Volume 3, No. 7
July 2024 (1390-1408)
p-ISSN 2980-4868 |
e-ISSN 2980-4841
https://ajesh.ph/index.php/gp
Analysis of Diaphragm Force on Reinforced
Concrete Building Structures with Horizontal Irregularities of Diaphragm Discontinuity
Renita
Safitri1*, Relly Andayani2
1,2Universitas Gunadarma,
Depok, DKI Jakarta, Indonesia
Email: renitasafitri@yahoo.com
ABSTRACT
The diaphragm plays a crucial role in
distributing seismic forces within buildings during earthquakes, affecting both
regular and irregular structures differently. This study investigates the
seismic behavior of diaphragms in various building
geometries resembling the letters I, T, L, and O, focusing on their influence
on structural performance and reinforcement requirements. Using analytical
methods, diaphragm seismic forces, slab shear stresses, and internal forces
were calculated for a sample of buildings with different geometrical
irregularities. The study reveals significant differences in diaphragm
earthquake forces between regular and irregular buildings, with irregular
geometries exhibiting distinct patterns of shear stress distribution.
Particularly, the building with an L-shaped plan and concentrated stress points
showed the highest maximum shear stresses in both orthogonal directions.
Analysis of internal forces—axial, shear, and moment—highlighted varying
reinforcement needs among the studied buildings. While axial and shear forces
necessitated minimal additional reinforcement across all structures, moment
forces indicated substantial reinforcement requirements, particularly in the
L-shaped building. These findings underscore the importance of tailored
diaphragm design strategies for buildings with irregular geometries to mitigate
potential structural vulnerabilities during seismic events. The study
contributes insights into optimizing diaphragm design practices and emphasizes
the need for further research in this critical area of structural engineering.
Keywords: Diaphragms, Irregular, Shear Stress, Reinforcement.
According to
Bambang Budiono et al. (2016), in their research on the behavior of
building structures with irregularities to earthquake loads, the performance of
earthquake-sheltered buildings shows that irregular buildings, due to geometric
variations that affect stiffness, have a deviant response compared to regular
building structures. The combination of more than one irregularity in one of
the floors reviewed gave the worst response compared to all the case studies
conducted.
In their research,
Mangesh S. et al. (2017) showed the effect of geometric
irregularities through the collapse rate of reinforced concrete multi-story
buildings, which were investigated based on non-linear static analysis,
concluded that regular buildings were the last ones to collapse. Regular
buildings are said to be more able to withstand earthquakes for a long time
compared to irregular buildings with the shape of O, H and L plans which have
the smallest resistance of all these forms. Therefore, if there is an increase
in irregularities in buildings whose volume is fixed, the performance of the
building will decrease (Mohsenian
et al., 2020; Munni & Chandra Mohan Rao, 2022).
Research conducted
by Annie Sweetlin et al. (2016), who compared the displacement of
regular and irregular buildings due to earthquake forces, shows that irregular
buildings with smaller dimensional directions provide greater displacement. In addition,
the displacement of irregular buildings is lower than that of regular buildings
because it is influenced by the structure's mass reduction.
Diaphragm analysis
is closely related to the assumption of a given stiffness. In a study conducted
by Alexander et al. (2018), the diaphragm on the floor of the
building structure is classified into a flexible diaphragm on the upper floors
and a semi-rigid diaphragm or a rigid diaphragm on the lower floors. A
semi-rigid diaphragm stimulates stiffness in a way parallel to the true plane
of the diaphragm. The flexibility in a semi-rigid diaphragm can affect the
horizontal distribution of earthquake forces to vertical elements (Eivani
et al., 2022; Tena-Colunga & Sabanero-García,
2023).
Research related to
diaphragm floors in reinforced concrete multi-story buildings conducted by
Jadhav Anupriya P, et al. (2017) presented the types of diaphragms assumed
for buildings with and without sliding walls. Based on the results of the
study, buildings without sliding walls indicate more accurately modelled rigid
diagrams, while buildings with sliding walls give very different results
because of the rigidity of the sliding walls. However, the result of a
semi-rigid and flexible diaphragm is influenced by the irregular gemotriosis of the building.
The analysis of the
diaphragm force is related to the diaphragm's role. Egan et al. (2018) analyzed the force and moment around the
cord elements and collector beams due to the earthquake. The study's results
show that the diaphragm functions as a buffer for gravity and lateral
resistance. The cord element requires additional reinforcement in the tensile
area, and some collector blocks require additional bending reinforcement (Janardhanraj et al., 2022; Rezaeian et al., 2020). The diaphragm
itself is designed against shear forces and does not require additional
reinforcement.
Prijasambada et al. (2018), in their research on the analysis of
the diaphragm force of cords and collectors according to SNI 1726:2012, stated
that buildings with sliding walls designed against diaphragm force require
additional reinforcement of the diaphragm to the sliding wall as friction shear
reinforcement, collector element reinforcement and cord reinforcement. The
amount of additional reinforcement depends on the irregular level of the
building being analyzed (Massone et al., 2021).
