7/23/2019 Bs 5268 Part 7 Sec 7.2 http://slidepdf.com/reader/full/bs-5268-part-7-sec-72 1/20 BRITISH STANDARD BS 5268-7.2: 1989 Structural use of timber — Part 7: Recommendations for the calculation basis for span tables — Section 7.2 Joists for flat roofs UDC [624.011.1 + 674.038.5 + 691.1.11]:[692.526:694.5]:001.4
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This British Standard, havingbeen prepared under thedirection of the CivilEngineering and BuildingStructures StandardsCommittee, was publishedunder the authority of theBoard of BSI andcomes into effect on30 June 1989
This Section of Part 7 of BS 5268 has been prepared under the direction of theCivil Engineering and Building Structures Standards Committee.
The general principles for the design of structural timber components are givenin BS 5268-2 and using these principles it is possible for span tables to beprepared for a wide range of components.
Experience has shown that different interpretations of these principles has led toinconsistencies in span tables prepared by different compilers. It is the purposeof BS 5268-7 to eliminate these differences by recommending the designequations and the loading to be used in the preparation of span tables. Part 7 isintended to ensure that different organizations produce span tables on aconsistent basis in the future, and is not necessarily intended for use by designersfor individual designs carried out in their day-to-day work, where simplifiedequations may produce adequate designs. Section 7.2 deals with joists for flatroofs. Other sections of BS 5268-7 published or in preparation are as follows.
— Section 7.1: Domestic floor joists;
— Section 7.3: Ceiling joists;
— Section 7.4: Ceiling binders;
— Section 7.5: Rafters;
— Section 7.6: Purlins supporting rafters;
— Section 7.7: Purlins supporting sheeting or decking.
BS 5268-2 gives grade stresses for very many combinations of species and gradeand it is considered impractical to publish in a British Standard span tables forall possible combinations of species, grades and sizes. BS 5268-7 is thereforerestricted to the basis of the calculations.
The solution of the design equations for many combinations of geometry andmaterial is most conveniently undertaken by computer. A program written by the
Timber Research and Development Association (TRADA) was used toprepare Appendix A and Appendix B. For users wishing to prepare their ownspan tables or computer programs Appendix A gives a samplecalculation. Appendix B gives span tables for three typical combinations ofspecies and grade. Although the presentation of span tables is not covered inBS 5268-7, it is recommended that tables for predetermined flat roof joist centresand loading follow this format.
A British Standard does not purport to include all the necessary provisions of acontract. Users of British Standards are responsible for their correct application.
Compliance with a British Standard does not of itself confer immunityfrom legal obligations.
Summary of pages
This document comprises a front cover, an inside front cover, pages i and ii,pages 1 to 14, an inside back cover and a back cover.
This standard has been updated (see copyright date) and may have hadamendments incorporated. This will be indicated in the amendment table on theinside front cover.
basis for the permissible clear span for joists for flatroofs and roofs with a slope of up to 10° Therecommendations apply to joists at a maximumspacing of 610 mm centre-to-centre, this being themaximum spacing for which the “load-sharing”assumption may be adopted as described inBS 5268-2. The method of calculation makes noallowance for any contribution of the roof decking tothe load resistance of the joists although it isassumed that the decking should be capable ofproviding lateral load distribution. It does not coverthe design of joists taking account of a structuralcontribution by sheet material supporting theroofing where such action can be provided byadequate design of its attachments as in a stressedskin panel roof.
The uniform and concentrated loads recommendedin BS 6399-1 and BS 6399-3 are considered.
This Section of BS 5268 is applicable to the speciesand grades of timber given in BS 5268-2.
NOTE The titles of the publications referred to in this standardare listed on the inside back cover.
2 Definitions
For the purposes of this Section of BS 5268, the
definitions given in BS 6100-4.2 to BS 6100-4.4,BS 6100-2.1 and BS 5268-2 apply, together with thefollowing.
2.1grade stress
stress that can safely be permanently sustained bymaterial of a specific section size and of a particularstrength class or species and grade
2.2load-sharing system
assembly of pieces or members that are constrained
to act together to support a common load2.3permissible stress
stress that can safely be sustained by a structuralmaterial under a particular condition
NOTE For the purposes of this Section of BS 5268 it is theproduct of the grade stress and the appropriate modificationfactors for section size, service and loading.
2.4strength class
classification of timber based on particular values ofgrade stress
2.5bearing length
length at each end of the joist in contact with thesupport
2.6notional bearing length
bearing length required for the calculation ofpermissible clear spans
2.7effective span
span from centre-to-centre of the minimum bearinglengths at each end
2.8
permissible effective spanlowest value of effective span found from thecalculations for bending strength, shear strengthand deflection
2.9permissible clear span
permissible unsupported span of a joist, measuredbetween the faces of the supports at its two ends
NOTE Permissible clear span is equal to permissible effectivespan less the notional bearing length.
