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Kamara, et al. USEP: Journal of Research Information in Civil Engineering, 9(2), 2012

227

Modelling the Prism of Termitarium-

Strawbale Composite Masonry for its BearingCapacity

V. S. Kamara 1, and D. P. Katale 2 and A. A. Adedeji 3 1,2Department of Civil Engineering, Namibia University of Science

& Technology (former Polytechnic of Namibia),Windhoek, Namibia

3Department of Civil Engineering, University of Ilorin, Ilorin, Nigeria

Abstract

The paper reports the response of termitarium-strawbale composite prism (T-SBP) under compression (vertical) and thermal (lateral)loads, using SAP2000 for the finite element method of analysis. Theanalysis was carried out considering the same thickness of T-SBPformed rectangular section with different heights. The parameters ofstresses under certain pressures and their comparative results were

obtained from stresses and applied loads. The comparison of theresults between the termitarium plastered strawbale masonry and thecement plastered strawbale masonry shows that the former has muchmore stresses affected by the loadings than the later, given thatmaximum allowable stress, due to compression and thermal loads,for termitarium plastered strawbale wall is 62.2kN/m 2 and of thecement is 9.6kN/m 2.

Keywords

SAP2000, termitarium, strawbale, prism, stress rectangularmasonry, composite, finite element method.

1 Introduction

1.1 Termitarium

Beca use of the c limatic con dition in most part of the Namibia ,shapes and si zes of habited an d aba ndoned termite mo ulds do exist ,

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plastic foams, styro-foam and expanded perlite (Manohar andYarbrough, 2003). Besides their long-term financial benefit are the

use of inorganic insulating materials that may be harmful to humanhealth and body and also can cause environmental pollution, such asemissions of toxic gas and particle, and stick to skin (Liang and Ho,2007). Also, the production of these materials is highly energyintensive and the eventual disposal is an environmental hazard(Panyakaew and Fotios, 2008). Therefore, alternative materialshaving same or better properties as the conventional material needtobe explored as it can offer lower cost (Mohd et al., 2011).

One of the alternative materials that has been widely investigated isthe strawbale material which is very innocuous and can be used as astructural and durable element for a two-storey building to replacesandcrete wall.

2. Methodology

A typical example of prototype stacked strawbale plastered withtermitarium soil is shown in Figure 1 from which different prism

heights were cut out, subjected to compression and thermal loads.The data collected for the proper execution of this project werecollected from these properties data are presented in the Table 1.

Special attention was paid to the wall models for its time-dependence due to static loads from thermal and compressive forcesfor the analyses and optimisation design. Eigen-value solutions wereembarked upon using two applications using SAP2000 and LISA. Inthe analysis, the masonry panels, in the form of prism, were

provided for the prescribed loads for various heights, while thestrawbale size remained constant for various termitariumthicknesses of 10, 15, and 25 mm.

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Table1 Materials property for termitarium-strawbale prism (T-SBP)Property of sample of T-SBP Detail Data (Static

analysis)Sample material Termitarium-

Strawbale PrismElastic modulus (E)

N/mm 2 Termitarium 6000.00Strawbale 200.00

Poisons ratio Termitarium 0.30Strawbale 0.23

Dimension of T-SBP Strawbale 890mm x 220mm x220mm

Vertical load, kN T-SBP 42Thermal horizontalequivalent load, kN

T-SBP 1.92

Moisture Contents Termitarium 17.50 %Strawbale 5.5%

(a) Composite wall

(b) One-string strawbale block

Figure 1 Plastering of stacked strawbale blocks with termitarium soil

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Quality of database was considered before proceeding formodelling

2.2 Initial and Boundary Conditions

These are to be fixed before the commencement of the analysisusing software: e.g., essential, natural and mixed boundaryconditions.

2.3 Solutions

Preparation of mathematical formulation Qualitative formulation: the need to explore without expletivelysolving qualitative analysis

Quantitative formulation: by taking into consideration theanalytical, physical and computation method.