The purpose of the
study is to design a building structure system with irregularities with plans
resembling I, T, L and O on the 2nd, 8th and 15th floors so that there is
horizontal irregularity of diaphragm discontinuity according to SNI 1726:2012
reference, analyze the diaphragm force that occurs on one floor and the
combination of earthquake force and analyze the shear stress of the floor plate
and analyze the internal force and calculate the need for additional
reinforcement due to the diaphragm force if Needed. With the results of the
calculation of the additional reinforcement requirements of the floor slab, a
more efficient design of building structure openings can be determined,
especially based on the need for extra cord reinforcement.
This study discusses regular and horizontal irregular buildings.
Buildings with horizontal irregularities are assumed to have openings or voids
with several schemes. They are designed with the same function, namely, an
office building, and they have the same earthquake load.
The general data of
the building structure analyzed are:
1.
Function :
Office Building
2.
Number of Floors : 17 Floors + 1 Roof
3.
Location :
South Jakarta
4.
Soil type :
Soft soil
5.
Building height : 63.7 m, with the floor height in
the following table.
Table 1. Building
Floor Height
|
It
|
Floor
|
Height
Between Floors (m)
|
|
1
|
1st Floor
|
4,5
|
|
2
|
Floors
2-17
|
3,5
|
|
3
|
Roof floor
|
3,2
|
Structure plan
The structural plan is delineated following the preliminary structural
plan to obtain openings in the floor plan under review (floors 2, 8, and 15)
that conform to the requirements of the building with type 3 horizontal
irregularities.
Figure 1. Floor
Plans of 2,8 and 15 Regular Buildings
Figure 2. Floor
Plans 2,8 and 15 Irregular Buildings
ETABS automatically calculates the loading data for the dead load
itself. For additional dead loads, the SIDL for a typical office floor is 3.29 kN/m2, and the SIDL for a roof floor is 1.48 kN/m2. Living load is the burden given due to the function
or use of the floor in the building. SNI 1727:2013 article 4.3.1 in table 4-1
has regulated the assumed cost of life. The living load for the office floor
from the table is 2.4 kN/m2, while for the
roof floor is 0.96 kN/m2. The preliminary design for
the structural components of the building was carried out in accordance with
the requirements of the SNI 1726:2012 earthquake and SNI 2847:2013 reinforced
concrete. So that it gets:
1.
The typical beam dimensions for the parent beam
are B40x70 and the daughter beam B30x50.
2.
The thickness of the plates used for the design,
H is 130 mm, and the roof plates are taken by 150 mm.
3.
Column dimensions:
12th – 17th floor: 600x600 mm.
Floor 6 – 11: 800x800 mm.
Floor 1 – 5: 1000x1000 mm.
This study uses a
calculation method and comparison of several structural analyses with building
modeling using ETABS v.16 software. Data collection is a software output that
is processed with equations that have been determined by the rules of structural
analysis. The calculation and checking of components also adjust to the
limitations of the structure. Systematically, here is a picture of the research
flow chart.
Irregularity
Checking
The irregularity
examination was carried out limited to horizontal irregularity examination
according to SNI 1726:2012 table 10. From the checks carried out, both regular
and irregular buildings do not have irregularities in torque and excess torque
(type 1a and 1b), irregularities in the inner corner (type 2), irregularities
in transverse shifts to the plane (type 4) and irregularities in non-parallel
systems (type 5). Regular buildings do not have type 3 horizontal
irregularities, namely diaphragm discontinuities, while these irregularities
are found in the following non-table buildings.
Table 2. Examination of diaphragm discontinuity
irregularities
|
Building Type
|
Floors reviewed
|
Full Floor Area
|
Opening Area
|
Percentage of Opening Area
|
Check Irregular Continuity of
Diaphragm Discontinuities
|
|
(m)
|
(m)
|
(%)
|
|
In the afternoon
|
Entire
|
1024
|
48
|
4.69
|
None
|
|
1st Irregular
|
2,8,15
|
1024
|
536
|
52,34
|
Exist
|
|
2nd Irregular
|
2,8,15
|
1024
|
536
|
52,34
|
Exist
|
|
3rd Irregular
|
2,8,15
|
1024
|
536
|
52,34
|
Exist
|
|
4th Irregular
|
2,8,15
|
1024
|
536
|
52,34
|
Exist
|
Diaphragm
Earthquake Force
The diaphragm
earthquake force for a certain floor is designed based on the equation contained in SNI 1726:2012 article 7.10.1.1. The
calculation data is in the form of structural analysis results in ETABS
software, such as diaphragm mass data, structural floor data and earthquake
lateral force calculation data according to dynamic earthquake analysis.
This procedure requires that the structural elements' strength be
adequate based on cross-sectional strength. This is done with concrete
run-design in ETABS, and the results obtained show that all structural
components are still safe based on cross-sectional strength with a combination
of loading. Based on the existing data, the table shows the diaphragm's
earthquake force design. These forces are assigned to each structural model for
diaphragm analysis on the 2nd, 8th, and 15th floors.
