Effect of P-Delta Due To Different Eccentricities in Tall Structures

International Journal of Engineering Science & Invention
ISSN (Online): 2319 – 6734, ISSN (Print): 2319 – 6726
www.ijesi.org ||Volume 6 Issue 6|| June 2017 || PP. 06-13
www.ijesi.org 6 | Page
Effect of P-Delta Due To Different Eccentricities in Tall
Structures
1
Dr. Latha M S, 2
Naveen Kumar B M
1
Associate Professor, Ph. D., 2
Assistant Professor, M. Tech.
Sri Venkateshwara College Of Engineering, Vidyanagar, Bia Road, Bangalore, Karnataka, India,
Highlights: Study Includes Comparison Of Symmetrical And Asymmetrical Building In Zone 4 & 5 Due To P-
Effect.
ABSTRACT: P-effect in structure mainly rises from the direct action of lateral forces and the structure in a
state of equilibrium where the deformed structure shape is a more responsible factor. This kind of effect is made
in the analysis of second order, where the geometry of the elements is come from their changed condition.
Gravitational loads on the construction elements, deform producing extra forces, which are not taken into
account during calculations of structures in un-deformed shape. The given gravitational loads are more
precisely defined, in the group of action forces in a structure, can't be said that their change from project
values, will be the determining factor in the effect of P-Delta, but in defining order remains the geometry of the
structure. More detail the geometry is defined as the correct second order effects could be considered in
structures. In this paper static & dynamic analysis has been performed using with and without P-delta for
symmetry & asymmetry Reinforced Concrete (RC) frame building models by varying different eccentricities
levels from 0, 10, 20 & 30 percent. Results of comparison between symmetrical & Asymmetrical building in
zone 4 & 5 are conferred and conclusions are made.
Keywords: Wind load (EQX), Displacement, and different level of eccentricity, P-delta analysis, Symmetry &
Asymmetry building.
I. Introduction
P-Δ effect on structure mainly arise from the direct action of lateral forces & terminate the structure in
a state of equilibrium where the deformed structure shape is a more determining factor. This kind of effect is
made in the analysis of second order, where the geometry of the elements comes from their changed condition.
Gravitational loads on their way through the construction elements, where this one are deformed to produce
additional forces, which are not taken into account during calculations of structures in un- deformed shape. The
given gravitational loads are the loads, more precisely defined, in the group of action of forces in a structure, we
can’t say that their change from project values, will be the determining factor in the effect of P-Delta, but in
deforming order remains the geometry of the structure.
II. Literature Survey
Some of the parametric studies on buildings considering effect of P-Delta by different eccentricities on
tall buildings by considering symmetry as well as asymmetry building with static and dynamic behavior with &
without P-Delta for different eccentricity level.
Rafael Shehu, 2014 [1], Building behaviour is an element of various elements and their interaction
versus outside activity picked by us. This exchange transcends the geometry of the structure, its hardness and
their connections capacities. The primary parameters of the connection capacities are loads at the current stage.
With loads we mean static and dynamic, while the calculation stage I refer to the stage conduct of the material
and structure, the flexible stage or post versatile stage, without distorted or twisted components. Every stage is
acknowledged or let’s say, inexact in estimations techniques and altering some standard methods. In this
discussion we will address in a compact manner, two key factors in the configuration of structures, which are
second order effects (P-Delta) and the ductility of structures. Both components have risen as a need of
approximating genuine complex conduct in a design system. Will would like to better comprehend the
connection of these two different methodologies, contemplating distinctive philosophy and way to deal with the
issue by looking at the outline necessities. What we remain for change, is to expand the exactness of basic
analyses for structures at the design stage of internal force. It is realized that a nonlinear examination is more
precise than a direct analyses, however then again is an inefficient analysis in term as time consuming with
calculations and PC memory. The arrangement for our situation would oblige a little memory and quick time.

