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July 2003 * The Indian Concrete Journal 1217
Seismic shear design of RC
bridge piers Part II:
Numerical investigation of
IRC provisions
Rupen Goswami and C.VRupen Goswami and C.V
Rupen Goswami and C.VRupen Goswami and C.V
Rupen Goswami and C.V.R. Murty.R. Murty
.R. Murty.R. Murty
.R. Murty
Part I of this paper1 reviewed the code provisions on seismic
shear design of RC bridge piers. The second part, presented
here discusses the numerical investigation of IRC provisions.
In this paper, monotonic lateral load-deformation relations of
reinforced concrete (RC) bridge piers, designed as per existing
IRC standards and bending in single curvature, are
analytically studied. A displacement-based pushover analysis
procedure is developed for the purpose. The analysis shows
that the design shear capacities of short piers are lower than
the corresponding shear demand under flexural overstrength
conditions. Also, buckling of longitudinal reinforcement is
commonly observed, which results in rapid strength loss and
subsequent failure of piers. Thus, the current transverse
reinforcement requirements of the Indian code are inadequate.
Also, additional radial links in hollow circular piers are found
to enhance the displacement ductility; the current code does
not have any reference to this. The Indian seismic bridge design
provisions need to be revised urgently.
Bridge piers should be designed and detailed for adequate
flexural ductility to ensure satisfactory performance under
strong seismic shaking. A review of the strength design
provisions of the Indian codes in comparison with those of
several international codes of practice was presented in Part
I of the paper1. This sequel paper presents the results of
analyses of a number of RC bridge piers designed as per the
existing IRC code provisions, and investigates the
vulnerability of such piers to brittle shear failure under strong
earthquake shaking.
RC bridge piers are of four types, namely wall type,
single-column type, multiple-column frame type, and linked-
column frame type. The framed bridge piers have high
redundancy and small ductility demand on individual plastic
hinges at the critical sections. In contrast, the single column
piers with superstructure simply resting on them are vertical
cantilevers with no redundancy; their overall response
critically depends on the satisfactory performance of a single
plastic hinge at the base. Thus, single column piers are most
vulnerable, but are most commonly used due to appealing
aesthetics. Hence, a detailed investigation is carried out on
the lateral load-deformation relations of such piers of four
different, but commonly used cross-sections.
Pushover analysis
An upper bound of lateral strength and deformation
characteristics of large bridge piers can be determined by
conducting a monotonic displacement controlled test on
prototype pier specimens. However, in India, the
infrastructure required to perform these tests is still not
available. Alternatively, an analytical method can be
employed, which provides sufficient information not only
for evaluating the performance of the piers being designed
currently, but also for the development of improved design
standards. Pushover analysis is one such tool. It is a
displacement-based nonlinear quasi-static scheme that
provides insight into the full response, that is, till failure, of
the piers. The pushover analysis of the most commonly used
piers, namely the single column piers bending in single
curvature, is described in the following.
The Indian Concrete Journal * July 20031218
Geometric model
In analytical models of bridge piers with large cross-sections,
the approach of idealising the member by its centroidal axis
and defining the inelastic action of the whole cross-section in
a lumped way does not accurately model the spread of
inelasticity either along the length of the member or across
the depth of the cross-section. Hence, a distributed plasticity
model is required, which is described below.
Model description
The pier is discretised into a number of segments along the
length, and each segment into a number of fibres across the
cross-section, Fig 1. Because an RC section is composed of
both concrete (confined and unconfined) and longitudinal
reinforcing steel, the section is further discretised into separate
concrete and steel fibres, Fig 2. Such a general approach of
discretising RC sections into a number of fibres has been in
practice for long, to accommodate general irregularities in
geometry, strain-hardening in steel, non-linear concrete
constitutive relations, and to capture the complex stress
distribution across the cross-section2. Also, procedures for
obtaining the tangent stiffness matrix of a segment discretised
into such fibres were presented earlier to cover any loading
condition, geometric irregularities, and geometric and
material non-linearities3,4. For analysis involving material and
geometric non-linearity, relations between incremental stress
resultants and incremental deformations are derived for all
the fibres, which are combined to form the incremental
equilibrium equation for a segment. Finally, the incremental
equilibrium equation of the entire member, or pier, is obtained
by assembling those of its segments. Large displacements
but small strains are considered in the analysis.
