Significance Analysis of Flexural Behaviour of Hybrid Sandwich Panels

doi:10.4236/ojce.2013.33B001

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Open Journal of Civil Engineering, 2013, 3, 1-7

http://dx.doi.org/10.4236/ojce.2013.33B001 Published Online September 2013 (http://www.scirp.org/journal/ojce)

Significance Analysi s of Fl e x ur al Be h aviour

of Hybrid Sandwich Panels

Jauhar Fajrin, Yan Zhuge, Frank Bullen, Hao Wang

Centre of Excellence in Engineering Composite (CEEFC), University of Southern Queensland Toowoomba, Toowoomba, Australia

Email: [email protected]

Received June 2013

ABSTRACT

This paper presents the significance analysis of a new type of hybrid composite sandwich wall panel which can be

manufactured as modular panelised system. Two different types of natural fibers reinforced plastics (NFRP) laminate

were incorporated into the new sandwich panel as an intermediate layer. The significance analysis in this research has

been carried out using analysis of variance (ANOVA). As the aim of the analysis is to select the most appropriate natu -

ral fiber composites for the intermediate layer, the experiments were arranged as a single factor experiment in which 3

levels of a factor have been examined. The factor refers to the type of intermediate layer used in the sandwich panel.

The result of this study shows that the incorporation of intermediate layer has significantly enhanced the load carrying

capacity of the sandwich panels.

Keywords: Hybrid Structure; Sandwich Panels; Significance Analysis; Natural F iber Composites; Buil ding

Construction

1. Introduction

Providing accommodation on a large scale at relatively

affordable price has always been a challenging task not

only for government but also for housing industry. There

are two key factors in order to solve these two challenges.

The first factor is to reduce the weight of the stru cture to

maintain affordable prices. In building construction, the

self-weight of a structure represents a large proportion of

the total load on a structure. The reduction of self-weight

of structure by adopting appropriate material results in

the reduction of element cross section, size of foundation

and supporting elements thereby reduce the overall cost

of the housing construction. The second factor is to util-

ize the panelized housing system to encourage the mass

production of houses. A panelized housing system is a

form of construction in which all housing components

are pre-fabricated at factory and shipped to the site for

erection. With this construction system, a house can be

built faster than stick-built homes. In most cases, pane-

lized homes can be assembled in a matter of days which

means that lesser labor is needed and more homes can be

built. Other advantages of panelized homes are such as

the system can eliminate costing delays, less weather

damage during construction and also precision engi-

neered to the highest quality.

In order to meet these challenges, a research project

has been carried out aimed at developing a new type of

hybrid composite sandwich wall panel which can be

manufactured as modular panelised system. The typical

sandwich panel used in building application commonly

consists of metal skins and soft core. Although oriented

strand board (OSB) is commonly employed for the skin

of sandwich structure in structural insulated panels (SIPs),

the observed shortcomings of this typical skin such as

mould build-up and disintegration in the presence of

flood water [1] have reduced their usage. In this study,

metal based skins such as aluminium or steel are adopted.

Metal skins are actually preeminent choice for their

many advantages, but the price is always a concern.

Consequently, reducing the thickness of the skin as much

as possible is the only way to keep a competitive and

reasonable overall cost. However, using thinner skins

may result in the early failure of sandwich structure, such

as face wrinkling or inundation. The sustainable hybrid

concept offered in this research has been considered as a

practical solution where an intermediate layer made from

natural fibers reinforced plastics (NFRP) laminate was

introduced. Natural fibers are a major renewable resource

material throughout the world especially in the tropics.

Statistical significance is a mathematical tool that is

commonly used to determine whether the outcome of an

experiment is the result of a relationship between specific

factors or merely the result of chance [2]. Commonly,

such concept is used in the fields in which research is

conducted through experimentation. It is frequent to

J. FAJRIN ET AL.

summarize statistical comparisons by declarations of

statistical significance or non -significance [2]. In a scien-

tific research, a hypothesis is proposed prior to data col-

lection and analyses. The statistical analysis of the data

will produce a number that is statistically significant if it

falls below a certain percentage called the confidence

level or level of significance. Further, Reference [2] ex-

plains that statistical significance is used to reject or ac-

cept what is called the null hypothesis, which usually

states that there is no relationsh ip between two variables.