Effect Of P-Delta Due To Different Eccentricities In Tall Structures
Yousuf Dinar, Nazim Uddin Rahi, Pronob Das, 2013 [2],
This paper assesses deflection of the steel skyscraper structure because of the P-Delta impact
considering the global slenderness of the entire structure. For simple and fast plan just Linear Static examination
is performed and secondary loading impact is neglected in a few underdeveloped and developing nations of
South Asia. Utilizing STAAD Pro v8i, 40 different models is recreated to watch the seriousness of the P-Delta
wonder against standard Linear Static system. 4 different stories were joined with 5 varying span in both
directions for differing the slenderness of the structure. During investigation lateral load imposed with UBC94
to perform the seismic events in two different seismic moderate danger zone of Bangladesh utilizing Bangladesh
National Building Code (BNBC) comparing coefficients however wind load is overlooked to watch the seismic
event impact in Steel skyscraper structure exclusively expecting result choice would be same if the reproduction
would accomplished for wind load too. This examination uncovers how pivotal side of the structure creates
different deflections with changing slenderness. Test outcomes were assessed by story deflection (in 'mm') and
rate of variety of deflection was performed by looking at P-Delta yields with Linear Static Method outputs.
Christoph Adam, Luis f. Ibarra, Helmut Krawinkler, 2011 [3]
This paper addresses the evaluation of destabilizing impacts of gravity, generally referred to as P-Delta
impacts, in exceptionally inelastic structures when subjected to seismic excitations. The proposed methodology
is taking into account an identical single-degree of freedom (ESDOF) system of the real building. Appropriate
properties of the ESDOF framework are characterized, taking into account after effects of a relating global
pushover analysis investigations. P-Delta impacts are consolidated by which is pivoted by a uniform stability
coefficient. The methodology is assessed for a few multi-story generic fame structures. The breakdown limit of
these structures is derived from a set of Incremental Dynamic Analysis (IDA) studies including 40 ground
movements whose power is expanded until P-Delta instability occurs. The results are translated from the
ESDOF area into the space of the multilevel of-opportunity (MDOF) framework, and used for the estimation of
P-Delta effects in MDOF structures. "Careful" results are contrasted from results of the investigations using
ESDOF frameworks. Assumption and limitations of the ESDOF framework methodology are examined. The
accentuation is on the level of reaction at which the structure approaches dynamic instability (sideway fall).
III. Details of Structure
In the present study, 3D RC frames of symmetry and asymmetry building with 5 x 5 bays and 8 x 4
bays with G+40 and G+ 41 storeys are taken into consideration. The RC frames to be designed as per BIS codes.
Namely, IS 456-2000, “Plain and Reinforced Concrete code of practice”, IS 1893-2002 (Part 1), “Criteria for
Earthquake Resistant design of structures” and, M25 concrete is assumed and both mild steel and tor steel are
used for reinforcement. But in this journal there is only static case with zone 4.
Symmetry case : Live load =4kN/m2
: Super dead load =1.5kN/m2
Asymmetry case : Live load =1.5kN/m2
: Super dead load =3.5kN/m2
IV. Details Of Frame
 Breadth of Beam, b = 0.23 m
 Depth of Beam, d = 0.60 m
 Breadth of Column, b = 0.90 m
 Depth of Column, d = 0.90 m
 Thickness of slab, = 0.230 m
 Height of masonry infill, h = 3.6 , 3 m (For Bottom &Other Floors)
 Grade of Steel = Fe 415
 Poisson’s ratio of concrete, μ = 0.20
V. Details Of Frame
 Breadth of Beam, b = 0.23 m
 Depth of Beam, d = 0.60 m
 Breadth of Column, b = 0.90 m
 Depth of Column, d = 0.90 m
 Thickness of slab, = 0.230 m
 Height of masonry infill, h = 3.6 , 3 m (For Bottom &Other Floors)
 Grade of Steel = Fe 415
 Poisson’s ratio of concrete, μ = 0.20