Each fibre is treated as a two-noded axial member with
no flexural property. However, the total stiffness of a segment,
modeled as a general frame member, accounts both axial and
bending actions, and also, separate shear action. In bridges
with large cross-section piers, shear deformation significantly
affects the overall deformation response of the pier. Thus,
the stiffness matrix derived for a general frame member is
such that it is valid for both a slender one with predominant
flexural behaviour, and for a stocky one with significant shear
dominated behaviour. This is achieved though the use of a
factor β, where β is the relative ratio of flexural lateral
translational stiffness and shear stiffness of the segment, given
by
β= LGA LEI
s
3
12 (1)
where,
β= relative ratio of flexural lateral translational
stiffness and shear stiffness of a segment
E= Youngs modulus
I= second moment of area of a section
L= length of fibre / segment
G= shear modulus
As= area resisting shear
A detailed description of the analytical formulation is given
elsewhere 6.
Material models
The load-deformation relationship of each fibre is derived
using material constitutive laws. In RC structures, the two
different material fibres, namely reinforcing steel and
concrete, require two different material constitutive law
models. Moreover, core concrete fibres are confined and the
cover concrete unconfined. Also, the longitudinal and
transverse steels can be of different grade and amount. The
transverse steel only affects the confinement of the core
concrete and influences the axial stress-strain relation of the
core concrete. On the other hand, longitudinal steel plays a
direct role in the axial, bending and shear resistance of the
section. Thus, only longitudinal steel is modelled.
In India, the most widely used reinforcing steel is high
yield stength deformed (HYSD) bars conforming to IS 1786 :
198513. A model representing the virgin stress-strain curve
for HYSD bars, developed through regression analysis of
experimental data from uniaxial tensile tests is used5.
Brief descriptions of some of the constitutive law models
of concrete available in literature are discussed elsewhere6.
Of the different constitutive models available, the analytical
Fig 1 Discretisation of a pier into segments and
segments into fibres
Fig 2 Discretisation of a hollow rectangular RC section
into concrete (core and cover) and longitudinal steel
fibres
July 2003 * The Indian Concrete Journal 1219
model applicable to hollow sections also is used in this study5;
this model is an extension to an earlier model7. Hollow sections
address a new situation, wherein the outer and inner hoops
are tied by links leading to two distinctly different confining
actions, namely hoop action and the direct action of links.
The falling branch as defined by the original single equation7,8
is too flat and remains above the experimental uniaxial stress-
strain data. Hence, the equation is modified6 beyond the strain
corresponding to the peak stress as
fc=o
r
o
occ xr xrf +−1
'
(2)
where,
ro=
()
r
r
/11
+(3)
r=sec
EE E
c
c
−, 1
'
sec ε
=cc
f
E, 69003320 '+= cc fE
....... (4)
x=1
ε
εc(5)
where,
fc= stress in concrete
'
cc
f= ultimate stress of confined concrete
Ec= Youngs modulus of concrete
Esec = secant modulus of elasticity confined concrete
at ultimate stress
1
ε= strain corresponding to ultimate stress of
confined concrete
'
c
f= characteristic compressive (cylinder) strength
of concrete
c
ε= strain in concrete.
During pushover analysis of the pier, initially all the fibres
are in compression under the action of gravity load. As the
pier tip is displaced laterally, Fig 1, the curvature at any section
is gradually increased; the compressive strain in some fibres
increases, while in others, it decreases and eventually becomes
tensile (unloading in compression and subsequent loading in
tension). At a certain curvature, spalling of cover concrete
occurs, which results in redistribution of stresses within the
section. There is possibility of unloading and reloading of
both concrete and steel fibres. However, for the purpose of a
monotonic pushover analysis, exhaustive hysteretic models
for material stress-strain curves may not be required; simple
loading, unloading and reloading rules are therefore used.
