Verification for modeling of ultimate load for lightweight palm oil clinker reinforced concrete beams with web openings using response surface methodology

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
TECHNOLOGY (IJCIET)
ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 3, Issue 2, July- December (2012), pp. 229-240
IJCIET
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VERIFICATION FOR MODELING OF ULTIMATE LOAD FOR
LIGHTWEIGHT PALM OIL CLINKER REINFORCED CONCRETE
BEAMS WITH WEB OPENINGS USING RESPONSE SURFACE
METHODOLOGY

Sadam Hade Hussein, Kamal Nasharuddin Bin Mustapha, Zakaria Che Muda,
Salmia Beddu
Universiti Tenaga Nasional, KM7, Jalan, Ikram-UNITEN, 43009 Kajang, Selangor,
Malaysia
engineer_archicad@yahoo.com

ABSTRACT
This paper suggests verification for modeling of ultimate load of lightweight Palm Oil
Clinker (POC) reinforced concrete (RC) beams with web openings using the
Response Surface Methodology (RSM). The proposed model is developed to predict
and verify the ultimate load for a comparison with the experimental measurements
and optimizes load capacity and design accordingly. The ultimate load has been
investigated against three parameters, namely depth of beams, location of openings
and length of openings. The results of this work show that the technologically
advanced model has good adaptability and high accuracy.

Keywords: palm oil clinker; beams with web openings; response surface
methodology
1. INTRODUCTION
Structural members are frequently confronted with the problem of having to provide
openings as passage for utility ducts and pipes to accommodate essential services such
as plumbing, heating, air conditioning, and telephone and electricity cables.
Obviously if openings through beams or girders can be made for ducts or pipes
without sacrificing structural integrity, the dead space in false ceilings can then be
eliminated and substantial construction cost savings can be realized. This is

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particularly important in multi-storey buildings where the use of openings in the
beams can reduces the total height of building, leading in turn to a multiplicity of
savings. A lot of researches for reinforced concrete (RC) beam with openings using
Normal Weight Concrete (NWC). Recently, the construction materials technologies
and building practice have evolved. Construction industry is the biggest energy
consuming sector. With increasing urbanization, natural resources are being utilized
in the construction. Environmental conscious buildings design has become important.
The green building concept is the construction of energy efficient buildings which
result in reduced air and water pollution, less water consumption, limited waste
generation and increased user productivity. The awareness of green building has
begun and with building industry poised for a major growth, green building industry
would be a mantra of the building industry in future. Going green is a sustainable
building technology for the environmentally harmonious cities. Malaysia, being the
world leading producer of palm oil, generates an enormous amount of waste in the
form of oil palm shell in the production process (D.C.L. Teo, et al., 2007; Mannan,
M.A. and Ganapathy, C., 2002; Teo et al., 2006; Basri, H. B et al., 1999). In
addition, the main advantage of using waste in nature and converting them to useful
material such as LWC will lead to environmental conservation and reduce pollution.
This is because this waste is expected to increase as the nation’s quest for renewable
energy from biological sources increases. This waste pollutes the vicinity where it is
deposited and constitutes an environmental nuisance. There is an enduring need to
obliterate this waste for a more conducive habitation. This can be achieved by
exploring an avenue of putting the waste into beneficial alternative uses. One of the
ways to do this is to use the waste as an aggregate in concrete. This would ensure
resource preservation by reducing the depletion of natural resources from rock
fragments, which are normally crushed to obtain aggregate for construction works.
So, the benefit of using POC lightweight aggregate is basically to reduce the dead
load of concrete structure without any loss in the strength of the structure. This is
possible since lightweight concrete can reduce the dead load by as much as 35% and
still provide the structure’s strength (Omar and Roslli, 2002). Therefore, the reduction
of the dead load of the structure will lead to a decrease in the cost of the construction
which is an important advantage of POC over normal weight concrete (NWC). In
addition, there was a problem that needed to be resolved, which the researcher faced

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at the beginning when he wanted to do the Design of Experiments (DOE), especially
in the field of structural engineering. In DOE, there is sometimes more than one
variable that cannot be determined accurately, or there may be a variable which is
more influential than the other, and a suitable number of samples has to be specified.
This paper will help to choose a suitable number of samples for studying by using the
Box-Behnken Design.

