construction and theoretical analyses of a roof truss … · the mid – span deflection on the...

*Corresponding Author’s E-mail: [email protected]

Unified Journal of Engineering and Manufacturing Technology (UJEMT) Vol 2(1) pp. 001- 018 March, 2018. http://www.unifiedjournals.org/ujemt Copyright © 2018 Unified Journals

Original Research Article

Construction and Theoretical Analyses of a Roof Truss Made of Gmelina

(Gmelina Arborea) Suitable for Cross River State of Nigeria

Agbonkhese, Kingsley A.

1*, Isemede, Eric E.

2, Omoikholo, Frank.

3, Eme, Sunday C.

4

1, 3,4

Department of Mechanical Engineering Technology, National Institute of Construction Technology

(NICT), Uromi, Edo State, Nigeria

2Department of Civil Engineering Technology, National Institute of Construction Technology (NICT),

Uromi, Edo State, Nigeria

Accepted 26th

February, 2018.

ABSTRACT

The research was done to determine the ability of roof truss made of Gmelina arborea to withstand deflection when

subjected to design loads. The design load was resolved to act on the joint of the truss. The truss was then manually

analyzed using the method of joints to determine the compressive and tensile axial forces on the truss members. The

type of truss analyzed for, was pitched roof trusses with emphasis on Howe Truss. The span of the roof truss was

6000mm while the spacing of truss members was 1500mm. Gusset plates of 12mm plywood, bolts and nuts were used

as fasteners. The cross sectional dimensions of the roof truss members is 1500mm. The truss members were analyzed

as simply supported beam. The mid – span deflection on the members were analyzed using the method of joints. The

result shows that the maximum possible deflection of 13.83mm was obtained and within the limit of permissible

deflection of 18mm (L/333) as stipulated in NCP 2 (the use of timber for construction 1976 code of practice) for

permissible stress design and this is in agreement with the analysis carried out. This result of our analysis helps to

recommend the use of Gmelina arborea for the construction of roof trusses.

Keywords: Gmelina arborea, deflection, Roof truss, Life load and dead load.

1205-4315

U n i f . J . E n g r . M a n u f . T e c h . A g b o n k h e s e K i n g s l e y A . e t a l . P a g e | 2

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1.0 INTRODUCTION

Gmelina arborea (Family: Verbenaceae) is a tropical,

evergreen tree, native to South Asia from Pakistan, to

Myanmar and Sri Lanka and has been widely planted in

Southeast Asia and tropical Africa and America. It is both

a plantation and smallholder timber crop [1];[2]. The

wood is one of the most widely grown tropical timbers,

useful for particle board, plywood core stock, matches,

and saw timber for light construction, furniture, general

carpentry, and packing. The timber of this plant is

generally not attacked by termites and wood borer. The

aqueous extracts from fresh fruits, tree bark leaves of

Gmelina exhibit insecticidal property against legume pod

borer and pod sucking bug [3]. The wood is relatively

light with a density of 420 to 640 kg/m3 and a calorific

value of about 4800 kcal/kg [4]. The growth rate for G.

arborea has been reported to be as high as 40–50

m3/ha/year in areas of good soils and rainfall [5].

Fig.1: Gmelina arborea wood

Wood as one of the basic engineering material is used for

different types of structural forms, such as beams,

columns, paneling, and furniture and roof trusses in

buildings. Wood, as a building material receives more

attention than other building materials, despite the

abundance of other alternatives. This is because among

other advantages, it is cheaper than most of these

alternatives due to its ready availability and ease of

conversion into any shape as the builders desires. Wood is

suited for all types of roof trusses. They are therefore used

for industrial buildings. Some of these trusses can serve

both for residential buildings and industrial buildings.

