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MALAYSIAN STANDARD
MS 327 : PART 2 : 1997
MS 544 : PART 11 : SECTION 2 : 2001
CODE OF PRACTICE FOR STRUCTURAL USE OF TIMBER : PART 11 : RECOMMENDED SPAN TABLES AND THEIR CALCULATIONS : SECTION 2 : CEILING 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
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and standardisation.
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OR
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MS 544 : PART 11 : SECTION 2 : 2001
CONTENTS
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Page
1 2 3 4 5 6 7 8
Committee representation…………..……………………………………………………
ii
Foreword…………………………………………………………………………………..
iv
Scope……………………………………………………………………………………….. Referenced documents………………………………………………………………….... Definitions …………………………………………………………………………..…… Symbols…………………………………………………………………………………….. Design considerations………………………………………………………………..…… Permissible spans…………………………………………………………………………. Bearing length…………………………………………………………………………….. Information to be given in span tables………………………………………………….
1 1 1 2 4 8 12 12
Recommended average densities of timber for purpose of calculation……..…...... Permissible clear spans for ceiling joists SG 1..………………………………......….. Permissible clear spans for ceiling joists SG 2..………………………………......….. Permissible clear spans for ceiling joists SG 3..………………………………......….. Permissible clear spans for ceiling joists SG 4..………………………………......….. Permissible clear spans for ceiling joists SG 5..………………………………......….. Permissible clear spans for ceiling joists SG 6..………………………………......….. Permissible clear spans for ceiling joists SG 7..………………………………......…..
14 17 18 19 20 21 22 23
Tables A1 C1 C2 C3 C4 C5 C6 C7
Figures 1
Roof construction (Typical example)……………………………………………....….… 5
2
Bearing length, permissible effective and permissible clear span…………………... 13
Appendices A
Recommended average densities of timber for purpose of calculation…………...… 14
B
Sample calculations for a ceiling joists…………………………………….……………. 15
C
Specimen span tables for ceiling joists………………………...……………………….. 17
i
MS 544 : PART 11 : SECTION 2 : 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 following 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 Masters 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. Mohamad bin Mohd Nuruddin 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 Standard 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. Ir. 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. Badorul Hisham bin Abu Bakar
Universiti Sains Malaysia
Prof. Ir. 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 Nor Zamri bin Mat Amin
Malaysian Timber Industry Board Malaysia
Ir. Yap Chin Tian
Malaysian Wood Industry Association
Tuan Hj. Mohamad Omar bin Mohamad Khaidzir
Forest Research Institute Malaysia
ii
MS 544 : PART 11 : SECTION 2 : 2001
Committee representation (Working Group)
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The Working Group on the Recommended Span Tables and Their Calculations which prepared this Malaysian Standard consists of the following representatives: Tuan Hj. Ir. Mohd. Shukari bin Midon (Chairman)
Forest Research Institute Malaysia
Encik Hamdan bin Husain (Secretary)
Forest Research Institute Malaysia
Puan Hanishahani binti Othman
Construction Industry Development Board Malaysia
Dr. Mohd Ariff bin Jamaludin
Universiti Putra Malaysia
Prof. Madya Ir. Dr. Mohd. Zamin bin Jumaat
Universiti Malaya
Encik Mohd. Nor Zamri bin Mat Amin
Malaysian Timber Industry Board Malaysia
Ir. Yap Chin Tian
Malaysian Wood Industry Association
Dr. Badorul Hisham bin Abu Bakar
Universiti Sains Malaysia
Encik Chu Yue Pun
Forest Research Institute Malaysia
Encik David Yeoh Eng Chuan
Politeknik Shah Alam
Encik Rahim bin Husain/Puan Haliza binti Abd. Aziz
Public Works Department
Tuan Hj. Mohamad Omar bin Mohamad Khaidzir
Forest Research Institute Malaysia
iii
MS 544 : PART 11 : SECTION 2 : 2001
FOREWORD This Malaysian Standard was developed by the Working Group on the Recommended Span Tables And Their Calculations 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 the construction industry.
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In the preparation of this standard reference was made to BS 5268 : Part 7 : 1989, ‘Recommendations for the calculation basis for span tables. Section 7.3 : Ceiling joists’. 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.
iv
MS 544 : PART 11 : SECTION 2 : 2001
CODE OF PRACTICE FOR STRUCTURAL USE OF TIMBER : PART 11 : RECOMMENDED SPAN TABLES AND THEIR CALCULATIONS : SECTION 2 : CEILING JOISTS 1.
