Page 1

Advanced Steel Construction 2 (2006) 87-108

AN INVESTIGATION ON STRUCTURAL PERFORMANCE OF

PROFILED STEEL SHEET TO DEVELOP SELF-SUPPORTING

ROOFING SYSTEM

S. M. Zahurul Islam*, A. A. Abang-Abdullah, M. S. Jafar

Housing Research Centre, Department of Civil Engineering, Universiti Putra Malaysia

*(Corresponding author: E-mail: smzislam190@yahoo.com)

Abstract: Profile steel shell structures are used popularly due to aesthetic and economical use of materials. The aim

of this research work is to develop a self-supporting roofing element using profiled steel sheet such as zincalume,

with potential for application in affordable quality housing. An analytical investigation using nonlinear finite element

method is carried out on the structural strength and behaviour of different types of self-supporting roofing elements.

An experimental study is conducted to validate the analytical investigation. Conventionally, profile steel sheet such

as zincalume is using in roof as a covering materials using different types of internal support without any attention

paid to their structural capability. Self-supporting of roofing system has significant advantages of removing the

internal trussing and support. An attempt has been made to find out efficient, economic and aesthetically pleasing

shape of shell elements to provide self- supporting roofing system on the basis of present results. The load–

deflection, stress- strain and deflected shape profiles for investigated roofing element is showed that parabolic

roofing element having crown height 1/6 of chord length is more efficient than others. It is observed that the

proposed roofing system has a great potential to be exploited for housing construction.

Keywords: Structural performance, profiled steel sheet (zincalume), self-supporting, roofing element, semi-loof

elements.

INTRODUCTION

The housing need is ever increasing due to rapid industrialization, urbanization and population

explosion. The roof protects the building and its occupants from the effects of weather, but it are

also is an architectural feature that gives the building a desired appearance.

Roof accounts to a substantial part (about 25%) of the total cost of a building whether it is

residential or industrial [1]. Therefore, it demands high technical and design specifications for both

of the individual products elements and for the roof as a whole in order to achieve a satisfactory

design life. Recent trends, research and developments are directed towards developing a

lightweight, economical and structurally strong material that can be precast or prefabricated and

easily erected. Conventionally, profile steel sheet such as zincalume and galvanized iron sheet is

using in roof as a covering materials using different types of internal support without any attention

paid to their structural capability. It is an innovative system that is self-supporting roofing system

where sheeting roofs run continuous lengths of roof sheeting from one end to other end support

through eliminating internal support. The use of the corrugated metal sheet goes back to the

beginning of this century. For a long time, corrugated metal sheets were used as covering materials,

without any attention paid to their structural capability. The reason for not considering them as

structural elements was the lack of sound basis for using these sheets together to form a continuous

self-supporting medium. This approach provides particularly neat and attractive roofing whilst

eliminating the ridge capping, thereby avoiding any possibility of leakage along this fitting. The use

of the corrugated metal thin shells in roofs, leads to considerable saving in materials, labour and

cost. Analytically critical loads of self-supporting cylindrical roofs can be found out by energy

theorem [2]. The possibility of using these sheets in folded plate roofs was investigated [3]. A study

has been performed on structural strength and practical applications of cylindrical shell roofs made

of corrugated metal sheets [4]. The exact differential equations used to explain the behavior of

orthotropic shells. More recently, a study was carried out to develop a procedure for the design of

88

S. M. Zahurul Islam et al.

steel roof subjected to non-uniform loads such as drifted snow using purlins frame [5]. Self-

supporting concept was not considered in their study. Rib steel deck ware used as a covering

materials, without any attention paid to their structural capability. Geometric and materials

nonlinearity also was ignored. Extensive study on support settlement of cylindrical shell roofs was

carried out [6-8]. Experimentally an investigation on structural strength and behaviour of

ferrocement semicircular roofing elements were conducted [9], Theoretical studies relating to

ferrocement have been reported in the literature observed and found out an optimum shape within

selected five shapes [10-11]. Thin cylindrical shell roof was solved [12] and was extensively used

for checking the performance of various types of shell elements. They used support along the

circumferential edge not straight edge as a self- supporting concept. Nonlinear analysis was not

carried out. Steel instead of ferrocement is very much use now a day in the design of lighter

structures. In ferrocement construction needs skilled, creative carpenters to produce good quality

items with fine finishes. Zincalume is lighter than ferrocement, which is easier for construction,

handling and efficiently erection. The self-supporting roofing element using profile steel sheeting

(zincalume); a thin shell, lightweight structure, is a structural load bearing system describe in an

earlier publication [13-14].

