Indi an Journal of Engineering & Materials Sciences Vol. 7, August 2000, pp. 181- 188

An experimental investigation of wind load on axisymmetrical shell structure houses

Gazi Md. Khalil

Department of Naval Architecture and Marine Engineering, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh

Received 11 August 1999: revised received 28 Februwy 2000

The purpose of this paper is to investigate the wind load on axisymmetrical shell structure houses. Twelve models of such houses are fab ricated with aluminium. The models are of circular cylindrical waJl and ellipsoidal, spherical and paraboloidal shell roofs with various height-to-span ratios. The models are tested in a wind tunnel at four different wi nd speeds (Reynolds numbers varying from 0.25 x 106 to 0.32 x 106

). The lift forces generated on the models are measured by a Three Component Aerodynamic Balance, Model No. B-1264 (made by the Plint and Partners Limited, England). The experimental results are plotted in terms of non-dimensional parameters and then physicall y interpreted. The results are reported wi th the available data in the literature. The findings of this investigation are expected to be useful in evolving an appropriate house building technology for the poor people who li ve in the cyclone-prone coastal area of Bangladesh.

Bangladesh is part of the humid tropics, with the Himalayas lying to the north and the funnel shaped coast touching the Bay of Bengal in the south. This pec uliar geographical location of Bangladesh produces not only the life-giving monsoon rains but also the catastrophic floods and cyclones. The Bay of Bengal is an ideal breeding ground for tropical cyclones and storm surges which frequently devastate the coastal areas and offshore islands of Bangladesh. Over the last one hundred years 56 severe cyclones have oCCULTed. Recurrence of these natural disasters has caused widespread loss of life and property in the coastal belt of the countr/.

House is one of the immovable properties and also one of the first casualties in a cyclone disaster. This is more so in the case of a developing country like Bangladesh where poor people live in their traditional houses built with indigenous materials and non­engineered conventional construction techniques. Most of the houses in the coastal area are built with mud walls and thatched roofs with low height. The roofs are pyramidal in shape.

In the choice of material s used in the construction of these houses, bamboo features most prominently, because it is the cheapest and most easily transportab le materi <l l. Houses made of bamboo can be expanded easily when more money is available later and as such it is the choice of those in the lowest income group. But in recent times the price of bamboo has shot up and consequently the poor people can afford only the thin bamboo which may last for

only one or two years. Poor quality bamboo framing is liable to be associated with walls made of bamboo­mat or jute stick panels which not only have poor durability but also limited protection against monsoon rains. Bamboo has other shortcomings. It is vulnerable to insect attack and has poor resistance to rotting.

Mud wall housing is still the choice of the poor people because of many reasons. Cohesive mud can be procured from ponds or river banks. By paying for a little transportation cost or price of labour, the mud itself can be obtained free of cost. But such construction (kutcha dwelling) is un suitable for this country. These houses exhibit little or no resistance to extreme winds. The roofs are blown off, walls collapse and houses flattened by strong winds . Neither mud nor bamboo provides a safe shelter2

.

There is no doubt that most people in the coastal region want stronger houses. But lack of fLl1ance prevents them from achieving thi s. The need , therefore, for finding out a procedure for constructing proper dwelling at a cost within the reach of the common man is most pressing today. Researchers are trying to evolve an affordable house building technology for the cyclone-prone coastal area of Bangladesh. As a part of this venture some works have been done in the development of extra thin shells made of concrete at a cost within the reach of the common man which appears to have a great potentiality in developing cheap housings3

.

182 INDIAN J. ENG. MATER. seL , AUGUST 2000

Before designing a shell structure, one must estimate the lift and drag forces that will be generated on the curved surface when the wi nd blows over it. The lift force tends to detach the roof whereas the drag force may tilt the structure aside. Naturally, therefore, the designer has to keep an eye on these two aerodynamic forces while prescribing the :lI1choring for the building.

From aerodynam ic considerati ons, with the possibilities of extreme wind blowing from any direction, the best shape would be a house of circular plan fo rm. From structural point of view, shell roofs consume minimum building materials. Hence, the knowledge of wind loads over such houses is essential 10 des ign the structure economically.

