tabulated values of nonstructural amplification factors may not adequately characterize the
actual seismic behavior of some nonstructural components since the values do not consider the
actual properties of the nonstructural components and the effect of actual support and bracing.
While ASCE 7-10 provides a formula for determining the actual period of mechanical and
electrical components, this formula is seldom used in actual practice. Determining the period of
vibration of a nonstructural component does not provide all of the information needed to assess
how a nonstructural component will respond during an earthquake since it does not consider the
predominant periods of vibration of the building.
The vibrational periods for some common nonstructural components are tabulated based on
considerations of material properties and dimensions. Data from component testing are also
summarized and compared to calculated values. The influence of support conditions are also
described. Recommendations for changes to building code requirements are presented.
Introduction
The design of nonstructural components for seismic loading is required for buildings in most
areas of moderate to high seismicity. Most building codes incorporate nonstructural seismic
design provisions that are based on requirements in ASCE 7-10 Minimum Design Loads for
Buildings and Other Structures [1], or its predecessor documents. The design procedure in
ASCE 7-10 for nonstructural components prescribes a horizontal seismic force be calculated and
applied to the component. This calculated seismic force provides a simplification of the complex
interaction of the behavior of nonstructural components attached to a building.
The response of a nonstructural component to earthquake shaking of the building to
which it is attached depends in large part on whether the nonstructural component vibrates in
1
Associate Principal, Wiss, Janney, Elstner Associates, Inc., Emeryville, CA 94608
Kehoe BE. Defining Rigid vs. Flexible Nonstructural Components. Proceedings of the 10th National Conference in
Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.
resonance with the vibration of the building. If the component is attached to the building such
that it effectively responds in synch with the portion of the building to which it is attached and
does not vibrate independently of the building, the seismic forces on the nonstructural
component are equal to the product of the weight of the component times the building
acceleration at the point where the component is attached. This is considered to be a rigid
nonstructural component.
Many nonstructural components are either attached to the building in a manner that will
allow the component to vibrate independently of the building, or the component itself has
inherent flexibility that allows it to vibrate. If the nonstructural component can displace
independently of its point of attachment to the building, the vibration of the nonstructural
component may be amplified due to resonance with the building vibration, thus increasing the
seismic forces on the nonstructural component. This is considered to be a flexible or flexibly
mounted nonstructural component.
For many years, building codes in the United States have considered the differing
response of nonstructural components that are rigidly attached to the structure, and therefore
respond with the response of the building, and those components that are flexible or flexibly
supported and therefore may respond in resonance with the structure. The component frequency
that generally is used to distinguish between rigid and flexible behavior is 16.67 Hertz, which
corresponds to a component period of vibration of 0.06 seconds.
The period of vibration of a nonstructural component can be calculated using principals
of dynamics. ASCE 7-10 includes the following equation (Eq. 1) for calculating the period of
vibration of nonstructural components that can be considered as a single degree of freedom
system.
=2
(1)
Where:
Tp is the period of vibration of the component,
Wp is the weight of the nonstructural component,
Kp is the stiffness of the nonstructural component, and
g is the acceleration of gravity
The nonstructural component seismic design force equation prescribed by ASCE 7-10
(Eq. 2) includes a factor, ap, that accounts for the amplification due to resonance of flexible
nonstructural components attached to a building and provides a simplification for designers to
avoid the need to calculating the period of vibration of every nonstructural component.
=
(1 + 2 )
Where:
Fp is the design lateral seismic force on the nonstructural component,
SDS is the design spectral acceleration at short periods
(2)
Ip is the component importance factor
ap is the component response amplification factor
Rp is the component response factor
z is the height of attachment of the nonstructural component to the building, and
h is the height of the building.
For typical architectural, mechanical, and electrical components, ASCE 7-10 includes
tables listing typical nonstructural components and provides a value of ap for these typical
nonstructural components. For components considered rigid, the value of ap is prescribed as 1.0,
indicating that the component does not experience any dynamic amplification due to resonance
with the structure. For components considered flexible or flexibly mounted, the value of ap is
prescribed as 2.5 to account for potential dynamic amplification of the component.