Pre-processing and post-processingWhen FEM is to be considered, the two above are carried out: Pre-processing, here parameters were given as domain

geometry, initial and boundary conditions and constants for the problem formulation.- Value of universal constants;- Formulation of grid; mesh generation of the domain into

mesh generation that encompasses decretisation of thedomain in to elements/nodal points;

- Dimensioning for 2D; and- Performing the real simulation of the problem with

particular numerical method.(In other words, this involves

modeling of the structure, specifying the type and strengthof the materials, applying all the relevant loads andspecifying the code to be used for the analysis and design)

Post-processing: Results were obtained and processed for thereflection in terms of tables, charts, graphs, contours, bar charts etc.(i.e. This stage involves the interpretation of the results produced bythe software (Adedeji, 2007).

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3. Analysis Investigation

In order to carry out the analysis, Eigenvalue solution was obtained by the application of SAP2000 in the following sequences:

- Creation of model;- Finite element incidences;- End conditions;- Load application;- Solution analysis types;- Analysis of the input; and- Extent of output results.

The prism masonry panel was systematically subjected tocompressive and horizontal thermal loads for various heights of the

panel. Response of the panels, leading to the variation in stresseswas observed to conclude results.

3.1 Termitarium-Strawbale Prism (panel) Dimensions

1 bale size is 890mm x 220mm x 220mm (L P x B P x H P) (Bruce,

2006)Prism (plastered strawbale at H p= 470 mm) has size: 890mm x240mm x 480mm (including termitarium plaster thickness t T =10mm on each side).Prism (plastered strawbale at H p = 710 mm) has size: 890mm x240mm x 710mm (including termitarium plaster thickness t T =10mm on each side).Prism (plastered strawbale at H p = 1040 mm) has size: 890mm x240mm x 1040mm (including termitarium plaster thickness t T =

10mm (minimum thickness on each side). See Figure 2 for thevariation in slenderness ratio.

3.2 Application of Loads

Vertical load N = N B + N T at N T=2N B, then load on N B = N = N T + 0.5N T Where N B = compression load on strawbale and N T = compressionload on termitarium panels. It is assumed that 2t T +t B = B P

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Figure 2Termitarium-strawbale prism of different slendernessratio ( )

4. Modal Analysis

4.1 Design of a Plastered Strawbale Wall

The optimal design using finite element was embarked upon andwas based on conduction, convection, cost function and loading.Analyses involved expressions for the constraints of conduction,convection, and cost function for the generation of loading equations,while data was input to obtain the required solutions. Figure 3 showsthe cross-section of strawbale wall of a building and also shows theloading applied to the wall. Where H P = height of the strawbale wall,tB = thickness of the strawbale (28t T mm), t T = thickness of the

plaster (15mm each), B P = total thickness of the plastered strawbalewall (30t T mm), b = breadth of the wall (assumed value = 1000mm),ww = wind load (0.33kN/m height (Asonibare 2007, Adedeji and Ige2011)), Q = heat transfer through the plastered strawbale wall, w f =foundation load, w r = roof load, u = earth pressure (upthrust).

= = 2 = = 3 = = 4

890 mm

tB tT

B p

890 mm 890 mm

tT

H p

B p

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tT

Figure 3 Cross section of a strawbale wall with applied loading.

In order to determine the stress generated in the T-SBP,isoparametric element represented in Figure 4 was used.

w r (kN/m)

Strawbale

Plaster(Termitarium soil)

w f (42 kN/m)

wh(kN/m)

Q

tB tT

BP

u (kN/m )

H p

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Figure 4 Isoparametric element definitions

4.2. Generation of Equations for the Discrete Elements.

The elements are higher order two dimensional isoparametricquadrilateral and triangular elements. For the quadrilateral elementsaselement type 1 is shown in Figure 4, while its shape function is

expressed in Equation (1) and other interpolation functions areshown in Equations (2) to (11).. The interpolation function (Shapefunction) is defined for the four nodal points as;

N1 =14

1 + r 1 + s

N2 =14

1 r 1 + sN3 =

1

41

r 1

s

N4 =14

1 + r 1 s (1)

Hence, the coordinate interpolation for the element is;

x = N 1 x1 + N 2 x2 + N 3 x3 + N 4 x4y = N 1 y1 + N 2 y2 + N 3 x3 + N 4 y4

(2)

4

12

3

b

a

r

s

Element type I

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And the displacement interpolation function is also given as;

u = N 1 u1 + N 2 u2 + N 3 u3 + N 4 u4v = N 1 v1 + N 2 v2 + N 3 v3 + N 4 v4 (3)