The purpose of this paper is to investigate the aerodynamic li ft forces generated on axisymmetrical shell structure houses of ellipsoidal, spherical and paraboloidal roofs with various height-to-span ratios.

Wind Loading and Building Response Wind gives ri se to pressure on the surface of

bu ildings, and the press ure generates forces (loads). Different parts of a building encounter different wind pressures and loads. For instance, when wind direction is perpendicular to a building, the windward wall experiences an externa l pressure that is higher than the ambient atmospheric pressure at the ground level, whereas the leeward and the side walls experience an external pressure lower than ambient. Thus the re lative pressure (i .e., wind pressure on the building minus the ambient pressure) on the windward wa ll is posi ti ve, while it is negative on the leeward and the side wa lls. The relative pressure on ordinary roofs is negative except on the windward part of a steep roof. Fig.1 depicts the pressure distribution over a typical rectangular building wi th a flat roof. Note that arrows pointi ng toward the building represent pos iti ve pressure (si mpl y 'press ure'), wherea~ arrows pointing away from the building k.prese lt negative pressure (,suction ') .

The pressure disc ussed in the previous paragraph is that generated on the external surfaces of buildings . It is ca lled the 'ex ternal pressure'. Wind also generates a pressure inside bui ldings termed the 'i nternal pressure'. The wind loads on bui lding cladding (i.e., walls, roofs and ce ilings) depend on the differences between the external and illternal pressures act ing on oppos ite sides of the cladding. Genera ll y, the net wind load , on any part of cladding is,

F=A(P'-~) . .. (1)

where A is the cladding area; P, is the average external pressure on the part of cladding for which F is calculated; and Pi is the internal pressure. When F is posit ive, the net wind load F is di rected toward the building. But when F is negative, the wind load ac ts away from the building.

It is important to reali ze that the external pressure Pe depends on build ing geometry and not on cladding openings. In contrast, the interna l pressure Pi depends strongly on cladding openings. For instance, with a window or door open on the windward wa ll , the internal pressure ri ses (becomes positi ve). However, cladding openings are on leeward and side wall s, the internal pressure drops (becomes negative). Very hi gh positive internal pressure can be generated by opening a door or a window on the windward wa ll in hi gh winds. Such high pressure often con tributes to the failure of lightweight roofs.

In general, the wind pressure P on a buildirig, for both internal or externa l pressures and for both pressure and suction, is proportion, 1 to the square of the wind veloc ity V in the foll owi ng manner:

pV 2

P =C - (2) " 2

where p is the density of the air, and the proportionali ty constant Cp is cailed the ' pressure coeffici ent ' . Substituting Eq. (2) into Eq. (1) yields

F = A(C"e - C I'J p~ 2 ... (3)

where Cpe and Cpi are the external and internal pressure coefficients, respecti ve ly.

Eq. (3) shows that accurate determi nat ion of wind loads on buildings requires an accurate knowledge of the external and internal pressure coeffi cients. Cpc and

WIND --- + -=-l -->.;

Fig. I - Wind-generated pressu re around J block·lype building.

KHALIL: WIND LOAD ON AXISYMMETRICALSHELL STRUCTURE HOUSES 183

Cpi. respectively. Values of Cpe are normally determined from wind tunnel tests, and are given in handbooks and standards such as ASCE4

. Values of Cpi for a given building, on the other hand, can be calculated in a simple manner if the cladding opening conditions are known , as discussed in Liu and Nateghi5 and Liu6

.

Determjnation of the wind loads on a building in high wind requires the use of Eq. (3) on various parts of the building, using different values of Cpe for different building parts. The value of Cpi in contrast, is uniform throughout the interiors of a building except in cases where the building has tightly sealed rooms, which give rise to different internal pressures in different rooms.

Experimental Set-up and Procedure The experimental facility consists of a subsonic

wind tunnel of test section 30.48 cm x 30.48 cm, a Three Component Aerodynamic Balance (Model No. B-1264) and a multi manometer (made by the Plint and Partners Limited, England).