2. EXPERIMENTAL PROCEDURE

2.1 Response Model

The RSM explores the relationships between several explanatory variables and one or
more response variables (Basim A. Khidhir and Bashir Mohamed; 2011). The main
idea of RSM is to use a sequence of designed experiments to obtain an optimal
response. RSM is a combination of experimental and regression analysis, and
statistical inferences. The concept of a response surface involves a dependent variable
y called the response variable and several independent variables x1, x2, . . .,xk (Basim
A. Khidhir and Bashir Mohamed; 2009; J. Grum and J. M, 2004; G.E.P. Box and K.P.
Wilson, 1951)

y = f (x1; x2; . . . ; xk) (1)

The goal is to optimize the response variable y. It is assumed that the independent
variables are continuous and controllable by the experimenter with negligible error.
The response or the dependent variable is assumed to be a random variable. In RC
beams with web openings, it is necessary to find a suitable combination of depth of
beam (x1 = D), location of opening (x2 = L), and length of opening (x3 = W), that
optimizes response. The observed response y as a function of the D, L and W, can be
written as:

y = f(x1, x2, x3,) +ε (2)

Where ε : Error observed in the response y
Usually a low order polynomial (first-order and second-order) in some regions of the
independent variables is employed. The first-order model is expressed as:

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k
y = β o + ∑βi x i + ε (3)
i =1

For the relationship between the response variable y for example, the ultimate load
and independent variables in our case are usually unknown. In general, the low-order
polynomial model is used to describe the response surface. A polynomial model is
usually a sufficient approximation in a small regain of the response surface.
Therefore, depending on the approximation of unknown function f , either the first
order or second- order model are employed (Teychenne, D.C.et al., 1988)

y = β 0 + β 1 x1 + β 2 x 2 + β 3 x 3 (4)

Where y is the response, x1= Depth of beam (D), x2 = Location of openings (L), x3 =
Length of openings (W). β0 = C and β1, β2 andβ3, are the model parameters.

The second-order model is flexible because it can take a variety of functional forms
and approximates the response surface locally. Therefore, this model is usually a good
estimation of the true response surface. In this study, the second order model has been
utilized:

‫ߚ = ݕ‬௢ + ∑௤ ߚ௝ ‫ݔ‬௝ + ∑௤ ߚ௝௝ ‫ݔ‬௝ଶ + ∑ ∑௜ழ௝ ߚ௜௝ ‫ݔ‬௜ ‫ݔ‬௝ + ߝ
௝ିଵ ௜ିଵ (5)

= ߚ௢ + ‫ݔ‬௜′ ߚ + ‫ݔ‬௜′ ߚ‫ݔ‬௜ + ߝ௜௝ (6)

Where ‫ݔ‬௜ = ൫‫ݔ‬ଵ௜ , ‫ݔ‬ଶ௜ , … , ‫ݔ‬௜௤ ൯, ߚ = ൫ߚଵ , ߚଶ , … , ߚ௤ ൯

2.2 Concrete Materials and Mix Proportion
POC lightweight aggregate has been selected as fine and course aggregate (100%)
rather than NWC in LWC mix without any admixture for producing lightweight
reinforced concrete beams with web openings. The clinker, which was produced from
local sources, is an unprocessed by- product material from palm oil clinker industrial.
Initially clinkers were taken in a form of hard porous lumps. The clinker was from the
bottom part of the boiler after the finishing of oil extraction process and the clinker
needs to be crushed to a smaller size. The sieve analysis of the POC was found
according to the requirement of (ASTM C136) which stated that any aggregates
passing the 5 mm sieve size are classified as fine aggregates. Also, the coarse
aggregate fractions are obtained by taking particles passing a particular maximum size

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ISSN 0976 – 6316(Online) Volume 3, Issue 2, July December (2012), © IAEME
July-

(14 mm) but retained on a 5 mm sieve size. A coarse lightweight aggregate of
structural coarse class has particle gradation in the range 14 mm to 5 mm. The clinker
was sieved and soaked in the water to achieve the Saturated Surface Dray (SSD)
condition of aggregate by using POC, and to remove the harmful substances from the
clinker. The strength and the workability of the mix were also expected to be
enhanced. The POC material is as shown in Figure 2.

