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Investigation of Rigid Floor Diaphragm Effects in Reinforced Concrete
Structures
Conference Paper · June 2020
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2. , Architecture
ineering
Civil Eng
International Congress on
.
th
4
and Urban Development
27-29 December 2016, Shahid Beheshti University , Tehran , Iran
Investigation of Rigid Floor Diaphragm Effects in
Reinforced Concrete Structures
Alireza Nazifkerdar1*, Taleb Moradi Shaghagi 2
1.Student of M.S Department of Civil Engineering group, Tabriz Branch, Islamic Azad University,
Tabriz, Iran,alirezanazifkerdar@gmail.com
2.Department of Civil Engineering group, Tabriz Branch, Islamic Azad University, Tabriz,
Iran,ta.moradi@yahoo.com
Abstract
Floor and roof systems are designed to carry gravity loads and transfer these loads to
supporting beams, columns or walls in addition they have a key role in distributing lateral
loads to vertical resisting systems and act as a diaphragm. Even though the assumption of
rigidity of floor diaphragm is used frequently, it can cause some error in some cases so
investigation of this assumption seems necessary. The main purpose of this paper is to
compare failure mechanism in reinforced concrete structures by using assumption of
flexible and rigid diaphragm and also Comparison of their response and comparing drifts,
columns and shear walls forces could be result of this paper. In the present study, five
main parametric models are used to investigate effects of rigidity of floor diaphragm in
behavior of reinforced concrete structures, these parameters are number of spans,
thickness of slab, existence of shear wall as a lateral load resisting system and thickness
of shear walls, all of the instances are modelled in two way, first with assumption of rigid
diaphragm and then with assumption of flexible diaphragm and linear and nonlinear time
history analyses are performed for each model and then their results are compared. It is
found that failure mechanism, with assumption of rigid diaphragm, is different from the
failure mechanism with assumption of flexible diaphragm in addition forces and drifts are
different when those two distinct assumption are used in modeling.
Keywords: Diaphragm, Rigidity, flexiblity, Time history linear and nonlinear analysis.
1. Introduction
In the analyses of multistory buildings subjected to lateral loads, a common assumption is that
the floor system undergoes no deformation in its own plane, building structures are typically
designed using the assumption that the floor systems serve as rigid diaphragm between the
vertical elements of the lateral load-resisting system [1].
The seismic response of buildings subjected to earthquake ground motion depends not only
on the characteristics of its vertical lateral force resisting systems, such as braces and frames,

3. , Architecture
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Civil Eng
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but also on horizontal lateral force resisting elements, the horizontal elements typically consist
of floor diaphragms[2].
In building structures subjected to lateral loads, the floor slabs which usually have the task of
transferring gravity loads to the vertical structural systems also act as a transfer medium for
inertial forces to the lateral load-resisting system in a diaphragm action, for the simplicity of
the analysis procedure and due to lack of understanding of the in-plane behavior of reinforced
concrete systems, floor slabs are frequently treated as perfectly rigid elements in current
design practice, however, experience and researches have demonstrated the importance of the
influence of flexible diaphragms on the seismic response of many types of buildings[3].
In the structural analysis of buildings, floor slabs are usually assumed to be rigid in their
planes at the mass center of each floor, there is a master node having three degrees of freedom
to represent the two in-plane transitions and one out-of-plane rotation of all the other nodes or
so-called slaved nodes in this floor [4].
A study which was done by Sashi K.Kunnah and Nader Panahshahi and Andrei M.Reinhorn
on 1991 shows that the in-plane deflections of floor slabs impose a larger demand on strength
and ductility of flexible frames than predicted values using the assumption of rigid or elastic
slabs [5].Another study which was done by S.H JU and M.C Lin on 1999 shows that for the
buildings without shear walls, the rigid-floor model is accurate as the flexible model even for
irregular floor systems and this is observed since the in-plane stiffness of the slab is much
larger than the out-of-plane column stiffness and for the buildings with shear walls, the rigid-
floor and flexible-floor analyses can differ greatly due to the very large lateral stiffness of the
shear wall system, the in-plane stiffness of the slab is relatively insignificant, and the slab in-
plane deformation cannot be ignored [4].
In this study, two main methods are used to analyse the samples. In the first method all cases
are modeled with assumption of rigid-floor diaphragm so three degrees of freedom are used to
represent each floor diaphragm, there are three degrees of freedom for transition and three
degrees of freedom which represent rotations in three-dimensional modeling for a node, and a
floor diaphragm is represented by a concentrated mass located in mass center of each floor. In
the second method all instances are modeled with assumption of flexible-floor diaphragm
which includes nodes in a diaphragm and each node has six degrees of freedom in a three-
dimensional modeling, there are three degrees of freedom for transitions and three degrees of
freedom for rotations, so the matrix of stiffness is larger than the matrix of stiffness with
assumption of rigid-floor diaphragm. The more nodes there are, the better in-plane
deformation you consider then the results of two distinct assumptions are compared.
In this paper, ETABS 2015 Ultimate V.15.0.0 are used for linear analyses and all nonlinear
analyses are performed by SAP 2000 Ultimate V 16.0.0.
2. The Feature of Models
Narrow and rectangular plans whose length-to-width ratios are 5 and 3 have been used in
modeling in addition story heights and column spaces (span dimensions) have been
considered 3200 mm and 6000 mm in row. It is important that all instances, used in this
paper, have rational structural elements so all structural elements, used in the models, have
been loaded and designed considering Iranian seismic code and concrete criterion and also
two way concrete slab system has been selected as a floor system in the all models. Table 1
shows parameters which is used in the models and table 1 and 2 show dimensions of
structural elements and figure 1, 2 and 3 indicate plans are used in this paper.

