EXPERIMENTAL MODELING OF IN FILLED RC FRAMES …€¦ · strength of infilled frames with openings...

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International Journal of Civil Engineering and Technology (IJCIET)

Volume 7, Issue 2, March-April 2016, pp. 95–106, Article ID: IJCIET_07_02_007

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ISSN Print: 0976-6308 and ISSN Online: 0976-6316

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EXPERIMENTAL MODELING OF IN

FILLED RC FRAMES WITH OPENING

M.E. Ephraim

Department of Civil Engineering, Rivers State University of Science and Technology,

P.M.B 5080 Port Harcourt, Rivers State, Nigeria

T.C. Nwofor

Department of Civil Engineering, University of Port Harcourt,

P.M.B 5323 Port Harcourt, Rivers State, Nigeria

ABSTRACT

Reinforced concrete frames are usually infilled with masonry walls but, in

most designs, both the shear strength capacity of these walls and the

contribution of the infill panel openings on the shear strength of the infilled

frame, especially in critical cases of seismic loading are generally ignored.

This paper reports the results of an experimental study of the influence of

central openings in the infill on the sway stiffness of reinforced concrete plane

frames. A series of 1:4 scaled structural models with opening ratios from 0 to

50 percent in steps of 10 percent were designed, constructed and tested in the

study to obtain the load - displacement profiles. The test results were validated

with output of FE models of the prototype walls using SAP 2000 analysis

software. The results confirm that 1:4 model adequately reproduces the

behavior of infilled frame with openings including lateral stiffness and

anisotropy. The six percent accuracy of predicted shear strength of infilled

frames under lateral loadings as a function of opening ratio is considered

sufficient for engineering design purposes.

Key words: Modeling, Similitude Requirement, Sway Deflection and

Stiffness.

Cite this Article: M.E. Ephraim and T.C. Nwofor, Experimental Modeling of

In Filled RC Frames with Opening, International Journal of Civil Engineering

and Technology, 7(2), 2016, pp. 95–106.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=7&IType=2

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=7&IType

M.E. Ephraim and T.C. Nwofor


1. INTRODUCTION

It has been established that the consideration of the infill panel in the design of RC

frame structures results in a complex modeling problem because of the large number

of interacting parameters and the many possible modes of failure that need to be

evaluated with a high degree of uncertainty[1 - 9]. The need to obtain a deeper

understanding of the influence of openings on the composite behavior of infilled

frames has further led to the development of more and more complex models with

ever increasing number of parameters [10-16]. An experimental study in which all

these factors could be taken into account is difficult to implement for obvious reasons

[17-19]. Thus, in most cases, the use of finite element approach has been considered a

most viable option in spite of its computational complexities and resource

requirements. For these reasons, the need for more simplified models of the composite

behavior of infilled frame has been recognized by researchers. In this regard, perhaps

the most popular of the simplified models remains the one-strut model (OSM),

proposed by Polyakov [10]. However, the major challenges in the development of this

model is in deciding the value of the width of the equivalent strut on the one side and

how to account for the effect of openings on the other. In this study, the shear

strength of infilled frames with openings was investigated using the structural

modeling theory and appropriate experimental techniques. The main aim of the study

was to obtain experimental data to assess the magnitude and trend of variation of the

shear strength of reinforced concrete infilled plane frames as a function of the opening

ratio. The brick masonry infill panel incorporated various sizes of square openings,

centrally located in the infill. The frame thus varied from the fully infilled frame to

the bare frame configurations. The effects of the opening ratio on the strength,

stiffness and drift of the infilled sway frames under lateral racky load were

investigated and the outputs compared with values obtained on the basis of numerical

analysis by the finite element method.

2. GEOMETRICAL CHARACTERISTICS OF MODEL FRAMES

The structural design of the prototype frame was carried out in accordance with

Eurocode 6, BS EN 1996 (2006) the lateral load capacity Q calculated. A series of 1:4

scaled reinforced concrete frame models with centrally located openings of varying

opening ratios was constructed and tested in the Structural Engineering Laboratories

of the Rivers State University of Science and Technology, Port Harcourt, Nigeria. The

details of the models and their construction are presented in 3.2

2.1. Similitude Requirements for Modeling

To obtain the appropriate loading for the models, the theory of dimensional analysis

and similitude mechanics was employed to determine the prediction and operating

dimensionless parameters for modeling the real prototype behavior [20-21]. The

theoretical framework was based on assumptions that the diagonal tensile stress σt of

an infill wall was dependent on the following variables: the magnitude of the racky

load Q, span L, thickness t, the modulus of elasticity E and Poisson’s ratio ν. The

relationship can be implicitly expressed as follows

Q, , , , , 0F L t E

(1)

