Performance based design of Tall RC Structures considering Uncertainty in plastic hinge length

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 07 | July 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 92
Performance based design of Tall RC Structures considering
Uncertainty in plastic hinge length
Madanlal C N1, Ashwini L K2, M.Keshava Murthy3
1PG Student, UVCE, Bengaluru,
2Assistant professor, RRCE, Bengaluru,
3Professor, Dept. of civil Engineering, UVCE, Bengaluru.
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Abstract - Different plastic hinge length are considered to be
effective parameter in the user defined hinge properties. Inthis
study the possible differences in the resultsofpushoveranalysis
due to default and user defined hinge length using various
hinge length formulation available in literature by considering
G+7 storied RC structures which is modeled in SAP 2000. In
present study is done assigning user defined hinges for beams
and columns we given calculated moment curvature relations
as input I account new plastic hinge length formula for this
study. Base shear and displacement capacity of the structures
for new formula are similar to various plastic hinge length
formula’s. The uncertainties in plastic hinge length does not
effect on the performance of the building. The observations
clearly show that the user-defined hinge model is better than
the default-hinge model in reflecting nonlinear behavior
compatible with the element properties. However, if the
default-hinge model is preferred due to simplicity, the user
should be aware of what is provided in the program andshould
avoid the misuse of default-hinge properties.
Key words: Performance based design, pushover analysis,
Moment curvature analysis, plastic hinge length.
1. INTRODUCTION
In Earthquake Engineering research area, which has been
significantly improved especially in the last 40-50 years,
recent researches havebeen significantlyconcentratedon the
idea of “performance-based earthquakeengineering(PBEE)”.
Performance-based design and assessment approaches have
gained more popularity. The main objective of the PBEE is to
answer the question of “what would be the performance
(dynamic response and resulting damage) of a structure
during the “expected earthquakes” at the site?” Performance
based methods require reasonably accurate estimates of
inelastic deformation and resulting structural damage.
The rapid growth of the urbanpopulationandtheconsequent
pressure on limited space have considerably influenced city
residential development. Thehighcostofland,desiretoavoid
a continuous urban sprawl, and the need to preserve
important agricultural production have all contributed to
drive residential buildings upward. Because of the local
topographical restrictions, tall buildings are the only feasible
solutions sometimes for housing needs. The probability and
interest of high rise structures have always dependentonthe
available materials, the level of construction technology and
the state of development of services necessary for the use of
the building. As a result significant advances have occurred
from time to time with the advent of a new material,
construction facility or form of service.
1.1 PLASTIC HINGE MECHANISM
Plastic hinges form at the maximum moment region of
reinforced concretesections. The determination of theplastic
hingelength is a critical step inpredictingthelateralload-drift
response of columns. As it is difficult to estimate the plastic
hinge length by using sophisticated computer programs, it is
often estimated based on experimental data or by using
empirical equations. However, several factors influence the
length of plastic hinge, such as: a) level of axial load; b)
moment gradient; c) the value of shear stress in the plastic
hinge region; d) the amount and mechanical properties of
longitudinal and transverse reinforcement; e) strength of
concrete; and e) level of confinementprovidedinthepotential
plastic hinge zone. The simplified equations available in
literature do not contain all or most of the aforementioned
factors.
1.2 SCOPE AND OBJECTIVES OF THE STUDY
Scope
The present study aims to evaluate the performance of the
Tall RC building considering the various plastic hinge length
formulations.
Objectives
Based on the review of literature survey, the following
objectives have been aimed.
1. Develop 3D RC framed building model based on
pushover analysis using SAP2000.
2. To evaluate the performance of the building
Considering Uncertainties in thePlastichingelength.
3. To study the possible differences in the results of
pushover analysis due to default and user defined
hinge length using various hinge length formulation.

4. To compare the inelastic behavior of the different
plastic hinge length.
2. FLOW CHART FOR METHODOLOGY 2
Fig -1: Flowchart for Methodology
3. PERFORMANCE BASED DESIGN
Table -1: Section and reinforcement details of Beam
Beam Dime
nsion
(mm)
Top
Reinforc
ement
Bottom
Reinforcem
ent
Transverse
Reinforceme
nt
B-1(0-
5storey)
300x
500
6-25ϕ 5-25ϕ 3L-8ϕ @
100C/C
B-2(6-8) 300x
500
5-25ϕ 5-25ϕ 2L-8ϕ @
100C/C
Table -2: Section and reinforcement details of Column
Column
Type
Dimensi
on
Main
Reinforcement
Transverse
Reinforcement
C1-L(0-2) 500X800 12-25ϕ 5L-8ϕ @ 200C/C
C1-M(3-5) 350X750 12-25ϕ 5L-8ϕ @ 200C/C
C1-H(6-8) 350X750 12-20ϕ 5L-8ϕ @ 200C/C
C2-L(0-2) 500X900 14-25ϕ 6L-8ϕ @ 200C/C
C2-M(3-5) 350X750 14-25ϕ 6L-8ϕ @ 200C/C
C2-H(6-8) 350X750 14-20ϕ 6L-8ϕ @ 200C/C
Fig -2: performance based design details
Performance based design using nonlinearpushoveranalysis
involves tedious and intensive computational effort, is a
iterative process needed to meet designer specified and code
requirements.
3.1 Structural Modelling
All beams are 300x500mm, columns dimensions of ground
storey and first storey of C1 is 500x800mm, C2 is
500x900mm and from 2nd storey to 8th storey the column
dimension 350x750mm. The gradeoftheconcreteisM26and
steel is Fe500.

