Construction and Theoretical Analyses of a Roof Truss … · The mid – span deflection on the members were analyzed using the method of joints. The ... These include Howe truss,
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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
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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).
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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.
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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
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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
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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
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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 =
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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
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D A
E F B
At joint D:
FDA
30
30
FBD
FDE
Resolving Vertically:
W1Cos30 = FDE
81.9928 x Cos30 = FDE
81.9928 x 0.8660 = FDE
FDE = 71.008N
Resolving Horizontally:
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
Resolving Vertically:
FAECos30 - FBECos30 = 0
FAE x 0.8660 – 81.9928 x 0.8660
FAE = = 81.9928N
Resolving Horizontally:
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/
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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
Resolving Vertically:
FBDSin30 + ½ = 0
FBDSin30 = -½ FBD = -½ x 2 = -1N
Resolving Horizontally: FBE -1 =0 =1N For joint D:
Resolving Vertically:
FAD Sin30 - FDE Cos30 = Sin30
FAD x ½ - FDE x = ½
FAD - FDE x = ½ x 2
FAD - FDE x 3 = 1 ……………………………………1
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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
Resolving Vertically:
FEA Cos30 = 0
FEA x = 0, FEA = 0N
Resolving Horizontally:
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
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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.
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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
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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
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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.
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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.
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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.
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 | 18
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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.
REFERENCES [1]. Hossain M. K (2001). Gmelina arborea: A popular
plantation species for the tropics. In: Roshetko J. M. (2001). Agroforestry species and technologies: a compilation of the highlights and fact sheets published by NFTA and FACT Net 1985-1999. Taiwan Forestry Research Institute and Council of Agriculture, Taiwan, Republic of China and Winrock International, Morrilton, Arkansas, USA. p. 232
[2]. Roshetko J.M, Mulawarman, Purnomosidhi P (2004).
Gmelina arborea – a viable species for smallholder tree farming in Indonesia? New Forests 28: 207-215.
[3]. Oparaeke, A. M (2005). Studies of insecticidal potential of extracts of Gmelina arborea products for control of field pests of cowpea, Vigna unguiculata (L) Walp: the pod borer,
Maruca vitrata and the coreid bug, Clavigralla omentosicollis. J. Plant Protect. Res.,45(1):1-7.
[4]. Gonzalvz Rubio, H. (2009). Stand structure development
effects on wood quality of GMelina (Gmelina arborea roxb). (Doctoral dissertation, University of Missouri - Columbia).
[5]. Zeaser, D. (1998). Vegetative propagation of Gmelina
(Gmelina arborea Roxb). In: CAMCORE. International Tree Breeding Short Course Book, North Carolina State University, Raleigh, North Carolina, USA, PP. 27-34.
[6]. Krenk, S., Hogsberg, J. (2013). A Textbook of Statics
and Mechanics of Structures. http://www.springer.com/978-94-007-6112-4. ISBN9789400761124.
[7]. Victor, E. S.; Lecture Notes in: Structural Concepts and
Systems for Architects. Department of Civil Environmental and Architectural Engineering, University of Colorado, Boulder, C080309 – 0 428.
[8]. Lavers, G. M. (1969). Strength Properties of Timbers.
Design Guide. A State – of –the – Art Engineering Resource for Light – Frame Homes, Apartments and Town houses. Second Edition.
CODES OF PRACTICES
Nigerian standard code of practice NCP2 (1976), “the use of timber for construction” published by the Nigerian Standard Organization (SON), UDC 674/694, Federal Ministry of Industries Lagos.
BS 5268 “Structural use of timber” British Standard code of
practice, part 2, 2002. BS 6399 “Dead and Imposed Loads on timber” British