The main objective of this study is to develop a self-supporting roofing system, with potential and

efficiency for application in affordable quality housing. Structural behavior of Inverted V shape,

Cylindrical, Parabolic, Doubly curve, Single pitch and Flat plane shell roofing system are

investigated analytically to provide as a self–supporting roofing system. This research was an

attempt to investigate the contribution of corrugated sheet in reducing the buckling and

displacement and enhances its load carrying capacity. An experimental program was undertaken in

the course of present study. The experimental results showed good agreement with those obtained

theoretically. The deflection and stress behavior of different types of roofing elements are

compared each other. The efficient and economic shape of self-supporting roofing elements has

been found out after a through investigation on the basis of present results.

ROOFING MATERIAL ZINCALUME

Shell structures are used popularly due to aesthetic and economical use of materials. Great variety

of shell roofs have been designed and constructed in many part of the world [15]. The use of the

shells in roofs, leads to considerable savings in materials. Normally corrugated metal sheet such as

zincalume is used in roofs as a covering only, while depending on different types of intermediate

support. A self-supporting roofing system is when a roof runs its continuous length from on end to

other end support by eliminating internal supports such as purlins, rafter, fastener and truss. This

method provides a particularly neat and attractive solution to roofing whilst eliminating the ridge

capping, thereby avoiding any possibility of leakage along this fitting. This roof can save material,

construction and erection cost.

The shape and size of precast/prefabricated roofing element is chosen to satisfy the general

requirements of strength and stiffness, lightness and economy, ease of handle and erection, proper

seating and leak proof joint. There are different types of materials for construction of roof frame

and roof covering. Common types of materials are metal sheet, ferrocement, plastic, and concrete

and clay tile for roof covering. Timber and metal are normally used for the trusses. For this

investigation the corrugation metal sheet zincalume was chosen in an effort to develop the self-

supporting roofing system. The main features of using of zincalume sheet as roofing material as

according to Bluescope-Lysaght are as follows:

An Investigation on Structural Performance of Profiled Steel Sheet to Develop Self-supporting Roofing System

89

(a)

Speedy installation; no shuttering required, less installation errors

(b)

30-40% cost saving over RCC roofing

(c)

Lower dead load on the walls, light weight and easy handling

(d)

High strength to weight ratio

(e)

Easy to for into complex shapes, new shape more efficiently allowing to be used.

(f)

Elegant profile and uniform sizes, large span possible with intermediate supports

(g)

Abundantly available, and inexpensive and corrosion-resistant

(h)

Fire registrant and material consistency high

(i)

Unaffected by termites and longevity and does not required paint

(j)

No materials wastage and recyclining system is applicable

(k)

Economical considering mean service life

Zincalume sheet can be considered as the best and most durable roofing elements for affordable

quality housing in the world. Zincalume consists of high strength steel substrate protected with

corrosion inhibitive treatments and coatings designed to provide the broad spectrum of performance

that is essential for long life and minimum maintenance. All steel sheets used in the manufacture of

the roofing sheets shall have a protective metallic alloy coating of zinc (43.5%), aluminium (55%)

and silicon (1.5%), applied by the hot dip process and having a coating thickness of 0.05mm as

stipulated in AS1397-1993 for coating class AZ 150. Chromic acid sealed, zinc phosphate

pretreatment is applied after alkaline cleaning for coating. Galvanized steel is treated on both sides

with phosphate conversion coating followed by application of an impervious epoxy primer

incorporating a corrosion inhibiting compound. Modified polyester coating of 20 micrometers is

used for finish coat to ensure maximum durability. Composition layer of zincalume is shown in

Figure 1.

Zincalume, which is used in the investigation, are locally available in Malaysia, Singapore and

Australian market. It is obtained strength as steel grade ASTM A446 E, minimum yield strength

550 MPa, Modulus of elasticity E = 210 GPa, poisons ratio ν = 0.30: mass = 4.7 kg/m2

(for

thickness of 0.47 mm sheet). Zincalume obtained two basic strength grades G 550 and G 300,

which are shown in Figure 2. High tensile steel G550 was used in this study to develop self-

supporting roofing elements.