Dynamic Behavior of Nonstructural Components
The actual behavior of nonstructural components within a building involves a complex
interaction of the nonstructural component and the building. Nonstructural components, even
ones that seem straightforward, can be complex and may not be represented as a single degree of
freedom system. For example, Notohardjono et. al. [2] performed finite element analyses and
shake table testing of a mainframe computer rack system to determine its vibration
characteristics, which varied depending the details of the construction of the frame and whether
the rack was populated with equipment. Their studies found that the frequency of vibration of the
frame can vary by nearly a factor of two depending on the amount of weight added to the frame
and whether the frame’s connections were reinforced. Testing of laboratory equipment benches
by Hutchinson and Chaudhuri [3] demonstrated that there are not only differences in the periods
of vibration of the tested benches in the two orthogonal directions but also that the benches
themselves have several characteristic periods of vibration. The vibrational characteristics of the
benches, or other support structure, can influence the characteristics of the components attached
to them.
While it would be ideal for the structural engineer designing anchorage for a
nonstructural component to know the component’s vibrational characteristics, this is seldom
done in practice for several reasons. Shake table testing of nonstructural components has become
more frequent; however the number of components tested on a shake table represents only a
small fraction of the number of components available. For many nonstructural components, there
is very little benefit gained from the knowledge of the component’s characteristics since the
anchorage of the component to the structure with four typical anchors would be more than
sufficient to resist the required lateral force regardless of the vibrational characteristics. For other
components, the vibrational characteristics are not available and the behavior is complex enough
that the effort required to obtain the vibrational characteristics, either by analysis or full scale
shake table testing, is not justified. Finally, if the anchorage is being designed by an engineer
other than the designer of the building, knowledge of the nonstructural component’s vibrational
characteristics would not affect the anchorage design since the vibrational characteristics of the
building are not available.
Building Code Limitations
The nonstructural design provisions in ASCE 7 include potentially conflicting requirements
regarding nonstructural components. ASCE 7 defines Component, Rigid as having a period of
vibration of less than or equal to 0.06 seconds [1] and Component, Flexible as having a period of
vibration greater than 0.06 seconds [1]. In addition, Section 13.2.4 requires that “The design and
evaluation of components, their supports, and their attachments shall consider their flexibility as
well as their strength.” Eq. 1 also provides a method for determining the period of vibration of a
component to be used to satisfy these requirements.
Eq. 1 however, is referenced only in the section of ASCE 7 that applies to mechanical
and electrical components, implying that this equation is not to be used for architectural
components. More importantly however, are the values of ap that are provided in Tables 13.5-1
and 13.6-1; however the values of ap provided for specific types of nonstructural components are
not directly related to the actual vibrational characteristics of the components. The values
prescribed in these tables relate only to the generic type of component without reference to the
component’s characteristics that may affect whether its behavior is rigid or flexible or the
specific method of attaching the component to the structure.
Although the footnotes in Tables 13.5-1 and 13.6-1 indicate that rigid components should
be assigned a value of ap equal to 1.0 and the value of ap cannot be taken as less than 1.0, there is
no explicit requirement that for components listed in the table, the component is required to be
assigned a value of ap that accounts for whether the component’s behavior, including that of its
support, is rigid or flexible. The values in these tables are based primarily on engineering
judgment, rather than on testing or analysis.
Table 13.5-1 in ASCE 7 indicates that all ceilings, regardless of their configuration
should be evaluated as rigid components with a value of ap equal to 1.0. Testing of gridded
ceiling systems by Reinhorn et. al. [4] has shown that the horizontal acceleration of the ceiling
grid is higher than that of the floor or roof system to which it is attached, indicating that some
amplification of response of the ceiling grid is occurring and thus the building code assumption
of ap of 1.0 seems to be unconservative. These tests also indicate that the period of vibration of
the ceiling system, as would be expected, varies depending on the weight of the ceiling system.
For each component listed in the tables in ASCE 7, there is a single value for ap, implying
that the behavior of the component would be the same in both orthogonal directions. For some
components, the lateral stiffness of the component would similar in each direction, such as a
ceiling or an exhaust stack. Other components however have substantially different vibrational
characteristics depending on the direction being considered. Walls, for example, are very stiff in
the in-plane direction while being more flexible in the out-of-plane direction. Cabinets and
shelving may also have different vibrational characteristics in each direction depending on the
horizontal dimensions and the type of bracing. Stairs are usually stiff in the direction of the
stringers, but long span stairs can be flexible in both orthogonal directions perpendicular to the
longitudinal direction of the stringers.
Wall Panel Example
Consider the case of a concrete wall panel in a building with a thickness of 5 inches and an
unsupported vertical span of 10 feet. The period of vibration in the out-of-plane direction of this
component, assuming it behaves as simply supported, is 0.014 seconds. Using the definition of
rigid nonstructural components in ASCE 7, this wall panel would be considered rigid and this
corresponds to the value of ap equal to 1.0 prescribed in Table 13.5-1.