Moment curvature analysis is a method to accurately
determine the load deformation behaviour of a concrete
section using nonlinear material stress-strain relationship. It
is the representation of strength and deformation of the
section in terms of moment and corresponding curvature of
the section. The relationship between the moment and
curvature of reinforced concrete sections is an important
parameter for carrying out pushover analysis considering
user defined hinge length. These moment curvature data
obtained from Microsoft excel office.
Chart -1: Moment curvature relationship for beams
Chart -2: Moment curvature relationship for columns
3.3 PLASTIC HINGE LENGTH FORMULATION
Various empirical expressions have been proposed by
investigators for the equivalent length of plastic hinge Lp.
1. Corley’s formula( park and pauley1975, corley 1966)
Lp= 0.5d+0.2√d (z/d)
2. Sawyer’s formula ( park and pauley1975, sawyer
1964)
Lp=0.25d+0.075z
3. Pauley- Priestley formula [ pauley & Priestley 1992 ]
Lp=0.08z+0.022dbfy
4. Mattock’s formula ( park and pauley1975, mattock
1967)
Lp=0.5d+0.05z
Where, z= distance of critical section from point of
contraflexure
d = effective depth of the member
db = diameter of main reinforcing bars
Based on the literatureaboveplastichingelengthformulas
are used. But research purpose I account new simple form of
plastic hinge length equation.
Lp = 0.25H
Where, H is the section depth
4. RESULTS AND DISCUSSION
The objective of this study is to see the variation of load-
displacement graph and check the maximum base shear and
displacement of the frame. From nonlinear static pushover
analysis conducted, base shear v/s roof displacement was
obtained from SAP2000. The resulting base shear and roof
displacement obtained considering uncertainties in plastic
hinge length
3.2 MOMENT CURVATURE RELATIONSHIPS

Chart -3: pushover curve (x direction) for different plastic
hinge length
Chart -4: pushover curve (y direction) for different plastic
hinge length
The maximum base shear of the structure in the user defined
hinge model is greater than the default hinge model in both X
and Y directions. Maximum roof displacement of the building
in the default hinge model is greater than user defined hinge
model in both X and Y directions.
4.1 PERFORMANCE EVALUATION OF BUILDING
The seismic performance of building is evaluated using
capacity spectrum method (CSM). The intersection point of
capacity spectrum and demand spectrum such that capacity
equals demand is performance point.. Tables 3.3 and 3.4
displays performance point of the structureforanearthquake
in X and Y direction respectively in terms of base shear, roof
displacement from FEMA 356 and spectral acceleration and
spectral displacement obtained from ATC 40
The performance of the building (base shear and
displacement capacity) are similar in various user defined
plastic hinge length formulation: the variation in the
performance of the structures is less than 5%.
Table 3.3: performance point (x direction) for different
plastic hinge length
Hinge
length
Plastic
hinge
length
formulas
Base
shear(kN)
Displacement
(m)
Default Default 3508.62 0.219
User
defined
Mattock’s 3492.061 0.218
Pauley-
Priestley
3491.87 0.218
Corley’s 3491.878 0.218
Sawyer’s 3492.596 0.218
new 3492.842 0.218
Table 3.4 : performance point (y direction) for different
plastic hinge length
Hinge
length
Plastic hinge
length formulas
Base
shear(kN)
Displacement
(m)
Default Default 4509.645 0.142
User
defined
Mattock’s 4754.77 0.149
Pauley-
Priestley
4759.011 0.149
Corley’s 4759.025 0.149
Sawyer’s 4761.001 0.149
new 4760.526 0.149
4.2 HINGES
4.2.1 Hinge status at ultimate : The details of the hinges
formed in the structure in X direction and Y direction is given
in the Table 6.5 and 6.6

Chart 5: performance level for default hinge length in Y
direction Chart 6: performance level for default hinge length in Y
direction
Table -3.5: Summary of plastic hinging for pushover analysis at different damage level
Plastic hinge
length
Direction A-B B-IO IO-LS LS-CP CP-C C-D D-E >E Total
Default X
418 24 16 0 0 6 0 0 464
Y
416 30 14 0 0 4 0 0 464
Table -3.6: Summary of plastic hinging for pushover analysis at different damage level
Plastic hinge
length
Direction A-B B-IO IO-LS LS-CP CP-C C-D D-E >E Total
User defined X
424 28 12 0 0 0 0 0 464
Y
418 41 5 0 0 0 0 0 464
Chart 7: performance level for user defined hinge length in
X direction.
Chart 8 : performance level for user defined hinge length in
Y direction.