2.10point load
concentrated load referred to in BS 6399-1, that isregarded as acting at a point for calculationpurposes
3 Symbols
For the purposes of this Section of BS 5268, thefollowing symbols apply.
NOTE The symbols used are in accordance with ISO 3898,published by the International Organization for Standardization,supplemented by the recommendations of CIB-W18-1 “Symbolsfor use in structural timber design”, published by theInternational Council for Building Research Studies andDocumentation, which takes particular account of timber
properties.
The symbols used are:
a Distance (notional bearing length)
b Breadth of joist
E Modulus of elasticity
F Total load per metre length
F d Dead load per square metre applied bymass of ceiling and roofing materials(excluding joist self weight)
It is recommended that where more than onesubscript is used, the categories should be separatedby commas.
Subscripts may be omitted when the context inwhich the symbols are used is unambiguous exceptin the case of modification factor K .
4 Design considerations
4.1 General
The design calculations recommended by thisSection of BS 5268 are based on engineers’ bendingtheory and are consistent with therecommendations of BS 5268-2. The design methodensures that the permissible bending and shearstresses, as given in BS 5268-2, are not exceededand that the deflection due to bending and sheardoes not exceed the recommended limitof 0.003 times the span.
NOTE A sample calculation is given in Appendix A and Table 1to Table 3 in Appendix B contain specimen span tables.
4.2 Qualifying assumptions
The calculations given in this Section of BS 5268
apply to systems of at least four roof joists, at amaximum spacing of 610 mm centre-to-centre, andhaving roofing adequate to provide lateral loaddistribution. Because load sharing takes place theload sharing modification factor K 8 and the meanmodulus of elasticity should be used.
Lateral support should be provided in accordancewith 14.8 of BS 5268-2:1988.
The bearing length required at each end of the joist,calculated in accordance with 5.5, may not besufficient for practical construction purposes.
4.3 Loading
The design calculations provide for flat roof loadswhich consist of the following.
a) Imposed load1)
1) with access: 1.5 kN/m2 uniformlydistributed, or a concentrated load of 1.8 kN,whichever governs the design;
2) without access: 0.75 kN/m2 uniformlydistributed, or a concentrated load of 0.9 kN,whichever governs the design.
The concentrated load, in accordance withBS 6399-1, is taken as a point load forcalculation purposes.
The point load is assumed to act in the positionwhich produces maximum stress or deflection.
The imposed distributed load should beconsidered as a medium term load for both roofswith access and those without access. Theimposed point load should be considered as ashort term load, as given in Table 8 ofBS 5268-3:1985.
b) Dead load. Dead load per square metre F d (in kN/m2) to provide for the mass of ceiling androofing materials, insulation, etc. Weights ofmaterials are given in BS 648.
c) Self weight. Self weight per metre length F j (in kN/m) to provide for the mass of the joists. Thetimber densities (in kg/m3) given in Table 9and 92 of BS 5268-2:1988 should be used.
4.4 Design loads
For roofs with or without access three loadingconditions should be considered.
a) A uniform imposed load condition, the loadingconsisting of uniformly distributed imposed load,dead load and member self weight. This loadingshould be considered as medium term.
l 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
w Deflection
Z Section modulus
Ô Density
Ö Stress
Ù Shear stress
c Compression
m Bending
adm Permissible
cl Clear
g Grade
max Maximum
tra or ¹ Perpendicular (to the grain)
1) The numerical values are examples of imposed loads, including snow load, specified in BS 6399-1. For other snow loadsreference should be made to BS 6399-3.
b) A point imposed load condition, the loadingconsisting of a point imposed load plus uniformly
distributed dead load and member self weight.This loading should be considered as short term.
c) A long term load condition, the loadingconsisting of uniformly distributed dead load andmember self weight with no imposed load. Thisloading should be considered as long term.
With access
For the uniform imposed load condition F (in kN/m)is given by the equation
For the point imposed load condition
F p = 1.8 kN
acting together with uniform dead load and selfweight (in kN/m)
For the long term load condition, i.e. dead load andself weight alone, F (in kN/m) is given by theequation
Without access
For the uniform imposed load condition F (in kN/m)is given by the equation
For the point imposed load condition
F p = 0.9 kN
acting together with uniform dead load and self
weight (in kN/m)
For the long term load condition, i.e. dead load andself weight alone, F (in kN/m) is given by theequation
In equations (1) to (6)
The value of F j (in kN/m) may be found from theequation
where
For the calculation of spans under loadingincorporating a point load, the combined effect ofuniform and point loads may be obtained using theequivalent uniformly distributed load F. F (in kN/m)is given by the following equations.