Considering the elastic modulus E and span L as dimensionally independent

variables for static structural modeling, equation (1) can now be expressed in

dimensionless products in the form

Experimental Modeling of In Filled RC Frames with Opening


2 , , , 0tQG

EL E L

(2)

The functional G must be the same for various scales of measurement and hence it

must be same in the model and prototype. Therefore, similitude requirements for

modeling will result from forcing the non-dimensional terms to be equal in model and

prototype. Thus,

Pr2 2ototype Model

Q Q

E L E L

(3)

From where

Qp = QM . SE . SL2 (4)

Here, Qm and QP represent the values of racky load in model and prototype,

respectively;

SE and SL – scale factors for material and geometry

Assuming the same material in prototype and model, and neglecting Poisson’s ratio

distortion, SE = S ν = 1.

Hence, the model load equals

2

L/SM PQ Q (5)

The linear scale factor SL equals to 4 for 1:4 scaled model adopted in this

investigation.

The design and structural detailing of a typical specimen are given in Table 1 and

Figure 1.

Table 1 Design Details of Prototype and Model RC Frame

Design Characteristics Prototype 1:4 Model

Total height (mm) 2800 725

Total length (mm) 3600 900

Cross section of columns (mm) 300 x 300 75 x 75

Cross section of beam 400 x 300 100 x 75

Longitudinal reinforcement of columns 4 Ø 16 4 Ø 4

Tensile and Compression rein. of the beam 2Ø 16 Top, 3Ø 16 Btm 2 Ø 4, 3 Ø 4

Stirrups Ø 10 @ 150mm c.c Ø 2.5 @ 50mm c.c



Figure 1 Structural Details of the Prototype Model

3. EXPERIMENTAL PROCEDURE

The experimental procedure consisted of instrumentation and testing single-bay,

single-storey reinforced concrete plane frames, infilled with one-quarter scale brick

masonry with centrally located opening of various sizes. The following nomenclature

was adopted for the frames: Model Frame (MF) followed by two digit suffixes

representing the percentage opening. Thus, for example, MF10, MF20, MF30 etc

represent model frames with 10, 20 and 30 percent opening ratios respectively. A total

of seven frame models were constructed and tested as detailed in section 3.2.

Appropriate tests were also conducted to determine the mechanical characteristics

which were required as input for the finite element validation of the experimental

results.

3.1. Modulus of Elasticity and Poisson’s Ratio for Model Materials

The basic mechanical properties of masonry were obtained from tests carried out on

the masonry units used. These mechanical properties are basic input parameters for

the finite element micro modeling of masonry infilled frame structure. The modulus

of elasticity and Poisson’s ratio of the masonry were determined through loading a

four-block wallet vertically and measuring the strains in the longitudinal (X) and

transverse (Y) directions. Mechanical strain gages of sensitivity 0.01mm were used in

the strain measurements. Prototype burnt bricks of dimensions 224 x 106 x 72mm

were set on 13mm mortar. Three mortar mixes, namely 1:3, 1:4.5 and 1:6, were

considered. The load was applied normal and parallel to the bedding and average

values taken as representative of the mechanical properties of the masonry. The tests

were conducted in accordance with BS EN 1996 (2006). Plates 1A, B, C demonstrate

the test set up and failed specimen.



A B

C

Plate 1 Test Setup for Determination of Mechanical Properties of Brickwork and Failed

Specimen

By measuring the compression load and the strains x and y, the values of

modulus of elasticity (E) and Poisson’s ratio (v) were obtained through the following

basic relationships

y

y

E

; y

xv

(6)

3.2. Sway Frame Model Construction, Test Set-up and Procedure

The main aim of the experimental program on the single bay, single storey reinforced

concrete infilled frames with openings was to obtain a load-displacement profile for

each specimen in order to capture the degree of reduction in the shear strength or

sway stiffness of the infilled frames as a function of the opening ratio. To maintain

good workmanship, the frame and the infill brickwork were constructed in horizontal

beds. The ground beam was constructed in-situ and allowance made in the column

pits to accommodate the erection of the precast frame and infill. Dial gauges Model

EL83-546 of 0.01mm sensitivity were installed to measure the horizontal

displacement as a result of the lateral in-plane loading. The general pre-test set-up is

shown in Plate 2. The lateral load was applied by the aid of a hydraulic jack at the

level of the horizontal axis of the beam. A 70 kN proofing ring, duly calibrated, was



used to measure the applied lateral load during the tests. The analysis and discussion

of results obtained are presented in section 5.

Plate 2 Test Set-up and Instrumentation for Determination of Sway Stiffness of Infilled

Frames with Various Opening Ratios

4. THE FINITE ELEMENT MODEL

To advance the comparison with another reliable model, the FE micro model was

executed using SAP 2000 version 14, a sophisticated software package for finite

element modeling with capacity to model infill openings. Minor details that do not

significantly affect the analysis were deliberately left out from the models for ease of

analysis. The comparative analysis of the experimental and finite element results is

presented in Table 4 under results.