The following are the salient features of the hysteretic
stress-strain model of steel used in this study, Fig 3.
(i) All unloading and initial reloading slopes, upto yield,
are equal to the initial elastic modulus, Es; there is no
stiffness degradation.
(ii) There is no strength deterioration
(iii) As the material unloads from the virgin curve, the
whole stress-strain curve translates along the strain
axis, the total translation being dependent on the
plastic strain history; a kinematic hardening approach
is utilised, wherein the stress-strain path translates with
accumulation of plastic strain, but without any change
in size or shape.
The salient features of the hysteretic stress-strain model
of concrete used in this study, Fig 4 are:
(i) linear unloading and reloading occur with tangent
modulus equal to the initial modulus
(ii) the residual strain capacity is calculated from the
accumulated plastic strain
(iii) the tensile strength of concrete is neglected.
The load-carrying capacity of compression reinforcement
in RC compression members is significantly affected by the
unsupported length of the longitudinal bars between the
transverse ties that are expected to provide lateral support
and thereby prevent buckling of longitudinal bars. In the
present study, longitudinal bars are considered to have
buckled if the axial compressive stress in them exceeds the
Fig 3 Hysteretic stress-strain model of HYSD bars used in
this study showing a possible strain path starting at O
Fig 4 Hysteretic stress-strain model of concrete in
compression used in this study
The Indian Concrete Journal * July 20031220
critical stress, bcr,
σ, given by
bcr,
σ =
[]
2
,
1
,
;
bcrbcr
Min σσ (6)
where,
bcr,
σ= critical stress for buckling of longitudinal steel
in piers
1,bcr
σ= elastic buckling stress of longitudinal steel in
piers
2,bcr
σ= inelastic buckling stress of longitudinal steel
in piers.
In Eq.(6), b
cr,
1
σis the critical buckling stress of the
longitudinal bar under clamped-clamped condition between
the transverse ties, given by
1,bcr
σ=
()
2
2
/4 b
s
ds
E
π(7)
where,
Es= Youngs modulus of steel
s= longitudinal spacing of transverse
reinforcement
db= nominal diameter of longitudinal
reinforcement.
Further,
2,bcr
σis the inelastic critical buckling stress, given
by 6
2,bcr
σ =
>
<
<
−
−
−
<
10
1055
5
)(
5
b
y
bb
yu
y
b
u
d
s
forf
d
s
for
d
s
ff
f
d
s
forf
(8)
where,
fu= ultimate strength of steel
fy= characteristic strength of steel.
Analytical procedure
The following procedure is employed to assess the inelastic
drift capacity of (circular and square, solid and hollow) RC
piers bending in single curvature. To begin with, a small
displacement increment is imposed at the tip of the cantilever
pier. Corresponding to this tip displacement, an initial
deformed profile is assumed along the height of the pier.
Usually, the deformed shape of an elastic cantilever with only
bending deformations under the action of a concentrated
load at the tip is a good approximation. For this assumed
displacement profile, the internal resistance vector {p} along
the degrees of freedom is calculated. The external load vector
{f} consists of vertical concentrated load at the top of the pier
due to gravity load of the superstructure and vertical dead
loads at all intermediate nodes from the self weight of the
pier segments. The unbalanced force
{}{}
uu pf − along all
unknown degrees of freedom is calculated. The deformed
geometry of the pier is corrected using the additional
incremental deformation
{}
u
x
&at the unknown degrees of
freedom obtained by solving
[]
{}{}{}
uuuuu pfx K −=
&(9)
where,
[]
uu
K= the iterating matrix corresponding to the
unknown degrees of freedom
{}
x = end-displacement vector of a segment in
global coordinates
{}
f= end-force vector of a segment in global
coordinates; external load vector on the
member in global coordinates
{}
p= internal resistance vector of the member in
global coordinates.