These include Howe truss, Warran truss, Fan truss, Fink

truss, Bowstring truss etc. Roof construction is a very

important aspect of building construction where wood can

be used. Other areas of roof construction where wood are

needed include roof cladding (e.g. shingles), fascia and

wall plate construction. Buildings with such roofs have

been found to be quite reliable in durability and are

comfortable to live in. However, roofs constructed in the

tropics are mostly destroyed by rain storms or heavy

wind. These problems are usually caused by poor design

of the roofs. In recent times, at the beginning of the rainy

season, comes heavy storms and so many people are

displaced and properties worth millions of naira are

destroyed. This project is aimed at providing substantial

solutions to the prevailing structural problems, especially

roof structures as part of the building and construction

industry using Gmelina arborea which is in abundance

and readily available in the southern part of Cross River

State of Nigeria. This project was constructed and

theoretically analysed in the department of Wood

Production Engineering, Cross River State University,

Calabar, Nigeria.

2.0 Truss structure Analyses and Calculation

The major roof truss analysis were on live load (rain load

and wind load), dead load due to asbestos – cement

roofing cladding, dead load due to timber purlin, bearing

capacity of the roof truss, resolution of forces at each

member and mid – span deflection of the truss structure.

2.1. Live Load

The table below shows the amount of rainfall in Calabar,

Cross River state of Nigeria for the year 2007 – 2011,

recorded in (mm).



Table 1: Monthly rainfall distribution in Calabar, Cross River State for year 2007 – 2011 in mm

MONTH

JAN.

FEB.

MAR.

APR.

MAY

JUN.

JUL.

AUG.

SEPT.

OCT

NOV.

DEC.

YEAR

2007

0.0

51.1

181.0

265.9

384.2

583.5

492.7

415.5

516.7

197.4

262.1

33.1

2008

15.1

1.0

108.0

216.9

286.8

437.0

597.7

509.2

217.9

315.0

105.1

77.1

2009

89.7

38.5

87.5

150.5

308.9

218.4

577.4

507.5

273.9

148.1

126.9

0.0

2010

31.8

88.2

63.6

130.4

306.5

611.3

384.0

406.7

451.3

269.6

272.1

56.2

2011

TR

183.4

123.1

208.8

340.9

388.6

648.6

573.7

251.8

519.9

325.2

438.8

SOURCE: Nigeria Meteorological Agency, Airport Station Calabar, Cross River State.



B E F C

D

16.225N

16.225N

8.1125N

2.1.1. Rain Load

The diameter of the rain gauge cylinder,

D = 20cm = 200mm

The maximum height (H) of rain water over period of five (5) years

H = 100cm = 1000mm

Water density, ꝭ = 1g/ = 1x

Weight of rain, W = X ꝭ (1)

=

Taking, g = 10m/ , where g = acceleration due to gravity

W =

W = 81541992N

From table 3, the density of Gmelina at 12% M.C = 481kg/

Actual weight of rain =

Rain gauge cross sectional area, A = =

= 31430

For an area of 31430 , we have a total rainfall = 169.52971

Therefore, for an area of 6m = 6000 we have,

= 32.453

Breaking down the rain load into concentrated loads at point A, D and B

A

G

At point B, load = x 32.453 = 8.1125N

At point D, load = x 32.453 = 16.225N

At point A, load = 2 x the load at point B

= 2 x 8.1125 = 16.225N



Since point A bears load on both sides of the roof truss, i.e. loads from point B and C, then, by

symmetry of structure:

Load B = Load C

Load D = Load G

2.1.2. Wind Load

TABLE 2: Shows monthly mean values of wind speed for Calabar, Cross River State for year 2007 - 2011

Wind speed in (m/s)

MONTH

JAN.

FEB.

MAR.

APR.

MAY

JUN

JUL.

AUG.

SEPT.

OCT.

NOV.

DEC. YEAR

2007

56.5

70.46

67.07

49.95

36.12

47.13

35.75

33.97

28.66

42.81

35.13

49.79

2008

51.77

59.77

21.85

54.00

60.39

48.66

11.35

45.67

41.67

49.69

39.18

48.87

2009

62.41

62.62

67.26

67.32

57.17

64.56

104.32

58.79

53.44

55.74

45.26

56.54

2010

25.37

60.68

31.51

36.21

32.29

27.62

27.31

11.43

XX

XX

XX

XX

2011

47.30

12.57

21.19

19.40

13.70

XX

XX

26.78

28.26

24.18

19.21

19.20

SOURCE: Nigeria Meteorological Agency, Airport Station Calabar, Cross River State.