Finsh coat (Normal 20µm)

Corrosion inhibitive primer (normal 5 µm)

Conversion coating

ZINCALUME steel Aluminum/ Zinc Coating 25 µm)

Steel Subtrate

ZINCALUME steel Aluminum/ Zinc Coating 25 µm Flash

Conversion coating

Corrosion inhibitive primer (normal 5 µm)

Backing coat (Normal 10µm)

Figure 1. Different composition layer of zincalume sheet

90

S. M. Zahurul Islam et al.

FINITE ELEMENT MODELS

The self-supporting roofing elements were models and analysed employing the finite element

software (LUSAS) [16]. The shell-roofing element was analysed as a 3-D problem. It was

discretised by means of 8-noded semi-loof elements having three translational displacements in the

global axes at the corner and mid side nodes and one rotation with respect to axes in the plane of

middle surface. The semi-loof element is probably one of the most efficient elements for the

solution of thin shell of arbitrary geometry [17-18]. At first an arc was drown by three Cartesian

points and then translate required width and corrugation for profile sheet. Width of different types

of roofing elements was considered as 0.76 m and 8.0 m for analysis. Thickness of flat sheet and

profile sheet were assigned as 1.2 mm and 0.47 mm respectively. A nonlinear FEM analysis was

carried out assuming zincalume to be elastic-plastic material. The model was subjected to global

distributed load along the vertical direction. Different types of roofing element such as Inverted V

shape, Cylindrical, Parabolic, Doubly curve, Single pitch and Flat plane have been subjected to

incremental global distributed load. The boundary conditions for the roofing element were assumed

as fixed, pin and simple supported to make a comparative study of effect of boundary condition.

Different mesh sizes and different numbers of element were tried so that accurate results could be

obtained. Material and geometric nonlinearity were considered in FEM analysis. Three different

types of profile sheet such as Trim, Spendek , and Klip-lok are model that is shown in Figures 3, 4,

and 5.

Figure 2. Stress-strain diagram for zincalume steel (Bluescope-Lysaght, 2003)

Figure 3. Finite element model of TRIM profile of parabolic shell roof

An Investigation on Structural Performance of Profiled Steel Sheet to Develop Self-supporting Roofing System

91

THEORETICAL FORMULATION OF DEGENERATED SHELL ELEMENT

A good number of finite elements have been developed for the analysis of thin, circular cylindrical

shells. These include flat elements and curved elements. Flat elements are lower- order elements

and hence may require refined mesh, where as curved elements are higher –order elements and may

more efficient than flat element [19]. The semi-loof element is probably one of the most efficient

for the solution of thin shell of arbitrary geometry. It was originally published by Irons and since

then it has been the object of much research with respect to its philosophy and performance in

various structural situation. Finite element modeling of general shells has been using semi-loof

elements, elements formulated on the basis of curved shell theory; and by means of degenerated

isoparametric elements. The semi-loof shell element is a thin, doubly curved, isoparametric element

formed by applying Kirchhoff constraints to a three-dimensional degenerated thick shell element

(LUSAS). It is able to predict properly the bending performance of thin shell structures. The final

nodal configurations are obtained corner and mid-side nodes at which displacement U, V, W along

respectively the axis X.Y, Z is used as parameter: loof nodes at which the parameters are θi

(rotation) which is shown in Figure 6.

The strain matrix B, relating the strain components in the local system to the element nodal variable

can be constructed as ε =∑

=

n

k

ii

dB

1

(1)

Figure 4. Finite element model of Spendek profile of parabolic shell roof

Figure 5. Finite element model of Klip-lok profile parabolic shell roof

92

S. M. Zahurul Islam et al.

Eq.(1) often written in the partitioned form

│

│

│

│

⌋

⌉

│

│

│

│

⌊

⌈

=

│

⌋

⌉

│

⌊

⌈

∑

∑

=

=

n

k

i

si

n

k

i

fi

s

f

dB

dB

1

1

ε

ε

(2)

In which εf and εs is the in plain strains and the transverse shear strains. The total potential energy

can be written as

П =

ddvBDB

d

d

BDB

d

d

DBdv

B

d

e

e

e

v

s

s

s

t

T

v

fdv

f

f

t

T

v

T

T

│

│

⌋

⌉

│

│

⌊

⌈

+

│

│

⌋

⌉

│

│

⌊

⌈

=

│

│

⌋

⌉

│

│

⌊

⌈

∫

∫

∫

2

1

2

1

2

1

(3)

Where the elasticity matrix D is divided into an in plane part Df and a transverse part Ds. Upon

finite element discretisation and subsequent minimization of total potential energy [20-22] with

respect to nodal variabled the following equations are obtained

i

j

ij

f

dK =

(4)

In which the stiffness matrix Kij linking nodes i and j has the following typical contributions

emanating from the in plane and transverse shear strain energy terms respectively.

dvBDB

K

dvBDB

K

sj

s

si

T

v

sij

e

v

fi

f

fi

T

fij

e

e

e

∫

∫

=

=

(5)

A 2-point integration rule through the shell thickness and a full integration rule in the ζ –η surface

can be used and

ζ

η

ξ

dddJ

dxdydz

dv

=

=

(6)

Where | J| is determinant of the Jacobian matrix

If the axes of the local coordinate system are parallel to those of the global coordinate system at all

points in the shell mid surface, then the formulas for the shell element are the same as those of the

