Department of Civil Engineering, N-W.F.P UET Peshawar A Monograph on Earthquake Resistant Design of R C Structures Prof. Dr. Qaisar Ali (http://www.eec.edu.pk) Page 1 of 56 Earthquake Resistant Design Of Reinforced Concrete Structures By Professor Dr. Qaisar Ali Earthquake Engineering Center, Civil Engineering Department N-W.F.P University of Engineering and Technology Peshawar, Pakistan.
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Department of Civil Engineering, N-W.F.P UET Peshawar A Monograph on Earthquake Resistant Design of R C Structures
Prof. Dr. Qaisar Ali (http://www.eec.edu.pk) Page 1 of 56
Earthquake Resistant Design
Of
Reinforced Concrete Structures
By
Professor Dr. Qaisar Ali
Earthquake Engineering Center, Civil Engineering Department
N-W.F.P University of Engineering and Technology
Peshawar, Pakistan.
Department of Civil Engineering, N-W.F.P UET Peshawar A Monograph on Earthquake Resistant Design of R C Structures
Prof. Dr. Qaisar Ali (http://www.eec.edu.pk) Page 2 of 56
1. Introduction:
Earthquake results from the sudden movement of the tectonic plates in the earth’s
crust, figure 01. The movement takes place at the fault lines, and the energy released
is transmitted through the earth in the form of waves, figure 02, that cause ground
motion many miles from the epicentre, figure 03. Regions adjacent to active fault
lines are the most prone to experience earthquakes. As experienced by structures,
earthquakes consist of random horizontal and vertical movements of the earth’s
surface. As the ground moves, inertia tends to keep structures in place, figures 04,
resulting in the imposition of displacements and forces that can have catastrophic
results, figure 05. The purpose of seismic design is to proportion structures so that
they can withstand the displacements and the forces induced by the ground motion.
Figure 01: Earth’s tectonic plates.
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Figure 02: Motions caused by body and surface waves.
Figure 03: Epicentre and focus.
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Figure 04: Effect of inertia in a building when shaken at its base.
Figure 05: Inertia force and relative motion within a building.
Figure 06: Arrival of seismic waves at a site.
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Historically, seismic design has emphasized the effects of horizontal ground motion,
because the horizontal components of an earthquake usually exceed the vertical
component and because structures are usually much stiffer and stronger in response to
vertical loads than they are in response to horizontal loads. Experience has shown that
the horizontal components are the most destructive.
For structural design, the intensity of an earthquake is usually described in terms of
the ground acceleration as a fraction of the acceleration of gravity, i.e., 0.1, 0.2, or
0.3g. Although peak acceleration is an important design parameter, the frequency
characteristics and duration of an earthquake are also important; the closer the
frequency of the earthquake motion is to the natural frequency of a structure and the
longer the duration of the earthquake, the greater the potential for damage.
Based on elastic behaviour, structures subjected to a major earthquake would be
required to undergo large displacements. However, recent design practices require
that structures be designed for only a fraction of the forces associated with those
displacements. The relatively low design forces are justified by the observations that
the buildings designed for low forces have behaved satisfactorily and that structures
dissipate significant energy as the material yield and behave in-elastically.
This nonlinear behaviour, however, usually translates into increased displacements,
which may result in major non-structural damage and require significant ductility.
Displacements may also be of such a magnitude that the strength of the structure is
affected by stability considerations.
Designers of structures that may be subjected to earthquakes, therefore, are faced with
a choice: (a) providing adequate stiffness and strength to limit the response of
structures to the elastic range or (b) providing lower-strength structures, with
presumably lower initial costs, that have the ability to withstand large inelastic
deformations while maintaining their load-carrying capability.
2. Structural Response:
The safety of a structure subjected to seismic loading rests on the designer’s
understanding of the response of the structure to ground motion. For many years, the
goal of earthquake design has been to construct buildings that will withstand
Department of Civil Engineering, N-W.F.P UET Peshawar A Monograph on Earthquake Resistant Design of R C Structures
Prof. Dr. Qaisar Ali (http://www.eec.edu.pk) Page 6 of 56
0
1
2
3
Displacement(a) (b) (c)
Stor
ey H
eigh
t
moderate earthquakes without damage and severe earthquakes without collapse.