Fig. 2 shows the schematic diagram of an axisym­metric shell structure house. Twelve models of such houses are fabricated with aluminium. The models are of circular cylindrical wall and ellipsoidal, spherical and paraboloidal shell roofs with various height-to­span ratios (R = bid). The projected area of the roof and the area of the walls of all the models are kept constant. It may be noted that the diameter and the height of the walls are 13.72 cm and 12.32 cm respectively for all the cylindrical models.

The models are tested in the above-mentioned wind tunnel and the lift forces are measured by the Three Component Aerodynamic Balance (see Figs 3 and 4). The experiments are performed at four different Reynolds numbers Rn (ranging from 0.25 x 106 to 0.32x106

) under two different conditions of wind flow, namely, (i) uniform wind ve locity field when the test section surface is smooth ; and (ii) wind having a velocity gradient due to the roughness given

I b

I ~---t-----1.l--.-l I I I _---...,: I /''' I /'/ 'X" I I . \ I I I \ I 1/ 'I \1 1----- -- - --- -- - ,

\~'" I ~I./ " '" ........ _- -_/

I-<---- d

Fig. 2 - Schematic di agram of the axisymmetrical shell structure house. (17 = 12.32 cm, d = 13 .72 cm and b = height of the roof)

Aerofoil Fan Aerodynamic Balance

Damper

Silencer

Test Section

Fig. 3-Schematic diagram of lhe Plint and Partners wind tLinnel filled with a Three Component Aerodynami c Balance and a shell house model.

184 INDI AN 1. ENG. MATER. SCI., AUGUST 2000

Cantileve r Springs

- --- _ ... _--- -------

Universal Jo ints

1\ tr~ I

~ ~, Dial Gauge

Microme ter

Ta e

I

Model Force Pl ate

o

SIDE VI EW FRO NT VIEW

Fig. 4 - Schematic diagram of the Three Component Aerodynamic Balance (made by the Plint and Partners Limited, England).

on the test section fl oor to simulate ground conditions by fixing al1ific ia l trees, bushes and grass on it. Reynolds numbers are varied by adjusting the position of the damper.

Having measured the lift force L generated on a shell roof the corresponding coefficient of lift CL is calculated using the well-known equation7

,

CL

= L ... (4)

~pV 2 S 2

where p is the dens ity of the air, V is the wind veloci ty and S is the projected area of the roof.

Results and Discussion Figs 5, 6 and 7 show the variati on of the coeffic ient

of lift with Reynolds number in uniform velocity field fo r ellipsoidal, spherical and paraboloidal she ll roofs respectively. F rom Figs 5 and 6, it is observed that for ellipsoidal and spherical shell roofs, the coefficient of lift increases with increase in height-to-span ratio R. But F ig. 7 shows that for the paraboloidal shell roofs , the coeffic ient of lift increases with the height-to-span ra tio upto about R = 1/6.5, but then sharply decreases wi th any further increase in R. Such va riati on of the coeffic ient of lift for the paraboloidal she ll roofs can be explai ned in the follow ing way. The coefficient of

1--'

~ -.J

u.. 0

I--z w '::! u.. u... w 0 u

3.0

2.8

2.6

2.4

..".

2.2

2.0

1.8

1.6 0.25

•

o

0.27

A R·o 1/4. 2

• R" 1/ 5 0 R ~ 117. S

'" -.A-_-&---_

• • "

o o

0.29 0.3 0. 33 0. 35

RN xl06

Fig. 5 - Vari ation of the coe ffi cient of lift with Reynolds number for elli psoidal shell roofs in uniform ve locity ricld.

KHALIL: WIND LOAD ON AXISYMMETRICAL SHELL STR UCTU RE HOUSES 185

--' w

>--u.. ::::; u.. 0

>-z ~

u.. u.. 4.J 0 w

2.S ,--------------- ----,

2.4

2.3

2.2

2 1 --('j

2.0

1.9 0·2S

• 0

0.27

• Q

El R= 1/3 A R = 114 • R= 1/6 o R= 117

• 0

0.29 0.31 0·33

RNx1()6

035

Fig. 6 - Variation of the coefficient of lift with Reynolds number for spherical shell roofs in uniform velocity fie ld .