In a simple expression, statistical sign ificance means that

there is a good re lat ionshi p exis ti ng bet ween two variables.

This paper focuses on the significance analysis of the

experimental results on the flexural behaviour of the sand-

wich pane l s develope d by the authors.

2. Significance Analysis

Although significance or statistical analysis is rarely

found as a primary approach in composite sandwich pan-

el research, it has actually been extensively used in the

field of composite material research. A number of re-

searches reported in the literature provide the idea of how

it was applied to composite material research. A study on

the significance effect of microwave curing on tensile

strength of carbon fibre composites was reported by [3].

The statistical analysis employed was two-way analysis

of variance (ANOVA) using statistical software SPSS

14.0. The results showed that the curing time and mi-

crowave process had significant effect on the tensile

strength of the carbon fibre composites. Reference [4]

reported their work on the optimization of processing

variables in wood-rubber composite panels manufactur-

ing process. The results of experiments were statistically

analysed using response surface method (RSM). The

Design-Expert statistical software was employed to de-

termine the significant factors that affected the properties

of the composite panels. It was concluded that the den-

sity and the interaction of different variables were the

significant factors affecting the final properties of the

boards.

Reference [5] used design of experiments (DoE) to

study the significance of low energy impact on modal

parameters for composite beams. The experiment was

designed as a 5 × 2 full factorial design. The results

showed that damping ratio is more sensitive parameter

for the damage detection than the natural frequency.

Reference [6] reported their work on the mechanical and

absorption properties of woven jute/banana hybrid com-

posites. Statistical analysis using one-way ANOVA was

employed to analyze the results of tensile, flexural and

impact tests of various composite configurations. The

results suggested that th e layering pattern had significant

effect on the mechanical properties of the composites.

A response surface methodology (RSM), which is a

statistical design of experiment method, was employed

by [7] to analyze the factors influencing deflection in

sandwich panels subjected to low-velocity impact. The

results revealed that the deflection increased with the

increasing of height of fall the mass of impactor. The

deflection was only slightly increased with the incr easing

in the core thickness.

It is worth to note that when a statistical test res ulted in

a significant outcome it means that a finding has a

chance of being true due to the relation between variables,

not just really a chance occurrence. Statistical signific-

ance does not always mean that the finding is important

or that it has any decision-making utility, so that the re-

searcher must always examine both the statistical and the

practical significance of any research finding.

3. Experimental Program

Before the significance analysis is performed, the flex-

ural testing program will be briefly reviewed in the fol-

lowing sections.

3.1. Testing Specimens

The sandwich samples were cut and shaped into a span

length of 450 mm and the size of 550 × 50 × 22 mm for

length, width and thickness, respectively. An aluminium

5005 H34 sheet with the thickness of 0.5 mm was used

as the skins for all samples. An expanded polystyrene

(EPS) is used for the core of this hybrid sandwich panel.

The thickness of EPS core for control level was 21 mm

and 15 mm for the other two levels to maintain a constant

overall thickness of 22 mm. Several types of natural fiber

composites have been investigated and the two best per-

formed natural fibers were employed as the intermediate

layer; jute and hemp fiber composites with a thickness of

3 mm. Each level was replicated 5 times; hence the total

of samples tested was 15 samples. The arrangements of

the flexural test specimens are shown in Table 1.

Sandwich panel specimens were manually prepared

using a pressing system. All constituent parts were cut

into the same length and width and glued together using

structural grade adhesive. The NFCs intermediate layers

were sanded-up using sanding machine to obtain uniform

thickness while alu minium sheet were roughed manually

using sandpaper. The EPS core was sliced using hot

knife foam cutter to obtain the required thickness. When

all constituents ready, they were glued and placed in the

pressure system. The process of sample preparation is

shown in Figure 1.