Mindilin plate element. Shell structural behavior and strength is predicted in LUSAS by the

following matrix:

Figure 6. Final nodal configuration for Semi-loof elements

An Investigation on Structural Performance of Profiled Steel Sheet to Develop Self-supporting Roofing System

93

│

│

│

│

│

│

│

│

⌋

⌉

│

│

│

│

│

│

│

│

⌊

⌈

+

│

│

│

│

│

│

│

│

⌋

⌉

│

│

│

│

│

│

│

│

⌊

⌈

Ψ

Ψ

Γ

-

│

│

│

│

│

│

│

│

⌋

⌉

│

│

│

│

│

│

│

│

⌊

⌈

Ψ

Ψ

Ψ

Γ

│

│

│

│

│

│

│

│

⌋

⌉

│

│

│

│

│

│

│

│

⌊

⌈

=

│

│

│

│

│

│

│

│

⌋

⌉

│

│

│

│

│

│

│

│

⌊

⌈

xyo

yo

xo

xyo

Yo

xo

xyo

yo

xo

xyo

yo

xo

xy

x

xy

y

x

xy

Y

x

xy

y

x

M

M

M

N

N

N

y

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

D

M

M

M

N

N

N

ψ

ε

ε

ε

ε

21

20

19

18

17

16

20

15

14

13

12

11

19

14

10

9

8

7

18

10

9

6

5

4

17

12

8

5

3

2

16

11

7

4

2

1

(7)

where

N

are the membrane stress resultants (Force per unit width)

M

are the flexural stress resultants (Moments per unit width)

D

are the Flexural and shear rigidies

Ε

membrane strains

ψx, ψy

, and ψxy

are the flexural strains in the local Cartesian system.

NUMERICAL EXAMPLES AND RESULTS

The primary effect of wind is visualized in the form of pressures normal to the structure’s exterior

surfaces. In this paper, the assessment of imposed load and wind loading was carried out according

to Uniform Building by Law (Malaysian code of practice) [23] and the British code of practice [24-

26]. With the help of well-known FEM based software package LUSAS, different benchmark

problem are solved. The LUSAS is used for the evaluation of deflection and stress-stran behavior

of different types of roofing elements. The numerical results are studied for Parabolic, Cylindrical,

Doubly Curve, Flat Plane and Single pitch roofing elements. The roofing elements are analyzed

with span length 3 m, width 0.76 m and thickness 0.47 mm and 1.2 m for profile sheet and flat

sheet respectively [27] Different types of roofing elements are shown in Figure 7.

The numerical results are studied for Parabolic, Cylindrical, Doubly Curve, Inverted V, Flat plane

and Single pitch roofing system. The roofing shell elements are analyzed with span length 3 m,

width 0.76 m and thickness 0.47 mm and 1.2 m for profile sheet and flat sheet respectively.

Figure 7. Different types of roofing elements

Parabolic shape

Cylindrical shape

Inverted V shape

Single pitch shape

Flat plane shape

Doubly curve shape

94

S. M. Zahurul Islam et al.

EXPERIMENTAL INVESTIGATIONS

In order to verify the validity of the finite element analysis of different types of roofing elements,

critical and limited model test was conducted. The dimension of the model was span 3 m, width

0.76 m and crown height 0.125 m, 0.25 m, 0.5 m, 1.0 m and 1.5 m respectively. All specimens were

tested to ensure curve edge free and straight edge hinged. U type metal channel were used to

provide hinge support at straight of cylindrical and parabolic shell roofing element to maintain self-

supporting condition. All the specimens were tested in the vertical position. Sand bag loading was

used to provide uniformly distributed load. Each bag was contained 5 kg load. The load was

applied manually by gradually increased until yield failure of the model. Four deformation gauge,

two LVDT and ten electronic strain gauges are used to measure deflection and stain. Deformation

gauge and LVDT were set at the centre of bottom surface for the specimen with required stand.

Strain gauges also were used the mid position of top surface of the specimen. Test setup was shown

in Figures 8, 9, 10 and 11.

RESULTS AND DISCUSSIONS

The results were collected into two parts namely the finite element analysis (FEM) results and

experimental results, which are then followed by the comparison section. The graphical

representation of load deflection and stress-strain behavior of different types of roofing element is

shown in Figures 12 and 13.