--' w

,..: u.. ::::; u.. 0

>-z ~ w u.. u.. U.J 0 w

2.8,----------- ----------

2.6

2.4

X x

2.2

0 o

2.0 f-

Ib

1.8 f-

0 •

1.6 e e

1.4 0.25 0.27

1

0.29

x

g

• 0

• R = 1/4.2 <I R = 1/6 X R = 1/65 D R = 117.4 OR= 1/9.8

x

• 0

I I

0.31 0.33 RN x10-6

0.35

Fig. 7 - Van<ltion of the coefficient of lift With Reynolds number for rnrabo!o idal ~hcl l roofs in Ul1I form velocity fiel d.

2.2 r-------- ------- ---,

2.1

2.0

ti:*' 1.9 ::::; u.. a .-z

w u:: u.. UJ o

1.8

1.7

1. 6

1.':> 0.25

•

0.27

• •

0

o 29 -6

RN x 10

o R= 1/4.2

• R= 115

o R = 1/7.':>

•

0.31 033 0.35

Fig. 8 - Vari ation of the coefficient of lift with Reynolds number fo r ellipsoidal shell roofs when ground condition is simulated in the test section.

u.. o I­Z UJ

u.. u..

2.3

2.2

2.1

2.0

1.9

d 1.8 w

1.7

1 6

0.25 0.2 7

El R = 1/3 • R = 1/4 • R = 1/6 o R = 117

0.29 0. 31 -6

RN x 10

0.33 0.3':>

Fig. 9 - V ~lr i at ion of the eoenicient of lift with Reynolds number for spherical shell roo fs when ground condition is sllllulated 111 the test section.

186 INDIAN J. ENG. MATER. SCI. , AUGUST 2000

lift depends upon the magnitude of pressure and its ve rtica l component. As R increases, the magnitude of pressure increases, but its vertical component decreases to a greater extent because the tangent to the paraboloidal she ll roof becomes steeper. The va lue of the coeffic ient of lift is contro lled more by the magnitude of pressure upto R = 116.5 and by the vel1ical component of pressure fo r R greater than 116.5.

Figs 8, 9 and 10 show the variati on of the coefficient of li ft with Reynolds nu mber fo r ellipsoidal , spherica l and paraboloidal shell roofs when ground condi ti on is simulated in the test section. By comparing Figs 5, 6 and 7 with Figs 8, 9 and 10 respectively, it is observed that the coe fficient of lift obtained in smooth test secti on is greater than that in rough test sec ti on where ground conditi on IS

simulated. Fig. 11 compares the coefficient of lift fo r the two­

dimensional ellipt ic shell roof tested by Husain8 with that for the ax isymmetrical ellipsoidal shell roof tested by the present author, the height-to-span ratios of both the shell roofs being the same (v iz. R = 1/5). It is observed that the li ft coefficient for the axisymmetrical ellipsoidal shell roof is much smaller than tha t for the corresponding two-dimensional elli ptic shell roof at all Rey nolds number.

-' u

1;::" :::; u. 0

I-z UJ

u u. u. UJ 0 U

2.7

2.3

• R ~ 114.2 6 R~ l ib

X R = l/b. S G R= 117. 4 o R = 1/9.8

2.1 ~-

- F.}-- -lil rr--U--1.9

b~ ~~

1.7

1.5

1.3 0.25

,..----"'--~&0

0. 27 0.29 0,31 0.33 -b

RN x 10

0.35

ri g. 10- Variation of the coefficient of lift with Reynolds number 1'0 1' paraboloidal shell roofs when ground condi ti on is simu lated in the test secti on.