Table 3. Diaphragm Earthquake Force
|
Floor
|
Regular Buildings
|
Irregular 1
|
Irregular 2
|
Irregular 3
|
Irregular 4
|
|
FPX-X
|
FPX-Y
|
1,25
FPX-X
|
1,25
FPX-Y
|
1,25
FPX-X
|
1,25
FPX-Y
|
1,25
FPX-X
|
1,25
FPX-Y
|
1,25
FPX-X
|
1,25
FPX-Y
|
|
(kN)
|
(kN)
|
(kN)
|
(kN)
|
(kN)
|
(kN)
|
(kN)
|
(kN)
|
(kN)
|
(kN)
|
|
ROOF
|
1257,11
|
1256,97
|
1218,65
|
1215,02
|
1217,64
|
1212,33
|
1217,83
|
1217,98
|
1223,25
|
1221,99
|
|
Story17
|
1266,41
|
1265,62
|
1241,67
|
1239,64
|
1243,27
|
1243,69
|
1241,81
|
1241,13
|
1245,24
|
1243,07
|
|
Story16
|
923,14
|
923,17
|
926,08
|
923,40
|
926,85
|
922,00
|
926,31
|
926,53
|
929,64
|
926,94
|
|
Story15
|
885,30
|
885,30
|
553,35
|
553,35
|
553,37
|
553,37
|
573,31
|
573,31
|
593,31
|
593,31
|
|
Story14
|
495,59
|
496,37
|
477,69
|
481,18
|
478,39
|
483,41
|
477,63
|
478,15
|
475,50
|
479,18
|
|
Story13
|
380,17
|
380,86
|
376,61
|
378,85
|
376,81
|
378,27
|
376,39
|
377,20
|
374,64
|
377,07
|
|
Story12
|
313,99
|
314,49
|
320,10
|
322,85
|
320,26
|
324,04
|
320,03
|
320,61
|
317,05
|
319,55
|
|
Story11
|
291,98
|
292,82
|
308,24
|
309,98
|
307,65
|
311,42
|
307,66
|
308,33
|
304,11
|
306,59
|
|
Story10
|
296,51
|
296,76
|
320,44
|
321,36
|
319,91
|
321,11
|
320,29
|
320,78
|
317,75
|
318,78
|
|
Story9
|
323,82
|
324,33
|
353,06
|
352,32
|
352,45
|
350,86
|
352,84
|
353,37
|
351,80
|
351,44
|
|
Story8
|
885,36
|
885,36
|
553,39
|
553,39
|
553,41
|
553,41
|
573,35
|
573,35
|
593,36
|
593,36
|
|
Story7
|
394,51
|
394,61
|
371,47
|
371,17
|
372,01
|
372,59
|
371,35
|
371,29
|
373,19
|
373,36
|
|
Story6
|
424,77
|
424,31
|
412,28
|
410,99
|
413,00
|
410,13
|
412,73
|
412,53
|
415,51
|
414,05
|
|
Story5
|
434,71
|
434,46
|
428,83
|
426,91
|
428,84
|
426,59
|
428,81
|
428,62
|
431,23
|
429,60
|
|
Story4
|
408,67
|
408,36
|
405,69
|
403,60
|
406,14
|
402,89
|
405,97
|
405,67
|
408,81
|
406,61
|
|
Story3
|
349,34
|
348,69
|
346,65
|
344,84
|
346,79
|
344,32
|
346,79
|
346,37
|
348,79
|
347,06
|
|
Story2
|
885,42
|
885,42
|
553,44
|
553,44
|
553,47
|
553,47
|
573,41
|
573,41
|
593,43
|
593,43
|
|
Story1
|
131,92
|
130,79
|
119,83
|
119,79
|
119,94
|
121,05
|
119,85
|
119,21
|
120,38
|
120,13
|
Based on the
calculation of the diaphragm earthquake force for regular buildings, the design
earthquake force does not need to be increased by 25% of the diaphragm
earthquake force.
Diaphragm Shear
Voltage Analysis
The stage of modelling the structure with the input of the floor
diaphragm force into a load case is carried out to check the diaphragm
structure. The first analysis is to check the shear stress of the plate. It
should be noted to limit the minimum thickness of the plate designed as a
diaphragm plate by not taking into account the sliding reinforcement. The shear
stress limitations that occur in diaphragm plates are:
The quality of the concrete floor slab in
the 1st irregular building is fc' = 30 MPa, then:
Based on modelling with ETABS v.16 in a building with an aura and
irregularity, the shear stress that occurs on the plate (S12) due to the
diaphragm design earthquake load case (Fpx) for the
floors reviewed is less than the allowable voltage limit that can occur on the
plate from both directions reviewed. The following is a table of plate shear
stresses.