3.2. Testing Results

The static flexural test was conducted in accordance with

J. FAJRIN ET AL.

the ASTM C 393-00 standard which is a standard test

method for flexural properties of sandwich constructions.

The testing set up is shown in Figure 2.

The failure loads and deflections of specimen tested

under flexural testing scheme in this experiment are

listed in Table 2. For a simplicity reason, the signific-

ance analysis in this paper is only made for the data of

load. As it can be seen from Table 2 that the coefficient

variation (CV) of the actual data ranges from 9.39 to

16.05. The CV values in this range are considered as

fairly acceptable. The ratio of mean to standard deviation

or CV should be of the order of 3 or more, but the value

of 33% has often been stated as the permissible upper

limit of CV (Patel et al., 2001).

The fluctuation in the distribution of exp erimental data

can be easily observed in Figure 3. It is clearly shown in

the figure that each level of samples has at least one out-

lier data. Removing these values, by conducting norma-

lization process, will produce more consistent or less

fluctuated data. For example, the failure loads of speci-

men 2 in CTR and JFC samples, and specimen 4 for HFC

samples are considered as an outlier, with the value of

415 N, 473 N and 734 N, respectively.

The experimental data resulting from the normaliza-

tion process are presented in Table 3.

As it can be noticed in Table 3, the coefficient varia-

tion of CTR, JFC and HFC for loads has now reduced to

3.83%, 5.17% and 8.7%, respectively. The previous CV

value for each level prior to the normalization process

was 15.23%, 9.39% and 11.68% for CTR, JFC and H FC,

respectively. The following significance analysis will use

data provided from the normalization process as listed in

Table 3.

Table 1. Experimental arrangements for flexural testing.

Samples

Code

Skin Intermediate Layer Core

0.5mm 3 mm 15 mm

CTR Aluminium None EPS (21 mm)

JFC Aluminium Jute EPS

HFC Aluminium Hemp EPS

Figure 1. Sandwich panel f ab rication pr oc ess.

Figure 2. Testing set up.

Table 2. Failure loads deflections of specimens un der flexural test.

Samples

number

Treatments based upon intermediate layer used

CTR JFC HFC

P (N) δ (mm) P (N) δ (mm) P (N) δ (mm)

1 321 11.92 414 56 628 42.24

2 415 15.4 473 62.18 579 36.37

3 307 12.18 379 45.22 524 47.04

4 293 9.89 378 56.53 481 37.86

5 302 13.2 414 64 635 35.09

Average 327.60 12.52 411.60 56.79 569.40 39.72

Stdev 49.90 2.01 38.64 7.34 66.53 4.90

CV 15.23 16.05 9.39 12.93 11.68 12.34

J. FAJRIN ET AL.

Figure 3. Dot-plot diagram for medium scale samples under flexural test.

Table 3. The results of normalization process for medium scale samples.

Samples number

Treatments based upon intermediate layer used

CTR JFC HFC

P (N) δ (mm) P (N) δ (mm) P (N) δ (mm)

1 321 11.92 414 56 628 42.24

2 307 12.18 379 45.22 579 36.37

3 293 9.89 378 56.53 524 47.04

4 302 13.2 414 64 635 35.09

Average 305.75 11.80 396.25 55.44 591.50 40.19

Stdev 11.70 1.39 20.50 7.73 51.44 5.53

CV 3.83 11.75 5.17 13.94 8.70 13.76

4. Analysis of Results and Discussion

The significance analysis in this research is carried out

using analysis of variance (ANOVA) as described in our

previous paper [8]. As the aim of the analysis is to select

the most appropriate NFCs for the intermediate layer,

either jute fibre composite or hemp fibre composite, the

experiments were arranged as a single factor experiment

in which 3 levels of a factor have been examined. The

factor refers to the type of intermediate layer used in the

sandwich panel and such factor was leveled as 0, 1 and 2

as required by Minitab 15 software. For the specimens

discussed in this paper, level 0 was the conventional

sandwich panel without intermediate layer or control

level (CTR) while level 1 and 2 refer to as jute fiber

composite (JFC) and hemp fiber composite (HFC), re-

spectively. For the analysis purpose, the data for ANOVA

are tabulated as follows in Table 4.

