International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 04, April 2019, pp. 1080-1088. Article ID: IJCIET_10_04_114
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=10&IType=04
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
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STRONG COLUMN WEAK BEAM CONCEPT BY
ANALYSING RCC MRF FRAME BY NON
LINEAR STATIC PROCEDURE
Ajay Singh Thakur
M.E Student, Department of Civil Engineering, Chandigarh University Garhuan
Jagdish Chand
Assistant Professor, Chandigarh University Garhuan
ABSTRACT
During past earthquakes column plastic hinges are more prominent than beam
hinges which gives rise to global structural damage and high life threatening risk. All
the structural components transfers their forces through column and column than
shares it with foundation to soil, so u can imagine if column fails whole structure can
collapse this is strong beam weak column concept. By making column more moment
resistant than beams the plastic hinges shifts to beam and avoids the global damage in
this case only beam will show flexure as a sign of beam damage and the people will
have adequate time to evacuate the place and beam failure will only limit to a particular
storey. This concept is strong column weak beam. In this paper three RC frame of 5, 8
and 12 storey height are investigated for strong column weak beam concept for zone 5
and medium soil and moment capacities are checked as per IS1893:2016. For checking
the performance of plastic hinges of column and beam non linear static analysis
(pushover analysis) is done in ETABS 2016 these hinges are checked and verified
according to acceptance criteria given in FEMA 356. Base shear and performance
point with displacement is checked for all frames.
Keywords: Etabs, pushover analysis, moment capacity ratio, performance point,
FEMA356.
Cite this Article: Ajay Singh Thakur and Jagdish Chand, Strong Column Weak Beam
Concept by Analysing RCC MRF Frame by Non-Linear Static Procedure, International
Journal of Civil Engineering and Technology, 10(4), 2019, pp. 1080-1088.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=04
1. INTRODUCTION
The formation of plastic hinges in beams helps to build the most desired and suitable energy
dissipating mechanism for structure in seismic conditions. If the plastic hinges are formed on
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Ajay Singh Thakur and Jagdish Chand
both ends of column then column is not able to spread the plasticity and collapses which can
lead to global failure. In previous earthquakes same things had happened column fails early in
compression than beams in flexure lead to life threatening condition of people in buildings.
The case study of previous earthquakes in India like 1897 Assam earthquake of magnitude
8.0Mw, 1905 Kangra earthquake of magnitude 7.8Mw, 1934 Nepal Bihar earthquake of
magnitude 8.0Mw, 2001 Bhuj earthquake of 7.7Mw magnitude, 2005 Kashmir earthquake of
magnitude 7.6Mw, 2015 Nepal earthquake of 7.8Mw shows that the Reinforced Concrete
structure have shown poor performance during strong earthquake in showing ductility of the
structure. The main and common failure was the beam column failure, storey failure, column
collapsing ahead of beam, short column effect. The irregular building invites large base shear
and they are in greater risk but the failure of regular frames without major structure irregularity
is the major concern in this paper. The failure modes in all the past earthquakes are almost
similar and strong beam weak column comes out to be a major problem which leads columns
to sway or sway mechanism and these structures also have lack of ductile detailing in beam
and column joints. All international codes follows strong column weak beam concept and have
different value of β (beta) for different country codes. The code provision says that the moment
in column should be β times stronger than beams.