If the wall panel has a vertical span of 16 feet and if one considers the effective stiffness
of the wall panel in the out-of-plane directionusing an effective stiffness of 0.3 times the gross
section, the period of vibration becomes 0.068 seconds This would no longer be considered a
rigid component and therefore should be considered as flexible and should be assigned a value of
ap equal to 2.5. ASCE 7 however does not prescribe dimensional limitations on the thickness or
span of a wall panel to be considered rigid and also does not define whether the stiffness used to
period of vibration should consider effective or gross stiffness properties.
Water Heater Example
Water heaters are listed in table 13.6-1 of ASCE 7 and are prescribed a value of ap equal to 1.0
implying that these are rigid components. Where water heaters are anchored directly to the
structure, this assumption is generally accurate. Consider however the case of a water heater that
is supported on a steel framed pedestal, 2 feet tall with four legs constructed of 3-inch steel
angles. For a water heater that weighs 400 pounds when filled with water (the approximate
weight of a 40 gallon water heater), the period of vibration of the system with the legs acting as
cantilevers is 0.073 seconds. This would be considered as a flexibly supported component and
should be assigned a value of ap equal to 2.5.
While it can be argued that a structural engineer should understand that placing a water
heater on a pedestal with cantilever legs should require an evaluation of the entire assembly to
assess the system’s overall vibrational characteristics, ASCE 7 provides little guidance for the
designer of the system, particularly for designers that are not experienced in structural dynamics
and the building code methodology to the requirements for nonstructural components who may
desire the simplification of choosing a value from a table rather than performing additional
calculations.
Effects of Building Response
In addition to a nonstructural component’s vibrational characteristics, the behavior of
nonstructural components is also dependent on the ratio of the component’s period of vibration
with those of the building to which it is attached. When the period vibration of a nonstructural
component is close to that of one of the significant periods of vibration of the building,
amplification due to resonance should be considered. Where the periods of the nonstructural
component and that of the building are not close, resonance need not be considered in the design
of the nonstructural component. This resonance effect is accounted for in ASCE/SEI 7-10 with
the ap factor being 2.5. This value of component amplification was suggested by Soong et al [5]
for the condition where the component period is similar to that of the period of the building.
Where the ratio of the component period to the building period varies by a factor of 2.0 (either
Tcomponent/Tstructure or Tstructure/Tcomponent) Soong et al proposed that there is no amplification of
component acceleration.
The amplification of nonstructural response due to resonance with the vibration of the
building should also consider multiple modes of vibration of the building. Most buildings have a
multiple periods of vibration and terefore a nonstructural component may respond in resonance
to any of the periods of vibration of the building. The periods of vibration of a building, for
example, may be substantially different in each orthogonal direction of the building due to
differences in the lateral force resisting systems. To consider the effects of the structural
response on the response of nonstructural components, floor response spectra can be generated to
describe the variation in response of nonstructural components at each floor level with the period
of vibration of the nonstructural component.
Figure 1 shows a floor response spectrum generated for the roof of a 12-story steel
moment-frame building subjected to the Newhall record of the 1994 Northridge earthquake from
a study by Kehoe and Hachem [6]. Note that the peaks in the spectrum correspond to the first
four modes of the building in the orthogonal direction of the building under consideration and
that the first mode period of 1.85 seconds does not produce the maximum spectral acceleration
for a component attached at the roof. The maximum spectral acceleration of 3.8 g occurs at a
period of 0.3 seconds, which is approximately the fourth significant mode of vibration. This
example, as well as other analyses, demonstrates that the response of nonstructural components
can be influenced by modes other than the fundamental modes of vibration of the building.
Acceleration (g)
4
Figure 1.
3
Mode 1
2
1
0
0
1
Tp (sec)
2
3
Floor response spectrum (assuming 5% damping) for the roof level of a 12-story steel
moment frame building subject to the Newhall record.
The actual effects of interaction of response of nonstructural components with those of
the building are seldom considered in practice for several reasons. The dynamic characteristics of
the building are generally not available to the engineers that are designing the nonstructural
components and their anchorages. The vibrational characteristics of the nonstructural
components may also not be known. In addition, the computation of floor response spectra is
tedious since it requires a response history analysis of the building and extraction of floor
response spectra at each floor level. However, a simplified procedure for determining floor
response spectra is presented in [6].
An Approach to Rationalization of Component Flexibility
It would be extremely difficult and time consuming to provide a detailed list of nonstructural
components in buildings along with the actual vibrational characteristics to provide the engineer
with the necessary information to characterize nonstructural components as rigid or flexible. A
practical approach however would be to provide limitations for some components that are
assumed to be rigid in tables 13.5-1 and 13.6-1 of ASCE 7. The limitations can be made on the
basis of dimensions or on the basis of calculated or tested component properties.