In bending strength calculations
In shear strength calculations
In deflection calculations:
For bending deflection
For shear deflection
In equations (8) to (11)
5 Permissible spans
5.1 General
The permissible effective span of a timber joistsubjected to the applied loads given in 4.3 should bethe shortest effective span resulting fromcalculations for bending strength, shear strengthand deflection, as given in 5.2, 5.3 and 5.4.
The permissible clear span should be calculated asthe permissible effective span less the notionalbearing length, calculated in accordance with 5.5.
(1)
(2)
(3)
(4)
(5)
(6)
s is the joist spacing (in mm);F d is the dead load (in kN/m2);
F j is the self weight of joist (in kN/m).
F j = 9.80665 × 10-9 × Ôbh (7)
Ô is the timber density (in kg/m3);
b is the joist breadth (in mm);
h is the joist depth (in mm).
(8)
(9)
(10)
(11)
F p = 1.8 kN with access or 0.9 kN without access;
or, inserting the expressions for equivalentuniformly distributed load,
With a deflection limitation of 0.003 L
With access
Uniform imposed load condition
Point imposed load condition
Without access
Uniform imposed load condition
Point imposed load condition
NOTE These equations lead to the following polynomials in L.
With access
Uniform imposed load condition
Point imposed load condition
Without access
Uniform imposed load condition
Point imposed load condition
5.5 Permissible clear spans
The calculation of clear span requires the deductionof a notional bearing length from an effective span.
The calculation of the notional bearing length to bededucted from the permissible effective span toproduce the clear span is made after finding Ladm,the smallest of the effective spans for a givencross section, as limited by:
From BS 5268-2, the permissible compressionperpendicular to the grain stress, Ö c,¹,adm (in N/mm2) is given by the equation
where
The notional bearing length a (in mm) required ateach end should be found from the equation
where b is the breadth of the joist (in mm).
Inserting appropriate expressions for the supportreaction, equation (54) gives the followingequations.
With access
Uniform imposed load condition
Point imposed load condition with bending stressor deflection governing
Point imposed load condition with shear stressgoverning
Long term load condition, i.e. dead load and selfweight alone
Without accessUniform imposed load condition
Point imposed load condition with bending stressor deflection governing
Point imposed load condition with shear stressgoverning
Long term load condition, i.e. dead load and selfweight alone
In equations (56) to (63)
The equation corresponding to the loading conditiongoverning the permissible effective span should besolved for a, and half the value of a should bededucted from each end of the span (total
deduction a, see Figure 1) to give the permissibleclear span. Lcl (in mm) is given by the equation
Ö c,¹, adm = Ö c,¹, g K 3 K 8 (54)
Ö c,¹, g is the grade compression perpendicular
to the grain stress (in N/mm2)
(see BS 5268-2)a;
K 3 is the load duration modification
factor, 1.0 for long term, 1.25 for mediumterm or 1.5 for short term (see Table 17of BS 5268-2:1988);
K 8 is the load sharing modificationfactor, 1.1 [see clause 13 item a) ofBS 5268-2:1988].
a BS 5268-2 provides two values for the grade compressionperpendicular to the grain stress. When the specificationspecifically prohibits wane at bearing areas, the higher valuemay be used, otherwise the lower value applies.(See footnotes to Table 9, Table 10, Table 11, Table 12 andTable 13 in BS 5268-2:1988). The span table should indicatewhether wane is permitted.
Although correct for the calculation of clear span the
procedure given in 5.5 for the calculation of notionalbearing length may not ensure that the permissiblecompression perpendicular to the grain stress is notexceeded for all loading cases.
The design of some members may be governed by aloading case which does not represent the greatesttotal load of all loading cases. For example, thegoverning design case may include a concentratedload, but another less critical loading case mayconsist of a greater total load uniformly distributedalong the span.
7 Information to be given in spantables
There are many possible formats for span tables. Atypical format suitable for flat roof joists atpredetermined centres and for quoted loading isgiven in Appendix B.
This Section of BS 5268 does not recommendformats for different components but whatever
format is used the following information should begiven in the heading or in the main body or in thefootnotes of the span tables, or in an introduction tothe tables:
a) the loading;
b) details of the arrangement of the members;
c) the member sizes and their maximumpermissible deviations and/or the standards thatdefine these quantities;
d) the species, stress grade or strength classand/or the standards that define these properties;
e) a statement specifying any requirements
additional to those given in the stress gradingrules, e.g. whether wane is prohibited atbearings;
f) a statement that the spans have beencalculated in accordance with therecommendations of BS 5268-2 and BS 5268-7.2;
g) a statement specifying any structuralrequirements that may be necessary to complywith the qualifying assumptions made in 4.2,e.g. lateral support requirements,accommodation of lateral thrust at supports;
Application of the design equations from 5.2 to 5.4 leads to the following solutions for effective span, L;
Appendix B Specimen span tables for flat roof joists
There are many possible formats for span tables and Table 1, Table 2 and Table 3 are typical examples.Whatever format is used, the information listed in clause 7 should be given.