Scope
This Section of MS 544 : Part 11 recommends a calculation basis for permissible clear span for ceiling joists with access at a maximum spacing of 610 mm centre-to-centre. It does not cater for the design of the ties of trussed rafters, whether prefabricated or otherwise.
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The uniform and concentrated loads recommended in Uniform Building By-Law (UBBL) : 1984 are considered. This Section of MS 544 : Part 11 is applicable to the species, strength groups and grades of timber given in MS 544 : Part 2 for both single and continuous span ceiling joists as shown in Figure 1.
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). BS 5268 : Part 3 : Roof truss system. Malaysian Grading Rules for Sawn Hardwood Timber : 1984.
3.
Definitions
For the purpose of this Section of MS 544 : Part 11, the definitions given in MS 544 : Part 1 and the following apply. 3.1
Bearing length
Length at each end of the joist in contact with the support. 3.2
Effective span
Span from centre-centre of the minimum bearing lengths at each end.
1
MS 544 : PART 11 : SECTION 2 : 2001
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 common load. 3.5
Permissible clear span
Permissible unsupported span of a joist, measured between the faces of the support at its two ends.
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NOTE. Permissible clear span is equal to permissible effective span less the notional bearing length.
3.6
Permissible effective span
Lowest value of effective span found from the calculations for bending strength, shear strength and deflection. 3.7
Permissible stress
Stress that can safely be sustained by a structural member of a particular cross section under the particular conditions of service and loading. 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 depth, service and loading.
3.8
Point load
Concentrated load referred to in UBBL : 1984 that is regarded as acting at a point for calculation purpose. 3.9
Notional bearing length
Bearing length required for the calculation of permissible clear spans. 3.10
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: a
distance (notional bearing length);
2
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MS 544 : PART 11 : SECTION 2 : 2001
b
breadth of joist;
E
modulus of elasticity;
F
total load per metre length;
Fd
dead load per square metre applied by mass of ceiling materials, insulation etc.(excluding joist self weight);
Fj
self weight of joist per metre length;
Fp
point load;
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: c
compression; and
m
bending.
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MS 544 : PART 11 : SECTION 2 : 2001
b) Significance: adm
permissible;
cl
clear;
g
grade; and
max
maximum.
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c) Geometry: //
parallel (to the grain); and
⊥
perpendicular (to the grain).
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 – Part 7. The design method ensures that the permissible bending and shear stresses, as given in MS 544 : Part 2, are not exceeded and that the deflection due to bending and shear does not exceed the recommended limit of 0.003 times the span. NOTE. A sample calculation is given in Appendix B. Tables C1 to C7 in Appendix C contain specimen span tables.
5.2
Qualifying assumptions
Although the calculations given in this Section envisage systems of ceiling joists at maximum spacing of 610 mm centre-to-centre, it is assumed that lateral load distribution is not adequate to allow stresses to be increased for `load sharing'. For members acting alone, i.e. without load sharing, the use of minimum modulus of elasticity is recommended in MS 544 : Part 2. However, for ceiling joists long experience has indicated that satisfactory performance can be achieved by the use of mean modulus of elasticity, and this practice is adopted in the equations for limiting deflection. For roof pitches greater than 20 degree the axial tension induced by rafter thrust when the ceiling joist is used to tie complementary rafter feet together may be ignored except that it should be considered in connection design. The importance of obtaining tensile continuity when the ceiling joist is acting as a tie is emphasised.
4
Figure 1. Roof construction (Typical example)
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MS 544 : PART 11 : SECTION 2 : 2001
5
MS 544 : PART 11 : SECTION 2 : 2001
The uniformly distributed dead and imposed loads are as given in UBBL : 1984 for ceiling joists. Ceilings with access are assumed. The 0.9 kN concentrated load is applied only once to the ceiling joist and not simultaneously in any other position. The design calculations given in this Section do not allow for water tank loads. Additional design calculation should be made if the ceiling joists were intended to carry water tank loads. 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 purposes. 5.3
Loading
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The design calculations provide for ceilings with access and consist of the following. a)
Imposed load 2
0.25 kN/m uniformly distributed, together with a concentrated load of 0.9 kN which, in accordance with UBBL : 1984, taken as a point load for calculation purposes. The point load is assumed to act in the position which produces maximum stress or deflection. The imposed distributed load should be considered as a long term load. The imposed point load should be considered as a short term load, as given in MS 544 : Part 8 and Table 7 of BS 5268 : Part 3. b)
Dead load 2
Dead load per square metre Fd (in kN/m ) to provide for the mass of ceiling materials, insulation etc. Weights of materials are given in UBBL : 1984. c)
Self weight Self weight per metre length Fj (in kN/m) to provide for the mass of the joists. The 3 timber densities (in kg/m ), given in Appendix A should be used.