The net incremental deformation in global coordinate is
then computed and the deformed geometry is updated using
{} {} {}
u
old
u
new
uxxx &
+= (10)
The internal resistance vector
{}
u
pis re-calculated for this
revised geometry of the pier considering the strength of the
materials, the deformation of the pier and the extent of
cracking in concrete. The iterations using Eq.(9) are repeated
until the unbalanced force
{}{}
uu pf −is within the specified
tolerance. Once force balance is reached within a displacement
step, the next displacement increment is imposed at the tip of
the cantilever pier. Again, a revised target geometry is set
based on the geometry at the end of the previous
displacement step, and the procedure of calculation of internal
and external force balance is repeated, until the two converge.
The above internal resistance calculation procedure is
repeated with additional displacement increments until the
pier reaches failure. Thus, the full lateral load-lateral
displacement response is traced. From this, the flexural
overstrength-based shear demand, max
Ω
V, on the RC pier
bending in single curvature is extracted as
max
Ω
V=max
H(11)
where
Hmax = is the maximum internal resistance of the pier
at its tip during the entire displacement
loading history, Fig 5.
max
Ω
V= flexural overstrength-based shear demand on
RC pier
Numerical study
The adequacy of strength design provisions is investigated
for solid and hollow RC piers of circular and rectangular
July 2003 * The Indian Concrete Journal 1221
cross-sections. Piers of typical 5 m height are designed as per
the strength design methodology outlined in IRC 21 : 198710.
The approximate initial choice of section size (cross-sectional
area) and probable load on the piers are taken from field
data of existing bridge piers. In this study, a 2-lane
superstructure is considered. The weight of the superstructure
is taken as 162.5 kN/m. Hence, for a span of 40 m, the piers
are subjected to a superstructure gravity load of 6500 kN.
The lateral and vertical seismic loads are calculated based on
the seismic coefficient method outlined in IRC 6 : 2000 for
seismic zone V, with importance coefficient of 1.5 and soil
foundation system coefficient of 1.09.
There is no provision for shear design of piers in
IRC 21 : 1987; nominal transverse reinforcement required by
the IRC 21 : 1987 is provided in first set of four piers (one each
of solid circular, solid rectangular, hollow circular and hollow
rectangular cross-section). These are named as CSWG, RSWG,
CHWG and RHWG. However, provisions for shear design in
beams and slabs are outlined in IRC 21 : 1987, wherein the
entire shear is attributed to the transverse steel only. Hence,
a second set of four more piers (namely CSSG, RSSG, CHSG
and RHSG) is designed for shear in line with these shear
design provisions. The overstrength-based shear demand of
the above eight piers are estimated from the monotonic
lateral load-deformation response. In addition, design shear
capacities of the sections are computed as per IS 456 : 2000,
wherein both concrete and transverse steel are considered to
contribute to the design shear strength12.
Next, the effect of pier slenderness on overall response is
investigated. A third set of eight piers is designed for two
slenderness ratios, namely 2, and 6. These piers (namely
CSWL-2, CSWL-6, RSWL-2, RSWL-6, CHWL-2, CHWL-6,
RHWL-2, and RHWL-6) are designed for the same
superstructure gravity load of 6500 kN, and a transverse
load of 650 kN (considering a average seismic coefficient of
0.1 for seismic zones IV and V) with nominal transverse
reinforcement. In all piers, the cross-sectional area is kept at
approximately 4.8 m2, giving a compression force of about
gc Af '
042.0 . Pushover analysis is performed for all the eight
piers to compare the overstrength shear demand with the
design shear capacity at the critical sections.
Finally, the effect of additional radial links on the load-
deformation behaviour of hollow circular piers is investigated.
The hollow circular piers with no radial links in the first
(CHWG) and second (CHWL-2) investigations are re-analysed
with 19 and 28 radial links of 8 mm diameter HYSD steel
bars, and the load-deformation responses are compared with
the corresponding original ones.