According to the non-linear finite analysis, parabolic shell roofing element is more efficient than

other types of roofing element due to its less deflections and stresses. Parabolic and cylindrical

roofing elements obtain arch action so load carrying capacity is higher those others as self-

supporting conditions. Nonlinear and non-planer parabolic system resist applied loads by direct

Figure 11. Experimental deflected shape of

cylindrical roofing element

Figure 10. Test setup for parabolic shell

roofing element

Figure 8. Test setup for cylindrical roofing element

Figure 9. Sand bag loading on cylindrical roof

An Investigation on Structural Performance of Profiled Steel Sheet to Develop Self-supporting Roofing System

95

stress, as opposed to membrane stress and bending stress. Experimental load-deflection profile of

different crown heights parabolic roof using 0.47 mm thick corrugated zincalume sheet, 3 m span,

0.76 m width and pin support along the straight edge are shown in Figure 14.

Figure 12. Load –deflection profile of different roofing element

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

0

50

100

150

200

250

300

350

Deflection (mm)

Applied L

oad (kN/m

2

)

Parabolic shape

Cylindrical shape

Inverted V shape

Doubly curve shape

Flat plane shape

Single pitch shape

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

0

0.025

0.05

0.075

0.1

0.125

0.15

Strain(m/m)

S

tress (N

/m

m

2

)

Parabolic shape

Cylindrical shape

Inverted V shape

Doubly curve shape

Flat plane shape

S ingle pit c h sha pe

Figure 13. Stress strain profile of different types of roofing element

Figure 14. Experimental load deflection profile of different crown height parabolic shell roofing element

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

0 5 10 15 20 25 30 35 40 45 50 55

Deflection (mm)

Ap

p

lied

L

o

ad

(KN/m

2

)

Crown height 0.125 m

Crown height 0.25 m

Crown height 0.50 m

Crown height 1.0 m

Crown height 1.5 m

96

S. M. Zahurul Islam et al.

Crown displacement is occurred due to two causes, (1) bending and (2) shortening of shell.

Bending of shell is created by bending field such as Mx, My, Mxy, Myx, Qx, and Qy and on the other

shortening is created by membrane field Nx, NY, Nxy, and Nyx. At crown height 1/6 of chord width

membrane field is predominant than bending field. As a result deflection is least. When crown

height is lower membrane force also lower than bending force. When crown height increase

membrane force also increases. After a certain limit of crown height membrane force also decrease.

Load carrying capacity higher and least deflection was obtained at crown height 1/6 of chord width

or span length. In order to validate the analytical work, a comparison between the finite element

analysis and experimental results are shown in Figures 15, 16, 17, 18 and 19. It is interesting to

note that both the central deflection and stresses are lower in parabolic shape of roofing element

with crown height of 0.5 m. When crown height decrease then deflection and stresses increase i.e.,

valid for less crown height of 0.5 m.

Figure 15. Load deflection profile at crown of parabolic roofing element for 0.125 m crown height

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

Deflection (mm)

A

pplied L

o

ad

( K

N

/m

2

)

Experimental results

Numerical results

Figure 16. Load deflection profile at crown of parabolic roofing element for 0.25 m crown height

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

0

5

10

15

20

25

30

35

40

45

50

55

Deflection (mm)

A

pplied L

o

ad

(K

N

/m

2

)

Experimental results

Numerical results

An Investigation on Structural Performance of Profiled Steel Sheet to Develop Self-supporting Roofing System

97

Figure 18. Load deflection profile at crown of parabolic roofing element for 1.0 m crown height

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

0

5

10

15

20

25

30

35

40

45

50

Deflection (mm)

App

lied

L

o

ad (KN/m

2

)

Experimental results

Numerical results

Figure 19. Load deflection profile at crown of parabolic roofing element for 1.5 m crown height

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0

5

10 15 20 25 30 35 40 45 50 55

Deflection (mm)

Ap

p

lied

L

o

ad

(KN

/m

2

)

Experimental results

Numerical results

Figure 17. Load deflection profile at crown of parabolic roofing element for 0.5 m crown height

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

0

5

10

15

20

25

30

35

40

45

50

Deflection (mm)

A

p

p

lied

lo

ad

( K

N

/m

2

)

Experimental results

Numercal results

98

S. M. Zahurul Islam et al.

The results showed load carrying capacity, deflection and stresses in parabolic roofing shell

elements with different crown height. Load carrying capacity was 1.059, 2.108, 2.80, 2.508 and

1.684 kN/m2 without geometrical failure for 0.125, 0.25, 0.5, 1.0 and 1.5 m crown height parabolic

and cylindrical roofing element respectively. Geometrical as well as yield failure load was found

due to 1.283, 2.23, 3.164, 2.71, 1.739 kN/m2 for 0.125, 0.25, 0.5, 1.0 and 1.5 m crown height

parabolic and cylindrical roofing element respectively.