The element strain is given as;

T = xx yy xy (4) where;

xx =

u

x:

yy =

v

yand

xy =

u

y+

v

x (5)

Evaluating the displacement, we need to evaluate

r = J x (6) Where J is the Jacobian operator, shown as;

rs= xr yrxs ys

xy (7)

For any value of r and s, 1 r + 1 and 1 s +1,r = r iand s = s j

The stiffness matrix is calculated from,

= T dvv

or = T tA (8)

The element stress is given as;

= = = xy

xy

(9)

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where

x =

E

1

2

xx +

E

1

2

y

y = E12xx + E12yxy = E2 1 2 xy (10)

also,

=1

2

1 01 0

0 0 12 (11)

5. A Typical Analytical Example

In order to verify the capability of this numerical procedure, thefollowing assumptions are made for the termitarium plasteredstrawbale wall and the properties in Table 1 were also considered.With the use of SAP2000 (Adedeji and Ige 2011, Lofti 2001), the

analytical example shown in Figure 5 refers to show the effects ofcontact between the strawbale and the plastering composition. A

particular value was entered on a computer system, using SAP2000,as the applied loads and quantities of the heat energies, which wastransferred by conduction and convection i.e. Composite (combined)stress constraint values of height, h, = 0.48, 0.71 and 1.01 m withtotal maximum thickness, B P, = 0.45m.

5.1 Stability Analyses

The loading on the strawbale structure used in this work is basicallythe static loading i.e. applied loads (both vertical and horizontalloading), the load due to the self weight of the wall and the upthrust.

These loadings are shown below:

(a) Vertical Loading

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(i) Upthrust, U = 0.5hbt for quadrilateral structures = 4.5 kN

In which = density of water, h = height of upthrust, b = breadth ofupthrust, t = thickness.

tT

Figure 5 Termiterium-strawbale wall under loads

wr (42 kN/m)

Strawbale

Plaster(Termitarium soil)

w f (42 kN/m)

wh(2.25kN/m)

H p(0.47, 0.71, 1.0m )

Q

tB 220

~ 240) tT

BP(240 ~ 450)

u 10.0 kN/m )

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(ii) Foundation load and roof load (assumed) W f = W r = 18kN

(iii) Plaster self weight,W T = V T= 8.83kN(iv) Strawbaleself weight,W B = V B= 10.04kN

Therefore, total vertical loading = 42.24 kN

(b) Horizontal Loading

(i) Heat transfer, W q= (0.3 + 1.62) = 1.92kN/m x 1 = 1.92kN

Therefore, total horizontal loading = 1.92 + 0.33 = 2.25kN

(c) Sliding Criteria

Factor of safety; F.S. = Net vertical loading= 18.67 Net Horizontal loading

Therefore, (18.67 kN> 1.6, Hence, sliding criteria is favorablysatisfied.

5.2 Stresses Analysis Using SAP2000

The Figures 6 12show the diagrammatic procedure for theanalytical example (combined loading) from SAP2000 on how thestructure has been analyzed for the prism slenderness ratio, = 2and 3). It should be noted that all the analysed prism have zero

coordinates origin at their principal axes.

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Figure 6Applied loads on termitarium plastered strawbale wall( = 2,3)

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Figure 7 Deformed shape of termitarium plastered strawbale wall ( =2,3)

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Figure 8 Shear force diagram of termitarium plastered strawbalewall ( = 2,3)

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Figure 9 Bending moment diagram of termitarium plasteredstrawbale wall( =2,3)

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Figure 10 Minimum stress diagram of termitarium plasteredstrawbale wall ( =3)

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Figure 11 Maximum stress diagram of termitarium plasteredstrawbale wall ( =3)

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Figure 12 Both minimum and maximum stress diagram oftermitarium-plastered strawbale wall( =3)

However, Figure 13 shows the discretization of the wall intofinite elements. The results shown in Table 3are the typical values of

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the stresses from the analytical example (combined loading) fromSAP2000 and the stresses between the plaster composition and the

strawbale as well as the stresses in the middle of the strawbale.