(a) (b) (c)

Figure 2: Lump Palm Oil Clinker

Three cylindrical (150 mm diameter and 300 mm height) compressive strength tests
at an age of 28 days pr
roduced compressive strengths of 25.4 MP which
Pa,
is higher than the mini
imum required strength of 17 MPa, for structural
concrete recommended b ASTM C330. The palm oil clinker is an industrial
by
waste by product of palm oil kernel; many tests have been conducted to obtain some
t kernel;
basic properties of these lightweight aggregates. The results of the tests were then
test
checked with appropriate standards to ensure the suitability of clinker aggregates to
aggregate
be used in lightweight concrete mixture (Abdullahi et al, 2008). The ingredients of
eight
t h e P O C are shown in Table 1
able 1.

Table 1 The ingredients of the POC
1:

POC Contents Unite POC as LWC
Cement Kg/m3 500
Coarse aggregate of POC Kg/m3 343.9
Fine aggregate of POC Kg/m3 739.3
Water /cement ratio - 0.44
Water Kg/m3 220
Additional water to coarse Kg/m3 105.6
aggregate to reach SSD
Additional water to fine aggregate Kg/m3 18.5
to reach SSD

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2.3 Lightweight POC RC beams with web openings: Instruments and Testing

Fifteen specimens of full scale lightweight palm oil clinker beams with web openings
were fabricated and tested. All the beams were simply supported and they were
subjected to a two point load. All beams tested had a rectangular cross section with a
total length of 2400 mm. The width of beams, depth of openings and shear span of
beams were kept constant and are shown in Figure 3. The selected beams differed in
their depths (D), location of openings (L) and length of openings (W). The bottom
reinforcement provided for all beams consist of three 16 mm diameter bars, and the
top reinforcement consist of two bars of 12 mm diameter. All tested beams were have
vertical stirrups of 8 mm diameter. The rectangular openings had vertical closely
spaced stirrups of diameter 8 mm around its openings as corner reinforcement.
Lightweight palm oil clinker reinforced concrete beams with web openings have been
tested with different boundary conditions to investigate all the various parameters
mentioned above. The fifteen beam specimens were obtained based on an analysis
using RSM. All the specimens were prepared for experimental tests to evaluate the
effect of the ultimate load on depth of beams, location of openings and length of
openings. The details of beam and its loading arrangement of a selected specimen are
shown in Figure 3.

Figure 3: Beams details and loading arrangement

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Figure 4: Beam instrumentations

Three linear vertical displacement transducers (LVDT) were used to measure vertical
displacement of the beam at web opening, at mid-span as shown in the Figure 4. The
loads were applied incrementally in a load control manner up to failure.

3. RESULTS AND DISCUSSION

3.1 Case Study 1

In order to study and model the effect of the ultimate load, the three kinds of design
parameters mentioned above: (D), (L) and (W) are chosen as the tuned variables.
Table 2 illustrates the levels of variables and coding identifications used in this case.
Table 3 shows the necessary Coded values for the application of this design for three
levels proposed by RSM using Minitab Software.

Table 2: Suggested values of corresponding levels

Level Low Medium High

Coding -1 0 1
D 350 400 450
L 275 325 375
W 250 325 400

The number of experiments and the corresponding levels proposed by Minitab
Software are shown in Table 3.

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Table 3: Experiments and the corresponding levels proposed by Minitab

D L W
Run order
1 0 -1 1
2 1 1 0
3 0 0 0
4 0 1 -1
5 1 -1 0
6 0 1 1
7 1 0 -1
8 0 -1 -1
9 1 0 1
10 0 0 0
11 -1 1 0
12 0 0 0
13 -1 -1 0
14 -1 0 -1
15 -1 0 1

3.1.1 Analysis of Results

The experimenta1 design used in this work comprises three factors; depth of beams,
location of openings and length of openings. The results of 15 numbered specimens of
LWPOC RC beams which were obtained from RSM and experimental data are shown
in Table 4.
Table 4: Predicted ultimate load data vs. Experimental ultimate load
D L W Ultimate Load Ultimate load
Run
(mm) (mm) (mm) (Experimental) (Predicted)
order
(kN) (kN)
1 400 275 400 158.2 158.5
2 450 375 325 180.5 181.7
3 400 325 325 162.9 162.6
4 400 375 250 169.8 169.5
5 450 275 325 192.7 193.0
6 400 375 400 147.8 147.2
7 450 325 250 199.4 198.8
8 400 275 250 174.7 175.2
9 450 325 400 176.3 175.9
10 400 325 325 162.9 162.6
11 350 375 325 135.4 135.0
12 400 325 325 162.9 162.6
13 350 275 325 141.9 140.6
14 350 325 250 145.1 146.0
15 350 325 400 128.6 129.8

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The process considered three input variables [depth of the beam (D), location of
opening (L), and length of opening (W)] to develop a model from the experimental
results using RSM. The polynomial model used is defined in Eq.7, (Sadam et al,
2011).