5. RESULTS

The results obtained from tests on infill wall specimens and infilled frame structures

are presented in the subheadings that follow.

5.1. Mechanical Properties of Model Materials

The summary of mechanical properties for brick infill obtained to aid the finite

element analysis of the models is given in Table 2.

Table 2 Summary of Test Results on Brick-Mortar Wall Specimens

Description

of Loading

Mortar

Mix

No. of

Specimen

Compressive

Strength (Fm)

(N/m2)

Strains

10-3

Modulus

of

Elasticity

(Em)

(kN/m2)

Poisson’s

Ratio

x y

Perpendicular

to bedding

plane

1:3 2 13.46 1.90 0.55 8.41 0.29

1:4 2 11.54 2.00 0.66 7.21 0.33

1:6 2 10.58 4.70 1.69 6.61 0.36

Parallel to

bedding plane

1.3 2 8.50 5.70 1.03 5.32 0.18

1.4 2 7.20 9.20 1.93 4.67 0.21

1.6 2 5.10 8.60 2.41 3.21 0.28



The variation of modulus of elasticity mE with compressive strength m measured

on specimens is shown in Table 2. An average relationship was obtained for modulus

Em and Fm in the form

Em1 = 634.66Fm1 (7)

Em2 = 640.00Fm2 (8)

Where the suffixes 1 and 2 denote values corresponding to compressive load

normal and parallel to mortar bedding respectively.

In order to be consistent as regards suitable mechanical property for masonry

infill, the following average values of modulus of elasticity and Poisson’s ratio were

adopted.

xE = 4.4 x 106

kN/m2;

yE = 7.41x 106 kN/m

2; Poisson’s ratio,

xy = 0.22; yx =

0.33

From the above results, the anisotropy of the masonry wall is obvious.

The mechanical properties of the concrete in the frame are considered to be fairly

stable and thoroughly documented. Hence, reference values were obtained from a

previous works for example [1], [14], [18], [21] among others.

Modulus of elasticity, xE = yE = 2.9 x 10

7 kN/m

2

Poisson’s ratio, xy= yx

= 0.20

5.2. Model and Prototype Deflections and Computed Sway Stiffnesses

The results of experimental tests and numerical analysis are summarized in Tables 3

and 4.

Table 3 Experimental Values of Deflection of Test Models

Model

Loads

Model lateral Displacements (mm)

MF 0 MF 10 MF 20 MF MF 40 MF 50 MF100

(KN) 30

3.125 0.38 0.40 0.42 0.42 0.45 0.77 0.82

6.25 0.72 0.76 0.93 0.95 1.20 1.25 1.31

9.375 0.93 0.96 1.27 1.35 2.20 2.07 2.19

12.5 2.25 2.34 1.97 2.12 2.75 2.87 3.01

15.624 3.64 3.75 4.30 4.00 4.82 5.75 6.15

18.75 5.38 5.75 5.55 6.62 7.00 9.00 9.72



Table 4 Comparative Analysis of Experimental Sway Deflections and Analytical Results

Specimen Opening

Ratio % Model

Deflection at different load application (mm)

50kN 100kN 150kN 200kN 250kN 300kN

MF 0 0% FE model 1.47 2.69 3.69 9.10 15.20 20.69

Exp. Model 1.52 2.88 3.72 9.00 14.56 21.52

Diff. % 0.33 6.59 0.81 1.11 4.40 3.86

MF10 10% FE model 1.53 3.10 4.01 9.21 14.59 21.09

Exp. Model 1.60 3.01 3.86 9.34 15.01 23.00

Diff. % 4.40 2.99 3.87 1.39 2.80 8.30

MF20 20% FE model 1.62 3.58 5.12 8.01 16.15 23.22

Exp. Model 1.70 3.70 5.10 7.90 17.20 22.20

Diff. % 4.71 3.24 0.39 1.39 6.50 4.60

MF30 30% FE model 1.67 3.70 5.51 8.20 17.10 25.95

Exp. Model 1.70 3.80 5.40 8.50 16.00 26.50

Diff. % 1.76 2.63 2.04 3.53 6.87 2.07

MF40 40% FE model 1.99 4.51 7.72 11.02 19.11 27.12

Exp. Model 1.80 4.80 8.80 11.00 19.30 28.00

Diff. % 1.06 6.04 12.27 0.18 0.98 3.14

MF50 50% FE model 2.79 5.79 8.05 12.44 22.45 34.12

Exp. Model 3.10 5.00 8.30 11.50 23.00 36.00

Diff. % 0.10 0.16 3.01 8.17 2.39 0.05

MF100 100% FE Model 2.89 5.40 8.50 13.00 23.10 36.02

Exp. Model 3.28 5.24 8.76 12.04 24.60 38.88

Diff. % 11.89 3.05 2.97 7.97 6.10 7.35

The value of lateral load applied to test models and the corresponding lateral

displacements were read from the proofing ring and dial gages. The experimental

results are presented in Table 3. The predicted prototype loads and the corresponding