In the nomenclature used in designating the above piers,
the first character (that is, C or R) indicates the type of
cross-section, namely circular or rectangular. The second
character (that is, S or H) indicates solid or hollow sections.
The third character (that is, W or S) indicates piers without
and with shear design. The fourth character (that is, G, or
L) indicates type of investigation undertaken on the piers,
namely effect of geometry or slenderness. The fifth set of
numbers in the investigation on effect of slenderness (that is,
2, 6) indicates slenderness ratio of the piers. In the
investigation on effect of additional radial links, the last
character (that is, L) indicates presence of additional radial
links. The character D in the graphical representations of
responses indicates design shear capacity of the pier computed
based on shear design methodology described in IS 456 :
2000.
In all numerical studies, concrete cover of 40 mm and
concrete grade of 40MPa are used. As required by IRC 21 :
1987, when the resultant tension due to direct compression
and bending under design loads exceeded permissible stress
given in IRC 21 : 1987, cracked section analysis was carried
out to arrive at the amount of longitudinal steel. The
permissible stresses used in design are increased by 50 percent
while using seismic load-combinations, as per
recommendation of IRC 6 : 2000.
Results
The investigation on effect of geometry shows that short
piers (with slenderness ratio of 1.7 2.8) with solid sections
with shear reinforcement perform better than the hollow
ones with approximately same cross-sectional area, Fig 6.
Fig 6 Effect of cross-section geometry: Lateral load-
deformation response of 5 m
tall piers. Piers having
solid circular and rectangular cross-sections and with
design shear reinforcement have stable post-yield
response
Fig 5 Maximum shear demand on the pier during the
entire displacement loading history
The Indian Concrete Journal * July 20031222
Table 3: Results of analyses of four types of piers of three slenderness ratio comparing
shear capacity with demand, and showing final form of failure
Pier L, Section, Area, Reinforcement Shear Shear Failure mode
name m m m2longitudinal Transverse capacity, demand,
kN kN
CSWL-2 5.0 2.50 φ4.91 66Y28 Y8 at 300 2333 6093 Buckling of
longitudinal steel
CSWL-6 15.0 2.50 φ4.91 66Y28 Y8 at 300 2333 1786 Buckling of
longitudinal steel
RSWL-2 6.0 3.0 ×1.6 4.80 64Y28 Y8 at 300 3114 6789 Buckling of
longitudinal steel
RSWL-6 18.0 3.0 ×1.6 4.80 64Y28 Y8 at 300 3114 1997 Buckling of
longitudinal steel
CHWL-2 7.0 3.5(OD), 4.71 84Y25 Y10 at 100 4554 6726 Compression
2.5(ID) of concrete
CHWL-6 21.0 3.5(OD), 4.71 84Y25 Y10 at 100 4554 1980 Compression
2.5(ID) of concrete
RHWL-2 8.0 2.8 × 4.0(OD), 4.80 156Y20 Y10 at 130 6419 8648 ——
2.0 × 3.2(ID)
RHWL-6 24.0 2.8 × 4.0(OD), 4.80 156Y20 Y10 at 130 6419 2579 ——
2.0´3.2(ID)
Hollow sections have larger section
dimension and therefore draw in
more lateral force. In piers with
circular cross-section, this increases
the overstrength-based seismic
shear demand without any
appreciable increase in
deformability. In piers with
rectangular cross-section, the pier
with hollow cross-section shows
increased deformability, apart from
the expected increased shear
demand, Fig 6. This is due to the IRC
21 : 1987 requirement that, in
rectangular sections, every corner
and alternate longitudinal bar be
laterally supported by the corner of
a tie, and that no longitudinal bar
be farther than 150 mm from such a laterally supported bar.
This forces additional intermediate ties in both directions in
the hollow rectangular sections, which enhance the effective
confinement of concrete (compare volumetric ratio of
transverse reinforcement in Table 2) and therefore increase
the maximum strain that concrete can sustain. This also results
in increased deformability of the hollow rectangular section
compared to the solid rectangular section with only nominal
transverse reinforcement. On the other hand, piers with solid
cross-sections with design transverse shear reinforcement
have better post-yield behaviour in the form of enhanced
deformability and displacement ductility.