Fig -3: default hinge model at ultimate
Fig -4: user defined hinge model at ultimate
Following are the discussion:
 It was observed that, both the models, the
performance level lied between Immediate
occupancy and lifesafety level for an earthquake in X
direction.
 It was observed that, both the models, the
performance level lied between B and Immediate
occupancy level for an earthquake in Y direction.
 It was found that, Default hinge length, 90.1% of
members are in A to B, 5.2% of members are in B to
immediate occupancy [ B-IO ], 3.5% of members are
in immediate occupancy to life safety [ IO- LS ] zone.
Remaining 1.2% of membersreach collapsezoneinX
direction.
 It was found that, Default hinge length, 89.6% of
members are in A to B, 6.5% of members are in B to
IO, 3% of members are in IO to LS zone. Remaining
0.86% of members reach collapse zoneinYdirection.
 Damage members can be strengthen or retrofitted
based on the requirement.
 It was found that, various user defined hinge length,
91.3% of members are in A to B, 6.2% of members
are in B to immediate occupancy [B-IO], 3.5% of
members are in immediate occupancy to life safety
[IO- LS] zone in X direction.
 It was found that, various user defined hinge length,
90% of members are in A to B, 9% of members are in
B to IO, 1% of members are in IO to LS zone in Y
direction.
 It was found that none of the membersreachcollapse
zone for user defined hinge model in both X and Y
direction. Hence the building poses some residual
strength.
 The present building model is safe for minor
earthquakes.
5. CONCLUSIONS
The following conclusions were observed:
 Performance of the building increases when the
sectional size of columns is increased while keeping
same reinforcement.
 The uncertainty in plastic hinge length does not
effect on the performance of the building. The
performance of the building (base shear and
displacement capacity)aresimilarindifferentplastic
hinge length: the variation in the performance of the
structures is less than 5%.
 The differences in Default hinges and user defined
hinges for various plastic hinge length has
considerable effects on the maximumbaseshearand
displacement capacityofthe structures;thevariation
in the base shear and displacement capacity is 10%
in X direction and 30% in Y direction.

 The stiffness of structure in the Y direction is more
than that in X direction. That is particularly due to
orientation of columns along Y axis.
 Comparison of hinging pattern indicates that both
models with default hinges and the various user
defined hinges estimate plastic hinge formation at
the ultimate state there are significant differences in
the hinging patterns.
 Most of the hinges developed in the beams and few
in the columns of both models it indicates strong
column and weak beam.
 This study is carried out to investigate the possible
differences between pushover analyses of the
default-hinge and user-defined hinge models. The
observations clearly show that the user-defined
hinge model is better than the default-hinge model
because damage is limited. However, if the default-
hinge model is preferred due to simplicity, the user
should be aware of what is provided in the program
and should definitely avoid the misuse of default-
hinge properties.
5.1 SCOPE FOR THE FUTURE WORK
 This study focuses on Non-linear Static Analysis
procedure to check the performanceofthestructure.
But, the study can be extended to Non-Linear Time
History Analysis and the results can be checked for
more accuracy.
 In this study pushover analysis was carried out.
Further studies compare the results with
experimental observations.
 To study the differences in results of various plastic
hinge length for different storey height.
REFERENCES
[1] Inel, M., & Ozmen, H. B. (2006). Effects of plastic hinge
properties in nonlinear analysis of reinforced concrete
buildings. Engineering structures, 28(11), 1494-1502.
[2] Hede, N. P., & Babunarayan, K. S. (2013, November).
Effect of variation of plastic hinge length on the resultsof
non-linear analysis. In International Journal of Research
in Engineering and Technology (IJRET), IC-RICE
Conference Issue (pp. 2319-1163).
[3] CM, R. K., Choudhary, V., Narayan, K. S., & Reddy, D. V.
(2014). Moment Curvature Characteristics for Structural
Elements of RC Building.
[4] Biradar, S. H. (2015, August) 3D RC Multistorey Building
Seismic Assessment with User Defined Hinges.
[5] Sonwane, D. P., & Ladhane, K. B. (2015). Seismic
performance based design of reinforced concrete
buildings using nonlinear pushover
analysis. International Journal of Engineering Research
and Technology, 4(06).
[6] Subramanian, N. (2009). Plastic Hinge Length of
Reinforced Concrete Columns. Paper by Sungjin Bae and
Oguzhan Bayrak. ACI Structural Journal, 106(2), 233.
[7] Ashraf Habibullah, S. E., & Stephen Pyle, S. E. (1998).
Practical three dimensional nonlinear static pushover
analysis. Structure magazine, winter.
[8] Bento, R., Falcao, S., & Rodrigues, F. (2004, August).
Nonlinear static procedures in performance based
seismic design. In Proceedings of the 13th world
conference on earthquake engineering, Vancouver,
Canada.

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Performance based design of Tall RC Structures considering Uncertainty in plastic hinge length