∑Mc ≥ β x ∑Mb
(1)
TABLE 1 Values of Moment Capacity Factor for Various International Codes
Value of β
1.2
1.4
1.4
1.4
International codes
American standard (ACI 318M-02)
New Zealand standard (NZS3101:1995
European standard (NZS3101:1995
Indian standard (IS13920:2016)
Pushover analysis is static non linear analysis and is know by pushover method which can
be performed with the help of guidelines given in FEMA356, 440 and ATC40 and this analysis
comes under static analysis and is absent from our IS1893:2016 so we have to follow FEMA
and ATC guidelines for approaching the performance of structure. Hinges were assigned to
column and beam after analysis for gravity load to check the plastic performance of
components and record and checks the hinge rotations for performance. This analysis can be
operated on various packages like Etabs, SAP2000 and STAAD Pro. This analysis is the main
keys for performance based design which helps in designing the key column and beams for
new structure and retrofits the old structure by checking the plastic hinge acceptance criteria
given by FEMA356. This picture shows the performance criteria of building in which IO
means Immediate Occupancy LS means life safety CP means collapse prevention which comes
in B to C which is plastic zone in which the structure ductility yields for plastic behaviour.
Figure 1 Shear Force vs. Deformation
Figure 2 a) Strong column weak beam behaviour
b) Weak column strong beam
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Strong Column Weak Beam Concept by Analysing RCC MRF Frame by Non-Linear Static
Procedure
A comparison of moment capacity ratio of beam and column was done by Yangbing Liu,
Yuanxin Liao & Nina Zhen 2012 by varing the capacity ratio from 0.8 to 2.2 to improve the
bearing capacity at node end of column and beam has suggested that with the decrease in
ductility column loses its strength and β = 1.2 gives first hinge on column base and β =1.6 gives
beam sway moment. Another research by Dooley & Bracci, 2001; Haselton et al., 2011;
Ibarra & Krawinkler, 2005 shows that for tall buildings the present over strength factor of
1.2 is not sufficient to prevent the mechanism of plastic hinges and for 4 storey and more the
over strength factor of 2 shows complete beam sway mechanism suggested by (Haselton et
al., 2011; Ibarra & Krawinkler, 2005). B Shiva kumara Swamy, S K Prasad, Sunil N 2015
concludes in their research that the structure with least stiffness ratio by varying the dimension
of beam and column are vulnerable to seismic excitation with the help of pushover analysis
and the results are compared for different zones and soil type. A total of 15 structures of 12, 18
and 24 storey with varying capacity ratio from 1.2 to 2.0 was analysed by Cagurangan (2015)
and numerical modelling was done on opensess and response of beams and column for
incremental dynamic analysis was plotted on research paper.
2. STRUCTURE GENERAL INFORMATION
The structural frame consists of 2 mid rise and 1 high rise RC building frame was selected
which comes in category of SMRF (special moment resistant frame) due to its zone type which
is zone 5 means the frame will be designed under IS456:2000 and IS1893:2002 and 2016 part1
and IS13920:2002 and 2016 . These frames is first designed for gravity loading and then the
results of rebar percentage, column beam capacity ratio and seismic results are checked and if
the result are passed then further pushover analysis is done for plastic capacity of structure by
assigning hinges in beam column and performance is checked for all frames but in some cases
beam and column dimensions are not sufficient for some combination for seismic and gravity
loading so the dimensions are modified to reduce the rebar percentage for economic purpose
and maintaining the column beam capacity ratio and then pushover is done to check the damage
and performance of 3 frames. These frames are without dual frame structure like shear wall,
dampers, struts which helps in dissipating energy or distributing seismic energy to check the
actual performance of frame.
