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MALAYSIAN STANDARD
MS 327 : PART 2 : 1997
MS 544 : PART 11 : SECTION 1 : 2001
CODE OF PRACTICE FOR STRUCTURAL USE OF TIMBER : PART 11 : RECOMMENDED SPAN TABLES AND THEIR CALCULATIONS : SECTION 1 : DOMESTIC FLOOR JOISTS
ICS : 91.080.20 Descriptors : permissible clear span, solid timber joist, design limitations, bearing length, timber size, joist spacing, sample calculations, span tables
© Copyright DEPARTMENT OF STANDARDS MALAYSIA 1
MS 327 : PART 2 : 1997
DEVELOPMENT OF MALAYSIAN STANDARDS The Department of Standards Malaysia (DSM) is the national standardisation and accreditation body.
The main function of the Department is to foster and promote standards, standardisation and accreditation as a means of advancing the national economy, promoting industrial efficiency and development, benefiting the health and safety of the public, protecting the consumers, facilitating domestic and international trade and furthering international cooperation in relation to standards and standardisation.
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Malaysian Standards are developed through consensus by committees which comprise of balanced representation of producers, users, consumers and others with relevant interests, as may be appropriate to the subject in hand. These standards where appropriate are adoption of international standards. Approval of a standard as a Malaysian Standard is governed by the Standards of Malaysia Act 1996 (Act 549). Malaysian Standards are reviewed periodically. The use of Malaysian Standards is voluntary except in so far as they are made mandatory by regulatory authorities by means of regulations, local by-laws or any other similar ways.
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For further information on Malaysian Standards, please contact:
Department of Standards Malaysia Tingkat 21, Wisma MPSA Persiaran Perbandaran 40675 Shah Alam Selangor D.E.
OR
Tel: 60 3 5519 8033 Fax: 60 3 5519 2497 http://www.dsm.gov.my
SIRIM Berhad 1, Persiaran Dato' Menteri P.O. Box 7035, Section 2 40911 Shah Alam Selangor D.E. Tel: 60 3 5544 6000 Fax: 60 3 5510 8095 http://www.sirim.my
Email:
[email protected]
2
MS 544 : PART 11 : SECTION 1 : 2001
CONTENTS
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Page Committee representation………………………………………………………………………..
iii
Foreword……………………………………………….………………………………………….
v
1
Scope…………………………………………………………………………………….
1
2
Referenced documents………………………………………………………………..
1
3
Definitions ………………………………………………………………………………
1
4
Symbols…………………………………………………………………………………
2
5
Design considerations…………………………………………………………………
4
6
Permissible spans………………………………………………………………………
6
7
Bearing length…………………………………………………………………………..
11
8
Information to be given in span tables………………………………………………..
12
Tables A1
Recommended average densities of timber for purpose of calculation…………….
13
C1
Permissible clear spans for domestic floor joists SG 1………..…....…………...…
16
C2
Permissible clear spans for domestic floor joists SG 2...………………..……….…
17
C3
Permissible clear spans for domestic floor joists SG 3..…………….………….….
18
C4
Permissible clear spans for domestic floor joists SG 4…………..……….……….
19
C5
Permissible clear spans for domestic floor joists SG 5…………..………………..