4. , Architecture
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Civil Eng
International Congress on
.
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Table 1: Parameters used in the models
Shear
wall
thickness
(
mm
)
Slab
thickness
(
mm
)
Story
heights
(
mm
)
Number
of
stories
Length-
to-
width
ratio
Dimension
of span
(
mm
)
Shape of
plans
Structural
system
Number
of
model
-
150
3200
3
3
6000
rectangular
Moment
frame
1
-
150
3200
3
5
6000
rectangular
Moment
frame
2
-
200
3200
3
5
6000
rectangular
Moment
frame
3
250
150
3200
5
5
6000
rectangular
dual
4
300
150
3200
5
5
6000
rectangular
dual
5
Table 2: dimensions of structural elements models 1 through 3
Dimensions
of beams
(
cm
)
Dimensions
of inner
columns
(
mm
)
Dimensions
of edge
columns
(
mm
)
stories
Number
of
stories
Span
dimension
(
mm
)
Structural
system
Number
of model
400×600
350×550
550×550
450×450
550×550
450×450
first
Second
and
third
3
6000
Moment
frame
1
400×600
350×550
550×550
450×450
550×550
450×450
first
Second
and
third
3
6000
Moment
frame
2
400×600
350×550
550×550
450×450
550×550
450×450
first
Second
and
third
3
6000
Moment
frame
3

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Table 3: dimension s of structural elements models 4 and 5
Figure 1: plan of model number 1
Figure 2: plan of models 2 and 3
Figure 3: plan of models 4 and 5
Dimensions
of beams
(mm)
Dimensions
of columns
in frame D
(
mm
)
Dimensions
of columns
in frames
B
and
E
(
mm
)
Dimensions
of edge
columns
(
mm
)
stories
Number
of
stories
Span
dimension
(
mm
)
Structural
system
Number
of
model
300×400
300×400
300×400
500×500
450×450
350×350
350×350
350×350
350×350
550×550
450
×
450
350×350
first
Second
and
third
fourth
and
fifth
5
6000
Dual
system
4
300×400
300×400
300×400
500×500
450×450
350×350
350×350
350×350
350×350
550×550
450
×
450
350×350
first
Second
and
third
fourth
and
fifth
5
6000
Dual
system
5