5.4
Design loads
Two loading conditions should be considered : a)
a point and uniform imposed load condition, the loading consisting of a point imposed load plus uniformly distributed imposed load, dead load and self weight. This loading should be considered as short term; and
b)
a uniform imposed load condition, the loading consisting of uniformly distributed imposed load, dead load and self weight. This loading should be considered as long term. For the point and uniform imposed and dead loads and self weight (in kN/m) Fp = 0.9 kN 6
MS 544 : PART 11 : SECTION 2 : 2001
acting together with uniform imposed and dead loads and self weight (in kN/m)
(0.25 + Fd )
+F j 1000 s
(1)
For the uniform imposed load condition, F (in kN/m) is given by the equation
s + F j 1000
F = (0.25 + Fd )
(2)
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where, s is the joist spacing (in mm); 2 Fd is the dead load (in kN/m ); and Fj is the self weight of joist (in kN/m). 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). For the calculation of spans under loading incorporating a point load, the combined effect of uniform and point loads may be obtained using the equivalent uniformly distributed load F. F (in kN/m) is given by the following equations. In bending strength calculations F=
1000 x 2F p L
+ (0.25 + Fd )
s +F j 1000
(4)
In shear strength calculations F=
1000 x 2Fp L
+ 1.25
(0.25 + F ) s + F d j 1000
(5)
where the factor 1.25 is inserted to allow for continuity (see 6.1). In deflection calculations: F=
1000 x 1.6 Fp L
(
+ 0.25 + Fd
s ) 1000 + Fj
In equations (4) to (6) Fp = 0.9 kN L is the span (in mm)
7
(6)
MS 544 : PART 11 : SECTION 2 : 2001
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.
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Ceiling joists may be single-span beams, i.e. supported only at both ends, or they may be supported within their length by binders or supporting walls. Both configurations are covered by the design equations which recognise that the greatest deflection and bending stress occur in the single-span case while the shear stress is greater for multi-span cases. 6.2
Limitation of bending stress
From MS 544 : Part 2 the permissible bending stress equation
2
σm,adm (in N/mm ) is given by the
σm,adm = σm,g K1K6
(7)
where, 2
σm,g
is grade bending stress (in N/mm ) (see MS 544 : Part 2);
K1
is the load duration modification factor, 1.0 for long term or 1.5 for short term (see Table 5 of MS 544 : Part 2); and
NOTE. There is no medium term load case.
K6
is the section depth modification factor (see 11.6 of MS 544 : Part 2).
Expanding the equation σm, adm =
(8)
M Z
leads to the following equations. Point and uniform imposed load condition
1800 + (0.25 + Fd ) L
σ m,g x 1.5 x K 6 =
s + F L2 6 1000 j 2 8 bh
(9)
Uniform imposed load condition
σm, g x 1.0 x K 6 = (0.25 + Fd )
s + F L2 6 1000 j 2 8 bh
NOTE. These equations lead to the following polynomials in L. Point and uniform imposed load condition.
8
(10)
MS 544 : PART 11 : SECTION 2 : 2001
2 1350 s L - σm,g x 1.5 K 6 = 0 + Fj L + (0.25 + Fd ) 4bh 1000 bh 2 3
2
(11)
Uniform imposed load condition 2 s + F j L - σm,g x 1.0 x K 6 = 0 (0.25 + Fd ) 4bh 1000 3
2
6.3
Limitation of shear stress
From MS 544 : Part 2 the permissible shear stress Licensed to GAN CHIN PHANG / Downloaded on : 15-Sep-2016 06:24:02 PM / Single user license only, copying and networking prohibited
(12)
τ
adm
=
τ adm (in N/mm2) is given by the equation
τg K1
(13)
where, 2
τg
is the grade shear stress (in N/mm )(see MS 544 : Part 2); and
K1
is the load duration modification factor, 1.0 for long term or 1.5 for short term (see Table 5 of MS 544 : Part 2);
NOTE. There is no medium term load case.