From the table of values, the critical wind speed value (V) = 104.32m/s

According to [7], P = 0.00256 (2)

Where P = stagnation pressure or Velocity pressure

1 Ib = 454g = 0.454kg

0.00256 = 454 x 0.00256g

= 454 x 0.00256 x 10

= 11. 6224N

1’ = 30cm = 0.3

1sqft = 0.3 x 0.3 = 0.09

0.09 = 0.454 x 0.00256 x 10

= 0.0116224N

1 = = 0.129138N/

1 lb/wt = 0.454 x 10 = 4.54N



B E F C

Ppsf = 0.00256 = = 0. 129138N/

If, 1’ = 30cm

1mile = 1760 x 3’ = = 1584m

1584m = 1mile

104.32m = = 0.0659miles

It means in Calabar, 0.0659miles are travelled in 1sec.

In 1hr, speed travelled in Calabar = 0.0659 x = 237.24mph.

104.32m/s = mph

1mph = = 0.44m/s

V =0.44m/s But,

P = 0.00256 = 0.00256 x = 4.95616 x

This gives a linear load intensity of 4.95616 ×

Breaking the total wind load into concentrated loads at point A, D and C

A

D G

At point B, load = 4.95616 x

= = = 0.012390N

At point D, load = 4.95616 x

= = 2.47808 x = 0.0247808N

At point A, load = 4.95616 x

= = = 0.012390N

Since point A, bears wind load on both sides of the roof truss, i.e. loads from point B and C, then, by symmetry of structure:

wind load at:

Point B = Point C

Point D = Point G

Total live load (rainfall + wind speed) = 32.453 + 4.95616 x

= 32.45349562



2.2. Dead Load The dead loads on the roof truss are due to the self-weight of the roof truss and the asbestos-cement roof cladding [9]. The

weight of the fasteners is negligible.

2.2.1. Dead Load due to Asbestos Cements Roofing Cladding

The distance between truss members = 1500mm

Superficial density of asbestos = 1.367 x

Dimension of asbestos = 600 x 2400

No. of asbestos needed = 10 (taking care of overlapping sheets)

Total dead load due to 10 asbestos sheets =

= 10 x 1.367 x x 600 x 2400

= 1968.48N

Converting to concentrated load at point B, D, and A

At point B =

At point D =

At point A = (since it bears asbestos sheet for both sides).

2.2.2. Dead Load due to Timber Purlin

Size of each purlin = 50 x 100mm

The total number of purlins needed = 3 x 2 pcs (since the length of each rafter = 300m x2).

Density of Gmelina at 12% M.C = 481

Weight of timber purlins = 6 x 481 x 50 x 100mm = 14430000

=

Total weight due to the timber purlins and asbestos =

= 16398.48

2.3 Bearing Capacity of the Roof Truss

Bearing capacity of the roof truss =

= = 16398.55

= = 16.39855kg/

Converting to concentrated load at point B, D, and A

At point B =

At point D =

At point A =



40.9965

300

2.4. Resolution of Forces at each Member

According to [6] trusses are resolved by the method of joints and section. The method of joint was used in analyzing the

truss.

40.9965N

A

81.9928N

D G

B E F C

RB=143.48755KN RC = 143.48755KN

RB = RC = =

= 143.48755KN

At joint B:

FBD

E

B FBE

RB = 143.48755KN

Resolving Vertically:

FBD Sin30 = 143.48755KN

FBD = = = 2.869751N

Resolving Horizontally:

FBD = Cos30 + FBE = 0

FBE = = = 3.313703N



D A

E F B

At joint D:

FDA

30

30

FBD

FDE


W1Cos30 = FDE

81.9928 x Cos30 = FDE

81.9928 x 0.8660 = FDE

FDE = 71.008N


W1Sin30 + FDA = FBD

81.9928 x 0.5 + FDA = 2.869751

FDA = 2.869751 – 81.9928 x 0.5

FDA = -38.126649N

At joint E:

FDE FAE

30

30

FBE FEF


FAECos30 - FBECos30 = 0

FAE x 0.8660 – 81.9928 x 0.8660

FAE = = 81.9928N


FEFSin30+ FBE Sin30 = 0

FEF = = =3.313703N

2.5 Determination of the Cross Sectional Area of the Truss

Let ‘A’ ( be the cross sectional area of each member of the truss.