From Table 4, some important parameters for theoret-

ical calculations can be determined such as replications

(n = 5), total number of samples (N = 12), and number of

levels or treatments (a = 3). The results of the theoretical

calculations are presented in Table 5, contains all im-

portant parameter for further use to make a significance

judgment. Such analysis obtained by statistical software

Minitab 15 is presented in Table 6.

As presented in Tables 5 and 6, the theoretical calcu-

lations were in good agreement with the ANOVA results

obtained by statistical software Minitab 15. It can be

noted here that the mean square between treatments

(85311) was few times larger than the mean square

within the treatments or error mean square which was

only 1068. This indicates that the treatments differ. The

other way to make a significance decision is by using the

F value (F0). The value of F0, as seen in Tables 5 and 6,

was 79.91. Instead, the F value obtained from the

F-distribution table for F(0.05;2,9) was 4.26. This value,

which called as F table, was obtained by using the signi-

ficance level of 95% (α = 0.05), 3 levels (a = 3) and 12

J. FAJRIN ET AL.

Table 4. Tabulated data for analysis of variance (ANOVA).

Factor levels Observations Totals Averages

1 2 3 4

Level 0 (CTR) 321 307 293 302 1223 305.75

Level 1 (JFC) 414 379 378 414 1584 396.25

Level 2 (HFC) 628 579 524 635 2366 591.50

Table 5. Analysis of variance table for single-factor experimental design.

Source of variations Sum of square Degrees of freedom Mean square F0

Between treatments

treatments i

SS y

= −

∑

1a−

treatments

0treatments

FMS

Error (within treatments)

E T treatments

SSSS SS= −

Na−

Total

()

T ij

SSy y…

= =

= −

∑∑

1N−

Table 6. The theoretical results of ANOVA for sandwich panels.

Source of variations Sum of square Degrees of freedom Mean square F0

Intermediate lay e r 170621.20 2 85310.58 79.91

Error 9608.50 9 1067.61

Total 180229.70 11

samples (N = 12). Since the value of F0 (79.91) was

much higher than the value of F table (4.26), the null

hypothesis (H0) should be rejected, meaning that there

are a significant difference in the treatment means.

For this experiment, the null hypothesis was actually

trying to state that the load carrying capacity of all types

of tested sandwich panels (CTR, JFC and HFC) were

equal. However, the statistical significance analysis

showed that the average values of the three types of

sandwich panels were significantly different. Since the

average values or means of the JFC and HFC was higher

than CTR, it can be concluded that the load carrying ca-

pacity of hybrid sandwich panels is significantly higher

than the conventional sandwich panels. In addition, as

the confidence level used in the Minitab analysis was

95%, it means that the finding has a 95% chance of being

true. Alternatively, the finding has a 5% of not being true

as it was analyzed with the assumption of the probability

error (α) of 0.05. A value of P, or frequently called as

P-value, could also be used for drawing a conclusion.

The rule is that if the P-value is less than α (0.05) which

is an error tolerance level, it can be concluded that there

has factor levels or treatments that have different means.

It is clearly presented in Table 6 that the P-value of me-

dium scale specimen was very small, which is approx-

imately 0.000.

A pairwise comparison between all factor levels might

be conducted to support the decisions drawn from

ANOVA results. There are several possible test methods

for this purpose such as Dunnet’s test, Tukey’s test and

Fisher’s test. The three pairwise tests were also con-

ducted using Minitab 15 software and the results are dis-

cussed as follows.