Assuming the ceiling tie member is installed to act as continuous over two spans and expanding the equation
τadm =
3 FL
(14)
2 2bh
leads to the following equations. Point and uniform imposed load condition
τg x 1.5 =
3 900
2 L
(
+ 0.625 x 0.25 + Fd
)
s 1000
L bh
+ Fj
(15)
Uniform imposed load condition
τ g x 1.0 =
3 s L x 0.625 x (0.25 + Fd ) + Fj 2 1000 bh
(16)
NOTE. These equations lead to the following polynomials in L.
Point and uniform imposed load condition 3 x 0.625 s 1350 − τ g x 1.5 = 0 + Fj L + (0.25 + Fd ) 2 bh bh 1000
9
(17)
MS 544 : PART 11 : SECTION 2 : 2001
Uniform imposed load condition 3 x 0.625 2 bh 6.4
s + F j L − τg x 1.0 = 0 (0.25 + Fd ) 1000
(18)
Limitation of deflection
From 11.7 of MS 544 : Part 2, the recommended deflection limitation δmax (in mm) for general application is given by the equation δmax = 0.003L
(19)
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The design equation limiting deflection* is: Point and uniform imposed load condition 4
δ max =
5 FL
384 EI
+
3 1 Fp L
(20)
48 EI
where, E is the mean modulus of elasticity or, inserting the expressions for equivalent uniformly distributed load
1000 x 1.6Fp 5 L4 s δmax = + (0.25 + Fd ) + Fj L 1000 384 EI
(21)
where, Fp = 0.9 kN with a deflection limitation of 0.003L. Point and uniform imposed load condition
1440
0.003 L =
L
(
+ 0.25 + Fd
5 L4 12 + Fj x 3 1000 384 E bh
)
s
(22)
NOTE. This equation leads to the following polynomial in L.
Point and uniform imposed load condition
3 225 2 s L - 0.003 = 0 + Fj L + (0.25 + Fd ) 3 32 Ebh Ebh 1000 5
3
(23)
* The deflection due to bending excludes shear deflection because the equation is based on apparent E which has taken into consideration the shear effect.
10
MS 544 : PART 11 : SECTION 2 : 2001
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 Ladm , the smallest of the effective spans for a given cross section, as limited by:
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a) b) c) d)
bending stress under uniform imposed load; shear stress under point and uniform imposed load; shear stress under uniform imposed load; and deflection under point and uniform imposed load.
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 K1
(24)
where, 2
σc,⊥,g
is the grade compression perpendicular to the grain stress ((in N/mm ) (see Table 4 of MS 544 : Part 2)); and
K1
is the load duration modification factor, 1.0 for long term or 1.5 for short term (see Table 5 of MS 544 : Part 2).
NOTE. There is no medium term load case. The notional bearing length a (in mm) required at each end should be found from the equation σc,⊥,adm ba = Support reaction
(25)
where, b is the breadth of joist (in mm). Inserting appropriate expressions for the support reaction, equation (25) gives: Point and uniform imposed load condition with bending stress or deflection governing
σ
900
c,⊥, g
x 1.5 ba =
Ladm
(
+ 0.25 + Fd
L + Fj adm 1000 2
)
s
(26)
Point and uniform imposed load condition with shear stress governing
σ
900
c,⊥ ,g
x 1.5ba =
L adm
+ 0.626 x (0.25 + Fd )
11
s + Fj Ladm 1000
(27)
MS 544 : PART 11 : SECTION 2 : 2001
Uniform imposed load condition
σ
c,⊥, g
(
x 1.0 ba = 0.25 + Fd
Ladm + Fj 1000 2
)
s
(28)
In equations (26) to (28)
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a b Ladm
is the notional bearing length (in mm); is the breadth of the joist (in mm); and is the permissible effective span (in mm).
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 2) to give the permissible clear span. Lcl (in mm) is given by the equation. Lcl = Ladm - a
(29)
NOTE. As the manner of support varies for ceiling joists, the calculation of bearing length assumes support on the underside of the joist and when preparing the span tables in Appendix C the same deduction has been applied to cater for all types of support.
7.
Bearing length
Although correct for the calculation of clear span the procedure given in 6.5 for the calculation of 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 case may consist of a greater total load uniformly distributed along the span.
8.
