Study of the plastic-hinge analysis of 3D steel frames applying nonlinear static analysis

Abstract

This paper provides a distinct study on the performance of different residential buildings with different height and length spans under the influence of applied loads according to the Turkish standard TS498. The research paper presents the nonlinear performance of the buildings and provides a clear picture of the plastic and its stages throughout the construction. The study explains the effect of the various stages of plastic and how it affects the rigidity of the building. The results portray the building's stiffness values and how they change. The results show that stiffness increases with length-increase and decreases by decreasing the height of buildings. All stiffness values were calculated according to the first plastic hinge formation. Software used is ETABS 2018 and all calculations and parameters used according to FEMA356-2000, ASCE 7-16, ACI-318, EURO code 8, and Turkish standard.

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International Journal of Advanced Engineering, Sciences and Applications (IJAESA)
Volume 1, Issue 3 (2020), Pages 24-29
ISSN: 2703-7266
DOI: https://doi.org/10.47346/ijaesa.v1i3.38
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Study of the plastic-hinge analysis of 3D steel frames applying nonlinear
static analysis
Haitham Kannas1*, Abdallah M. S. Wafi1
1Civil Engineering Department, Near East University, Nicosia, Via Mersin 10, Turkey
A R T I C L E I N F O
ARTICLE HISTORY:
Received: 24 February 2020
Revised: 06 May 2020
Accepted: 06 May 2020
Published: 28 June 2020
KEYWORDS:
Pushover analysis, plastic
hinge, stiffness, lateral load
A B S T R A C T
This paper provides a distinct study on the performance of different residential buildings
with different height and length spans under the influence of applied loads according to
the Turkish standard TS498. The research paper presents the nonlinear performance of the
buildings and provides a clear picture of the plastic and its stages throughout the
construction. The study explains the effect of the various stages of plastic and how it
affects the rigidity of the building. The results portray the building's stiffness values and
how they change. The results show that stiffness increases with length-increase and
decreases by decreasing the height of buildings. All stiffness values were calculated
according to the first plastic hinge formation. Software used is ETABS 2018 and all
calculations and parameters used according to FEMA356-2000, ASCE 7-16, ACI-318,
EURO code 8, and Turkish standard.
1. INTRODUCTION
All global codes are now looking to work with
performance-based design, a small part of it being Pushover
Analysis. This study focuses on knowing, what is
performance-based design and Pushover Analysis? Also,
how the global codes will be used and how traditional
methods such as equivalent static and response spectrum are
not used commonly anymore.
Typically, if engineers wanted to enter the earthquake
load on the building, they would consider that the load is
10% of the building’s weight value (NCSC2015). With
updated knowledge regarding the science of ground motion,
engineers started taking into perspective the dynamic
characteristics. They discovered that different facilities
respond in different ways to the same earthquake according
to the time-period and the ductility of the building. Also,
how the ductility is expressed by codes through a parameter
which is R. R is an estimated value, which causes difficulty
since it is not accurate. If a building is designed based on
the unknown value of R and an earthquake were to occur,
the building could very easily collapse. Therefore, the idea
of designing a building to perform on its own came to
question. That can be done by studying the performance of
the building during an earthquake. Through that, the idea of
performance-based design formed (Macedo et al., 2019;
Leelataviwat et al., 2015).
Force-based design is a traditional method that we
depend on in modern day designing, providing strength in
order for the building to resist any external load that might
affect it, and stiffness to strengthen the serviceability
requirements of the building. Force-based design is also a
method that counters the static method and relies on the
building for an estimated force capacity and design force
capacity and the force it provides must not exceed its design
force capacity (Habibullah & Pyle, 1998).
This method is reliable in case of small earthquakes and
is useless in the case of large earthquakes. Therefore, we
turned to deformation and the nonlinear relationship
between strength and deformation. Whereas instead of
saying there is a force capacity that should not be
overlooked, we say that there is deformation that should not
be missed.
Deformation based design, the strength that the building
can withstand, will not be discussed. Rather the amount of
deformation that can happen to the building. It simply
means that instead of asking what the force capacity is, the
question should be the deformation capacity, which is the