3. METHODOLOGY WITH BUILDING DESCRIPTION
The buildings consist of 5x5 grid of plan area 22.5m2 (4.5x4.5) m with bottom storey height
which includes the distance of foundation from plinth beam and storey height is kept same as
3.3m with varying floors (g+5, g+8, g+12) in north India with average imposed load 3KN/m2
for residential building per IS875:1987 Part 2 table 1 which includes one or multy family
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Ajay Singh Thakur and Jagdish Chand
dwelling house, apartment, lodging houses and residential hotels. Dead loads are taken from
IS875:1987Part 1 in which floor finish is taken to be 1.5KN/m2 and wall load is calculated as
per bricks unit weight (20-21KN/m3) which is uniformly distributed in the beams in
ETABS2016. The material property for concrete is M30 and Rebar for main bars TMT500 is
used and for confinement Fe415 bars is chosen. Beam of size 230x600 mm and column size of
300x600mm for G+5, G+8 frame and 400x800 mm columns for G+12 were chosen. Property
modifiers were applied as per IS1893:2016 new code for column and beam as per clause
6.4.3.1. Beams and column dimensions were chosen keeping in mind the updated clause 6.1
and 7.1 of IS13920:2016 by following the general requirements and minimum reinforcement
requirements. Slab thickness is taken as 120mm and slab are taken as membrane due to its in
plane property and its can be changed according to behaviour of slabs as out of plane , in plane
as shell thin and thick. Wall thickness is taken as 230mm to make it compatible with beam
width. In load pattern wall load and floor finish is taken as super dead and seismic cases for x
and y direction is added with zone 5 and importance factor 1.5. After modelling the frames are
analysed for gravity load and after passing the section in gravity load seismic cases are run to
check the model capacity ratio , rebar percentage and the rebar for columns are checked for
economic purpose and the section is modified for decreasing rebar percentage. After analysing
for gravity load pushover analysis is done by unlocking the model and assigning push x and
pushy in load pattern and then in load cases convert dead case to nonlinear from linear and then
modify push x and push y from starting pushover over analysis after dead case for analysing
frames after linear load. Beams are selected for hinges having parameter M3 (flexural case)
and columns for P-M2-M3 at distance of 0 and 1 from both ends and then relative distance
of 0.02 is auto selected by Etabs. After assigning hinges the analysis was run only for dead and
push cases with load combinations and results of Base shear vs. Displacement and performance
point was located and frames are checked for that specific performance in which beams and
column hinges was checked as per acceptance criteria in FEMA 356.
4. RESULTS AND DISCUSSION
4.1. a) Base shear vs. Monitored displacement for G+ 5 storeys and Hinge results.
Step
Monitored
Displacement
0
1
2
3
4
5
6
7
8
9
10
11
12
0.003
60.725
93.941
112.907
137.43
161.632
183.158
227.151
242.008
278.833
326.188
328.335
328.335
Base
Force
kN
0
2068.3783
2921.9216
3167.9284
3320.4682
3386.0808
3420.9655
3464.6354
3474.3627
3509.4416
3558.3566
3553.8273
3553.8277
A-B
B-C
C-D
D-E
>E
A-IO
IOLS
LSCP
>CP
Total
1560
1556
1416
1350
1276
1224
1178
1164
1164
1150
1150
1150
1150
0
4
144
210
284
336
382
396
396
410
408
406
406
0
0
0
0
0
0
0
0
0
0
2
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1560
1560
1560
1560
1556
1548
1542
1508
1478
1336
1300
1300
1300
0
0
0
0
0
0
0
28
58
198
208
206
206
0
0
0
0
0
0
0
0
0
0
24
22
22
0
0
0
0
4
12
18
24
24
26
28
32
32
1560
1560
1560
1560
1560
1560
1560
1560
1560
1560
1560
1560
1560
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Strong Column Weak Beam Concept by Analysing RCC MRF Frame by Non-Linear Static
Procedure
Performance point of G+5 frames and Sa vs. Sg curve
Step
0
1
2
3
4
5
6
Monitored
Displacemen
t
mm
0.005
118.805
124.082
163.516
185.056
207.728
230.876
Base
Force
KN
0
4027.6632
4206.5844
5228.8925
5524.2412
5677.2806
5751.1532
A-B
B-C
C-D
D-E
>E
A-IO
IOLS
LSCP
>CP
Total
2340
2340
2332
2112
1968
1892
1852
0
0
8
228
372
448
488
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2340
2340
2340
2340
2340
2338
2338
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2340
2340
2340
2340
2340
2340
2340
4.2. b) Base shear vs. Monitored displacement for G+8 storeys and Hinge results.