A b d, where b = the load in each member .

d = the maximum bending strength of each member.

From table 3: The maximum bending strength of Gmelina at 12% M.C = 64N/



D FBD

B E

A

E

300

For area, ABD =2.869751 x 64 =183.66

For area, ABE = 3.313703 x 64 = 212.08

For area, ADE = 71.008 x 64 = 4544.51

For area, ADA = -38.126649 x 64 = -2440.11

For area, AAE =81.9928 x 64 = 5247.54

For area, AEF = 3.313703 x 64 = 212.08

By symmetry of structure;

ABD = ACG, ABE =ACF, ADE = AGF, ADA = AGA, AAE = AAF, AEN = AFN.

2.6 Testing of Mid-Span Deflection

Let a unit load of 1N be acting on the mid-span. By symmetry of structure, the reactions at support B and C will be;

At point B =1 x ½ = ½N

At point C = 1 x ½ = ½N

For joint B:

30 FBE


FBDSin30 + ½ = 0

FBDSin30 = -½ FBD = -½ x 2 = -1N

Resolving Horizontally: FBE -1 =0 =1N For joint D:


FAD Sin30 - FDE Cos30 = Sin30

FAD x ½ - FDE x = ½

FAD - FDE x = ½ x 2

FAD - FDE x 3 = 1 ……………………………………1



F B

FEA

FBE FEF

Resolving horizontally:

FAD Cos30 + FDE Sin30 = Cos30

FAD x + FDE x ½ =

Dividing through by 2;

FAD x 3 + FDE = 3 …………………………………. 2

Equation 1 x 3 3FAD - 3FDE = 3 …………..… 3

Equation 2 – 3, 4 FDE = 0

FDE = 0N

Substituting into equation 1,

FAD - FDE x 3 = 1

FAD = 1N

For joint E:

A

30

60


FEA Cos30 = 0

FEA x = 0, FEA = 0N


FBE = FEF = 0

1 = FEF = 1N

FFC, FCG, FFG, FGA and FAF, are deduced by symmetry of structure.

2.7 Length of Various Members

The lengths of various members of the roof truss are shown below

DE = 1m

X

BD = 1.5m



B E F C

D

A

G

BE x Sin30 = 1

BE = 2m

DA/DE = Cos 30 = √3/2 x Cos 30

DA = 1.5m

AE = 2m

By symmetry of structure:

BD = CG, DA = GA, DE = GF, AE = AF, BE=CF, (EN + FN=EF)

3.0 MATERIAL AND METHODS

3.1 Description of Materials The roof truss was made from the following choice materials; timber (Gmelina arborea), wood, wall plates, fasteners, tie,

rafters, purlin and brace.

I. Timber (Gmelina arborea): The timber used was Gmelina arborea. This specie of wood is found abundantly in West

Africa, although it is not indigenous to the region. Gmelina arborea has very pale brown to grey brown colour having

average density of 481Kg/m3 at 12% moisture content. It texture is medium and even. It grains are straight, and often

interlock. It is very slow in drying, but dries well without degradation and retains shape. It is durable and resistance to

termites and borers. It can be worked on easily. It is medium light weight. [8] gives the strength properties of Gmelina

arborea as shown in table 3 below.