International Journal of Advanced Engineering, Sciences and Applications (IJAESA)
Volume 1, Issue 3 (2020), Pages 24-29
ISSN: 2703-7266
DOI: https://doi.org/10.47346/ijaesa.v1i3.38
25
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method of deformation-based design. Also, in which we
have been dealing with the nonlinearity that is happening
instead of relying on the linear behaviour in the force
method-based design. Therefore, it should be depending on
the amount of deformation capacity in the building
(Sullivan et al. 2018).
So, there are two important factors to consider:
● The deformation capacity is the amount of deformation
allowed for the building. Which depends on the
ductility and the amount of cracking in the building.
● The deformation demand, which is caused by the
earthquake.
If the length of the deformation demand caused by the
earthquake is less than the deformation capacity, our
building is safe.
Even this method is flawed because it neglects the
building's performance. Therefore, instead of defining one
value which is the deformation capacity, it is possible to
define more than one value according to the building
performance level and this is the performance-based design
method.
The performance-based design does not rely on only one
aspect, which is the deformation capacity but takes into
account the building performance level, and we are able to
determine more than just the capacity point. Each point
represents a specific performance level of the building
(Shah & Patel, 2011; Tyagi & Tyagi, 2018).
2. BUILDINGS SPECIFICATIONS
All building models consist of a ground floor and other
storeys with an elevation of 3.2 m for all storeys.
Fig. 1. 3D model of N10-L5
The steel modelled low-rise, mid-rise and high-rise
buildings consisted of G+3 (4-storey), G+6 (7-storey) and
G+9 (10-storey) structures, with 3 different types of spans
length, 5, 5.5, 6 m. They have regular plans as shown in Fig.
1 The location was chosen at Lefkosa city in Northern
Cyprus. All structures are modeled as frames and secondary
beams under floor decks. Floor decks are modeled as a one-
way membrane element, the diaphragm is defined as semi-
rigid (Alkhattab et al., 2019).
3. METHODOLOGY
All models were designed in accordance with Euro code
3, using ETABS 2018 software, the smallest section has
been chosen which can carry out the applied loads.
The loads applied as follow, dead load is calculated by
the software, the live load is assumed 2 kN/m2, super dead
load has taken 1.5 kN/m2, and wind speed is assumed 15 m/s
according to TS498, Earth quick load with 10% exceedance
within 50 years (NCSC2015) (Alkhattab et al., 2019).
3.1. Linear static analysis
The first step we must analyse is to design all buildings
to have the best sections for all members.
Linear static analysis was used to apply all load
combinations according to Turkish standard TS 498-97 for
wind load definition, TSC-2007 for earthquake parameters,
and earthquake loads, both X and Y direction were used for
positive and negative (Naughton et al., 2017).
Finally, all section was chosen as shown in Fig. 2.
Fig. 2. Steel sections details N10-L5

International Journal of Advanced Engineering, Sciences and Applications (IJAESA)
Volume 1, Issue 3 (2020), Pages 24-29
ISSN: 2703-7266
DOI: https://doi.org/10.47346/ijaesa.v1i3.38
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3.2. Nonlinear static analysis
It is a non-linear static approximation to the response
shown by the origin when exposed to a dynamic seismic
load. Based on its primitive form on the representation of
the multi-degree of freedom MDOF response. In response
to an equivalent sentence with a single degree of freedom
ESDOF (AISC 2016, 2019).
This approximation includes the application of a side
load distributed to the height of the model of origin subject
to its vertical loads. This model takes into account the non-
linear properties of the elements, which are represented by
the general non-linear behaviour curve (strength -
transmission) for each type of element that is resistant to
side loads (Abhilash et al., 2009).
3.3. Performance level
An essential step before starting the procedures for non-
linear static analysis of any origin is to determine the level
of performance required of it when it is exposed to certain
seismic risk and to characterize the permissible damage in
structural and non-structural elements at this level.
The level of performance is defined according to (ATC-
40) as the condition in which the studied origin is desired
after being exposed to a specific ground movement. In other
words, it is the maximum level of damage permitted in a
building as a result of its exposure to a certain level of
seismic risk. The codes classified the performance levels for
any of the structures to a structural level SP and a non-
structural performance level NP (Monavari & Massumi
2012).
Structural performance levels are known as:
● Immediate Occupancy (IO):
Limited structural damage is permitted with structural
elements that resist vertical and horizontal loads
maintaining their properties and capacity, allowing the
facility to be used immediately after the earthquake.
● Life Safety (LS):
And in it, when an earthquake occurs, there will be
damage to some of the structural elements and they are
capable of repairing them, and damage will occur to the
non-structural elements and it will not be suitable for
repairing them.
● Collapse Prevention (CP):
Here, major damage occurs in the structural elements,
but there will be no collapse of the building. Also, at
this stage, injuries and deaths are expected to occur for
individuals present in the building. At this point, the
building cannot be repaired.
● Collapse:
The building collapses as well as some structural
elements.
Thus, when designing the building, the designer
should decide in determining the level of performance
of the building he wants, meaning that he wants the
building up to the IO, LS, or CP.
3.4. Pushover Analysis (PA)
The first step in any Pushover Analysis is to run a
gravity analysis. Yielding will rarely occurs in the gravity
analysis, however, the pattern of moment and forces that
develop in the individual structural components will have
an effect on the location and sequencing of hinges in the
lateral load phase of the analysis. The gravity load analysis
will also cause gravity-related P-Delta effects to be
activated (if such effects are explicitly included in the
analytical model (FEMA 451) (Honneshgowda & Chandra
2017; Hoang et al., 2015).
3.4.1 Pushover analysis procedure
● Design all structure members using
linear static analysis.
● Decide push displacement value considers a joint on the
highest level of the building.
● Define loads, convert dead load to nonlinear static load.
● Define Push overload on X and Y direction.
● Assign hinge properties to the column and beam.
● Select all members then choose hinge to overwrite to
have better results.
● Set loads to run, here just nonlinear load will set.
● Display pushover curve and calculate the stiffness as
per the found values.
● Display Pushover Curve, base shear vs displacement,
an example is shown in Fig. 3.
Fig. 3. Base shear (kN) vs monitored displacement (mm)
of N10-L6
3.5. Lateral loads used in nonlinear static analysis
One of the most important factors influencing the
sideload shape used in the non-linear static analysis in the
result of the analysis due to its expression in the distribution