Building codes have undergone regular modification as major earthquakes have
exposed weaknesses in existing design criteria.
Design for earthquakes differs from design for gravity and wind loads in the
relatively greater sensitivity of earthquake-induced forces to the geometry of the
structure. Without careful design, forces and displacements can be concentrated in
portions of a structure that are not capable of providing adequate strength or ductility.
Steps to strengthen a member for one type of loading may actually increase the forces
in the member and change the mode of failure from ductile to brittle.
a. Structural consideration:
The closer the frequency of the ground motion is to one of the natural frequencies
of a structure, the greater the likelihood of the structure experiencing resonance,
resulting in an increase in both displacement and damage. Therefore, earthquake
response depends strongly on the geometric properties of a structure, especially
height. Tall buildings respond more strongly to long-period (low frequency)
ground motion, while short buildings respond more strongly to short period (high
frequency) ground motion. Figure 07 shows the shapes for the principal modes of
vibration of a three storey frame structure. The relative contribution of each mode
to the lateral displacement of the structure depends on the frequency
characteristics of the ground motion.
Figure 07: Modal shapes for a three storey building (a) first mode; (b) second mode;
(c) third mode.
Department of Civil Engineering, N-W.F.P UET Peshawar A Monograph on Earthquake Resistant Design of R C Structures
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The first mode, figure 07a, usually provides the greatest contribution to lateral
displacement. The taller a structure, the more susceptible it is to the effects of
higher modes of vibration, which are generally additive to the effects of the lower
modes and tend to have the greatest influence on the upper stories. Under any
circumstances, the longer the duration of an earthquake, the greater the potential
of damage.
The configuration of a structure also has a major effect on its response to an
earthquake. Structures with a discontinuity in stiffness or geometry can be
subjected to undesirably high displacements or forces. For example, the
discontinuance of shear walls, infill walls or even cladding at a particular story
level, will have the result of concentrating the displacement in the open, or “soft,”
story, figure 08, 09. The high displacement will, in turn, require a large amount of
ductility if the structure is not to fail. Such a design is not recommended, and the
stiffening members should be continued to the foundation.
Figure 08: Upper storeys of open ground storey move together as single block.
Department of Civil Engineering, N-W.F.P UET Peshawar A Monograph on Earthquake Resistant Design of R C Structures
Prof. Dr. Qaisar Ali (http://www.eec.edu.pk) Page 8 of 56
Figure 09: Ground storey of reinforced concrete building left open to facilitate
parking.
Similarly, any kind of horizontal or vertical mass or stiffness irregularity in
structures places them in undesirable position against earthquake forces.
Buildings with simple geometry in plan, figure 10a, perform well during strong
earthquakes. Buildings with re-entrant corners, like those U, V, H and + shaped in
plan, figure 10b, have sustained significant damage in past earthquakes. Many
times, the bad effects of these interior corners in the plan of buildings are avoided
by making the buildings in two parts. For example, an L-shaped plan can be
broken up into two rectangular plan shapes using a separation joint at the junction,
figure 10c.
Figure 11 shows buildings with one of their sizes much larger or much smaller
than the other two. Such shapes do not perform well during the earthquakes.
Buildings with vertical setbacks (like the hotel buildings with a few storeys wider
than the rest) cause a sudden jump in earthquake forces at the level of
discontinuity, figure 12.
Within a structure, stiffer members tend to pick up a greater portion of the load.
When a frame is combined with a shear wall, this can have the positive effect of
reducing the displacements of the structure and decreasing both structural and
non-structural damage. However, when the effects of higher stiffness members,
Department of Civil Engineering, N-W.F.P UET Peshawar A Monograph on Earthquake Resistant Design of R C Structures
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such as masonry infill walls, are not considered in the design, unexpected and
often undesirable results can occur.