The shear capacities of circular and rectangular sections,
both solid and hollow, with nominal transverse reinforcement
as recommended by IRC 21 : 1987 are insufficient for the
shear demands due to flexure for short piers, Tables 1 and 2.
Premature brittle shear failure of piers will occur before the
full flexural strength is achieved. Amongst the four types of
piers of same height and cross-sectional area, and subjected
to the same axial compression, the solid circular piers have
the least shear capacity. This is
attributed to the presence of only
a single circular hoop in solid
circular piers. In rectangular
sections, the intermediate ties in
both the directions enhance the
shear capacity. Thus, the ratio of
transverse reinforcement
required (to prevent shear failure)
to that provided is maximum
(6.80) in pier with solid circular
section and least (1.15) in pier with
hollow rectangular section, Table
2.
Also, in hollow sections, the
IRC 78 : 198311 requirement of
minimum area of transverse steel
of 0.3 percent of wall cross-section
exceeds the IRC 21 : 1987
reinforcement requirements.
However, even this transverse
Table 1: Results of analyses of four types of piers comparing shear capacity and demand,
and showing final form of failure
Pier Section, Area, Longitudinal Transverse Shear Shear Failure
(L=5m) m m2reinforcement, reinforcement capacity, demand, mode
kN kN
CSWG 1.80 φ2.54 54Y22 Y8 at 260 1379 2471 Buckling of
longitudinal steel
CSSG 1.80 φ2.54 54Y22 Y12 at 110 2197 2494 —-
RSWG 2.5×1.0 2.50 46Y25 Y8 at 300 1823 4236 Buckling of
longitudinal steel
RSSG 2.5×1.0 2.50 46Y25 Y10 at 200 2607 4283 —-
CHWG 2.4(OD), 1.7(ID) 2.25 57Y22 Y10 at 140 2464 3834 Buckling of
longitudinal steel
CHSG 2.4(OD), 1.7(ID) 2.25 57Y22 Y10 at 140 2464 3834 Buckling of
longitudinal steel
RHWG 1.2×3.0(OD), 2.45 100Y16 Y10 at 140 3726 5057 Buckling of
0.5×2.3(ID) longitudinal steel
RHSG 1.2×3.0(OD), 2.45 100Y16 Y10 at 140 3726 5057 Buckling of
0.5×2.3(ID) longitudinal steel
Table 2: Transverse reinforcement requirement to prevent
shear failure in piers of four types of cross-section in
investigation on effect of geometry
Pier Shear Shear Percentage of transverse Ratio,
capacity, demand, reinforcement, percent p
s
r
sρρ
kN kN Provided p
s
ρRequired r
s
ρ
CSWG 1379 2471 0.0447 0.304 6.80
CSSG 2197 2494 0.239 0.312 1.30
RSWG 1823 4236 0.142 0.524 3.69
RSSG 2607 4283 0.333 0.617 1.85
CHWG 2464 3834 0.416 0.930 2.23
CHSG 2464 3834 0.416 0.930 2.23
RHWG 3726 5057 0.768 0.879 1.14
RHSG 3726 5057 0.768 0.879 1.14
steel is inadequate to resist the overstrength moment-based
shear demand in short piers, Table 2.
In most piers where only nominal transverse
reinforcement is provided, buckling of longitudinal
July 2003 * The Indian Concrete Journal 1223
reinforcement occurred, Table 1, resulting in sudden loss of
load carrying capacity. This is due to the large spacing of
transverse reinforcement adopted along the member length;
the spacing adopted is as per IRC 21 : 1987 which is the
minimum of
(i) 12 times the diameter of smallest longitudinal
reinforcement bar
(ii) 300 mm
The investigation on the effect of pier slenderness reveals
that the nominal transverse reinforcement requirements are
inadequate for short piers (slenderness ratio of 2). On the
other hand, for slender piers (slenderness ratio of 6 or more),
the nominal design shear capacity is higher than the demand,
Tables 3 and 4. Thus, slender piers exhibit a ductile behaviour.