Table 3: Strength properties of Gmelina arborea

Source: The strength properties of timber: by Gwendoline Lavers; London; Her Majesty’s stationery office

1969

SPEC

IES

OR

IGIN

ori

gin

MO

ISTU

RE

CO

NTE

NT

DENSITY

Max

imu

m b

end

ing

stre

ngt

h

stif

fnes

s

ENERGY

CONSUMED BY

BENDING

Res

ista

nce

to

su

dd

en

load

Max

imu

m c

om

pre

ssio

n

stre

ngt

h

Max

imu

m s

hea

rin

g

stre

ngt

h

Res

ista

nce

to

split

tin

g

50%

M. C

12%

M.C

R

adia

lly

Tan

gen

tial

ly

Gmelina

Wes

t A

fric

a

Wes

t A

fric

a

%

Kg/m3

Kg/m3

N/mm2

N/mm2

N/mm2

N/mm2

N

N/mm2

Green

stage

100

625

54

5900

0.080

0.225

0.69

25.6

3250

8.5

Dry stage

12

481

64

6300

0.43

36.3

3070

11.4



II. Wood: It has adequate dimensional stability in service and high in weight. It is fast to regenerate by coppicing and

grows fast when planted in seeds. In Cross River State, as a case study, it is readily available in large proportion

and affordable.

III. Wall plates: The dimension of the wall plates used is 75 x 100 x 3000 for effective strength to withstand

the load that is transmitted to it by other members of the roof truss

IV. Fasteners: The type of fasteners used for securing the various members and joints of the roof truss in this design

is bolt and nut for stronger joints and gusset plates for assembling of various members together to guard against

unnecessary overlapping of members and splitting as all members are in one plane. A total number of 20 bolts and

nuts of size 10mm were used for the construction and fastening of various joints. The gusset plates used for the

assembling of various members together was 12mm plywood. This is to guard against loose joints and splitting

fastened with bolts to various members.

V. Tie: For purpose of inter-changeability of members, the tie dimension used was 50mm x 100mm.

VI. Rafters: The rafters used for this design were of size 50 x 100 x 3000 , each rafter is half the span of the

truss.

VII. Purlin: For this particular design, the purlins used were of dimension 50 x 100 x 3000 each and a total of

eight purlins are used depending on the span of the design and the dimension of the rafters used.

VIII. Brace: A total of number of four (4) braces was used for the design of the roof truss. They are of varying length

but the same dimension of 50mm x 100mm.

IX. Span and spacing of truss members: In accordance with the Nigerian Code of Practice for Timber Engineering

(NCP 3) used in construction. The span of a timber roof truss should not exceed 12m to avoid deflection and the

spacing of various members should be 1500mm. Therefore, to conform to the stated criteria, 6m span of roof truss and

1500mm spacing of truss members were used. This is to check for effective strength and life in service of the design

structure as well as guard against deflection of members if the span is too large because the structural application was

purely residential.

3.2. METHODS

3.2.1. Cutting List

Table 4. Cutting list in mm of roof members

MEMBER

LENGTH

( )

WIDTH

( )

THICKNESS

( )

VOLUME

( )

BD 1500 50 100 7500000

BE 2000 50 100 10000000

DE 1000 50 100 5000000

DA 1500 50 100 7500000

AE 2000 50 100 10000000

CG 1500 50 100 7500000

CF 2000 50 100 10000000

GF 1000 50 100 5000000

GA 1500 50 100 7500000

AF 2000 50 100 10000000

EF 2000 50 100 10000000

TOTAL = 90000000

= 9.0 X 10

3.2.2. Preparation of Wooden Members

The wood was planed to 50 x 100mm; it was cut into various truss members with the dimension made according to the

cutting list. The ends of the members were shaped to conform to the desired shape of the roof truss and also to facilitate the

assembling in one plane.

3.2.3. Assembly of the Roof Truss

The members (tie beam, rafters, tie struts, wall plate) were arranged to check that they were ready to be assembled into the

desired roof truss and all necessary adjustments were made. They were then assembled with pre-drilled plywood gusset plates



at each of the joints to ease the use of bolts in fastening the joints. The number of bolts at each joint depended on the number

ends of other members meeting at a point and the perpendicular member.

Fig 2: Assembly of the truss members Fig 3: Assembly of joints with gusset plate

METHODOLOGY

The truss constructed was theoretically analysed using all the information gathered from table 1, 2 and 3 respectively. The

wind and rain loads were converted into live loads while the self-weight of the truss, timber purlin and asbestos cement roof

cladding were converted to dead load. These loads were made to act on the truss as point or concentrated load on each joint.

The analysis of the truss was carried out manually.