VI. Parameters
Symmetric building the plan regular building structure consists of 5 X 5 bays i.e. 5 bays along each X and Y
direction. Dimensions of plan area 20m X 20m.
Figure-1: Model 1 Symmetrical Building (Plan & Elevation)
Model type 1: 5 m X 5 m, G+41, at 0, 10, 20, and 30 percent of eccentricity level with p delta and without p
delta is evaluated using ETABS analysis software, and compared with seismic zone 4 with earthquake loading
in X direction.
Table-1: Displacement for Static Case along X Direction
For symmetrical building in zone 4 the equivalent static case with P-delta along EQX direction table -1 gives a
clear explanation regarding the maximum displacement along various storey levels with improving its
eccentricity levels up to 30 percent.
Comparison of EQX with p delta
Story eqx0 eqx10 eqx20 eqx30
STORY40 190.1784 215.1094 240.0397 264.9696
STORY35 176.9113 200.7886 224.6652 248.5416
STORY30 157.7328 179.5496 201.3657 223.1815
STORY25 133.9044 152.8549 171.8048 190.7545
STORY20 106.8846 122.3754 137.8657 153.3556
STORY15 78.0449 89.6649 101.2844 112.9037
STORY10 48.6479 56.137 63.6258 71.1144
STORY5 20.1351 23.3874 26.6395 29.8915
STORY1 1.9376 2.2723 2.6069 2.9416

Figure-2: Displacement for static case along x direction with p-delta.
In the Table-1 and Figure-2, the maximum displacement at 40 storey level is 190.178mm along X
direction for 0 eccentricity for 10 percent of eccentricity 215.1094mm for 20 percent eccentricities 240.397mm
similarly for 30- percent eccentricity 264.9696mm. Since in all the level of storey as the eccentricity increases
the level of displacement also increases as shown in the Figure-1 with P-Delta.
Table-2: Displacement for Static Case Along X Direction Without P-Delta
Comparison of EQX without p delta
STORY40 157.604 194.0638 217.2544 240.4449
STORY35 146.1777 180.6271 202.783 224.9388
STORY30 129.6829 160.7359 180.8916 201.0474
STORY25 109.4198 136.0219 153.435 170.8481
STORY20 86.7847 108.2213 122.3729 136.5246
STORY15 63.0155 78.8614 89.4192 99.9771
STORY10 39.1759 49.2427 56.0228 62.8028
STORY5 16.3322 20.6568 23.6115 26.5661
STORY1 1.6187 2.0652 2.376 2.6867
For symmetrical building in zone 4 the equivalent static case without P-delta along EQX direction
Table -2 gives a clear explanation regarding the maximum displacement along various storey levels with
improving its eccentricity levels up to 30 percent.

Figure-3: displacement for static case along x direction without p-delta
Table -3: Displacement for static case along X direction with p-delta.
Asymmetric building the plan irregular building structure consists of 8X4 bays. Dimensions of plan area 42m
X 18m

Figure-4: model 2 asymmetrical building (plan & elevation)
Model type 2: 8 m X 4 m, G+40, at 0, 10, 20, and 30 percent of eccentricity level with p delta and
without p delta is evaluated using ETABS analysis software, and compared with seismic zone 4 with earthquake
loading in X direction.
Table-3: displacement for static case along x direction with p-delta
STORY40 226.12 244.93 277.67 297.7
STORY35 212.97 230.43 257.33 275.55
STORY30 187.45 201.89 222.03 236.87
STORY25 158.59 170.34 185.79 197.78
STORY20 124.92 133.64 144.66 153.52
STORY15 93.671 100.2 108.22 114.83
STORY10 59.768 63.929 68.968 73.182
STORY5 24.58 26.291 28.345 30.076
STORY1 1.789 1.9132 2.0621 2.1878
In the Table-3 and Figure-3, the maximum displacement at 40 storey level is mm along X direction, for
0 eccentricity 226.12mm for 10 percent of eccentricity 244.93mm for 20 percent eccentricities 277.67mm
similarly for 30- percent eccentricity 297.7mm. Since in all the level of storey as the eccentricity increases the
level of displacement also increases as shown in with P-Delta.