Since the surface area also increases with the crown height, it is found that optimum crown height

will be more economical due to materials. Both end fixed and pin support showed almost same

results with minor changes. Horizontal displacement of simple supported condition was more than

that of pin and fixed supporting condition. The behaviour of this structure depends on the load-

transferring action of its member and connection. The graphical representation of stress-strain

behaviour of selected roofing element is shown in Figures 20, 21 and 22.

0

100

200

300

400

500

600

700

800

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Strain (mm/mm)

Stress (N

/m

m

2 )

Crown height 0.125 m

Crown height 0.25 m

Crown height 0.5 m

Crown height 1.0 m

Crown height1.5 m

Figure 20. Stress strain profile of different crown height parabolic roofing element

Figure 21. Stress strain profile of crown height 0.5 m parabolic roofing element

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Strain (mm/mm)

S

tress (N

/m

m

2

)

N

An Investigation on Structural Performance of Profiled Steel Sheet to Develop Self-supporting Roofing System

99

Nine types of roofing elements are studies in the present work. The presence of corrugation in the

metal roofing element resulted in a significant improvement on the roof’s structural performance

compared to flat sheet element.

Good agreement was found between the results from non-linear analysis and those obtained

experimentally. The load –deflection, stress strain and deflected shape profiles for investigated

roofing element showed that parabolic roofing element having crown height 1/6 of chord width is

more efficient than others as self supported condition. It was observed that a parabolic shape

roofing element with optimum crown height was structurally and economically able to use as a self-

support roofing system for 8 m span lengths using 1.2 mm thick corrugated zincalume. Deflection

along the arc length of different crown height of parabolic shell roof is shown in Figure 23 due to

service load 0.528 kN/m2. Form the analysis, it was seen that maximum deflection obtained at the

center point of curve roofing element.

Figure 23. Deflection profile of different crown height parabolic roofing element along the arc length

-30

-27.5

-25

-22.5

-20

-17.5

-15

-12.5

-10

-7.5

- 5

-2.5

0

2 .5

5

0

0 .5

1

1 .5

2

2 .5

3

D is t a n c e a lo n g t h e a r c le n g t h ( m )

Deflection (m

m

)

C r o w n h e i g h t 0 . 1 2 5 m

C r o w n h e i g h t 0 . 2 5 m

C r o w n h e i g h t 0 . 5 0 m

C r o w n h e i g h t 1 . 0 m

C r o w n h e i g h t 1 . 5 m

Figure 22. Stress strain profile of crown height 1.0 m parabolic roofing element

0

100

200

300

400

500

600

700

800

0

0.01

0.02

0.03

0.04

Strain (mm/mm)

S

tress ( N

/m

m

2

)

Experimental resul

Numerical results

100

S. M. Zahurul Islam et al.

It was observed that both the central deflection and stresses are lower parabolic shape of roofing

element with crown height of 0.5 m. When crown height decreased then deflection and stresses

increased i.e., valid for lower crown height of 0.5 m. The results showed optimum crown height,

deflection and stresses in parabolic roofing shell elements. Since the surface area also increases

with the crown height, it was found that optimum crown height would be more economical due to

materials.

Nine types of roofing elements are studies in the present work. It was found that support condition

has a great impact on behavior of shell structure. Both end fixed and pin support showed almost

same results with minor changes. Horizontal displacement of simple supported condition was more

than that of pin and fixed supporting condition. Figure 4 shows different shapes of roofing

elements; Doubly curve shape of roofing element is architecturally beautiful. The parabolic roofing

element is suitable to use as a self- supporting roofing system up to 8 m. On the basis of the

present analysis, it is found that the corrugated parabolic roofing element is the most economical,

efficient, architecturally pleasing shape in self- supporting condition. Three types of profile sheet

were analyzed which deflection behaviour is shown in Table1.

Table 1. Deflection of different types of profile sheet

TRIM profile Spandek profile

Klip-lok

Thickness of

Materials (mm)

Applied load for

Analysis kN/ m2

Deflection (mm)

0.528

4.99

4.52

5.13

0.633

5.98

5.42

6.16

0.47

(Profile Sheet)

0.950

8.98

8.13

9.23

In shell elements, it was observed that corrugated sheet is structurally 10 times stiffer than flat

sheet, which is shown in Table 2. Profile sheet is stronger because of its rib and section modulus.

Generally, based on the results obtained, the objectives of this work have been achieved where the

parabolic corrugated steel roofing element was able to show good structural performance under

self-supporting condition.