20
C6
Permissible clear spans for domestic floor joists SG 6...…………………..………
21
C7
Permissible clear spans for domestic floor joists SG 7...……………………..……
22
Figure 1 Bearing length, permissible effective and permissible clear span.…………….…
i
12
MS 544 : PART 11 : SECTION 1 : 2001
CONTENTS (continued) Page
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Appendices A
Recommended average densities of timber for purpose of calculation……...…….. 13
B
Sample calculation for a domestic floor joists…..………………….…………...…….. 14
C
Specimen span tables for domestic floor joists…..………………….……………..…. 16
ii
MS 544 : PART 11 : SECTION 1 : 2001
Committee representation The Building and Civil Engineering Industry Standards Committee (ISC D) under whose supervision this Malaysian Standard was developed, comprises representatives from the organisations :
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Association of Consulting Engineers Malaysia Chartered Institute of Building Malaysia Construction Industry Development Board Malaysia Department of Standards Malaysia Jabatan Bekalan Elektrik dan Gas Jabatan Bomba dan Penyelamat Malaysia Master Builders Association Malaysia Ministry of Housing and Local Government (Housing Department) Ministry of Works (Public Works Department) Pertubuhan Akitek Malaysia The Institution of Engineers, Malaysia Universiti Teknologi Malaysia The development of this Malaysian Standard is under the supervision of the following representatives of the CIDB Standards Committee : Ir. Mohamed bin Mohd Nuruddin Encik Megat Kamil Azmi bin Megat Rus Kamarani Puan Zainora binti Zainal Puan Hanishahani binti Othman
General Manager, Technology Development Division Senior Manager, Standard and Quality Unit Manager, Standard and Quality Unit The Secretary of CIDB Standards Committee
The Technical Committee on Structural Use of Timber which developed this Malaysian Standards consists of representatives from the following organisations : Dr. Abdul Rashid bin Hj. Ab. Malik (Chairman)
Forest Research Institute Malaysia
Puan Hanishahani binti Othman (Secretary)
Construction Industry Development Board Malaysia
Tuan Hj. Mohd Shukari bin Midon
Forest Research Institute Malaysia
Encik Zainuddin bin Kader
Public Works Department
Puan Dang Anom binti Md. Zin
Housing Department
Prof. Madya Dr. Sabaruddin bin Mohd./ Dr. Badurol Hisham bin Abu Bakar
Universiti Sains Malaysia
Prof. Dr. Zainai bin Mohamed/ Dr. Abd. Latif bin Saleh
Universiti Teknologi Malaysia
Prof Madya Ir. Dr. Mohd Zamin bin Jumaat
Universiti Malaya
Dr. Mohd Ariff bin Jamaludin
Universiti Putra Malaysia
Encik Mohd Nor Zamri bin Mat Amin
Malaysian Timber Industry Board Malaysia
Ir. Yap Chin Tian
Timber Trade Federation Malaysia
Tuan Hj. Mohamad Omar bin Mohamad Khaidzir
Forest Research Institute Malaysia
iii
MS 544 : PART 11 : SECTION 1 : 2001
Committee representation (Working Group)
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The Working Group on Recommendations For The Calculation Basis For Span Tables which developed this Malaysian Standard consists of the following representatives: Tuan Hj. Mohd Shukari bin Midon (Chairman)
Forest Research Institute Malaysia
Encik Hamdan bin Husain (Secretary)
Forest Research Institute Malaysia
Encik Zainuddin bin Kader/ Cik Sarina bin Husain
Public Works Department
Puan Hanishahani binti.Othman
Construction Industry Development Board Malaysia
Ir. Yap Chin Tian
Timber Trade Federation Malaysia
Prof. Madya Ir. Dr. Mohd Zamin bin Jumaat
Universiti Malaya
Dr. Mohd. Ariff bin Jamaludin
Universiti Putra Malaysia
Encik Chu Yue Pun
Forest Research Institute Malaysia
Encik Mohd Nor Zamri bin Mat Amin
Malaysian Timber Industry Board
Encik David Yeoh Eng Chuan
Politeknik Shah Alam
Tuan Hj. Mohamad Omar bin Mohamad Khaidzir
Forest Research Institute Malaysia
Dr. Badurol Hisham bin Abu Bakar
Universiti Sains Malaysia
iv
MS 544 : PART 11 : SECTION 1 : 2001
FOREWORD This Malaysian Standard was developed by the Working Group on Recommendations For The Calculation Basis For Span Tables established at the Construction Industry Development Board Malaysia (CIDB) under the authority of the Building and Civil Engineering Industry Standards Committee. CIDB is the Standards-Writing Organisation (SWO) appointed by SIRIM Berhad to develop standards for construction industry. In the development of this standard, reference was made to BS 5268 : Part 7 : 1989 “Recommendations for the calculation basis for span tables. Section 7.1 : Domestic floor joists”’.