Tabulation of Limiting Values
There are common building components whose vibrational characteristics can be easily
approximated calculations using fundamentals of dynamics. For these components, tables can be
developed that provide values of nonstructural component periods to characterize the
components as rigid or flexible. Table 1 provides values for the maximum length between
supports of pipes for several typical types and sizes of pipes for which the pipe, when filled with
water, would be considered to behave rigidly. The values in the table have been adapted from
Seismic Design for Buildings developed for the Departments of the Army, the Navy, and the Air
Force [8]. The stiffness of these pipes is based on the assumption that the pipes are simply
supported. This table also assumes that the pipes behave as simply supported between lateral
bracing and are significantly more flexible than the lateral bracing.
Table 1.
Maximum length of piping between supports for the piping to have a period of
vibration less than 0.06 seconds.
Pipe
Diameter
(inches)
Lateral Support Spacing (feet)
Schedule 40
Schedule 80
Copper Tube
Type K
Copper Tube
Type L
1
7.1
7.1
5.5
5.2
1-1/2
8.2
8.5
6.3
6.0
2
9.3
9.3
7.1
7.1
2-1/2
10.1
10.4
7.9
7.7
3
11.2
11.5
8.5
8.2
4
12.6
12.9
9.9
9.6
6
15.1
15.3
11.8
11.5
Similarly, limitations on spans of interior nonstructural walls and exterior wall panels can
also be developed based on typical wall configurations. Table 2 provides values for maximum
span of several sizes of steel studs for a range of unit weights of wall. The values assume that the
studs are spaced at 16 inches and they ignore the contribution of the wall sheathing on the
stiffness.
Table 2.
Maximum height of steel stud walls with a period of vibration less than 0.06 seconds
Stud Size
Unbraced Wall Height (feet)
Wall Weight
= 8 psf
Wall Weight
= 10 psf
Wall Weight
= 12 psf
Wall Weight =
16 psf
350S162-43
7.7
7.3
6.9
6.5
362S137-54
8.0
7.6
7.2
6.7
400S137-43
8.0
7.6
7.3
6.8
400S162-54
8.8
8.3
7.9
7.4
600S137-43
10.2
9.7
9.3
8.6
600S162-54
11.1
10.5
10.0
* Stiffness of studs based on effective stiffness of 33ksi steel
9.3
Component Support Conditions
Nonstructural components can be attached, anchored, or braced to a structure in a variety of
ways. Where the component is directly attached to the structure, the vibrational response of the
component is dependent on the vibrational characteristics of the component. However, when the
nonstructural component is attached or braced to a structure, the response of the component can
be altered based on the stiffness characteristics of the anchorage or bracing structural system.
Current building code provisions, [1], provide little or no guidance on whether the effects of the
support system has been considered in the determination of the ap values in the building code and
what assumptions have been made regarding the support or bracing for the components
identified in the building code tables.
The assumption implicit in the building code is that the characterization of a component
as rigid or flexible with the assignment of a value of ap of 1.0 or 2.5, respectively, is that the
behavior is based on that of the component without consideration of the effects on the method
used to attach the component to the structure. Where a nonstructural component is attached to a
structure through a supporting structure, Eq. 1, should be used to assess whether the stiffness of
the supporting structure causes the nonstructural component to behave as a flexible component
rather than a rigid component. This effect of the support system on the overall behavior of the
nonstructural component had been explicitly required in previous building codes [9], which
treated both flexible components and flexibly supported components as requiring an
amplification to account for dynamic interaction.
Conclusions
The response of nonstructural components to seismic loads is well known to be affected by the
interaction of the vibrational response of the nonstructural component with that of the building to
which it is attached. Current building code provisions for the design of nonstructural components
attempts to consider this interaction with an amplification factor that varies depending on
whether the component is considered rigid - and thus not experiencing any dynamic
amplification - or flexible - and thus experiencing amplification due to resonance of the
nonstructural component with that of the building to which it is attached. This approach has
resulted in the development of tabulated values for an amplification factor, ap, which is based
primarily on judgment. This code approach provides a simplification for engineers unfamiliar
with structural dynamics, however, like many “black boxes”, the use of tabulated values to
choose whether a nonstructural component will behave as rigidly or flexibly, can lead to
inaccurate characterization of nonstructural components as rigid.