Table 2. Displacement of parabolic roofing elements with different span length

Span length (m)

3

4

5

6

7

Roofing System

Thickness (mm)

Load

kN/ m2

Deflection (mm)

0. 65 (Flat sheet)

0.528

44

171

384

688 1210

Parabolic shell

roof

0.47 (Profile-sheet)

0.528

4.9

9.5

21

42

228

Experimentally load vs strains were measured by electronic strain gauge. Then load was converted

to equivalent stresses using LUSAS. These parabolic and cylindrical roofing elements were a

complex geometry due to presences of corrugation. It was quiet difficult to find out equivalent

stress under UDL using classical formulla. The scalar stress state obtained by combining the

individual component stresses at a point according to the classical von Mises failure criterion which

is known as generalised stress, equivalent stress, von Mises stress or effective stress. The equivalent

stress is most universally accepted yield criterion for metals (LUSAS Theory Manual, 2003) [28].

Stress – strain graphical presentation are shown in Figures 24, 25, 26, 27 and 28.

An Investigation on Structural Performance of Profiled Steel Sheet to Develop Self-supporting Roofing System

101

The failure occurs when the energy of distortion reaches the same as energy for yield/failure in

uniaxial tension. Mathematically, this is expressed as:

( )

0

,

=

│

│

⎠

⎞

│

│

⎝

⎛

-

=

-

-

p

e

F

κ

σ

κ

σ

(8)

Where

( )2/1

2

3 J

=

-

σ

Equivalent, generalized or effective stress

-

σ is calculated by the following formula.

(

) (

) (

)

[

] 2

2

1

3

2

3

2

2

2

1

2

1

y

σ

σ

σ

σ

σ

σ

σ

≤

-

+

-

+

-

(9)

Figure 25. Stress-strain profile at crown of parabolic roofing element for 0.25 m crown height

0

50

100

150

200

250

300

350

400

450

500

550

600

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

Strain (mm/mm)

E

q

u

iv

a

le

n

t stre

ss ( N

/m

m

2

)

Vertical strain

Horizontal Strain

Equivalent strain

Figure 24. Stress-strain profile at crown of parabolic roofing element for 0.125 m crown height

0

50

100

150

200

250

300

350

400

450

500

550

600

0

0.003 0.006 0.009 0.012 0.015 0.018 0.021 0.024 0.027

Strain (mm/mm)

E

quivalent S

tress ( N

/m

m

2

)

Vertical strain

Horizontal strain

Equivalent strain

102

S. M. Zahurul Islam et al.

Figure 27. Stress-strain profile at crown of parabolic roofing element for 1.0 m crown height

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Strain (mm/mm)

E

q

uiva

le

nt S

tre

ss (N

/m

m

2

)

Vertical strain

Horizontal strain

Equivalent strain

Figure 28. Stress-strain profile at crown of parabolic roofing element for 1.5 m crown height

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Strain (mm/mm)

E

q

u

ivale

nt S

tre

ss (N

/m

m

2

)

Horizontal strain

Vertical strain

Equivalent strain

Figure 26. Stress-strain profile at crown of parabolic roofing element for 0.5 m crown height

0

50

100

150

200

250

300

350

400

450

500

550

600

650

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Strain (mm/mm)

E

q

uivalen

t S

tress ( N

/m

m

2

)

Vertical strain

Horizontal strain

Equivalent strain

An Investigation on Structural Performance of Profiled Steel Sheet to Develop Self-supporting Roofing System

103

DEFLECTED SHAPE

In order to validate the proposed models a comparison between analytical and experimental

deflected shape were carried out as shown in Figures 29 to 38. It was found that when the crown

height of parabolic shape was increased, the central deflection decreased until optimum crown

height.

Figure 31. Analytical deflected shape of 0.25m crown height parabolic roofing element

Original shape

Analytical deflected shape

Figure 29. Analytical deflected shape of 0.125 m crown height parabolic roofing element

Original shape

Analytical deflected shape

Figure 30. Experimental deflected shape of 0.125 m crown height parabolic roofing element

Figure 32. Experimental deflected shape of 0.25 m crown height parabolic roofing element

104

S. M. Zahurul Islam et al.

Figure 33. Analytical deflected shape of 0.5m crown height parabolic roofing element

Original shape

Analytical deflected shape

Figure 35. Analytical deflected shape of 1.0 m crown height parabolic roofing element

Original shape

Analytical deflected shape

Figure 34. Experimental deflected shape of 0.5 m crown height parabolic roofing element

Figure 36. Experimental deflected shape of 1.0 m crown height parabolic roofing element

An Investigation on Structural Performance of Profiled Steel Sheet to Develop Self-supporting Roofing System

105

DETAILED STUDY ON 8M PARABOLIC ROOFING ELEMENTS

The FEM investigation was extended to explore the feasibility of usage of zincalume as a self-

supporting roofing system. Based on FEM investigation and experimental validation, this study was

extended up to 8 m span using 1.33 m crown parabolic roofing element for using as self-supporting

condition for affordable quality housing. According to the FEM results analysis, it was seen that the

parabolic roofing element can be used efficiently as a self supporting roofing system using 8 m

span and 1.25 mm thick profile zincalume sheet for affordable quality housing. Load- deflection

and stress–strain graphical presentation are shown in Figures 39 and 40 respectively.