RESULT PRESENTATION

The roof truss was constructed with Gmelina arborea of density 481kg/m3 at 12% moisture content. For easy analysis, the

properties of Gmelina at 12% moisture content are

1. Maximum bending strength – 64N/mm2

2. Stiffness – 6300N/mm2

3. Maximium shearing strength – 3070N

4. Maximum compressive strength – 36.3N/mm2

5. Resistance to splitting - 11.4N/mm2

DEFLECTION LIMITS

Acceptable deflection limits for tissues have been adopted by some organization and are recognized and generally acceptable

worldwide. These limits were given based on researches and are experimentally supported. The limits are given by the

following bodies:

a. Timber Research Association and development of America (TRADA)

b. Department of Civil Enginering, Monash University.



Table 5(a): Trada Acceptable Limits of Deflection

Uses Limit value For 1600mm

Spanning over plastered over plastered ceilings L/360 4.44mm

Spanning over plastered over unplastered

ceilings

L/240 6.67mm

For higher bridges L/200 8.00mm

Springers in rail load, bridges and trestlers L/300 5.33mm

L = LENGTH OF THE BOTTOM CHORD WHICH IS 1600MM

As given by Timber Research Association and Development of America (TRADA)

Table 5(b) : Monash University LC Deflection Limits

Members Long term effects Short term effect Wind load

Floor members, joint and

beevers

L/300 OR 10MM L/500 OR 7MM

floor members cantilevered L/150 OR 5MM L/300 OR 4MM

roof beams, raffers and

purlings

L/300 OR 15MM L/300 OR 15MM

wall plates L/250 OR 15MM L/250 OR 15MM

LINTEL L/300 OR 10MM L/300 OR 7MM

As given by the Department of Civil Engineering Monash University, Austria.



Table 6: Results for Internal Loads and deflections for Various Members of the Roof Truss calculated

manually.

MEMBERS

(N)

(N)

L

(mm)

A

(mm2)

Max.

shearing

strength

(N/mm2)

E

AE

(deflection)

BD 2.869751 -1 1500 183.66 3070 -89.736 -8.9736

BE 3.313703 1 2000 212.08 3070 138.163 13.8163

DE 71.008 0 1000 4544.51 3070 0 0

DA -38.126649 1 1500 -2440.11 3070 -1192.236 -119.2236

AE 81.9928 0 2000 5247.54 3070 0 0

CG 2.869751 -1 1500 183.66 3070 -89.736 -8.9736

CF 3.313703 1 2000 212.08 3070 138.163 13.8163

GF 71.008 0 1000 4544.51 3070 0 0

GA -38.126649 1 1500 -2440.11 3070 -1192.236 -119.2236

AF 81.9928 0 2000 5247.54 3070 0 0

EF 3.313703 1 2000 212.08 3070 138.163 13.8163

From the table: = 13.8163mm

But the maximum permissible deflection of timber is given as ,

Where

L is the span of the truss = 6000mm

Therefore,

=

Since 13.8163mm, the actual mid span deflection is less than 18mm which is the maximum permissible deflection limit (13.8163mm < 3L/1000) therefore, it is adequate for the design.



4.0 CONCLUSION AND RECOMMENDATIONS

4.1 CONCLUSION

The results of the theoretical analysis of the roof truss

shows a deflection value of 13.82mm which is less and

within the limit of permissible deflection when compared

to the maximum permissible deflection standard of

3L/1000 (18mm) as recommended by Nigerian standard

code of practice NCP 2 (1976).

4.2 RECOMMENDATIONS

Based on the result obtained from the theoretical analysis,

we recommend that:

1. The acceptable stage where Gmelina arborea

can be effectively used is when dried to 12%

moisture content.

2. The maximum span and spacing of roof truss

members should be 6000mm and 1500mm

respectively.

3. There is the need to adequately use fasteners like

gusset plates, bolts and nuts for proper strength

in the various joints.

4. Howe roof is recommended for better

performance because it is strongest and has the

ability to withstand deflection because it is more

triangulated.

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BS 5268 “Structural use of timber” British Standard code of

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