The maximum base shear for the building under push x is 5757.1532KN and the performance
point for this frame is 5685KN which is acceptable and in Sa VS Sg graph the reading are with
respect to time and shown in below picture the values of t(secent and effective) are given. The
dispcement and time with respect to this graph is matched with pushover curve (base shear vs
displacement ) and hinges are checked only for those points (performance point) and hinges
moments and results is checked and the results of 8 storey frame shows that the displacement
of performance point is 210.298mm which is between 207.728 mm and 230.876mm and plastic
hinges are formed upto immidiate occupancy as shown in above table 1b) in step 5-6 only 2
hinges are greater than collapse prevention which can be modified with the help of increasing
size of columns or by changing the oriantation of column.
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Performance point of G+8 frames and Sa vs. Sg curve
4.3. c) Base shear vs. Monitored displacement og G+12 storeys and Hinge results.
Step
0
1
2
3
4
5
6
7
8
9
10
11
Monitored
Displacemen
t
mm
0.014
97.332
126.602
174.51
348.148
530.388
557.514
706.09
706.115
706.173
706.176
707.003
Base
Force
kN
0
2207.3565
2697.8315
3009.1402
3489.2293
3752.7342
3783.1108
3888.9235
3888.9316
3888.9802
3888.9474
3889.474
A-B
B-C
C-D
D-E
>E
A-IO
IOLS
LSCP
>CP
Total
3380
3370
3122
2942
2722
2606
2582
2544
2544
2544
2544
2544
0
10
258
438
658
774
798
836
836
836
836
836
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3380
3380
3380
3380
3380
3136
3078
2870
2870
2870
2870
2870
0
0
0
0
0
242
298
500
500
500
500
500
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
2
4
8
8
8
8
8
3380
3380
3380
3380
3380
3380
3380
3380
3380
3380
3380
3380
The performace point for 12 storey frame is 3778 KN which comes near to maximum base
shear it shows that with the increasing of storey height the buildings need shear wall to resist
the sway and reduce the shear force for dissipating energy as we know the shear wall is more
stronger than columns and the displacement is 553.293 mm which comes between step 5-6 in
table 1c) the plastic hinges is this step is also safe because the size of column is increased for
this building to satisfy the capacity moment ratio and rebar percentange.
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Strong Column Weak Beam Concept by Analysing RCC MRF Frame by Non-Linear Static
Procedure
Performance point of G+12 frames and Sa vs. Sg curve
The hinges formed in G+12 storeys frame first appeared in beam and follows same patterns
indicate the beam failure in flexure than column in axial compression in push x.
Figure A) Hinge state coloured as per B, C, D, and E point. B) Hinge state coloured for IO, LS, and
CP.
The above Figures depicts the maximum hinge moments for maximum deflection in push
x case for 12 storey frame and some columns in figure b are in collapse condition which can
be fixed but this is for maximum push case in which only 8 hinges are in collapse prevention
so for this case the bottom storey column size can be increased for some storeys or shear wall
can reduce the hinges moment and reduce the base shear and displacements
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Figure c) Step 1 of push x case in 2d in elevation d) step 11 of push x case in elevation
The c and d figure are hinges as per B, C, D and E criteria and the green colour shows the
hinges in b to c zoneich shows the first hinge in beam and supports the strong column weak
beam concept and shows beam sway.
5. CONCLUSION
The results concluded that the cross section of beam and column matters a lot in designing
capacity-based design based on strong column weak beam concept which is systematically
represented by the hinges formed during pushover analysis.
The moment capacity ratio plays a major role in increasing the ductility of column and
moment resistivity of column is increased as per the code guidelines.
The frame follows mixed pattern in which only the bottom node of column in ground floor
shows hinge formation and rest follows beam mechanism.
With the increasing of storey height the performance point and displacement also increased
which implies the need of shear walls for lowering the displacement and increasing the strength
of building.
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