Ideally, the tabulated values for the amplification factors in the tables in the building code
should be based on testing or analysis. While shake table testing of nonstructural components has
become more prevalent, such testing is not practical for the majority of nonstructural components
with a building. Where such shake table testing has been performed, the results should be
tabulated and either incorporated into the building code or provided by the manufacturers of the
components. Analytical methods should also be used to establish limiting dimensional and
material property values for common nonstructural components that define rigid and flexible
behavior. Two such tables, for piping and steel stud walls, have been presented above as
examples of the use of simple analytical models can be used to provide guidance to engineers
designing these nonstructural components for seismic forces.
In addition to the dynamic properties of the component, the influence of the support
system should also be considered in characterizing a nonstructural component as rigid or
flexible. The term “flexibly mounted’ used in older building codes [9] has unfortunately been
lost from the current building code and as a result, the support conditions for nonstructural
components are seldom considered explicitly. The building code should include limitations on
the structural characteristics of the support structure for nonstructural components to be
considered rigid. Where those limitations are not met, the engineer should be required to
explicitly calculate the period of vibration of the nonstructural component, including the effect of
its support.
Although floor response spectra are known to demonstrate that dynamic amplification of
a nonstructural component varies depending on the characteristics of the component and that of
the building, explicit consideration of this effect is seldom justified. For critical structures
however, a more rigorous approach to calculating the interaction of nonstructural and structural
response may be warranted on a benefit-cost basis. Building code provisions should include a
methodology for evaluating floor response spectra and the dynamic amplification as a function
of the ratio of component period to the predominant periods of the building as suggested in [6].
Another consideration is the effect of nonlinear response of the structure on the response
of nonstructural components. Wieser et al [7] pointed out that the work of several researchers has
demonstrated that floor accelerations of a building are reduced when accounting for nonlinear
behavior of the building. While explicit consideration of nonlinear building behavior is difficult
to account for in building code provisions, one approach would be to use a level of earthquake
shaking that approximates the elastic limit of the building for the design of nonstructural
components rather than the use of an earthquake level that is expected to result in nonlinear
behavior of the building.
Although the seismic behavior of nonstructural components is complex, for the design of
most nonstructural components, a simplified approach is justified. As building codes for new
buildings, standards for design and evaluation of existing buildings, and other design criteria
evolve into more of a performance-based approach, the seismic design of the nonstructural
components requires a methodology that considers actual component behavior rather than
prescriptive code requirements. The approach described herein provides one step in the process
of a more rational understanding of the seismic behavior of nonstructural components.
References
1.
ASCE/SEI. ASCE/SEI 7-10 Minimum Design Loads for Buildings and Other Structures, American Society of
Civil Engineers, Virginia, 2010.
2.
Notohardjono B, Ecker R, Zheng, J, Torok J. Seismic Testing and Analysis of Main Frame Computer Structure
Proceedings of the ASCE/SEI Structures Congress 2012. American Society of Civil Engineers: Virginia, 2012.
3.
Hutchinson TC, Chaudhuri SR, Bench- and Self-Mounted Equipment and Contents: Shake Table Experiments,
Seminar on Seismic Design, ATC-29-2 Performance, and Retrofit of Nonstructural Components in Critical
Facilities, Applied Technology Council, California, 2003.
4.
Reinhorn AM, Ryu K, Maddoaloni G, MCEER-10-0004 Modeling and Seismic Evaluation of Nonstructural
Components: Testing Frame for Experimental Evaluation of Suspended Ceiling Systems, University at Buffalo,
State University of New York, June 30, 2010.
5.
Soong TT, Chen G, Wu Z, Zhang RH, Grigoriu M, NCEER-93-0003 Assessment of the 1991 NEHRP
Provisions for Nonstructural Components and Recommended Revisions, National Center for Earthquake
Engineering Research, University at Buffalo, State University of New York and Cornell University, March 1,
1993.
6.
Kehoe BE, Hachem M, Procedures for Estimating Floor Accelerations, ATC 29-2 Seminar on Seismic Design,
Performance, and Retrofit of Nonstructural Components in Critical Facilities, Applied Technology Council,
California, 2003.
7.
Wieser JD, Pekcan G, Zaghi AE, Itani AM, Maragakis E, MCEER-12-0008 Assessment of Floor Accelerations
in Yielding Buildings, University at Buffalo, State University of New York, October 5, 2012.
8.
Joint Departments of the Army, Navy, Air Force, TM 5-809-10/NAVFAC P-355/AFM 88-3 Seismic Design for
Buildings, 20 October 1992.
9.
International Conference of Building Officials, Uniform Building Code, Whittier, California, 1994.