Finally, any discussion of structural considerations would be incomplete without
emphasizing the need to provide adequate separation between structures. Lateral
displacements can result in structures coming in contact during an earthquake,
resulting in major damage due to hammering, figure 13. Spacing requirements to
ensure that adjacent structures do not come into contact as a result of earthquake
induced motion are specified in relevant codes.
Figure 10: Simple plan shape buildings do well during earthquake.
Figure 11: Buildings with one of their overall sizes much larger or much smaller
than the other two.
Department of Civil Engineering, N-W.F.P UET Peshawar A Monograph on Earthquake Resistant Design of R C Structures
Prof. Dr. Qaisar Ali (http://www.eec.edu.pk) Page 10 of 56
Figure 12: Buildings with setbacks.
Figure 13: Hammering or Pounding.
b. Member Considerations:
Members designed for seismic loading must perform in a ductile fashion and
dissipate energy in a manner that does not compromise the strength of the
structure. Both the overall design and the structural details must be considered to
meet this goal.
The principal method of ensuring ductility in members subject to shear and
bending is to provide confinement for the concrete. This is accomplished through
the use of closed hoops or spiral reinforcement, which enclose the core of the
beams and columns. When confinement is provided, beams and columns can
undergo nonlinear cyclic bending while maintaining their flexural strength and
Department of Civil Engineering, N-W.F.P UET Peshawar A Monograph on Earthquake Resistant Design of R C Structures
Prof. Dr. Qaisar Ali (http://www.eec.edu.pk) Page 11 of 56
M- M+
MC1
MC2
(a) (b)
without deteriorating due to diagonal tension cracking. The formation of ductile
hinges allows reinforced concrete frames to dissipate energy.
Successful seismic design of frames requires that the structures be proportioned
so that hinges occur at locations that least compromise strength. For a frame
undergoing lateral displacement, such as shown in figure 14a, the flexural
capacity of the members at a joint, figure 14b, should be such that the columns are
stronger than the beams. In this way, hinges will form in the beams rather than the
columns, minimizing the portion of the structure affected by nonlinear behaviour
and maintaining the overall vertical load capacity. For these reasons, the “weak
beam-strong column” approach is used to design reinforced concrete frames
In Pakistan, the design criteria for earthquake loading are based on design procedures
presented in chapter 5, division II of Building Code of Pakistan, seismic provision
2007 (BCP, SP 2007), which have been adopted from chapter 16, division II of UBC-
97 (Uniform Building Code), volume 2, attached for reference in Appendix A of this
document.
The total design seismic force imposed by an earthquake on the structure at its base is
referred to as base shear “V” in the UBC. The UBC-97 calculates the base shear from
Department of Civil Engineering, N-W.F.P UET Peshawar A Monograph on Earthquake Resistant Design of R C Structures
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the total structure weight and then appropriates the base shear in accordance with
dynamic theory. The design seismic force can be determined based on the UBC-97
static lateral force procedure [sec. 1630.2, UBC-97 or Sec. 5.30.2, BCP 2007] and/or
the dynamic lateral force procedure [sec. 1631, UBC-97 or sec. 5.31, BCP-2007].
The static lateral force procedures (section 1630 of the UBC-97) may be used for the
following structures:
1. All structures, regular or irregular, in Seismic Zone 1 and in Occupancy
Categories 4 and 5 in Seismic Zone 2.
2. Regular structures under 240 feet (73152 mm) in height with lateral force
resistance provided by systems listed in Table 16-N, except where section
1629.8.4, Item 4, applies.
3. Irregular structures not more than five stories or 65 feet (19812 mm) in height.
4. Structures having a flexible upper portion supported on a rigid lower portion
where both portions of the structure considered separately can be classified as
being regular, the average story stiffness of the lower portion is at least 10 times
the average story stiffness of the upper portion and the period of the entire
structure is not greater than 1.1 times the period of the upper portion considered
as a separate structure fixed at the base.