6. , Architecture
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1-2- procedure of Modeling
In this study, shell-thin element is used to model floor diaphragms and shear walls in addition
this element consists on in-plane behavior of floor diaphragm so all degrees of freedom are
free and it can transfer moments and shear forces. At each floor level, each panel of span has
divided into 6 pieces along X and Y axes and then shell-thin element has been assigned. The
rigid-floor diaphragm can be assigned in software if the master node is defined so all degrees
of freedom in a floor depend on master node which has only six degrees of freedom. Beam
and column elements has been used to model all beams and columns and all instances are
modeled and evaluated in 3 dimensions so it will be possible to consider the effects of floor
diaphragm.
The Northridge, Cape Mendocino and Tabas ground motion records are used to assigned as
lateral loads along Y axis and linear and nonlinear time history analyses are performed. The
linear time history analyses are used to compare forces and drifts in structural elements and
the nonlinear time history analyses are used to compare failure mechanism.
3. Analyses and Results
1-4- Model 1
With assumption of rigid diaphragm, the first model was subjected to Cape and Northridge and Tabas
ground motion and the first plastic hinge appears at 3.86th second in frame A, column A2; at 4.8th
second in frame A, column A2; at 10.84th second in frame B, column B1 in row. With assumption of
flexible diaphragm, it was subjected to Cape and Northridge and Tabas ground motion and the first
plastic hinge appeared at 5.42nd second in frame B, column B2; at 5th second in frame B, column B1;
in frame A column A2 in row. Figure 4 indicates development of plastic hinges at model 1 subjected to
Cape ground motion with assuming flexible and rigid diaphragm left to right in row.
Figure 4: development of plastic hinges in model 1 subjected to Cap ground motion
2-3- Model 2
With assumption of rigid diaphragm, the second model was subjected to Cape and Northridge
and Tabas ground motion and the first plastic hinge appears at 4th
second in frame B, column
B2; at 4.4th
second in frame B and C, column B2 and C2; at 10.76th
second in frame A, column
A2 in row. With assumption of flexible diaphragm, the second instance was subjected to Cape
ground motion as lateral load serving in operational performance level while subjected to
Northridge ground motion, collapse occur in the ground floor columns at 3.9th
second and
subjected to Tabas ground motion, the failure occurs in frame C, column C1 at 12.58th
second
of the analysis. Figure 5 shows development of plastic hinges at second model subjected to
Cape ground motion with assumption of flexible and rigid diaphragm left to right in row.

7. , Architecture
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Figure 5: Development of plastic hinges in model 2 subjected to Cape ground motion
3-3- Model 3
With assumption of rigid diaphragm, the thrid model was subjected to Cape and Northridge
and Tabas ground motion and the first plastic hinge appears at 4th
second in frame C, column
C1; at 5.02nd
second in frame C, column C1; at 10.78th
second in frame C, column C2 in row.
With assumption of flexible diaphragm, the third instance was subjected to Cape ground
motion as lateral load reaching operational performance level while subjected to Northridge
ground motion, collapse occured in frame A, column A2 at 3.98th
second and subjected to
Tabas ground motion, the failure occured in frame C, column C2 at 11.30th
second of the
analysis. Figure 6 shows development of plastic hinges at third model subjected to Cape
ground motion with assumption of flexible and rigid diaphragm left to right in row.
Figure 6: Development of plastic hinges in model 3 subjected to Cape ground motion
4-3- Model 4
With assumption of rigid diaphragm, the structure was subjected to Cape ground motion as a
lateral load reaching operational performance level while subjected to Northridge ground
motion, there was no plastic hinge during the analysis. Tabas ground motion was used as
lateral load and the structure reached operational performance level while the first hinge
appeared at 10.32nd
second of the analysis.
With assumption of flexible diaphragm, the fourth instance was subjected to Cape and
Northridge and Tabas ground motion and the first plastic hinge appeared at 6th
second in
frame A, column A2; at 5.2th second in frame A, column A1; in frame A column A1 in row.

8. , Architecture
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Figure 7 indicates development of plastic hinges at model 4 subjected to Cape ground motion
with assuming flexible and rigid diaphragm left to right in row.
Figure 7: Development of plastic hinges in model 4 subjected to Cape ground motion.
5-3- Model 5
With assumption of rigid diaphragm, the structure was subjected to Cape ground motion as a
lateral load reaching operational performance level while subjected to Northridge ground
motion, there was no plastic hinge during the analysis. Tabas ground motion was used as
lateral load and the structure reached operational performance.
With assumption of flexible diaphragm, the fifth instance was subjected to Cape and
Northridge and Tabas ground motion and the first plastic hinge appeared at 7.32nd
second in
frame A, column A2; in frame A, column A1 at the ground floor columns; at 10.4th
in frame A
column A1 in row. Figure 8 indicates development of plastic hinges at model 5 subjected to
Cape ground motion with assuming flexible and rigid diaphragm left to right in row.
Figure 8: Development of plastic hinges in model 5 subjected to Cape ground motion.
6-3- Forces and drifts comparing
The linear time history analyses are used to compare story drifts and shear forces in columns
and shear walls then the results are compared to achieve final conclusion in terms of
considering rigid and flexible diaphragm effects. The below figures illustrate the comparison
between these values.
In first model, the maximum difference in amount of drifts is 6 percent related to Tabas
ground motion and the maximum difference in shear forces is 8 percent related to Cape
ground motion in column C4 at 3rd
floor. See figure 9 through 11.