In large hollow rectangular piers, better distribution of
longitudinal steel and enhanced concrete confinement due to
intermediate links result in superior post-yield response than
in the other three types of sections considered in this study,
Fig 7. Also, with increase in slenderness, the shear demand
reduces and the deformability increases. This is due to greater
flexibility of piers with increased slenderness. Thus, the target
deformability of a pier seems to be a function of its
slenderness. However, as in the first study, failure is primarily
initiated by buckling of longitudinal steel, Table 3.
Providing radial links in hollow circular sections increases
ductility of piers, Table 5 and Fig 8). By providing nominal
radial links of Y8 bars (increase of 25 percent to 40 percent in
volumetric ratio of transverse reinforcement), the drift
capacity increases by at least about 1 percent even in short
piers with slenderness ratio of 2. This is
because the links not only increase the
amount of transverse reinforcement and
affect the concrete confinement, but also
cause the transfer of tension from outer
hoop to the inner hoop and thereby
prevent compression failure of inner
hoop.
Conclusions
The results of the investigations provide
significant insight into the effectiveness
of IRC provisions to prevent brittle shear
failure in single-column type RC bridge
piers. The implications of these results
Fig 7 Effect of pier slenderness: Lateral load-deformation
response of solid-circular, solid-rectangular, hollow-
circular, and hollow-rectangular piers having
slenderness ratios
2
and
6
. Their corresponding nominal
shear capacities are also shown. Short piers with
slenderness of
2
are vulnerable in shear
Table 4: Transverse reinforcement requirement to prevent
shear failure in piers in investigation on effect of slenderness.
Pier Shear Shear Transverse reinforcement, percent Ratio,
capacity, kN Demand, kN Provided p
s
ρRequired r
s
ρp
s
r
sρρ
CSWL-2 2333 6093 0.0277 0.516 18.62
CSWL-6 2333 1786 0.0277 0.0277 1.00
RSWL-2 3114 6789 0.135 0.385 2.85
RSWL-6 3114 1997 0.135 0.135 1.00
CHWL-2 4554 6726 0.374 0.798 2.13
CHWL-6 4554 1980 0.374 0.374 1.00
RHWL-2 6419 8648 0.604 0.800 1.32
RHWL-6 6419 2579 0.604 0.604 1.00
Table 5: Results of analyses of hollow circular piers with and without radial links,
comparing percentage lateral drift
Pier L, m Section, m Area, Longitudinal Transverse Ratio, Drift
OD ID m reinforcement reinforcement 12 ss ρρ percent
CHWG 5.0 2.4 1.7 2.25 57Y22 Y10 at 140 —- 1.34
(1
s
ρ= 4.16 ´ 10-3)
CHWG-L 5.0 2.4 1.7 2.25 57Y22 Y10 at 140 + 19 Y8 1.25 2.24
Radial links ( 2
s
ρ= 5.22 ´ 10-3)
CHWL-2 7.0 3.5 2.5 4.71 84Y25 Y10 at 100 —- 1.86
(1
s
ρ = 3.74 ´ 10-3)
CHWL-2-L 7.0 3.5 2.5 4.71 84Y25 Y10 at 100 + 28 Y8 1.40 3.43
Radial links ( 2
s
ρ= 5.23 ´ 10-3)
Fig 8 Effect of radial links: Lateral load deformation
response of hollow circular piers CHWG, and CHWL-2
with and without radial links. Radial links enhance drift
capacity and ductility in hollow circular piers
The Indian Concrete Journal * July 20031224
are important in light of the large stock of bridge piers that
are to be built in India as part of the ongoing National
Highway Development Project and the urban development
projects. These are given below.