The dynamic lateral force procedure of section 1631 shall be used for all other
structures including the following:
1. Structures 240 feet (73152 mm) or more in height, except as permitted by Section
1629.8.3, Item 1.
2. Structures having a stiffness, weight or geometric vertical irregularity of Type 1, 2
or 3, as defined in Table 16-L, or structures having irregular features not
described in Table 16-L or 16-M, except as permitted by Section 1630.4.2.
3. Structures over five stories or 65 feet (19812 mm) in height in Seismic Zones 3
and 4 not having the same structural system throughout their height except as
permitted by Section 1630.4.2.
4. Structures, regular or irregular, located on Soil Profile Type SF, which have a
period greater than 0.7 second. The analysis shall include the effects of the soils at
the site and shall conform to Section 1631.2, Item 4.
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3.1. Static lateral force procedure:
The static procedure is also referred to as the equivalent static lateral force procedure.
UBC-97 sec. 1630.2 provides the provisions for determining base shear by static
lateral force procedure as follows:
The total design base shear in a given direction can be determined from the following
formula:
V = (CνI/RT) W
Where,
Cν = Seismic coefficient (Table 16-R of UBC-97 given below in Table 1 of
this document).
I = Seismic importance factor (Table 16-K of UBC-97 given in Appendix A)
R = numerical coefficient representative of inherent over strength and global
ductility capacity of lateral force-resisting systems (Table 16-N or 16-P
given in Appendix A of this document).
W = the total seismic dead load defined in Section 1630.1.1 as follows:
Seismic dead load, W, is the total dead load and applicable portions of other
loads listed below.
i) In storage and warehouse occupancies, a minimum of 25 percent of the
floor live load shall be applicable.
ii) Where a partition load is used in the floor design, a load of not less than 10
psf (0.48 kN/m2) shall be included.
iii) design snow loads of 30 psf (1.44 kN/m2) or less need not be included.
Where design snow loads exceed 30 psf (1.44 kN/m2), the design snow
load shall be included, but may be reduced up to 75 percent where
consideration of siting, configuration and load duration warrant when
approved by the building official.
iv) total weight of permanent equipment shall be included.
The total design base need not exceed the following:
V = (2.5CaI/R) W
Ca = Seismic coefficient (Table 16-Q of UBC-97 given below in Table 2)
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The total design base shear shall not be less than the following:
V = 0.11CaIW
In addition for seismic zone 4, the total base shear shall also not be less than the
following:
V = (0.8ZNνI/R) W
Nν = near source factor (Table 16-T of UBC-97 given below in Table 3)
Z = Seismic zone factor (Table 16-I of UBC-97 given below in Table 4)
Note: Table for soil profile type is given in appendix A of this document.
Table 1: Seismic Coefficient Cν
Seismic Zone Factor, Z Soil Profile Type Z = 0.075 Z = 0.15 Z = 0.2 Z = 0.3 Z = 0.4
SA 0.06 0.12 0.16 0.24 0.32Nv SB 0.08 0.15 0.20 0.30 0.40Nv SC 0.13 0.25 0.32 0.45 0.56Nv SD 0.18 0.32 0.40 0.54 0.64Nv SE 0.26 0.50 0.64 0.84 0.96Nv SF See Footnote 1
1 Site Specific geotechnical investigation and dynamic site response analysis shall be performed to determine seismic coefficients for Soil Profile Type SF.
Table 2: Seismic Coefficient Ca Seismic Zone Factor, Z Soil Profile
Type Z = 0.075 Z = 0.15 Z = 0.2 Z = 0.3 Z = 0.4 SA 0.06 0.12 0.16 0.24 0.32Na SB 0.08 0.15 0.20 0.30 0.40Na SC 0.09 0.18 0.24 0.33 0.40Na SD 0.12 0.22 0.28 0.36 0.44Na SE 0.19 0.30 0.34 0.36 0.36Na SF See Footnote 1
1 Site Specific geotechnical investigation and dynamic site response analysis shall be performed to determine seismic coefficients for Soil Profile Type SF.