Table 4. Shear Tension Diaphragm Plate Floors 2,8 and 15
|
Floor
|
Regular Buildings
|
Irregular 1
|
Irregular 2
|
Irregular 3
|
Irregular 4
|
|
Direction X
|
Direction Y
|
Direction X
|
Direction Y
|
Direction X
|
Direction Y
|
Direction X
|
Direction Y
|
Direction X
|
Direction Y
|
|
(N/mm2)
|
(N/mm2)
|
(N/mm2)
|
(N/mm2)
|
(N/mm2)
|
(N/mm2)
|
(N/mm2)
|
(N/mm2)
|
(N/mm2)
|
(N/mm2)
|
|
Story2
|
2,27
|
2,81
|
1,64
|
1,19
|
1,94
|
0,55
|
3,79
|
3,93
|
1,14
|
0,68
|
|
Story8
|
3,04
|
3,08
|
1,94
|
1,34
|
2,25
|
0,6
|
4,03
|
4,11
|
1,46
|
0,85
|
|
Story15
|
3,27
|
3,34
|
2,05
|
1,38
|
2,42
|
0,66
|
4,24
|
4,32
|
1,51
|
0.92
|
From the table above, the plate's shear stress due to the diaphragm's
earthquake force is still below the allowable shear stress. Therefore, the
thickness of the building slabs for the 2nd, 8th, and
15th floors is still sufficient (OK).
Force Analysis in
Diaphragm
The next analysis to determine the influence of the design's lateral
force is to analyze the internal force that occurs in the diaphragm plate.
According to the plate's identification as a cord diaphragm, the internal force
is moment, axial force, and shear force.
Style capture in the diaphragm using section-cut tools provided by the
ETABS v.16 program. The location of the section cut is taken based on the
identification of the cord diaphragm according to each orthogonal direction due
to the earthquake force of the diaphragm design (Fpx-X
and Fpx-Y).
Based on the section cut made on the floor plate, the force in F11,
F22 and M. F11 is the force value in the direction of the force being reviewed,
so it is the shear force on the diaphragm plate. Meanwhile, F22 is the axial
force of attraction or compression on the diaphragm plate, and M is the bending
moment that occurs due to the lateral force of the diaphragm.
Section cut analysis was carried out for the 2nd, 8th and 15th floors
of regular and irregular buildings according to the cord diaphragm's location
and the section's position according to the initial identification. The
following are the results of the deep style from the section-cut analysis.
Table 5. Summary of
Styles in Regular Building Plates
|
Floor
|
Section Cut
|
Axial Force
|
Sliding Force
|
Momen
|
|
kN
|
kN
|
kNm
|
|
Floor2
|
SCut-A
|
0
|
153,8
|
2078,4
|
|
|
SCut-B
|
0
|
112,7
|
2436,1
|
|
Floor8
|
SCut-A
|
0
|
145,2
|
3146,0
|
|
|
SCut-B
|
0
|
98,2
|
3634,1
|
|
Floor15
|
SCut-A
|
0
|
167,8
|
4303,3
|
|
|
SCut-B
|
0
|
117,0
|
4901,8
|
Table 6. Summary of
Styles in 1st Irregular Building Slabs
|
Floor
|
Section Cut
|
Axial Force
|
Sliding Force
|
Momen
|
|
kN
|
kN
|
kNm
|
|
Floor2
|
SCut-A
|
27,7
|
67,4
|
789,7
|
|
|
SCut-B
|
0
|
70,4
|
1280,5
|
|
Floor8
|
SCut-A
|
48,8
|
72,8
|
1091,2
|
|
|
SCut-B
|
0
|
49,7
|
1767,7
|
|
Floor15
|
SCut-A
|
60,7
|
97,1
|
1541,1
|
|
|
SCut-B
|
0
|
70,8
|
2342,5
|
Table 7. Summary of
Styles in 2nd Irregular Building Slabs
|
Floor
|
Section Cut
|
Axial Force
|
Sliding Force
|
Momen
|
|
kN
|
kN
|
kNm
|
|
Floor2
|
SCut-A
|
26,75
|
144,75
|
213,37
|
|
|
SCut-B
|
146,83
|
210,55
|
668,28
|
|
|
SCut-C
|
28,45
|
109,58
|
174,43
|
|
|
SCut-D
|
31,86
|
79,08
|
266,39
|
|
Floor8
|
SCut-A
|
29,1
|
164,15
|
266,39
|
|
|
SCut-B
|
157,62
|
202,37
|
813,52
|
|
|
SCut-C
|
32,69
|
102
|
189,61
|
|
|
SCut-D
|
43,44
|
70,19
|
220,71
|
|
Floor15
|
SCut-A
|
38,81
|
175,51
|
329,28
|
|
|