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MS 544 consists of the following parts and sections, under the general title “Code of practice for structural use of timber”: Part Part Part Part
1 2 3 4
: : : :
General Permissible stress design of solid timber Permissible stress design of glued laminated timber Timber panel products Section 1 : Structural plywood Section 2 : Marine plywood Section 3 : Cement bonded particleboard Section 4 : Oriented strand board OSB) Part 5 : Timber joints Part 6 : Workmanship, inspection and maintenance Part 7 : Testing Part 8 : Design, fabrication and installation of prefabricated timber for roof trusses Part 9 : Fire resistance of timber structures Section 1 : Method of calculating fire resistance of timber members Part 10 : Preservative treatment of structural timbers Part 11 : Recommendation for the calculation basis for span tables Section 1 : Domestic floor joists Section 2 : Ceiling joists Section 3 : Ceiling binders Section 4 : Domestic rafters Part 12 : Structural laminated veneer timber for structural application.
Compliance with a Malaysian Standard does not of itself confer immunity from legal obligations.
v
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MS 544 : PART 11 : SECTION 1 : 2001
CODE OF PRACTICE FOR STRUCTURAL USE OF TIMBER : PART 11 : RECOMMENDED SPAN TABLES AND THEIR CALCULATIONS : SECTION 1 : DOMESTIC FLOOR JOISTS
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1.
Scope
This Section of MS 544 : Part 11 recommends a calculation basis for the permissible clear span for simply supported domestic floor joists of solid timber. The recommendations apply to joists at a maximum spacing of 610 mm centre-to-centre, this being the maximum spacing of which the `load-sharing' assumption may be adopted as described in MS 544 : Part 2. The method of calculation makes no allowance for any contribution of the flooring to the load resistance of the joists where such action can be provided by adequate attachments between the elements as in a stressed skin panel floor. Only uniform loading is considered whereas concentrated or line loads applied by partition, trimmers and other similar causes are excluded. This Section of MS 544 : Part 11 is applicable to the species, strength and grades of timber given in MS 544 : Part 2.
2.
Referenced documents
The following referenced documents contain provisions which, through reference in this text, constitute provisions of this Malaysian Standard. For dated references, where there are subsequent amendments to, or revisions of, any of these publications do not apply. However, parties to agreements based on this Malaysian Standard are encouraged to investigate the possibility of applying the most recent editions of the referenced documents. For undated references, the latest edition of the publication referred to applies. MS 544 : Part 1 to Part 8 - Code of practice for structural use of timber. Uniform Building By-Laws 1984, (G.N. 5178/85) (UBBL).
3.
Definitions
For the purpose of this Section of MS 544 : Part 11, the definitions given in MS 544 : Part 1 apply, together with the following: 3.1
Bearing length
The length at each end of the joist in contact with the support.
1
MS 544 : PART 11 : SECTION 1 : 2001
3.2
Effective span
Span from centre-to-centre of the minimum bearing lengths at each end. 3.3
Grade stress
Stress that can safely be permanently sustained by material of a specific section size and of a particular strength group and grade. 3.4
Load-sharing system
Assembly to pieces of members that are constrained to act together to support a common load. 3.5
Notional bearing length
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Bearing length required for the calculation of permissible clear spans.
3.6
Permissible clear span
Permissible unsupported span of a joist, measured between the faces of the supports at its two ends. NOTE. Permissible clear span is equal to permissible effective span less the notional bearing length.
3.7
Permissible effective span
Lowest value of effective span found from the calculations for bending strength, and deflection. 3.8
Permissible stress
Stress that can safely be sustained by structural material under a particular condition. NOTE. For the purpose of this section of MS 544 : Part 11, it is the product of the grade stress and the appropriate modification factors for section size, service and loading.
3.9
Strength group
Grouping of solid timber based on particular values of grade stress.
4.
Symbols
For the purposes of this Section of MS 544 : Part 11, the following symbols apply. The symbols used are: a
distance (notional bearing length);
b
breadth of joist;
2
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MS 544 : PART 11 : SECTION 1 : 2001
E
modulus of elasticity;
F
total load per metre length;
Fd
dead load per square metre applied by mass of ceiling and flooring materials (excluding joist self weight);
Fj
self weight of joist per meter length;
G
shear modulus;
h
depth of joist;
I
second moment of area;
K
modification factor (always with a subscript);
L
effective span;
Ladm
permissible effective span;
Lcl
permissible clear span;
M
bending moment;
s
spacing of joists, centre-to-centre;
δ
deflection;
Z
section modulus;
ρ
density;
σ
stress; and
τ
shear stress.