(i) IRC code prescribed design shear capacities of short
piers are lower than the expected shear demand during
strong earthquake shaking; in general, nominal
transverse reinforcement requirements prescribed in
the IRC code need to be enhanced up to 6-7 times the
current code values.
(ii) Increasing the amount of transverse reinforcement
increases the displacement ductility of piers, and
produces improved post-yield response; transverse
reinforcement requirement in the IRC code can be
made a function of the required displacement ductility
of piers.
(iii) Buckling of longitudinal reinforcement occurs,
resulting in rapid strength loss and subsequent failure
of piers; maximum limit on the spacing of transverse
reinforcement prescribed in the IRC code is grossly
inadequate in preventing buckling of longitudinal steel
and subsequent failure of piers under strong seismic
shaking.
(iv) Providing additional radial links in hollow circular
piers increases displacement ductility; new
specification for use of radial links needs to be urgently
incorporated in the IRC code.
References
1. GOSWAMI, R, and MURTY, C.V.R. Seismic shear design of RC bridge piers Part
I: Review of codal provisions, The Indian Concrete Journal, June 2003, Vol 77,
No 6, pp 1127-1133.
2. WARNER, R.F. Biaxial moment thrust curvature relations, Journal of the
Structural Divison, ASCE, 1969, Vol 95, No ST5, pp 923-940.
3. SANTATHADAPORN, S. and CHEN, W.F. Tangent stiffness method for biaxial
bending, Journal of the Structural Division, ASCE, 1972, Vol 98, No ST1,
pp 153-163.
4. MURTY, C.V.R. and HALL, J.F. Earthquake collapse analysis of steel frames,
Earthquake Engineering and Structural Dynamics, 1994, Vol 23, No 11, pp 1199-
1218.
5. DASGUPTA, P. Effect of confinement on strength and ductility of large RC hollow
sections, Master of Technology Thesis, 2000. Department of Civil Engineering,
Indian Institute of Technology Kanpur, India.
6. GOSWAMI, R. Investigation of seismic shear design provisions of IRC code for RC
bridge piers using displacement-based pushover analysis, Master of Technology
Thesis, 2002. Department of Civil Engineering, Indian Institute of Technology
Kanpur, India.
7. RAZVI, S.R. and SAATCIOGLU, M. Confinement model for high-strength concrete,
Journal of Structural Engineering, ASCE, 1999, Vol 125, No 3, pp 281-289.
8. POPOVICS, S. A numerical approach to the complete stress-strain curve of
concrete, Cement and Concrete Research, 1973, Vol 3, pp 583-599.
9. ______Standard specifications and code of practice for road bridges, Section: II,
loads and stresses, IRC: 6-2000, The Indian Road Congress, New Delhi.
10. ______Standard specifications and code of practice for road bridges, Section: III,
cement concrete (plain and reinforced), IRC 21 : 1987, The Indian Road Congress,
New Delhi.
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11 ______Standard specifications and code of practice for road bridges, Section: VII,
foundations and substructure, IRC 78 : 1983, The Indian Road Congress, New
Delhi.
12. ________ Indian standard code of practice for plain and reinforced concrete, IS
456 : 2000. Bureau of Indian Standards, New Delhi.
13. ______Specification for high strength deformed steel bars and wires for concrete
reinforcement, IS 1786 : 1985, Bureau of Indian Standards, New Delhi.
Mr Rupen Goswami is currently a doctoral student
in the department of civil engineering at The Indian
Institute of Technology (IIT) Kanpur. His area of
research is development of ductile seismic design of
RC bridge piers.
Dr C.V.R. Murty is currently associate professor in
the department of civil engineering at IIT Kanpur.
His areas of interest include research on seismic
design of steel and RC structures, development of
seismic codes, modelling of nonlinear behaviour of
structures and continuing education. He is a member
of the Bureau of Indian Standards Sectional
Committee on earthquake engineering and the Indian Roads
Congress Committee on bridge foundations and substructures
and is closely associated with the comprehensive revision of the
building and bridge codes.