SCut-B
|
168,22
|
211,64
|
873,08
|
|
|
SCut-C
|
47,54
|
144,89
|
283,19
|
|
|
SCut-D
|
61,45
|
94,44
|
386,34
|
Table 8. Summary of
Styles in 3rd Irregular Building Slabs
|
Floor
|
Section Cut
|
Axial Force
|
Sliding Force
|
Momen
|
|
kN
|
kN
|
kNm
|
|
Floor2
|
SCut-A
|
175,3
|
102,7
|
809,3
|
|
|
SCut-B
|
389,2
|
97,2
|
1257,5
|
|
Floor8
|
SCut-A
|
168,2
|
97,6
|
761,5
|
|
|
SCut-B
|
415,3
|
131,8
|
1122,3
|
|
Floor15
|
SCut-A
|
162,4
|
106,2
|
711,3
|
|
|
SCut-B
|
434,9
|
177,7
|
810,5
|
Table 9. Summary of the Force in the 4th Irregular Building Plate
|
Floor
|
Section Cut
|
Axial Force
|
Sliding Force
|
Momen
|
|
kN
|
kN
|
kNm
|
|
Floor2
|
SCut-A
|
198,5
|
58,5
|
206,9
|
|
|
SCut-B
|
19,7
|
46,1
|
167,5
|
|
|
SCut-C
|
48,3
|
32,0
|
121,8
|
|
|
SCut-D
|
48,6
|
31,4
|
119,8
|
|
Floor8
|
SCut-A
|
71,3
|
52,0
|
125,9
|
|
|
SCut-B
|
48,0
|
5,7
|
114,7
|
|
|
SCut-C
|
52,1
|
9,9
|
125,5
|
|
|
SCut-D
|
52,0
|
10,5
|
130,1
|
|
Floor15
|
SCut-A
|
14,2
|
123,1
|
230,0
|
|
|
SCut-B
|
7,3
|
28,2
|
110,4
|
|
|
SCut-C
|
61,7
|
9,8
|
171,0
|
|
|
SCut-D
|
61,7
|
9,8
|
172,3
|
Diaphragm Plate
Auxiliary Reinforcement
The floor slab was initially analyzed based on the gravity load
according to the floor function. In this study, the burden given is for office
buildings with a special load, namely the burden of the office lobby. The
thickness of the floor slab is t = 130 mm, and the reinforcement installed
based on the combination of gravity loads is D10-200 for both positive
reinforcement and negative reinforcement in both directions.
Furthermore, the plate is designed with a lateral force diaphragm, and
according to the section-cut analysis that has been carried out, the internal
force of the plate is used as a parameter for calculating the rebar
requirement. In the literature review, equations have been presented to obtain
the nominal strength value of the structural components. The calculation is in
the form of nominal axial force (φTn), nominal shear force (φVn) and nominal cord moment (φMn).
The deep force analysis was carried out on all pieces of each floor
reviewed for regular and irregular buildings. This analysis shows that the
internal force in the form of axial and shear does not exceed the nominal
strength provided by the concrete and the rebar attached to the gravity loading
plate. However, the force in the moment in some pieces exceeds the nominal
capacity of the plate, so it is necessary to add reinforcement, namely the
moment reinforcement of the cord. The summary of the results of the force
analysis on the diaphragm floor plate is as follows:
Table 10. Summary
of Force Analysis in Regular Building Slabs
|
Floor
|
Section Cut
|
Check Axial Force
|
Check Sliding Force
|
Check the Cord Moment
|
|
Your
|
Tn
|
Cheque
|
Vu
|
ϕVn
|
Cheque
|
In the
|
ϕMn
|
Cheque
|
|
kN
|
kN
|
|
kN
|
kN
|
|
kNm
|
kNm
|
|
|
Floor2
|
SCut-A
|
64,95
|
1336,32
|
OK
|
153.80
|
4308,67
|
OK
|
2078.40
|
3848,60
|
OK
|
|
|
SCut-B
|
76,13
|
1336,32
|
OK
|
112.70
|
4308,67
|
OK
|
2436.10
|
3848,60
|
OK
|
|
Floor8
|
SCut-A
|
98,31
|
1336,32
|
OK
|
145.20
|
4308,67
|
OK
|
3146.00
|
3848,60
|
OK
|
|
|
SCut-B
|
113,57
|
1336,32
|
OK
|
98.20
|
4308,67
|
OK
|
3634.10
|
3848,60
|
OK
|
|
Floor15
|
SCut-A
|
134,48
|
1336,32
|
OK
|
167.80
|
4308,67
|
OK
|
4303.30
|
6841,96
|
OK
|
|
|
SCut-B
|
153,18
|
1336,32
|
OK
|
117.00
|
4308,67
|
OK