Figure 13 Discretization of the plastered strawbale wall

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Table 3 Stresses within the termitarium plastered strawbale wall.Area AreaElem S11Top S22Top SMaxTop SMinTop SAngleTop

Text kN/m 2 Degrees

12 1 1.91 44.56 47.09 -0.62 -76.682

12 1 -9.38 14.4 16.7 -11.68 -73.456

12 1 3.77 -15.52 6.49 -18.24 -19.387

12 1 -1.32 -44.44 1.19 -46.95 -13.191

13 2 -4.58 -60.78 -1.23 -64.13 13.344

13 2 2.51 -21.78 6.69 -25.96 20.96213 2 -10.84 20.12 23.57 -14.3 72.414

13 2 4.68 60.8 64.16 1.33 76.639

14 3 -9.93 14.29 15.16 -10.8 -79.43

14 3 -0.28 4.78 6.03 -1.54 -65.978

14 3 -1.01 -5.04 0.43 -6.49 -27.228

14 3 4.23 -15.43 5.29 -16.49 -12.737

15 4 2.97 -21.69 5.06 -23.77 15.588

15 4 -0.65 -3.2 3.59 -7.43 38.304

15 4 -0.73 2.92 6.76 -4.57 54.419

15 4 -11.41 20 21.69 -13.09 77.294

16 5 -1.62 4.51 5.35 -2.47 -70.846

16 5 -0.74 4.16 5.13 -1.7 -67.883

16 5 -0.2 -4.34 0.89 -5.43 -24.482

16 5 0.74 -4.69 1.66 -5.61 -20.884

17 6 1.06 -2.86 4.4 -6.2 34.163

17 6 0.41 -1.93 4.27 -5.79 38.248

17 6 -1.01 1.82 5.49 -4.69 53.058

17 6 -2.35 2.6 5.63 -5.39 58.345

18 7 -1.81 46.45 49.42 -4.77 -76.474

18 7 -0.092 44.16 47.26 -3.19 -75.645

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-0.74 4.69 2.51 5.67 -1.72 68.615