Information to be given in span tables
There are many possible formats for span tables. A typical format suitable for ceiling joists at predetermined centres 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;
12
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MS 544 : PART 11 : SECTION 2 : 2001
d)
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
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.
statement that the spans have been calculated in accordance recommendations of MS 544 : Part 2 and MS 544 : Part 11 : Section 2;
a
L cl
a/2
with
a
a/2 L adm
Figure 2. Bearing length, permissible effective and permissible clear span
13
the
MS 544 : PART 11 : SECTION 2 : 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/m3
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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
14
MS 544 : PART 11 : SECTION 2 : 2001
Appendix B (normative) Sample calculations for a ceiling joists
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The object is to find the permissible clear span, given the following data as applicable to 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/m 2 = 0.25 kN/m 2 together with 0.9 point load
Grade stress and density
kN
(see 5.3 (b)) (see 5.3 (a)) (see 5.3 (a))
MS 544 : Part 2 = 10.5 N/mm 2 = 0.99 N/mm 2 = 11000 N/mm 2
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, ρ
Table 4 Table 4 Table 4
= 1.54 N/mm 2 = 750 kg/m 3
Table 4 Appendix A (MS 544 : Part 11)
= 1.0 long term = 1.5 short term = 1.0 (300/h) 0.11
Table 4 Table 4 Clause 11.6
Modification factors Uniform load, load duration K1 Point load, load duration, K1 Depth, K6
15
MS 544 : PART 11 : SECTION 2 : 2001
Permissible stresses and recommended deflection limitation
MS 544 : Part 11 : Section 2
Permissible bending stress, σ m,adm (in N/mm 2)
= σm,g K1K6 = 15.75 N/mm 2 for point and uniform load or = 10.50 N/mm 2 for uniform load (long term)
Clause 6.2
= τg K1 = 1.49 N/mm 2 for point and uniform load or = 0.99 N/mm 2 for uniform load (long t term)
Clause 6.3
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Permissible shear stress, stress τadm (in N/mm 2)
Recommended deflection limitation δmax (in mm) Permissible compression perpendicular to the grain stress, σ c ,⊥,adm (in N/mm 2)
= 0.003L
Clause 6.4
= σc,⊥ ,g K1 = 2.31 N/mm 2 for point and uniform load or = 1.54 N/mm 2 for uniform load (long term)
Clause 6.5
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, point and uniform imposed load
L = 2070 mm (equation (11))
b)
Limitation of bending stress, uniform imposed load
L = 7394 mm (equation (12))
c)
Limitation of shear stress, point and uniform imposed load
L = 12,066 mm (equation (17))
d)
Limitation of shear stress, uniform imposed load
L = 10,999 mm (equation (18))
e)
Limitation of deflection, point and uniform imposed load
L = 1399 mm (equation (23))
The permissible effective span Ladm is therefore Ladm = 1399 mm The appropriate equation is selected from 6.5 to calculate the notional bearing length, a, as 7 mm. The permissible clear span Lcl for the joist is then Lcl = Ladm - a Lcl = 1392 mm 16
Appendix C (normative)
Specimen span tables for ceiling joists Table C1. Permissible clear spans for ceiling joists SG 1 Dry Nett Size (mm)
Dead load supported by joist 0.25 kN/m 400
2
450 1613 2331 3142 3801 4629 5454 6274 1837 2636 3527 4245 5140 6024 6897 4630 5576 6505 7415 6862 7797
1597 2302 3095 3740 4549 5356 6157 1817 2600 3474 4176 5051 5917 6771 4555 5481 6392 7286 6747 7666
0.50 kN/m Centre to centre spacing of joists (in 600 400 1552 2222 2972 3580 4341 5100 5854 1763 2507 3332 3994 4820 5638 6447 4357 5234 6098 6948 6446 7324
mm 450 1552 2222 2972 3580 4341 5100 5854 1763 2507 3332 3994 4820 5638 6447 4357 5234 6098 6948 6446 7324
NOTES : 1. 2. 3. 4. 5. 6.
For species in this strength group see Table 3 of MS 544 : Part 2. The permissible clear spans as given, are of the minimum value between the dry and wet size calculation. All permissible stress calculations in this span tables are based on common grade stresses and minimum modulus of elasticity. The tables are computed on the basis that the specification include wane at bearing. The spans have been calculated in accordance with the recommendations of MS 544: Part 11 : Section 1. Lateral support should be provided in accordance with 11.8 of MS 544 : Part 2. The material should be stress graded in accordance with Malaysian Grading Rules 1984.