|
4901.80
|
6841,96
|
OK
|
Table 11. Summary
of Force Analysis in 1st Irregular Building Slab
|
Floor
|
Section Cut
|
Check Axial Force
|
Check Sliding Force
|
Check the Cord Moment
|
|
Your
|
Tn
|
Cheque
|
Vu
|
ϕVn
|
Cheque
|
In the
|
ϕMn
|
Cheque
|
|
kN
|
kN
|
|
kN
|
kN
|
|
kNm
|
kNm
|
|
|
Floor2
|
SCut-A
|
49,36
|
668,16
|
OK
|
67,4
|
2017,62
|
OK
|
200,448
|
962,15
|
OK
|
|
|
SCut-B
|
40,02
|
1336,32
|
OK
|
70,4
|
4308,67
|
OK
|
400.90
|
3848.60
|
OK
|
|
Floor8
|
SCut-A
|
68,20
|
668,16
|
OK
|
72,8
|
2017,62
|
OK
|
200.45
|
962.15
|
Cheque
|
|
|
SCut-B
|
55,24
|
1336,32
|
OK
|
49,7
|
4308,67
|
OK
|
400.90
|
3848.60
|
OK
|
|
Floor15
|
SCut-A
|
96,32
|
668,16
|
OK
|
97,1
|
2017,62
|
OK
|
200.45
|
962.15
|
Cheque
|
|
|
SCut-B
|
73,20
|
1336,32
|
OK
|
70,8
|
4308,67
|
OK
|
400,90
|
3848,60
|
OK
|
Table 12. Summary
of Force Analysis in 2nd Irregular Building Slabs
|
Floor
|
Section Cut
|
Check Axial Force
|
Check Sliding Force
|
Check the Cord Moment
|
|
Your
|
Tn
|
Cheque
|
Vu
|
ϕVn
|
Cheque
|
In the
|
ϕMn
|
Cheque
|
|
kN
|
kN
|
|
kN
|
kN
|
|
kNm
|
kNm
|
|
|
Floor2
|
SCut-A
|
26,67
|
334,080
|
OK
|
144,75
|
803,74
|
OK
|
213,37
|
240,54
|
OK
|
|
|
SCut-B
|
63,05
|
442,66
|
OK
|
210,55
|
1064,96
|
OK
|
668,28
|
422,29
|
Cheque
|
|
|
SCut-C
|
16,46
|
442,66
|
OK
|
109,58
|
1064,96
|
OK
|
174,43
|
422,29
|
OK
|
|
|
SCut-D
|
25,13
|
442,66
|
OK
|
79,08
|
1064,96
|
OK
|
266,39
|
422,29
|
OK
|
|
Floor8
|
SCut-A
|
33,30
|
334,08
|
OK
|
164,15
|
803,74
|
OK
|
266,39
|
240,54
|
Cheque
|
|
|
SCut-B
|
76,75
|
442,66
|
OK
|
202,37
|
1064,96
|
OK
|
813,52
|
422,29
|
Cheque
|
|
|
SCut-C
|
17,89
|
442,66
|
OK
|
102
|
1064,96
|
OK
|
189,61
|
422,29
|
OK
|
|
|
SCut-D
|
20,82
|
442,66
|
OK
|
70,19
|
1064,96
|
OK
|
220,71
|
422,29
|
OK
|
|
Floor15
|
SCut-A
|
41,16
|
334,08
|
OK
|
175,51
|
803,74
|
OK
|
329,28
|
240,54
|
Cheque
|
|
|
SCut-B
|
82,37
|
442,66
|
OK
|
211,64
|
1064,96
|
OK
|
873,08
|
422,29
|
Cheque
|
|
|
SCut-C
|
26,72
|
442,66
|
OK
|
144,89
|
1064,96
|
OK
|
283,19
|
422,29
|
OK
|
|
|
SCut-D
|
36,45
|
442,66
|
OK
|
94,44
|
1064,96
|
OK
|
386,34
|
422,29
|
OK
|
Table 13. Summary
of Force Analysis in 3rd Irregular Building Slabs
|
Floor
|
Section Cut
|
Check Axial Force
|
Check Sliding Force
|
Check the Cord Moment
|
|
Your
|
Tn
|
Cheque
|
Vu
|
ϕVn
|
Cheque
|
In the
|
ϕMn
|
Cheque
|
|
kN
|
kN
|
|
kN
|
kN
|
|
kNm
|
kNm
|
|
|
Floor2
|
SCut-A
|
101,16
|
334,08
|
OK
|
102,7
|
803,74
|
OK
|
809,3
|
240,54
|
Cheque
|
|
|
SCut-B
|
118,63
|
442,66
|
OK
|
97,2
|
1064,96
|
OK
|
1257,5
|
422,29
|
Cheque
|
|
Floor8
|
SCut-A
|
95,19
|
334,08
|
OK
|
97,6
|
803,74
|
OK
|
761,5
|
240,54
|
Cheque
|
|
|
SCut-B
|
105,88
|
442,66
|
OK
|
131,8
|
1064,96
|
OK
|
1122,3
|
422,29
|
Cheque
|
|
Floor15
|
SCut-A
|
88,91
|
334,08
|
OK
|
106,2
|
803,74
|
OK
|
711,3
|
240,54
|
Cheque
|
|
|
SCut-B
|
76,46
|
442,66
|
OK
|
177,7
|
1064,96
|
OK
|
810,5
|
422,29
|
Cheque
|
Table 14. Summary
of Force Analysis in 4th Irregular Building Slabs
|
Floor
|
Section Cut
|
Check Axial Force
|
Check Sliding Force
|
Check the Cord Moment
|
|
Your
|
Tn
|
Cheque
|
Vu
|
ϕVn
|
Cheque
|
In the
|
ϕMn
|
Cheque
|
|
kN
|
kN
|
|
kN
|
kN
|
|
kNm
|
kNm
|
|
|
Floor2
|
SCut-A
|
51.73
|
167.04
|
OK
|
58.5
|
401.87
|
OK
|
206.9
|
60.13
|
Cheque
|
|
|
SCut-B
|
41.88
|
167.04
|
OK
|
46.1
|
401.87
|
OK
|
167.5
|
60.13
|
Cheque
|
|
|
SCut-C
|
25.64
|
198.36
|
OK
|
32.0