Similarl y, Fig. 12 compares the coeffi cient of lift fo r the two-dimensional parabolic shell roof tested by Husa in8 with that for the ax isYlTlmetrk al paraboloidal shell roof of the present investigation, the height-to­span rati os of both the shell roofs be ing the same (viz. R = 117 .4). The coeffi cient of li ft for the ax isymme­trica l paraboloidal shell roof is founel to be sma ll er than that for the two-dimensional parabo lic shell roof at all Reynolds number.

It is, however, necessary to say a few words about the limitat ions of the present in vesti gati on. The experimental faci lity consi sts of a small wind tunnel of test section 30.48 cm x 30.48 cm whereas the cy lindrical model is of di ameter 13.72 cm and height 12.32 cm. The blockage rati o of 18.2% at test section is large enough to influence the lift coeffic ients measured. Moreover, as the fetch length before test sec tion is insignifican t perfect simulation of surface roughness of ground is not possible.

A model wi ll yield useful quantitative info rmat ion about the characteri sti cs of the prototype if it is completely similar to its prototype. Complete similarity can be obtained between the model and its prototype if the two systems are geometrically, kinematica ll y and dynamica lly similar. The model and its prototype are geometrica ll y i mi lar when they

8

6

4

1

•

8 • - TWO - DIMEN SIONAL EL LIPTIC SHELL ROOF

0 - AX ISY M MEiRl CAL ELLIP SOID AL SH ElL ROOF

R = 11 5

• • •

-o~--~0----~e7---~or------

0·25 0·27 0·29 0·31 0· 33 0.35

RNx l f6

Fig. I I - Variation of the coe ffi cient or' lift with Reynolds number for two-dimensional ellipli c shell roof and ax isymmelri cal ell ipsoidal shell roof.

KH ALI L: WI ND LOA D ON AXISYMM ETRICA L SH ELL STR UCTURE HOUSES 187

~

4· 6

4· 2

3.8

3· 4

3. 0

2.6

2.2

• - n"O -DIMENSIONAL PARABOLIC SHELL ROO F8

o -AXISYMMETRICA L PARABOLOIDAL SH ELL ROOF

R = 117.4

,-------.. ~--~.~-.----------•

r

<;) ~----~O~----~O~~0~·----------

1. 8 '-------l------'----__ --'--____ -'-____ -'-__ ---...J

0. 25 0.27 0.29 0. 31 0.33 0. 35 0.37

Fig. 12 - Variation of the cocrficielll of lift with Reynolds number for two-dimensional parabolic shell roof and axisymmetrical paraboloidal shell roar.

are identical in shape but d iffer only in size. In other words, fo r geometric similarity to ex ist between the model and its prototype, the rat ios of corresponding linear d imensions of mode l and prototype must be constant.

It may be noted that the behav iour of the prototype as predic ted by two models wi th different sca le ratios is genera lly not the same. Th is di ffe rence in the predicted behav iour of the prototype is att ributed to difference in scale rat ios and is known as scale effect. The d iscrepa ncy due to scale effect creeps in because it is imposs ible to have complete simili tude sati sfy ing all the requirements. In model in ves tigations, on ly two or three fo rces which are predominant are considered and the effect of the rest of the fo rces which are not signifi cant is neglected. T hese fo rces which are not so importalll ca use small but varying effect on the model depending upon the scale of the model. Because of th is variation in the effect of such forces on the model , sca le effect creeps in. Sometimes, the di screpancy due to sca le effect is caused owing to imperfec t si mulati on in d iffe ren t models. Scale effect can be detected by test ing a large number of models with different scale ratios . The exact behaviour of prototype can then be predicted by intelligent interpretation of the results.

It is interesting to note that for R = 1/4.2, there is a sudde n drop in CL va lue from about 2.3 in F ig. 5 to about 1.7 in Fig. 7 . It clearly shows that the e llipsoidal she ll roof experiences much greater lift forces than the parabolo idal she ll roof when the he ight-to-span rati o is R = 1/ 4 .2.