-1.19 2.83 -4.84 6.06 -4.42 -56.288

-0.13 1.99 -4.82 5.87 -4.01 -51.205

-1.34 -2.29 -4.82 3.03 -6.66 -42.21

0.11 -3.05 -4.84 3.62 -6.56 -35.962

-0.6 -46.94 12.32 2.47 -50.01 14.004

-2.32 -44.64 12.1 0.9 -47.85 14.879

-0.38 44.1 12.1 47.18 -3.45 75.726

-1.95 46.43 12.32 49.38 -4.91 76.502

1.47 63.53 -15.61 67.24 -2.23 -76.648

2.89 60.45 -15.39 64.3 -0.97 -75.929

-6.26 -61.12 -15.39 -2.24 -65.14 -14.649

Table 3 cntdSVMBot S13Avg S23Avg SMaxAvg SAngleAvg

KN/m 2 Degrees

46.94 -8.96 -27.37 28.8 -108.13

23.79 -8.96 -7.67 11.8 -139.43

22.86 4.04 -7.67 8.67 -62.257

47.95 4.04 -27.37 27.66 -81.612

63.74 5.63 38.03 38.44 81.577

30.21 5.63 11.46 12.77 63.839

32.04 -12.32 11.46 16.83 137.066

62.93 -12.32 38.03 39.97 107.954

21.62 7.65 -8.45 11.4 -47.822

6.8 7.65 -1.81 7.86 -13.329

7.1 -4.16 -1.81 4.54 -156.458

20.4 -4.16 -8.45 9.42 -116.23

27.12 -2.88 12.26 12.59 103.201

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9.75 -2.88 0.4 2.9 172.084

9.58 8.47 0.4 8.48 2.703

29.37 8.47 12.26 14.9 55.359

6.5 9.96 -2.78 10.34 -15.591

5.96 9.96 -2.55 10.28 -14.349

6.05 -10.31 -2.55 10.62 -166.123

6.7 -10.31 -2.78 10.68 -164.918

9.11 -8.48 1.63 8.64 169.141

8.6 -8.66 1.06 8.72 173.0368.58 15.36 1.03 15.4 3.829

8.94 14.98 1.57 15.06 6.003

51.29 19.16 -28.79 34.59 -56.351

48.31 19.16 -27.25 33.32 -54.884

49 -17.44 -27.25 32.35 -122.614

52.01 -17.44 -28.79 33.66 -121.201

68.38 -15.74 40.29 43.26 111.338

64.79 -15.74 38.26 41.37 112.359

64.05 20.94 38.26 43.62 61.312

6. Discussion of Results

It was observed from the analysis that the minimum and maximumstresses between the plaster compositions and the strawbale materialshows that the use of termitarium plaster can hold a strawbale fromdeflecting for the wall prism of H P = 2. The adequacy of this type ofdesign can be measured in terms of the minimum acceptable drift ofthe strawbale work system. The minimum acceptable drift is given

by as 1m H P 4m and 0.36m BP 0.45 m, where B P is themaximum thickness attained, H P is the height of the strawbale wall.For the height of the strawbale H P = 1m and thickness, B P = 0.45m,the maximum stresses allowable and calculated using SAP2000 are

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also shown in the Tables 4 and 5 for both cement (Adedeji, 2011)and termitarium plaster composition.

Table 4.Minimum and maximum stresses between each of the plaster compositions and the straw bale material.

Outside plaster

Inside plaster

Plastercomposition

Minimumstress

Maximumstress

Minimumstress

Maximumstress

*Cement -9.8 9.6 -19.3 18.3

Termitarium -60.0 62.2 -6.3 6.5*Adedeji (2011)

Table 5Differences between the allowable and calculated stressesfor both plaster compositions.

Wall composition Maximumallowable stressMaximum calculatedstress using SAP2000

*Cement plasteredstrawbale wall 70.14kN/m

2 38.836kN/m 2

Termitarium plasteredstrawbale wall 73.14kN/m

2 67.452kN/m

2

*Adedeji (2011)

7. Concluding Remarks

Termitarium plastered strawbale wall as a material has shownadequate resistance against vertical loading, as there are referencedevidences in this case. In the same vein, the comparison of theresults between that of termitarium plastered strawbale wall and ofthe cement show that the earth wall has much more stresses affected

by loading than the cement (i.e. maximum stress for termitarium plastered strawbale wall is 62.2kN/m 2 and of cement is 9.6kN/m 2).This implies that under higher load, which is above the allowablestresses, the collapse or response of the strawbale Termitariummasonry will be significantly higher compared to that of cementstrawbale masonry.

Also the allowable stresses (i.e. 70.14kN/m 2 for cement plastered strawbale masonry and 73.14kN/m 2 for termitarium

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plastered strawbale masonry) are lower than that of the calculatedstresses using SAP2000, i.e. 38.836kN/m 2 for cement plastered

strawbale masonry and 64.2kN/m2

for the termitarium plasteredstrawbale masonry, which implies that the stress stability of the plastered strawbale wall are adequate after using the best fitvariables for wall design.

From this work, it could also be recommended that further work bedone on this project to incorporate other aspects on other plastercomposition to produce optimum solutions to engineering problems.

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Adedeji, A. A. (2010), Interaction Analysis and Optimal Design of

Composite Action of Plastered Straw Bale, MultidisciplineModeling in Materials and Structures, Emerald Group PublishingLimited, Vol. 7 No. 2, 2011, pp. 146-169, DOI10.1108/15736101111157091

Adedeji, A. A. (2007), Introduction and Design of Straw baleMasonry, Olad Publishers & Printing Enterprises.

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Manohar, K., Yarbrough, D.W. (2003). A comparison ofBiodegradable Fiber Insulation with Conventional FibrousInsulation, Proceedings of the International Conference on ThermalInsulation, Volume 18, January 13 15, White Sulphur Springs, WestVirginia,U.S.A., Product Safety Corporation, pp.133-140.

Miller, B. E. (1992), Optimization of building design variables, MS,Department of Mechanical Engineering, Colorado State University,Fort Collins, Co.

Mohd, Y.Y., H. Sihombing, A. R. Jeefferie, M. A. Z. Ahmad, A. G.Balamurugan, M. N. Norazman, A. Shohaimi. 2011. Optimizationof coconut fibers toward heat insulator applications. GlobalEngineers & Technologist Review, Vol.1, No.1, pp.35-40.
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