lateral displacements, based on the similitude requirement obtained in section 2.1, are

presented in Table 4 under the appropriate rows for each model tested. The prototype

loads and deflections were extrapolated from the experimental values obtained from

model tests using the similitude expressions as follows:

2

P M LQ Q S and P M LS

, where 4LS

for 1:4 model.

5.3. Sway Deflection of Infilled Frames and Validation of Results

The dependence of corner deflection with load for the various opening ratios is

presented in Figure 2, from where it can be seen that there is approximately linear

relationship up to a load value of about 150kN for all values of opening ratios

investigated. This portion of the graph is followed by a more rapid increase of

deflection underscoring the non linear character of the force deflection curve.

The comparative analysis of the experimental results with those from numerical

analyses is presented in Table 4. It can be seen that lateral displacements obtained



from the test models are within 4 percent of the values based on the finite element

model. The close agreement between the results from experimental tests and

numerical analysis confirms the adequacy of the model to reproduce the strength and

deformation of the infilled frame including its anisotropy.

Figure 2 Force-Deflection Curves for Test Models with various Opening Ratios

5.4. Variation of Lateral Stiffness of the Infilled Frame with Openings

The values of lateral stiffness, computed as the ratio of the prototype load to the

corresponding sway deflection, are plotted in Figure 3 for different values of opening

ratio . From the graphs of Figure 3, it can be seen that the observed increase in

lateral deflection due to increase in opening ratio of the infill as depicted in Table 4,

generally leads to a reduction in the computed sway stiffness of the infilled frames. It

was also observed from the plots that the stiffness increases with the solidity ratio

with the curve exhibiting a peak somewhere around 150kN load, followed by a falling

branch of slope gradually reducing with increasing opening ratio. It is important to

note that the peakness or kurtosis of the sway stiffness curves decreased with the

opening ratio, thus reflecting the reduction in the stress concentration effect of the

openings as the ratio increased from 0 to 100 percent.

A highly reduced rate of increase in sway stiffness in the linear zone was observed

for MF50 structural frame corresponding to 0.5 . This in line with the trend

observed in previous investigations [23], namely, that the influence of the opening

ratio beyond 50% is relatively insignificant up to a complete bare frame ( 1.0 ).

0

5

10

15

20

25

30

35

40

45

0 50 100 150 200 250 300 350

Late

ral D

efl

ect

ion

(m

m)

Applied Sway load (kN)

MF0

MF10

MF20

MF30

MF40

MF50

MF100



Figure 3 Graphical Plot of Infill Frame Stiffness against Sway Load.

6. CONCLUSIONS

The following specific conclusions can be drawn from this study.

1. The 1:4 experimental model is able to reproduce the shear resistance of the infilled

frame with reasonable accuracy. The experimental values are within 4 percent of the

corresponding results based on finite element model.

2. The experimental values of the elastic modulus in the directions normal and parallel

to the mortar bedding are in the ratio of about 1.68:1. This corresponds to the range of

documented values for burnt clay brick masonry. The close agreement of the results

from the experimental test with those from finite element model confirms that the 1:4

model adequately reproduces the anisotropy of the masonry infill.

3. There is approximately linear force-displacement relationship up to a lateral racky

load of about 150kN for all values of opening ratios investigated. This portion of the

graph is followed by a more rapid increase of deflection, indicating the non linear

character of the force deflection curve beyond this load. At about 150kN, the stiffness

curves exhibit a sharp peak, followed by a falling branch of slope gradually reducing

with increasing opening ratio.

4. The peakness or kurtosis of the sway stiffness curve sharply decreased with the

opening ratio, reflecting the reduction in the stress concentration effect of the opening

ratio as it is increased from 0 to 100 percent.

5. A highly reduced rate of increase in sway stiffness in the linear zone was observed for

the test frame with opening ratio 0.5 . This in line with the observations in

previous investigations namely, that the influence of the opening ratio beyond 50% is

relatively insignificant up to a complete bare frame configuration for which 1 .

0

5

10

15

20

25

30

35

40

45

0 50 100 150 200 250 300 350

Sti

ffn

ess

(kN

/mm

)

Sway Load (kN)

B=0.1

B=0.2

B=0.3

B=0.4

B=0.5



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