Conclusions T his paper in vestigates the aerodynamic lift forces

generated on ax isy mmetrical she ll structure houses of e llipsoida l, spherica l and parabolo idal roofs with vari ous height-to-span rati os. T he fo llowi ng conc lus ions can be drawn fro m the present inves ti gati on: (a) For the ell ipsoid al and spherical she ll roofs, the

coefficient o f lift increases with increase in he ight-to-span ratio R.

(b) For the parabolo idal shell roofs, the coefficient of lift increases with increase in height-to-span ratio up to about R = 1/6.5 but then sharply decreases wi th any further increase in R.

(c) T he coefficient of li ft for each she ll house model is reduced when it is pl aced in a test section where ground conditi on is simul ated. It is, therefore, recommended that trees and bushes should be pl anted around houses in order to reduce the intens ity of w ind loads.

(d) For the same c urvature and the sa me he ight-to­span ratio R, the lift fo rce generated on the ax isymmetri c mode ls (v iz. , the e llipsoi dal, the spherical and the paraboloida l she ll roof) is a lways less than that deve loped on the correspond ing two-d ime nsional models (viz., the ell iptic, the circu lar and the parabolic she ll roof). Hence, it is adv isable on r.his count that the ax isy mmmetric shell roofs should be preferred to the two-dimensional ones.

(e) T he shell house mode ls on whi ch experiments have been performed are of geometric shape. The structural features like the doors , windmvs, louvres, overhangs e tc. in a buildi ng will affect the pressure distribution over the wall and the roof. So the exact wind load on a building is to be determined by testing a similar mode l.

(f) From aerodynamic considerations, with the possibil ities of extreme wind blowi ng from any direction, the best shape would be a house of circular plan form. From st ructural point of view, shell roofs consu me minimum bui lding materials. Hence, the knowledge of wind loads over sllch hOll ses will be useful in design ing the structure economicall y.

188 I DIAN 1. ENG. MATER. SC I.. AUGUST 2000

Nomenclature A cladding area b hei ght of the shell roof CL coefficient of Ii ft CI' coefficient of pressure C

",. ex ternal pressure coefficient

Cl'i internal pressure coefficien t d diameter of the circular cylindrical wall F net wind load on any part of cladd ing h height of the circular cy lindrical wall L lift force P P,.

Pi R RN S V

j.1

P

wind pressure on a buildin g average ex ternal pressure on an y part of cladd ing intern al pressure height-to-span ratio of the shell roof (= bid) Reynolds number (= pVdlj.1) projected area of the roof wind veloci ty coefficient of viscosity of the air dens ity of the air

References I Khalil G M, Natural Hazards, 6 (1992) 11-24. 2 Lewis J & Chisholm M P, in IlIlplelllenting 1-lazard-Resiswllt

Ilousillg, Proc First 1111 HOllsillg & Hazards Workshop to Explore Practical Buildillg for Safety SOllitiollS, edited by Hodgson R L P. Seraj S M & Choudhury J R, Dhaka, 1996, 29-38.

3 Haque S M N, Developlllell i of eXIra thill shell for cheap hOIiSillg , presented in Seminar on Low Cost Pucca Housing, Lions Club, Dhaka, 1970.

4 Minimum design loads for buildings and other structures, ASCE Stalldard 7, American Society of Civ il Engineers (ASCE), 1988, 94.

5 Liu H & Nateghi F. ASCE J Aerospace Ellg. 1(2) (1988). 6 Liu H, Willd Ellgilleerillg-A !-falldbook f or Stmctllral Ellgilleers

(Prentice-Hall , Englewood Cliffs, New Jcrs.y), 1991 , 209. 7 Sumer 13 M & Fredsoe J, lIydrodYllalllics arolilld cylilldrical

stmclllres (World Scienti fi c Pu bli shi ng Co. Pte. Ltd .. Singapore), 1997.

8 Ilusain H S, All Experilllell tal Ill vestigatioll of AerodYllalllic Lift Force 0 11 Shell St ructllre HOllse, M Sc Thesis, Department of Mechanical Engineering, B::lIlgladesh University of Engineeri ng and Technology, Dhaka, 1970.