1
Wet Nett Size (mm)
2
600 1532 2187 2919 3510 4251 4990 5725 1738 2465 3269 3915 4720 5518 6307 4270 5126 5971 6803 6315 7175
1478 2095 2779 3331 4023 4712 5398 1673 2356 3109 3713 4466 5213 5954 4050 4853 5647 6431 5979 6794
38x75 100 125 150 175 200 225 50x75 100 125 150 175 200 225 63x150 175 200 225 75x200 225
MS 544 : PART 11 : SECTION 2 : 2001
35x72 95 120 140 165 190 215 47x72 95 120 140 165 190 215 60x140 165 190 215 72x190 215
17
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MS 544 : PART 11 : SECTION 2 : 2001
Dry Nett Size (mm)
Dead load supported by joist 0.25 kN/m 400 35x72 95 120 140 165 190 215 47x72 95 120 140 165 190 215 60x140 165 190 215 72x190 215
2
450 1533 2221 3001 3637 4437 5238 6035 1748 2515 3375 4070 4939 5800 6651 4448 5369 6277 7168 6634 7552
1518 2194 2957 3579 4361 5143 5922 1729 2482 3324 4004 4853 5696 6529 4376 5277 6167 7041 6521 7423
0.50 kN/m Centre to centre spacing of joists (in 600 400 1477 2120 2841 3427 4163 4898 5630 1679 2394 3190 3831 4631 5426 6213 4185 5038 5880 6710 6225 7085
mm 450 1477 2120 2841 3427 4163 4898 5630 1679 2394 3190 3831 4631 5426 6213 4185 5038 5880 6710 6225 7085
NOTES : 1. 2. 3. 4. 5. 6.
For species in this strength group see Table 3 of MS 544 : Part 2. The permissible clear spans as given, are of the minimum value between the dry and wet size calculation. All permissible stress calculations in this span tables are based on common grade stresses and minimum modulus of elasticity. The tables are computed on the basis that the specification include wane at bearing. The spans have been calculated in accordance with the recommendations of MS 544: Part 11 : Section 1. Lateral support should be provided in accordance with 11.8 of MS 544 : Part 2. The material should be stress graded in accordance with Malaysian Grading Rules 1984.
2
Wet Nett Size (mm)
2
600 1458 2087 2791 3361 4077 4793 5505 1657 2355 3131 3756 4535 5310 6078 4102 4934 5756 6567 6097 6938
1408 2000 2659 3191 3859 4526 5190 1596 2253 2979 3563 4291 5016 5735 3891 4670 5441 6205 5769 6564
38x75 100 125 150 175 200 225 50x75 100 125 150 175 200 225 63x150 175 200 225 75x200 225
MS 544 : PART 11 : SECTION 2 : 2001
Table C2. Permissible clear spans for ceiling joists SG 2
18
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MS 544 : PART 11 : SECTION 2 : 2001
Dry Nett Size (mm)
0.25 kN/m 400
2
450
35x72 95 120 140 165 190 215
1423 2069 2804 3406 4166 4929 5690
1410 2044 2764 3353 4095 4840 5584
47x72 95 120 140 165 190 215
1626 2348 3161 3822 4650 5474 6291
1609 2318 3115 3761 4570 5376 6175
60x140 165 190 215
4187 5068 5940 6799
72x190 215
6292 7178
Dead load supported by joist 0.50 kN/m Centre to centre spacing of joists (in 600 400 1374 1978 2659 3213 3912 4611 5309
mm 450
600
1374 1978 2659 3213 3912 4611 5309
1357 1948 2612 3152 3832 4513 5192
1312 1869 2491 2996 3629 4263 4895
38x75 100 125 150 175 200 225
1564 2238 2991 3600 4362 5121 5875
1564 2238 2991 3600 4362 5121 5875
1544 2203 2937 3530 4272 5012 5746
1489 2109 2797 3351 4044 4734 5420
50x75 100 125 150 175 200 225
4119 4981 5835 6677
3941 4755 5562 6359
3941 4755 5562 6359
3864 4657 5445 6223
3665 4408 5146 5876
63x150 175 200 225
6183 7053
5899 6727
5899 6727
5776 6586
5463 6226
75x200 225
NOTES :
1. 2. 3. 4. 5. 6.
Wet Nett Size (mm)
2
For species in this strength group see Table 3 of MS 544 : Part 2. The permissible clear spans as given, are of the minimum value between the dry and wet size calculation. All permissible stress calculations in this span tables are based on common grade stresses and minimum modulus of elasticity. The tables are computed on the basis that the specification include wane at bearing. The spans have been calculated in accordance with the recommendations of MS 544: Part 11 : Section 1. Lateral support should be provided in accordance with 11.8 of MS 544 : Part 2. The material should be stress graded in accordance with Malaysian Grading Rules 1984.