The following subscripts are used: a) Type of force, stress etc.:
b)
c
compression; and
m
bending.
Significance : adm
permissible;
cl
clear;
g
grade; and 3
MS 544 : PART 11 : SECTION 1 : 2001
max c)
maximum.
Geometry : //
parallel (to the grain); and
⊥
perpendicular (to the grain).
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It is recommended that where more than one subscript is used, the categories should be separated by commas. Subscripts may be omitted when the context in which the symbols are used is unambiguous except in the case of modification factor K.
5.
Design considerations
5.1
General
The design calculations recommended by this Section of MS 544 : Part 11 are based on engineers’ bending theory and are consistent with the recommendations of MS 544 : Part 1 to Part 7 and the shear stresses as given in MS 544 : Part 2 are not exceeded and that the deflection does not exceed the recommended limit of 0.003 times the span or 14 mm (see 11.7 of MS 544 : Part 2) whichever is smaller. NOTES: 1.
A sample calculation is given in Appendix B.
2.
Tables C1 to C7 in Appendix C contain specimen span tables.
5.2
Qualifying assumptions
The calculations given in this Section apply to systems of at least four domestic floor joists, at a maximum spacing of 610 mm centre-to-centre and having adequate flooring to provide lateral load distribution. Because load sharing take place the load sharing modification factor K2 and the mean modulus of elasticity should be used. Lateral support should be provided in accordance with 11.8 of MS 544 : Part 2. The bearing length required at each end of the joist, calculated in accordance with 6.5, may not be sufficient for practical construction purpose. 5.3
Loading
The design calculations provide for domestic floor loads which consist of the following.* a) Imposed load i)
for an effective span equal to or greater than 2400 mm, the imposed load is 2 1.5 kN/m uniformly distributed;
* Concentrated or line loads applied by partitions, trimmers and other similar causes are excluded.
4
MS 544 : PART 11 : SECTION 1 : 2001
ii)
for an effective span less than 2400 mm, the imposed load is 3.6 kN per metre width of floor (measured perpendicular to the span) uniformly distributed over the span.
NOTE. This imposed load of 1.5 kN/m2 entirely fulfils the recommendations of UBBL : 1984. The maximum imposed load of 3.6 kN per metre width is a more onerous load applied to ensure that very small joist sizes do not result from the calculations for small spans.
The imposed load should be considered as a long term load. b)
Dead load 2
Dead load per square metre Fd (in kN/m ) to provide for the mass of ceiling and flooring materials, puggings, etc. Weights of materials are given in UBBL : 1984.
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c)
Self weight
Self weight per metre length Fj (in kN/m) to provide for the mass of the joists. The timber 3 densities (in kg/m ), given in Appendix A should be used. 5.4
Design loads
The total load per metre length of span, F, is found in different ways depending on whether the span is less than or greater than 2400 mm. For spans equal to or greater than 2400 mm, F (in kN/m) is given by the equation
s +F j 1000
F = (1.5 + Fd )
(1)
For spans equal to or less than 2400 mm, F (in kN/m) is given by the equation
F =
3600 + F s + F d j L 1000
(2)
where, s
is the joist spacing (in mm);
L
is the effective span (in mm);
Fd
is the dead load (in kN/m ); and
Fj
is the self weight of joist (in kN/m);
2
NOTE. At a span of 2400 mm, equations (1) and (2) give the same value for F.
5
MS 544 : PART 11 : SECTION 1 : 2001
The value of Fj (in kN/m) may be found from the equation -9
Fj = 9.80665 x 10 ρbh
(3)
where, 3
ρ
is the timber density (in kg/m );
b
is the joist breadth (in mm); and
h
is the joist depth (in mm).
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NOTE. The value of F is regarded as being in N/mm in the equations given in Clause 6, where all values are in newtons and millimetres because MS 544 : Part 2 gives stresses in N/mm2.
6.