Table 3: Near source factor Nν Closest Distance To Known Seismic Source
Seismic Source Type ≤ 2 km 5 km 10 km ≥ 15 km A 2.0 1.6 1.2 1.0 B 1.6 1.2 1.0 1.0 C 1.0 1.0 1.0 1.0
Table 4: Seismic zone factor Z Zone 1 2A 2B 3 4
Z 0.075 0.15 0.20 0.30 0.40
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Table 5: Near source factor Na Closest Distance To Known Seismic Source
Seismic Source Type ≤ 2 km 5 km ≥ 10 km A 1.5 1.2 1.0 B 1.3 1.0 1.0 C 1.0 1.0 1.0
Table 6: Seismic source type.
Seismic Source Definition2 Seismic Source
Type
Seismic Source Description
Maximum Moment Magnitude, M
Slip Rate, SR
(mm/year)
A Faults that are capable of producing large magnitude events and that have a high rate of seismic activity M ≥ 7.0 SR ≥ 5
B All faults other than Types A and C M ≥ 7.0
M < 7.0 M ≥ 6.5
SR < 5 SR > 2 SR < 2
C Faults that are not capable of producing large magnitude earthquakes and that have a relatively low rate of seismic activity M < 6.5 SR ≤ 2
Figure 15: Seismic zoning map of Pakistan.
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Structural period: The value of T shall be determined from one of the following
methods:
a. Method A: For all buildings, the value T may be approximated from the
following formula:
T = Ct (hn)3/4
Where,
Ct = 0.035 (0.0853) for steel moment-resisting frames.
Ct = 0.030 (0.0731) for reinforced concrete moment-resisting frames
and eccentrically braced frames.
Ct = 0.020 (0.0488) for all other buildings.
hn = Actual height (feet or meters) of the building above the base to the
nth level.
Alternatively, the value of Ct for structures with concrete or masonry shear
walls may be taken as 0.1/√Ac (For SI: 0.0743/√Ac for Ac in m2).
The value of Ac shall be determined from the following formula:
Ac = ∑Ae[0.2 + (De/hn)2]
The value of De/hn used in formula above shall not exceed 0.9.
Where, Ac = the combined effective area, in square feet (m2), of the shear
walls in the first story of the structure.
Ae = the minimum cross-sectional area in any horizontal plane in the
first story, in square feet (m2) of a shear wall.
De = the length, in feet (m), of a shear wall in the first story in the
direction parallel to the applied forces.
b. Method B: The fundamental period T may be calculated using the
structural properties and deformational characteristics of the resisting
elements in a properly substantiated analysis. The analysis shall be in
accordance with the requirements of Section 1630.1.2. The value of T from
Method B shall not exceed a value 30 percent greater than the value of T
obtained from Method A in Seismic Zone 4, and 40 percent in Seismic Zones
1, 2 and 3.
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12'-0"w = 800 kip1
w = 800 kip2
w = 800 kip3
w = 800 kip4
w = 700 kip5
60'-0"
The fundamental period T may be computed by using the following formula:
Where,
wi = that portion of W located at or assigned to Level i.
δi = horizontal displacement at Level i relative to the base due to
applied lateral forces, f.
g = acceleration due to gravity.
fi = lateral force at Level i.
The values of fi represent any lateral force distributed approximately in
accordance with the principles of Formulas (30-13), (30-14) and (30-15) in
UBC-97 or any other rational distribution. The elastic deflections, δi, shall be
calculated using the applied lateral forces, fi.
Example: Calculate the base shear and storey forces of a five storey building
given in figure 16. The structure is constructed on stiff soil which comes under
soil type SD of table 16-J of UBC-97. The structure is located in zone 3.
Figure 16: Two storey frame structure.
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Solution:
i) Base shear: According to static lateral force procedure the total design base
shear in a given direction can be determined from the following formula:
V = (CνI/RT) W
From table 16-R, Cν = 0.54
From table 16-K, I = 1.00, standard occupancy structures.
From table 16-N, R = 8.5, Concrete SMRF (will be discussed later).