|
477.22
|
OK
|
121.8
|
84.80
|
Cheque
|
|
|
SCut-D
|
25.22
|
198.36
|
OK
|
31.4
|
477.22
|
OK
|
119.8
|
84.80
|
Cheque
|
|
Floor8
|
SCut-A
|
31.48
|
167.04
|
OK
|
52.0
|
401.87
|
OK
|
125.9
|
60.13
|
Cheque
|
|
|
SCut-B
|
28.68
|
167.04
|
OK
|
5.7
|
401.87
|
OK
|
114.7
|
60.13
|
Cheque
|
|
|
SCut-C
|
26.42
|
198.36
|
OK
|
9.9
|
477.22
|
OK
|
125.5
|
84.80
|
Cheque
|
|
|
SCut-D
|
27.39
|
198.36
|
OK
|
10.5
|
477.22
|
OK
|
130.1
|
84.80
|
Cheque
|
|
Floor15
|
SCut-A
|
57.50
|
167.04
|
OK
|
123.1
|
401.87
|
OK
|
230.0
|
60.13
|
Cheque
|
|
|
SCut-B
|
27.60
|
167.04
|
OK
|
28.2
|
401.87
|
OK
|
110.4
|
60.13
|
Cheque
|
|
|
SCut-C
|
36.00
|
198.36
|
OK
|
9.8
|
477.22
|
OK
|
171.0
|
84.80
|
Cheque
|
|
|
SCut-D
|
36.27
|
198.36
|
OK
|
9.8
|
477.22
|
OK
|
172.3
|
84.80
|
Cheque
|
Based on the table above, only the force in the chord moment requires
additional reinforcement. The additional reinforcement requirements for the
required floors are based on the regular and irregular building sections-cuts
in the following table.
Table 15. 1st
Irregular Building Auxiliary Reinforcement
|
Floor
|
Section Cut
|
Additional Reinforcement
|
Additional Tonnage
|
|
Kg
|
|
8th Floor
|
SCut-A
|
D10 - 400
|
429
|
|
15th Floor
|
SCut-A
|
D10 - 400
|
429
|
Table 16. 2nd
Irregular Building Auxiliary Reinforcement
|
Floor
|
Section Cut
|
Additional Reinforcement
|
Additional Tonnage
|
|
Kg
|
|
2nd Floor
|
SCut-B
|
D10 - 400
|
216
|
|
8th Floor
|
SCut-A
|
D10 - 400
|
118
|
|
8th Floor
|
SCut-B
|
D10 - 400
|
216
|
|
15th Floor
|
SCut-A
|
D10 - 400
|
118
|
|
15th Floor
|
SCut-B
|
D10 - 400
|
216
|
Table 17. 3rd
Irregular Building Auxiliary Reinforcement
|
Floor
|
Section Cut
|
Additional Reinforcement
|
Additional Tonnage
|
|
Kg
|
|
2nd Floor
|
SCut-A
|
D10 - 200
|
326
|
|
2nd Floor
|
SCut-B
|
D10 - 200
|
471
|
|
8th Floor
|
SCut-A
|
D10 - 200
|
326
|
|
8th Floor
|
SCut-B
|
D10 - 400
|
235
|
|
15th Floor
|
SCut-A
|
D10 - 200
|
326
|
|
15th Floor
|
SCut-B
|
D10 - 400
|
235
|
Table 18. 4th
Irregular Building Auxiliary Reinforcement
|
Floor
|
Section Cut
|
Additional Reinforcement
|
Additional Tonnage
|
|
Kg
|
|
2nd Floor
|
SCut-A
|
D10 - 200
|
155
|
|
2nd Floor
|
SCut-B
|
D10 - 300
|
104
|
|
2nd Floor
|
SCut-A
|
D10 - 400
|
92
|
|
2nd Floor
|
SCut-B
|
D10 - 400
|
92
|
|
8th Floor
|
SCut-A
|
D10 - 400
|
78
|
|
8th Floor
|
SCut-B
|
D10 - 400
|
78
|
|
8th Floor
|
SCut-A
|
D10 - 400
|
92
|
|
8th Floor
|
SCut-B
|
D10 - 400
|
92
|
|
15th Floor
|
SCut-A
|
D10 - 200
|
155
|
|
15th Floor
|
SCut-B
|
D10 - 400
|
78
|
|
15th Floor
|
SCut-A
|
D10 - 400
|
92
|
|
15th Floor
|
SCut-B
|
D10 - 400
|
92
|
The reinforcement for the cord moment is installed like the repetition
of the bending moment of a typical plate. The length of the rebar installed
corresponds to the cut diaphragm's length and the cord plate's width.
Comparison of Calculation Results
The results of the analysis of the shear stress and force in the
diaphragm plate are very verifiable. The relatively same diaphragm seismic
force loading input for an irregular building provides a maximum shear stress
value that tends to differ in the two directions reviewed (Akelyan et al., 2020). Likewise, the value of force in the diaphragm, where there is
additional reinforcement due to the moment of the chord. The following is a
comparison of the variables of the calculation results.
Table 19.