Permissible spans
6.1
General
The permissible effective span of a timber joist subjected to the applied loads given in 5.3 should be the shortest effective span resulting from calculations for bending strength, shear strength and deflection, as given in 6.2, 6.3 and 6.4. The permissible clear span should be calculated as the permissible effective span less the notional bearing length, calculated in accordance with 6.5. 6.2
Limitation of bending stress
From MS 544 : Part 2, the permissible bending stress
σ
2
m, adm
(in N/mm ) is given by the equation
σ m, adm = σ m, g K1K2K6
(4)
where, 2
σm,g
is the grade bending stress (in N/mm ) (see MS 544 : Part 1);
K1
is the load duration modification factor, 1.0 for long term (see Table 5 of MS 544 : Part 2);
K2
is the load sharing modification factor, 1.1 (see Clause 10 item (a) of MS 544 : Part 2); and
K6
is the section depth modification factors 1.0 (see.11.6 of MS 544 : Part : 2).
Expanding the equation
σ
m,g, adm
=
M
(5)
Z
6
MS 544 : PART 11 : SECTION 1 : 2001
leads to the following equations: Effective span, L ≥ 2400 mm L2 6 s σ m,g x 1.0 x K 6 x 1.1 = (1.5 + Fd ) + Fj 2 1000 8 bh
(6)
Effective span, L ≤ 2400 mm 3600 L2 6 s σ m,g x 1.0 x K 6 x 1.1 = + Fd + Fj 2 1000 L 8 bh
(7)
NOTE. These equations lead to the following polynomials in L.
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L ≥ 2400 mm 2 s + Fj L - σm,g x 1.0 x K 6 x 1.1 = 0 (1.5 + Fd ) 4bh 1000 3
(8)
2
L ≤ 2400 mm 2 2700 s s + Fj L + L - σm,g x 1.0 x K 6 x 1.1 = 0 Fd 4bh 1000 bh 2 1000 3
2
6.3
(9)
Limitation of shear stress
From MS 544 : Part 2, the permissible shear stress τ
2
adm
(in N/mm ) is given by the equation:
τadm = τg K1 K2
(10)
where, 2
τg
is the grade shear stress (in N/mm ) (see MS 544 : Part 2);
K1
is the load duration modification factor, 1.0 for long term (see Table 5 of MS 544 : Part 2); and
K2
is the load duration modification factor, 1.1 [see clause 10 Item (a) of MS 544 : Part : 2].
Expanding the equation
τ
adm
=
3 FL
(11)
2 2 bh
7
MS 544 : PART 11 : SECTION 1 : 2001
leads to the following equations: Effective span L ≥ 2400 mm
τg x 1.0 x 1.1 =
L s + Fj (1.5 + Fd ) 2 1000 2bh 3
(12)
Effective span L ≤ 2400 mm
τg x 1.0 x 1.1=
3600 L s + Fd + Fj 2 L 1000 2 bh 3
(13)
NOTE. These equations lead to the following polynomials in L.
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L ≥ 2400 mm
s + Fj L - τg x 1.0 x 1.1= 0 (1.5 + Fd ) 4bh 1000 3
(14)
L ≤ 2400 mm
s 2700 s + Fj L + - τg x 1.0 x 1.1= 0 Fd 4 bh bh 1000 1000 3
6.4
(15)
Limitation of deflection
From MS 544 : Part 2, the recommended deflection limitation δmax (in mm) is given by the equation δmax = 0.003L
(16)
with an overriding limitation of 14 mm (see 11.7 of MS 544 : Part 2).
8
MS 544 : PART 11 : SECTION 1 : 2001
The design equation limiting deflection is
δ
max
=
4
5
FL
384
EI
(17)
NOTE. In addition to the deflection due to bending, the shear deflection can be significant and has been taken into account.
where, E is the mean modulus of elasticity or, inserting the expressions for equivalent uniformly distributed load, for an effective span L ≥ 2400 mm
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δ
max =
5 L4 s ( ) 1.5 + F + F j x d 1000 384 EI
(18)
and for an effective span L ≤ 2400 mm 3600 5 L4 s δ max = + Fd + Fj x 1000 L 384 EI
(19)
With a deflection limitation of 0.003L for an effective span L ≥ 2400 mm
0.003 L
5 L4 12 s = (1.5 + Fd ) + Fj x 3 1000 384 E bh
(20)
and for an effective span L ≤ 2400 mm
3600 5 L4 12 s 0.003 L = + Fd + F j x 3 1000 L 384 E bh
(21)
A further design equation is required for the 14 mm limitation on deflection of spans greater than or equal to 2400 mm: this is similar to equation (20) but with '0.003L' replaced by ‘14'. The deflection of spans less than 2400 mm will be limited to less than 14 mm by equation (21). NOTE. The three design equations lead to the following polynomials in L.