Table 1, Table 2 and Table 3 apply only to flat roofs where no access is provided to the roof (other than thatnecessary for cleaning and repair). The tables should not be used for the design of flat roofs with permanentaccess. Load span tables covering both types of loadings and covering a wider range of timber sizes areavailable from a number of trade organizations.
BS 5268-7.2 reference
Permissible compression
perpendicular to the grainstress, Ö c,¹, adm (in N/mm2) = Ö c,¹ g K 3 K 8 5.5
= 2.3375 N/mm2 for uniform load
(medium term)
or = 2.805 N/mm2 for point load
or = 1.87 N/mm2 for uniform load
(long term)
a) limitation of bending stress, uniform imposed load L = 4 916 mm [equation (20) or (23)];
b) limitation of bending stress, point imposed load L = 5 964 mm [equation (21) or (24)];
c) limitation of bending stress, long term load alone L = 6 638 mm [equation (22) or (25)];
d) limitation of shear stress, uniform imposed load L = 1 4940 mm [equation (34) or (37)];
e) limitation of shear stress, point imposed load L = 35 752 mm [equation (35) or (38)];
f) limitation of shear stress, long term load alone L = 47 517 mm [equation (36) or (39)];
g) limitation of deflection, uniform imposed load L = 4 230 mm [equation (50) or (52)];
h) limitation of deflection, point imposed load L = 4 484 mm [equation (51) or (53)];
The permissible effective span Ladm is therefore
Ladm = 4 230 mm
The appropriate equation is selected from 5.5 to calculate the notional bearing length, a, as 15 mm.
The permissible clear span Lcl for the joists is then
NOTE 1 The tables are computed on the basis that the specification does not exclude wane at bearings.
NOTE 2 The spans have been calculated in accordance with the recommendations of BS 5268-2 and BS 5268-7.2. Lateral supportshould be provided in accordance with 14.8 of BS 5268-2:1988.
NOTE 3 The material should be stress graded in accordance with BS 4978.NOTE 4 The sizes and their maximum permissible deviations should be in accordance with BS 4471.a For species/grade combinations in this strength class, see Table 3 to Table 7 of BS 5268-2:1988.b Regularized sizes are given in BS 4471.
NOTE 1 The tables are computed on the basis that the specification does not exclude wane at bearings.
NOTE 2 The spans have been calculated in accordance with the recommendations of BS 5268-2 and BS 5268-7.2. Lateral supportshould be provided in accordance with 14.8 of BS 5268-2:1988.
NOTE 3 The material should be stress graded in accordance with NLGA rules.
NOTE 4 The sizes and their maximum permissible deviations should be in accordance with Appendix A of BS 4471:1987.a CLS sizes are given in Appendix A of BS 4471:1987.
BS 648, Schedule of weights of building materials.
BS 4471, Specification for sizes of sawn and processed softwood.
BS 4471-1, Sizes of sawn and planed timber.BS 4978, Specification for timber grades for structural use.
BS 5268, Structural use of timber.
BS 5268-2, Code of practice for permissible stress design, materials and workmanship.
BS 5268-3, Code of practice for trussed rafter roofs.
BS 5268-7.1, Domestic floor joists3).
BS 5268-7.3, Ceiling joists3).
BS 5268-7.4, Ceiling binders3).
BS 5268-7.5, Rafters3).
BS 5268-7.6, Purlins supporting rafters3).
BS 5268-7.7, Purlins supporting sheeting or decking 3).
BS 6100, Glossary of building and civil engineering terms.
BS 6100-2.1, Structural design and elements.
BS 6100-4.1, Characteristics and properties of timber and wood based panel products.
BS 6100-4.2, Sizes and quantities of solid timber.
BS 6100-4.3, Wood based panel products.
BS 6100-4.4, Carpentry and joinery.
BS 6399, Loading for buildings .
BS 6399-1, Code of practice for dead and imposed loads.
BS 6399-3, Code of practice for imposed roof loads.
ISO 3898, Bases for design of structures — Notations — General symbols.
CIB-W18-1, Symbols for use in structural timber design. International Council for Building ResearchStudies and Documentation, Post Box 20704, 3001 JA Rotterdam, The Netherlands.
NLGA 1979, The national grading rules for dimension lumber. National Lumber Grades Authority, 1450-1055 West Hastings Street, Vancouver, British Columbia, Canada V6E 2G8.
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