The stress distributions along the arc of 8 m span parabolic roofing elements were observed with

stress contour plot. It was seen that the stresses were not uniformly distributed all over the element.

Maximum equivalent stress 406.1 N/mm2 was found at the lower part of the element, which is

connected with the support. The displacement distribution of 8 m parabolic roofing elements was

observed by Displacement contour plot. The maximum displacements obtained at crown height

were 39.69 mm, under service load 0.612 kN/m2. Deflection and equivalent stress obtained within

permissible limit 40 mm and 550 N/mm2 respectively.

Figure 37. Analytical deflected shape of 1.5 m crown height cylindrical roofing element

Original shape

Analytical Deflected Shape

Figure 38. Experimental deflected shape of 1.5 m crown height cylindrical roofing element

106

S. M. Zahurul Islam et al.

COST ANALYSIS

The cost of the various zincalume roofing elements (per m2) are computed based on the material

market cost in Kula Lumpur, Selangor Darul Ehsan, Malaysia. Zinaclume is manufactured

mechanically in Bluescope Lysaghat Sdn Bhd. So, labour costs are included in its market prize. As

a self-supporting condition, that easily can be handled and erected. So, labour cost will be very

lower. Hence, labour cost of erection was not considered in this cost analysis. The cost analysis of

zincalume roofing element as self-supporting condition is shown in Table 3

Table 3. Cost analysis for different types of roofing elements with 3 m span

Material-s

Roofing elements types

Quantity

(m2)

Rate

(RM/m2)

Cost (RM)

Cylindrical( C.H.-1.5 m)

3.58

120.0

Parabolic (C.H.-1.0 m)

2.90

97.25

Parabolic (C.H. 0.5 m)

2.44

81.84

Parabolic (C.H. 0.25 m)

2.33

77.92

Parabolic (C.H.125 m)

2.29

76.74*

Inverted V (C.H.0.5 m)

2.40

80.40*

Doubly curve (C.H. 0.5 m)

2.46

82.41*

Single pitch (C.H.0.5 m)

2.31

77.43*

Lysaghat Crim

Curve Trimdek Hi-

Tensile Zinaclume

(0.47mm thickness)

Flat plane shape

2.28

33.5

76.38*

Note: * Structurally not efficient

C.H. – Crown Height

CONCLUSIONS

Conventionally, metal sheet such as zincalume is using in roof covering through truss as a costume.

It has been implemented a novel and new approach to provide self- supporting roofing system. The

behaviour of nine different types of roofing element is studied to find out an economical, efficient,

architecturally pleasing shape in self -supporting condition. Nonlinear effect has been adopted in

the finite element analysis. From the parametric study, it is found that the central deflection and

stresses are lower in parabolic shape of roofing element with crown height about 1/6 of chord

length. Optimum crown height is obtained at about crown height 1/6 of chord width due to higher

load carrying capacity and lower deflection and stress. Internal horizontal reaction in parabolic

shape roofing element always reduced shear force and bending moment.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0

20

40

60

80

100

120

140

160

180

200

Deflection (mm)

A

p

p

lie

d Lo

a

d

(K

N

/m

2

)

Figure 39. Load –deflection profile of 8 m span

parabolic roofing elements

Figure 40. Stress-strain profile at crown of 8 m span

parabolic roofing elements

0

100

200

300

400

500

600

700

800

900

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Strain (mm/mm)

E

q

u

iv

a

le

n

t S

tr

e

s

s

(N

/m

m

2 )

An Investigation on Structural Performance of Profiled Steel Sheet to Develop Self-supporting Roofing System

107

On the basis of the present analysis, it is found that the corrugated zincalume shell element is the

most economical, efficient, architecturally pleasing shape in self- supporting condition. Based on

the results obtained, the objectives of this work have been achieved where the parabolic corrugated

roofing element showed significant improvements to the roof’s structural performance. It was

observed that corrugated parabolic shell element which, have 8 m span and 1.25 mm thickness

could be used efficiently as self -supporting roofing system in housing construction.

ACKNOWLEDGEMENTS

The authors would like to thank the Construction Industry Development Board (CIDB) Malaysia

for financial support and Blue scope Lysaght (Malaysia) Sdn Bhd for the free supply of

experimental test specimens. The present study is part of graduate research of civil engineering

department, Universiti Putra Malaysia (UPM) and National Research Programme on Affordable

Quality Housing.

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