9. , Architecture
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Figure 9: Story drifts and column forces in model 1 subjected to Cape ground motion
Figure 10: Story drifts and column forces in model 1 subjected to Northridge ground motion
Figure 11: Story drifts and column forces in model 1 subjected to Tabs ground motion
In second model, the maximum difference in amount of drifts is 2 percent related to Cape
ground motion and the maximum difference in shear forces is about 3 percent related to Cape
ground motion in column C5 at 1st
floor. See figure 12 through 14.

10. , Architecture
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Figure 12: Story drifts and column forces in model 2 subjected to Cape ground motion
Figure 13: Story drifts and column forces in model 2 subjected to Northridge ground motion
Figure 14: Story drifts and column forces in model 2 subjected to Tabas ground motion
In third model, the maximum difference in amount of drifts is 2 percent related to Cape
ground motion and the maximum difference in shear forces is about 3 percent related to Cape
ground motion in column C2 at 1st
floor. See figure 15 through 17.

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Figure 15: Story drifts and column forces in model 3 subjected to Cape ground motion
Figure 16: Story drifts and column forces in model 3 subjected to Northridge ground motion
Figure 17: Story drifts and column forces in model 3 subjected to Tabas ground motion
In fourth model, the maximum difference in amount of drifts is 51 percent related to Tabas
ground motion and the maximum difference in shear forces is about 54 percent related to
Northridge ground motion in w2 at 2nd
floor. See figure 18 through 20.

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Figure 18: Story drifts and shear wall forces in model 4 subjected to Cape ground motion
Figure 19: Story drifts and shear wall forces in model 4 subjected to Northridge ground motion
Figure 20: Story drifts and shear wall forces in model 4 subjected to Tabas ground motion
In fifth model, the maximum difference in amount of drifts is 83 percent related to Northridge
ground motion and the maximum difference in shear forces is about 42 percent related to
Northridge ground motion in w1 at 2nd
floor. See figure 21 through 23.

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Figure 21: Story drifts and shear wall forces in model 5 subjected to Cape ground-motion
Figure 22: Story drifts and shear wall forces in model 5 subjected to Northridge ground-motion
Figure 23: Story drifts and shear wall forces in model 5 subjected to Tabas ground motion
4. Acknowledgments
In the structures without shear walls as lateral load resisting system, the assumption of rigid
floor diaphragm can be as accurate as the assumption of flexible floor diaphragm. However,
this assumption can cause some error in the amount of drifts and shear forces but these errors
are rather insignificant. In the structures with shear walls as lateral load resisting system, the
amount of these errors are noticeable so they can result in unwanted collapse in the structural
elements.
The failure mechanism, with assumption of rigid floor diaphragm, is different from the
assumption of flexible floor diaphragm in the same structure and this issue is more important
when shear walls exist in the structures as lateral load resisting system.

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References
[1] Morteza Moeini, Behzad Rafezy. Investigation into Floor Diaphragms Flexibility in Reinforced
Concrete Structures and Code Provision. Global Journal of Researches in Engineering, Global
Journals Inc (USA); 11(1): 25-36, 2011.
[2] Hadianfard M A, Sedaghat S. Investigation of joist floor diaphragm flexibility on inelastic
behavior of steel braced structures. Scientia Iranica, Sharif University of Technology; 20(3): 445-453,
2012.
[3] Nader Panahshahi, M Reinhorn Andrei, K Kunnath, Sashi, Lu,Le-Wulu, Ti Huang , Kai Yu.
Seismic Response of a 1:6 R.C Scale-Model Structure With Flexibile Floor Diaphragm. ACI
Structural Journal, ACI; 88(3): 315-324, 1991.
[4] S H Ju, M C Lin . Comparison of Building Analyses Assuming Rigid or Flexible Floors. Journal of
Structural Engineering, J Struct Eng; 125(1): 25-31, 1999.
[5] Sashi K Kunnah, Nader Panahshahi, Andrei M Reinhorn. Seismic Response of R.C Buildings With
Inelastic Floor Diaphragms. Journal of Structural Engineering,J Struct Eng; 117(4): 1218-1237,1991.
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