The result of Tukey’s test for medium scale sandwich

panels is presented in Table 7. The rule for making a

decision is that whenever the Tukey’s confidence inter-

vals contain zero number, it means that the means are not

different or in other word if none of the Tukey’s confi-

dent intervals equals to zero, it indicates that all of the

means are different. As can be observed from Table 7,

all the confidence intervals have a positive number. The

comparison of level 0 to level 1 and level 2 has the value

of 25.97 and 221.22 fo r the lower values and 155. 03 and

350.28 for the upper values. While for the comparison of

level 0 to level 2, the lower value was 130.72 and 259.78

for the upper value. Since all the confidence intervals

included only positive numbers, it can be concluded that

all the treatment means differ. This sugges ts that the load

carrying capacity of hybrid sandwich panels with JFC

and HFC intermediate layer is significantly different with

the conventional sandwich panels (CTR). The term of

“significantly differ en t” h as the same meaning with “sig-

nificantly higher” because the load carrying capacity of

hybrid sandwich panels was higher than conventional

sandwich panels.

The second pairwise comparison method was the

J. FAJRIN ET AL.

Table 7. Analysis of variance results for sandwich panel obtained by statistical software Minitab 15.

One-way ANOVA: Flexural Load versus Intermediate Layer

Source DF SS MS F P

Intermediate Layer 2 170621 85311 79.91 0.000

Error 9 9609 1068

Total 11 180230

S = 32.67 R-Sq = 94.67% R-Sq(adj) = 93.48%

Individual 95% CIs For Mean Based on Pooled StDev

Level N Mean StDev ---+---------+---------+---------+------

0 4 305.75 11.70 (---*--)

1 4 396.25 20.50 (---*--)

2 4 591.50 51.44 (---*---)

---+---------+---------+---------+------

300 400 500 600

Pooled StDev = 32.67

Dunnet’s test that only compares the reference levels or

control with other factor levels. This means that the

Dunnet’s test only compares level 0 to level 1 and level 2,

it is not comparing level 1 to level 2. Likewise the Tu-

key’s method, the approach for making a significance

judgment is by checking whether confidence intervals

contain zero number. The result of Dunnet’s test con-

ducted with Minitab 15 shows that all confidence inter-

vals include only a positive numbers. Another way of

drawing a decision is by looking at the critical value of

each level. The results indicated that the critical value of

reference level was 2.61. This value is much lower than

the critical value of level 1 and level 2 which was 90.50

and 285.75, respectively. Overall, it can be concluded

that the load carrying capacity of level 1(JFC) and level 2

(HFC) is much higher than level 0 (CTR).

The third pairwise method is a Fisher’s test which is

pretty similar to the Tukey’s test. Th e result of Fisher test

indicated that none of the confident intervals contain zero

number meaning that all levels differ. It is also noticeable

that the critical values or th e center confident levels were

comparable to the critical values obtained on Tukey’s

test. The difference is only for their lower and upper

values.

5. Conclusion

The significance analysis has been carried out to the

testing data of ultimate load from flexural test of hybrid

and conventional sandwich panels. The experiments were

designed following the principle of statistical design of

experiments and the works reported in this paper was

specifically designed as a single factor experiments. Two

types of hybrid sa ndwich panels were compared with the

conventional sandwich panels without intermediate layer.

The primary conclusion drawn was that the incorporation

of intermediate layer has significantly enhanced the load

carrying capacity of sandwich panels. The results also

indicated that the value of F0 was much higher than the F

value obtained from the F-distribution (F(0.05;2,9)). The F0

was 79.91 while the F-table was only 4.26. Therefore, the

null hypothesis (H0) should be rejected, meaning that

there are significant differences in the treatment means.

All pairwise tests Tukey’s, Dunnet’s and Fisher’s tests

obtained positive confident intervals which suggest the

means of treatments differ. The inference statements

suggested that the load carrying capacity of hybrid sand-

wich panels with JFC and MDF intermediate layer was

significantly higher than the conventional sandwich pa-

nels.

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