Figure-5: Displacement for Static Case Along X Direction With P-Delta
Table-4: Displacement for Static Case Along X Direction Without P-Delta
STORY40 221.74 240.88 260.02 279.16
STORY35 205.48 222.84 240.2 257.56
STORY30 177.98 192.03 206.08 220.13
STORY25 148.86 160.16 171.46 182.76
STORY20 116.02 124.32 132.62 140.93
STORY15 86.221 92.378 98.535 104.69
STORY10 54.656 58.557 62.457 66.358
STORY5 22.532 24.136 25.739 27.343
STORY1 1.6787 1.7972 1.9158 2.0343
In the Table-4 and Figure-5, the maximum displacement at 40 storey level is mm along X direction, for
0 eccentricity 226.12 .for 10 percent of eccentricity 244.93mm for 20 percent eccentricities 277.67mm similarly
for 30-percent eccentricity 297.7mm. Since in all the level of storey as the eccentricity increases the level of
displacement also increases as shown in with P-Delta.
Figure-6: Displacement for Static Case Along X Direction Without P-Delta.

VII. Conclusions
1. In the elastic static analyses, impact of P-Delta dependably increased, as number of stories of structures or
their eccentricity will increase.
2. In the dynamic analyses, the impacts of P-Delta becomes more reduce the response. The reason is to
execute P-Delta analyses in implementing change in stiffness matrix of building, consequently the normal
periods and other dynamic properties of the building will change. On the other hand acceleration comparing
to the new natural time of building, response spectrum of the earthquake, is not as much as increasing speed
reaction relating to the first normal period, then decrease in building reactions for the case were P-Delta can
be normal.
3. "Effect of different eccentricities of building due to tall structures" basically relies on upon the type of
horizontal Load resisting system of building. The outcomes show that the kind of horizontal load resisting
system assumes a vital part in degree that torsion changes the P-Delta effects. It is reasoned that the
qualities of lateral load resisting framework has significantly more significance stand up in comparison with
the number of stories in building.
4. It is seen that the impacts of P-Delta is quite sensitive to ground movement, for example, the frequency
content of quake. The affectability is still vital however not exactly the dynamic cases. All in all, the
affectability to ground motion increases, as the eccentricity increases.
5. In flexible or inelastic dynamic analyses, increase in eccentricity causes change in the impact of P-Delta.
The change is essential in elastic analysis and is fairly less critical in inelastic analysis. Then again, the
variation does not have a constant expanding or decreasing pattern. One of the reasons is the way that with
expansion in the eccentricity, the mass moment of inertia has not expanded in all cases.
6. From the above results it can be reasoned that the impact of "P-Delta" analyses is discovered higher in static
and dynamic analyses and the impact of "P-Delta" analyses is much higher when the plan of building is
asymmetric with respect to symmetric building.
References
[1]. Rafael Shehu., “The P-Δ-Ductility Effect: Overview the Effect of the Second Order in the Ductile Structures”, European Scientific
Journal, 2014; 3; 1857 – 7881.
[2]. Yousuf Dinar., Nazim Uddin Rahi., Pronob Das., “Variation of Deflection of Steel High-Rise Structure Due to P-Delta Effect
considering Global Slenderness Ratio” , International Journal of Emerging Technology and Advanced Engineering, 2013; 3(12);
2250-2459.
[3]. Christoph Adam., Clemens Jager., “A Rough Collapse Assessment of Earthquake Excited Structural Systems Vulnerable to the P-
Delta Effect”, COMPDYN 2011 III ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and
Earthquake Engineering, 2011; 25–28

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