3
MS 544 : PART 11 : SECTION 2 : 2001
Table C3. Permissible clear spans for ceiling joists SG 3
19
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MS 544 : PART 11 : SECTION 2 : 2001
Table C4. Permissible clear spans for ceiling joists SG 4 Dry Nett Size (mm)
0.25 kN/m 400
2
450
35x72 95 120 140 165 190 215
1260 1840 2505 3052 3747 4447 5147
1250 1820 2472 3007 3686 4369 5053
47x72 95 120 140 165 190 215
1443 2094 2833 3437 4197 4957 5713
1429 2069 2793 3384 4127 4870 5609
60x140 165 190 215
3776 4589 5397 6196
72x190 215
5732 6560
Dead load supported by joist 0.50 kN/m Centre to centre spacing of joists (in 600 400 1220 1764 2382 2887 3526 4167 4809
mm 450
600
1220 1764 2382 2887 3526 4167 4809
1206 1739 2342 2834 3456 4080 4705
1168 1672 2238 2698 3278 3859 4440
38x75 100 125 150 175 200 225
1392 2002 2687 3244 3944 4643 5339
1392 2002 2687 3244 3944 4643 5339
1375 1972 2640 3183 3864 4545 5223
1329 1892 2519 3026 3662 4297 4930
50x75 100 125 150 175 200 225
3717 4512 5303 6085
3560 4311 5057 5796
3560 4311 5057 5796
3492 4223 4951 5672
3317 4001 4681 5357
63x150 175 200 225
5633 6446
5376 6146
5376 6146
5264 6016
4980 5687
75x200 225
NOTES : 1. 2. 3. 4. 5. 6.
Wet Nett Size (mm)
2
For species in this strength group see Table 3 of MS 544 : Part 2. The permissible clear spans as given, are of the minimum value between the dry and wet size calculation. All permissible stress calculations in this span tables are based on common grade stresses and minimum modulus of elasticity. The tables are computed on the basis that the specification include wane at bearing. The spans have been calculated in accordance with the recommendations of MS 544: Part 11 : Section 1. Lateral support should be provided in accordance with 11.8 of MS 544 : Part 2. The material should be stress graded in accordance with Malaysian Grading Rules 1984.
4
MS 544 : PART 11 : SECTION 2 : 2001
20
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MS 544 : PART 11 : SECTION 2 : 2001
Dry Nett Size (mm)
0.25 kN/m 400
2
450
35x72 95 120 140 165 190 215
1151 1688 2306 2816 3467 4126 4787
1142 1670 2276 2776 3412 4055 4700
47x72 95 120 140 165 190 215 60x140 165 190 215
1321 1925 2615 3180 3896 4615 5332 3504 4273 5040 5802
1310 1903 2579 3133 3832 4534 5235 3450 4202 4952 5697
72x190 215
5366 6159
5273 6050
Dead load supported by joist 0.50 kN/m Centre to centre spacing of joists (in 600 400 1116 1621 2196 2668 3267 3870 4475
mm 450
600
1116 1621 2196 2668 3267 3870 4475
1104 1599 2160 2621 3203 3790 4378
1071 1539 2067 2497 3040 3586 4133
38x75 100 125 150 175 200 225
1277 1844 2484 3006 3664 4324 4983 3307 4016 4723 5425
1277 1844 2484 3006 3664 4324 4983 3307 4016 4723 5425
1262 1817 2442 2951 3591 4234 4875 3245 3935 4623 5308
1222 1745 2332 2807 3405 4004 4601 3084 3729 4372 5012
50x75 100 125 150 175 200 225 63x150 175 200 225
5031 5765
5031 5765
4926 5642
4659 5330
75x200 225
NOTES :
1. 2. 3. 4. 5. 6.
Wet Nett Size (mm)
2
For species in this strength group see Table 3 of MS 544 : Part 2. The permissible clear spans as given, are of the minimum value between the dry and wet size calculation. All permissible stress calculations in this span tables are based on common grade stresses and minimum modulus of elasticity. The tables are computed on the basis that the specification include wane at bearing. The spans have been calculated in accordance with the recommendations of MS 544: Part 11 : Section 1. Lateral support should be provided in accordance with 11.8 of MS 544 : Part 2. The material should be stress graded in accordance with Malaysian Grading Rules 1984.