Comparison of Diaphragm Force, Shear Tension, Cord Moment and Additional
Reinforcement Calculation Results
|
Floor
|
Building Type
|
Fpx-Design
|
Fair. Geser-Max
|
Momen Kord-Max
|
Additional Reinforcement
|
|
FPX-X
|
FPX-Y
|
FPX-X
|
FPX-Y
|
Direction X
|
Direction Y
|
|
(kN)
|
(kN)
|
(kN/m2)
|
(kN/m2)
|
(kNm)
|
(kNm)
|
(Kg)
|
|
Floor
|
Regular
|
885.42
|
885.42
|
2.27
|
2.81
|
2078.4
|
2436.1
|
0
|
|
2
|
1st Irregular
|
553.44
|
553.44
|
1.64
|
1.19
|
789.7
|
1280.5
|
0
|
|
|
2nd Irregular
|
553.47
|
553.47
|
1.94
|
0.55
|
668.3
|
266.4
|
216
|
|
|
3rd Irregular
|
573.41
|
573.41
|
3.79
|
3.93
|
809.3
|
1257.5
|
613
|
|
|
4th Irregular
|
593.43
|
593.43
|
1.14
|
0.68
|
206.9
|
121.8
|
422
|
|
Floor
|
Regular
|
885.36
|
885.36
|
3.04
|
3.08
|
3146.0
|
3634.1
|
0
|
|
8
|
1st Irregular
|
553.39
|
553.39
|
1.94
|
1.34
|
1091.2
|
1767.7
|
429
|
|
|
2nd Irregular
|
553.41
|
553.41
|
2.25
|
0.60
|
813.5
|
220.7
|
364
|
|
|
3rd Irregular
|
573.35
|
573.35
|
4.03
|
4.11
|
761.5
|
1122.3
|
433
|
|
|
4th Irregular
|
593.36
|
593.36
|
1.46
|
0.85
|
125.9
|
130.1
|
324
|
|
Floor
|
Regular
|
997.10
|
996.96
|
3.27
|
3.34
|
4303.3
|
4901.8
|
0
|
|
15
|
1st Irregular
|
553.35
|
553.35
|
2.05
|
1.38
|
1541.1
|
2342.5
|
429
|
|
|
2nd Irregular
|
553.37
|
553.37
|
2.42
|
0.66
|
873.1
|
386.3
|
364
|
|
|
3rd Irregular
|
573.31
|
573.31
|
4.24
|
4.32
|
711.3
|
810.5
|
433
|
|
|
4th Irregular
|
593.31
|
593.31
|
1.51
|
0.92
|
230.0
|
172.3
|
398
|
From the table above, it can be seen that based on the calculation
results, regular buildings are given the largest diaphragm force because
regular buildings have a full floor plan without voids that are>50% of the
total area of a floor plan. Meanwhile, the earthquake force of the irregular
building diaphragm has a relatively similar value. The difference is due to the
arrangement and beams of different floor plans. The order from the largest is
the 4th, 3rd, 2nd and 1st irregular buildings for all floors. The diaphragm
shear voltage is still below the allowable shear stress. The order for X
Direction of the largest is that the 3rd, 2nd, 1st and 4th irregular buildings
are consistent for all floor zones. For the Y direction, the order is the 3rd,
1st, 4th and 2nd buildings.
The force in the plate presented is the value of the moment of the
cord, where the greatest value occurs in a regular building because the width
of the cut diaphragm covers the entire plan. For irregular buildings, the
moment of the cord is very varied, considering the width of the diaphragm or
the length of the section cut, which is different according to the floor plan. The
need for additional reinforcement is required based on the moment the cord
occurs. Overall here is the total need for additional
reinforcement.
Table 20. Total
Reinforcement Needs
|
Building Type
|
Additional Reinforcement
|
|
(kg)
|
|
In the afternoon
|
0
|
|
1st Irregular
|
858
|
|
2nd Irregular
|
944
|
|
3rd Irregular
|
1479
|
|
4th Irregular
|
1144
|
Based on the results of analysis and
calculations, the researcher concluded that the regular and irregular buildings
with horizontal discontinuities of diaphragms (letter plans I, T, L, O) on the
2nd, 8th, and 15th floors, which are given lateral loads in the form of
diaphragm force show the need for additional details on the diaphragm cord
plates. The shear stress shows a large value in irregular buildings L, and the
greatest chord moment reinforcement is produced with the deep force used for
the calculation. However, there are factors such as the geometry of the
building that also influence it. The calculation of diaphragm force in
irregular buildings shows relatively the same value but produces very varied
internal forces. Forces in axial and shear plates do not require additional
repetition details, while cord moments require additional reinforcement. This
deep force analysis shows the number of reinforcement requirements, where the
largest total requirement is a regular building with an L plan, and then O, T,
I, and regular buildings do not require additional reinforcement. The researcher
suggests that the next research study should review the irregularities of other
buildings and/or buildings with more than 1 irregularity. In addition, it is
necessary to develop other structural variables, such as the distribution and
rigidity of the structure due to diaphragm earthquake forces.
Akelyan, M. S., Brandow, G., Carpenter,
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Renita
Safitri, Relly Andayani
(2024)
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