3.1.2 Model for Ultimate Load

Several polynomial model for ultimate load prediction were considered. This model
includes a full quadratic. The analysis was conducted at a 95% confidence interval
and a 5% level of significance.

3.1.3 Full Quadratic Model (Second-order Model) for Ultimate Load
The full quadratic model for ultimate load is given by the following equations:

Ultimate load = - 135 + 0.823 D + 0.262 L + 0.165 W - 0.000570 D*L - 0.000440 D*W
- 0.000367 L*W (7)

The process considered three input variables [depth of the beam (D), location of
openings (L), and length of opening (W)] in order to develop models from the
experimental results and RSM. The polynomial model has been used as defined by
Eq. 7 for ultimate load.

3.2 Case Study 2

3.2.1 Verification for Modeling of Ultimate Load of POC RC beams with Web
Opening

Additional specimen was designed on the same scale as LWPOC RC beams with web
openings. They were fabricated and tested, but not before taking on board the new
dimensions of the variables or (Factors), that is, the depth of the beam (D) is equal to
375 mm, the location of an opening (L) is equal to 225 mm and the length of an
opening (W) is equal to 360. These were the compensated values of the variables in
Eqs. 7 were obtained based on an analysis using RSM to compare with the values of
those obtained from the experimental work.

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3.2.2 Model Check

A model of the ultimate load will compensate the values of the new dimensions in Eq.
7 of three factors as mentioned above. This will verify the model of ultimate load
obtained. The details of the compensated values of three factors are as found below:

Ultimate load = - 135 + 0.823 (375) + 0.262 (225) + 0.165 (360) - 0.000570
(375*225) - 0.000440 (375*360) - 0.000367 (225*360) = 154.75 kN

The result of the ultimate load obtained from the experimental test equal to 148.3 kN
means it is clear that the predicated values obtained via the response surface method
are in good agreement with the data taken from the experimental test within an
acceptable percentage of error. This indicates that the obtained model is useful in
predicting values of ultimate load.

In order to judge the accuracy of the prediction model, the percentage deviation (∅݅௜ )
ഥ
and the average percentage deviation (∅) were used as defined below:

หோ௔೐ೣ೛ ିோ௔೛ೝ೐ ห
∅௜ = ோ௔೐ೣ೛
‫%001ݔ‬ (8)

Where ∅୧ = Percentage deviation of a single experiment data

Raୣ୶୮ = actual Ra by Experimental work

Ra୮୰ୣ= predicted Ra generated by a multiple regression equation.
೙
ഥ ∑ ∅
∅ = ೔సభ ೔ (9)
௡
ഥ
Where ∅: average percentage deviation of all experiments,
n: the size of sample data

This method tests the average percentage deviation of the result of experimental work
and predicted result as well as its ability to evaluate the prediction of this model. The
regression model could predict the ultimate load from experimental data sets with an
acceptable error percentage is equal to 4.34%.

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4. CONCLUSIONS

In the present research, the second-order model based on RSM is developed to predict
and verify the ultimate load of LWPOC RC beams with web openings. The results
shows the developed model is sufficient to predict the ultimate load with good
adaptability and high accuracy, Moreover, the advantage of this research lies in the
fact that it can be developed for use in the future in order to provide the expected
ultimate load of LWPOC RC beams with web openings for designers in cases where
he or she wishes to assess the expected ultimate load of a particular design embarking
on the implementation and final design phases. Additionally, the verification for
model of ultimate load has proved that the designer or experimenter can depend on
the models obtained from statistical programs using RSM to estimate the values or
data of experimental work within an acceptable percentage of error. To the best of the
researcher's knowledge, there is no research which has sought to identify the use of
POC RC beams with web openings nor has any study attempted to obtain the
prediction data of ultimate load of LWPOC RC beams with web openings.

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Clinker Reinforced Concrete Beams with Web Openings Using Response Surface
Methodology” International Journal of Civil Engineering and Technology
(IJCIET), Volume 3, Issue 1.

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Verification for modeling of ultimate load for lightweight palm oil clinker reinforced concrete beams with web openings using response surface methodology

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Verification for modeling of ultimate load for lightweight palm oil clinker reinforced concrete beams with web openings using response surface methodology