Limitation 0.003L L ≥ 2400 mm 3 s + F j L - 0.003 = 0 (1.5 + Fd ) 1000 32 Ebh 5
3
9
(22)
MS 544 : PART 11 : SECTION 1 : 2001
and for an effective span L ≤ 2400 mm
s 118000 L2 s F + Fj + - 0.003 = 0 3 d 3 32 Ebh 1000 32 Ebh 1000 3
5L
(23)
Limitation 14 mm L ≥ 2400 mm
s + Fj - 14 = 0 (1.5 + Fd ) 32 Ebh 1000 4
5L
(24)
3
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6.5
Permissible clear spans
The calculation of clear span requires the deduction of a notional bearing length from an effective span. The calculation of the notional bearing length to be deducted from the permissible effective span to produce the clear span is made after finding L adm , the smallest of the effective spans for a given cross section, as limited by: bending stress, L ≥ 2400 mm;
a)
b) bending stress, L ≤ 2400 mm; c) shear stress, L ≥ 2400 mm; d) shear stress, L ≤ 2400 mm; e) deflection, limitation 0.003L, L ≥ 2400 mm; f)
deflection, limitation 0.003L, L ≤ 2400 mm; and
g) deflection, limitation 14 mm. From MS 544 : Part 2, the permissible compression perpendicular to the grain stress σc,⊥,adm 2 (in N/mm ) is given by the equation σc,⊥,adm = σc,⊥,g K1K2
(25)
where, 2
σc,⊥,g
is the grade compression perpendicular to the grain stress (in N/mm ) (see Table 4 of MS 544 : Part 2);
K1
is the load duration modification factor, 1.0 for long term (see Table 5 of MS 544 : Part 2); and
10
MS 544 : PART 11 : SECTION 1 : 2001
K2
is the load sharing modification factor, 1.1 (see clause 10 item (a) of MS 544 : Part 2).
The notional bearing length a (in mm) required at each end should be determined from the equation
σc,⊥, adm ba =
(26)
FL adm 2
where, b
is the breadth of the joist (in mm); and
Ladm
is the permissible effective span (in mm).
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Inserting the expressions for F, equation (26) gives for an effective span L ≥ 2400 mm
σ
c, ⊥,g
L adm s x 1.0 x 1.1 ba = (1.5 + Fd ) + Fj 1000 2
(27)
for L ≤ 2400 mm
σ
c,⊥ ,g
3600 Ladm s x 1.0 x 1.1 ba = + Fd + Fj 1000 Ladm 2
(28)
The equation corresponding to the loading condition governing the permissible effective span should be solved for a, and half the value of a should be deducted from each end of the span (total deduction a, see Figure 1) to give the permissible clear span. Lcl (in mm) is given by the equation Lcl = Ladm - a
7.
(29)
Bearing length
Although correct for the calculation of clear span the procedure given in 6.5 for the calculation of notional bearing length may not ensure that the permissible compression perpendicular to the grain stress is not exceeded for all loading cases. The design of some members may be governed by a loading case which does not represent the greatest total load of all loading cases. For example, the governing design case may include a concentrated load, but another less critical loading may consist of a greater total load uniformly distributed along the span.
11
MS 544 : PART 11 : SECTION 1 : 2001
8.