5
MS 544 : PART 11 : SECTION 2 : 2001
Table C5. Permissible clear spans for ceiling joists SG 5
21
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MS 544 : PART 11 : SECTION 2 : 2001
Table C6. Permissible clear spans for ceiling joists SG 6 Dry Nett Size (mm)
22
0.25 kN/m 400
2
450
35x72 95 120 140 165 190 215 47x72 95 120 140 165 190 215
1038 1527 2094 2564 3166 3778 4395 1193 1746 2380 2904 3569 4240 4913
1030 1512 2068 2529 3118 3715 4317 1183 1727 2349 2862 3512 4168 4825
60x140 165 190 215
3208 3926 4646 5364
3160 3862 4566 5268
72x190 215
4960 5711
4874 5608
Dead load supported by joist 0.50 kN/m Centre to centre spacing of joists (in 600 400 1008 1470 1999 2434 2989 3550 4114 1156 1676 2266 2750 3362 3978 4595
mm 450
6.
600
1008 1470 1999 2434 2989 3550 4114 1156 1676 2266 2750 3362 3978 4595
998 1451 1968 2393 2933 3478 4026 1143 1652 2229 2701 3297 3896 4496
969 1399 1886 2283 2787 3295 3805 1108 1590 2132 2573 3129 3687 4246
38x75 100 125 150 175 200 225 50x75 100 125 150 175 200 225
3032 3694 4356 5017
3032 3694 4356 5017
2977 3621 4266 4909
2832 3434 4035 4635
63x150 175 200 225
4650 5343
4650 5343
4554 5229
4308 4939
75x200 225
NOTES : 1. 2. 3. 4. 5.
Wet Nett Size (mm)
2
For species in this strength group see Table 3 of MS 544 : Part 2. The permissible clear spans as given, are of the minimum value between the dry and wet size calculation. All permissible stress calculations in this span tables are based on common grade stresses and minimum modulus of elasticity. The tables are computed on the basis that the specification include wane at bearing. The spans have been calculated in accordance with the recommendations of MS 544: Part 11 : Section 1. Lateral support should be provided in accordance with 11.8 of MS 544 : Part 2. The material should be stress graded in accordance with Malaysian Grading Rules 1984.
6
MS 544 : PART 11 : SECTION 2 : 2001
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MS 544 : PART 11 : SECTION 2 : 2001
Dry Nett Size (mm)
Dead load supported by joist 0.25 kN/m 400 35x72 95 120 140 165 190 215 47x72 95 120 140 165 190 215 60x140 165 190 215 72x190 215
23
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Table C7. Permissible clear spans for ceiling joists SG 7 2
450 879 1452 1996 2450 3033 3626 4226 1133 1665 2277 2783 3429 4083 4741 3082 3782 4487 5166 4796 5479
870 1437 1972 2417 2986 3565 4150 1118 1647 2247 2743 3374 4012 4654 3036 3720 4408 5076 4716 5384
0.50 kN/m Centre to centre spacing of joists (in 600 400 843 1389 1906 2326 2862 3405 3953 1079 1598 2168 2636 3229 3828 4429 2913 3557 4203 4841 4496 5138
mm 450 843 1389 1906 2326 2862 3405 3953 1079 1598 2168 2636 3229 3828 4429 2913 3557 4203 4841 4496 5138
NOTES : 1. 2. 3. 4. 5.
For species in this strength group see Table 3 of MS 544 : Part 2. The permissible clear spans as given, are of the minimum value between the dry and wet size calculation. All permissible stress calculations in this span tables are based on common grade stresses and minimum modulus of elasticity. The tables are computed on the basis that the specification include wane at bearing. The spans have been calculated in accordance with the recommendations of MS 544: Part 11 : Section 1. Lateral support should be provided in accordance with 11.8 of MS 544 : Part 2. 6. The material should be stress graded in accordance with Malaysian Grading Rules 1984.
7
Wet Nett Size (mm)
2
600 831 1361 1877 2286 2808 3336 3868 1061 1576 2132 2588 3166 3749 4333 2859 3486 4114 4739 4401 5031
798 1289 1798 2182 2668 3159 3652 1013 1517 2039 2466 3004 3546 4088 2720 3304 3889 4474 4160 4758
38x75 100 125 150 175 200 225 50x75 100 125 150 175 200 225 63x150 175 200 225 75x200 225
MS 544 : PART 11 : SECTION 2 : 2001
MS 544 : PART 11 : SECTION 2 : 2001