International Journal of Advanced Engineering, Sciences and Applications (IJAESA)
Volume 1, Issue 3 (2020), Pages 24-29
ISSN: 2703-7266
DOI: https://doi.org/10.47346/ijaesa.v1i3.38
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of inertial forces arising in the elements of the studied
building during its shock to the floor (Youcef et al., 2018).
The basic codes identified some side loads of linear and
stationary shape during the stages of analysis that push the
origin in one direction. They are used in the methods of
analysis called Conventional Analysis Pushover (Maheri et
al., 2003).
3.6. Labelling system applied
Since all frames have same steel properties, simple
labelling has been used as ST-N-L-H-𝑓
𝑦.
where:
● ST: The structure type and ST refers to the steel
structure
● N: Number of storeys
● L: span length
● H: Floor height
● 𝑓
𝑦: steel compressive strength
For short labelling used in figures N-L as the same 𝑓
𝑦
(S275) and the same type of floor heights had been used.
4. STRENGTH AND STIFFNESS
Buildings along with other structures, and all parts
thereof, shall be designed and constructed with adequate
strength and stiffness to provide structural stability, protect
nonstructural components and systems (ASCE).
Structural systems, and members thereof, should be
designed under service loads to have enough stiffness to
limit deflections, lateral drift, vibration, or any other
deformations that adversely affect the intended use and
performance of buildings and other structures based on the
requirements outlined in the applicable codes and standards,
or as specified in the project design criteria (Hashemi et al.,
2018).
4.1. The relation between plastic hinges and stiffness
Fig. 4 shows the relation between base shear and
stiffness.
Fig. 4. Relation between base shear and stiffness
As the relation displacement-base shear is linear the
stiffness does not change unless there are no hinges formed
(Papanikolaou et al., 2008)
5. RESULTS AND DISCUSSIONS
The results are shown in Figs 5 to 10.
Fig. 5. Plastic hinges formation, ST-10-6-3.2-S275
Fig. 6. Formation places of plastic hinges N7-L6

International Journal of Advanced Engineering, Sciences and Applications (IJAESA)
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5.1. The effect of buildings height on stiffness factor (K)
The stiffness increases by increasing the height of the
building.
Fig. 7. Initial stiffness factor comparison of N4, N7, N10
buildings for same spans length
5.2. The effect of span length on the stiffness factor
The following figures show the effect of span length for
the same height stiffness factor.
Fig. 8. Initial stiffness factor comparison of N4 buildings
for different spans length
Fig. 9. Initial stiffness factor comparison of N7 buildings
for different spans length
Fig. 10. Initial stiffness factor comparison of N10
buildings for different spans length
The results prove that stiffness increases with the
increasing span length for the same height of buildings.
6. CONCLUSION
This paper provided a clear study on the plastic-hinge
analysis for 3D frames with different span lengths and
different floor heights. It then gave a clear procedure for
non-linear analysis step by step, first, by applying linear
analysis and then with results a study about the stiffness of
different number of floors.
Three kinds of buildings have been studied, high-rise,
mid-rise, and low-rise, buildings with three different span
lengths.
The results have shown that the stiffness becomes less
as the height of the building increases. This brings us to
believe that low-rise buildings are stiffer than high-rise
buildings and stiffness of the building declines as the span
length decreases. In conclusion, 3D frames become stiffer if
we increase the base area of the building.
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Volume 1, Issue 3 (2020), Pages 24-29
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DOI: https://doi.org/10.47346/ijaesa.v1i3.38
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