Information to be given in span tables
There are many possible formats for span tables. A typical format suitable for domestic floor joist at predetermined centers and for quoted loading is given in Appendix C. This Section of MS 544 : Part 11 does not recommend formats for different components but whatever format is used the following information should be given in the heading or in the main body or in the footnotes of the span tables, or in an introduction to the tables: a) the loading; b) details of the arrangement of the members; c) the member sizes and their maximum permissible deviations and/or the standards that define these quantities;
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d) the stress grade or strength group and/or the standards that define these properties; e) a statement specifying any requirements additional to those given in the stress grading rules, e.g. whether wane is prohibited at bearings; f)
a statement that the spans have been calculated in accordance with the recommendations of MS 544 : Part 2;
g) a statement specifying any structural requirements that may be necessary to comply with the qualifying assumptions made in 5.2, e.g. lateral support requirements, accommodation of lateral thrust at supports; and h) the permissible clear spans.
a
L
cl
a/2
a
a/2 L adm
Figure 1. Bearing length, permissible effective and permissible clear span
12
MS 544 : PART 11 : SECTION 1 : 2001
Appendix A (normative) Recommended average densities of timber for purpose of calculation
Table A1. Recommended average densities of timber for purpose of calculation Units in kg/m
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Strength group
Recommended average densities Dry
Wet
SG1
1050
1200
SG2
950
1100
SG3
850
1000
SG4
750
900
SG5
650
800
SG6
550
700
SG7
450
600
13
3
MS 544 : PART 11 : SECTION 1 : 2001
Appendix B (normative) Sample calculation for a domestic floor joists
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The objective is to find the permissible clear span, given the following data as applicable to a particular design case. Timber
Strength group, SG4, dry
Dimensions
Joist breadth, b Joist depth, h Joist spacing, s
Loading
Dead load, F d Imposed load
(see Table 4 of MS 544 : Part 2) = 47 mm = 72 mm = 600 mm = 0.25 kN/m2 = 1.5 kN/m2 or = 3.6 kN/m width of floor
(see 5.3 (b))
(L ≥ 2400 mm, see 5.3 (a)) (L ≤ 2400 mm, see 5.3 (a))
The following data are given in MS 544 : Part 2 : 2000 Grade stress and density Common grade bending stress, σm,g Common grade shear stress, τg Mean modulus of elasticity, E Common grade compression perpendicular to the grain stress (with wane permitted), σc,⊥,g Density (dry), ρ
MS 544 : Part 2 2
= 10.5 N/mm = 0.99 N/mm2 = 11000 N/mm2
Table 4 Table 4 Table 4
= 1.54 N/mm2 = 750 kg/m3
Table 4 Appendix A (MS 544 Part 11)
Modification factors Load duration, K1 Load sharing, K2 Depth, K6
MS 544 : Part 2 = 1.0 long term = 1.1 = 1.0
Table 17 Clause 10 Clause 11.6
Permissible stresses and recommended deflection limitation
MS 544 : Part 11 : Section 1
Permissible bending stress, σ m,adm (in N/mm2)
= σm,gK1K2 = 11.55 N/mm2
Clause 6.2
= τgK1K2 = 1.09 N/mm2
Clause 6.3
Permissible shear stress, τadm (in N/mm2) Recommended deflection limitation δmax (in mm) Permissible compression perpendicular to the grain Stress, σ c,⊥,adm (in N/mm2)
= 0.003L or = 14 mm
= σc,⊥,g K1K2 = 1.69 N/mm2
14
Clause 6.4
Clause 6.5
MS 544 : PART 11 : SECTION 1 : 2001
Application of the design equations from 6.2 to 6.4 leads to the following solutions for effective span L : a)
Limitation of bending stress
L = 1868 mm (equation (8)) or L = 1544 mm (equation (9));
b)
Limitation of shear stress
L = 4571 mm (equation (14)) or L = 15,744 mm (equation (15));
c)
Limitation of deflection (0.003L)
L = 1510 mm (equation (22)) or L = 1248 mm (equation (23));
d)
Limitation of deflection (14 mm)
L = 2003 mm (equation (24)).
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NOTE. Solutions to all seven design equations have been provided in (a) to (d) for illustrative purposes but in practice fewer solutions would be required for any individual permissible span calculation. Some solutions are invalid; for example the solution of equation (9) is invalid because it exceeds 2400 mm.
The permissible effective span Ladm is therefore, Ladm = 1248 mm The appropriate equation is selected from 6.5 (i.e. in this case for L
