Design of Free Standing Walls Feb 1984

8/3/2019 Design of Free Standing Walls Feb 1984

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J. O . A. KORFF BSc CEng FIStructE MICE

DESIGNOrrREESTANDINGWALLS

e l/SfS' (21) ' F ',

February 1984


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THEBRICKDEVELOPMENTASSOCIATION

Information notes prepared in August 1995 relevant toDESIGN OF FREESTANDING WALLSBy J . O. A. KorffBDA Design Guide 12, February 1984

IntroductionThe Design of Freestanding Walls DG12 was firstpublished by BDA in February 1983 and subsequentlyrevised and reprinted in February 1984. Due to itspopularity with designers and because much of theguidance is still relevant, DG12 is being retained in theBDA's Publications List.Codes, Standards and other reference material havechanged during the intervening 12years since the guidewas reprinted in 1984, and the purpose of theseinformation notes is to highl ight those importantreference changes which have a significant influenceon the use of the guide. These updated references willneed to be fully considered by designers in theinterpretation and use of DG12.It is not possible to issue a teJduralline-by-lineaddendumsheet to the guide and no attempt is being made to dothis . In due course when all the essential Codes,Standards and other reference sources which arecurrent ly changing have come into effect, it is theAssociation's intention to completely revise DG12.Des ign fo r Exposure/Durabi l ityPages 4 to 8 inclusive of DG12 provide advice onexposure , durability and assoc iated deta ilingconsiderations for the design of freestanding walls .Some of this guidance has been superseded by moreup-to-date information and reference material. The"special" and "ordinary" qualities classification of clay

W ind LoadsDG12 derives wind loadings in accordance with BSCP3:Chapter V:Part 2:1972:Wind Loads. At the presenttime this Code is still relevant to wind loading derivation,although the current version has been amended fromthe 1972 edition. Consequently figure 3 on page 11 ofDG12 - Bas ic wind speed In mls requires revising inaccordance with the latest amendment of CP3.During 1995 it is expected that BS 6399:Loading fo rBulldings:Part 2:1995 :Code of prac t ice for w indloads , will be published by the British StandardsInstitution. This new wind load code will be a completerevision of CP3. BS 6399:Part 2 is likely to coexistalongside CP3:Chapter V:Part 2 for about 12 months,after which time CP3 will be withdrawn. BS 6399:Part2 will contain specific information for the derivation ofwind loads on freestanding walls.DG12 can be used in either the context ofCP3:ChapterV:Part 2 or BS 6399:Part 2. If wind loading derivation isin accordance with BS 6399:Part 2 then Table 2 (page12) of DG12 becomes redundant whilst Figure 7 (page18) of DG12 continues to be relevant if "p., the designwind pressure is derived fully in accordance with BS6399:Part 2 and incorporates the appropriate partialfactor of safety for loading (Y) from BS 5628 (usually YI= 1.2). This latter requirement also applies to DG12guidance in respect of the use of "p". the design windpressure, referenced on pages 17, 18, 19,2 0,21 and23 for unreinforced brickwork des ign and to similar


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of 0.15 N/mm2 is taken into account the pier designdemonstrated remains adequate.Pages 26 to 34 inclus ive of DG12 demonstratereinforced brickwork design using two alternativemethods. Thefirstis a permissiblestressdesignmethodbased on CP 111 :Part 2:1970, while the second is limitstates based to SP91. Reference to SP91 should bereplaced by BS 5628 :Use of Masonry:Part2:1985:Structural use of reinforced and prestressedmasonry. BS5628:Part2 becameavailableafterDG12was published. The detailed design approach andworkedexamplesfor limit statesdesign shown inDG12from pages 29 to 34 inclusive need to be modified inrespect of the recommendations of BS 5628: Part2:1985, although the basic principles of reinforcedmasonry design using this Code remain the same asthose given in SP91 . SP91 was a forerunner to BS5628:Part 2.An amended version of BS5628:Part 2 is expected tobe published in the Autumn of 1995. Upon publicationby theBritish Standards Institution this Code shouldbesubstituted for the 1985 edition. Major changes willinclude guidance on design for durability of reinforcingsteels (coverand infillconcrete quality) andchanges todesign methods for laterally loaded masonry panelsincorporating bed-joint reinforcement. References willalso be brought fully up-to-date.ReferencesThe list of references on page 35 of DG12 should beamended as follows (others not amended remaincurrent):(1) BS 3921 :1985. Specification fo r clay bricks.

British Standards Institution.

Note that in due course CP3:Chapter V:Part 2is likely to be withdrawn.(10) BS 5628:Use of Masonry:Part 1:1992:

Structural use of unreinforced masonry.British Standards Institution.

(12) Replace reference to SP91 :1977 by:BS5628:Use of Masonry:Part 2:1985:Structuraluse of reinforced and prestressedmasonry.British Standards Institution.

Note that in due course BS 5628:Part 2:1995 willsupersede BS 5628:Part 2:1985.Add new references:(13) BS 6649:1985. Specification fo r clay and

cal ci um sil icate mod ul ar b ri cks. BritishStandards Institution.

(14) BS 5628 :Use of Masonry:Part 3:1985:Materials and components, design andworkmanship. British Standards Institution.

(15) J R Harding & R A Smith. Design Note 7 Brickwork Durabil ity. 1986. BOA.

(16) MHammell & J Morton. The Design of CurvedBrickwork. 1991 . BOA.

(17) B A Haseltine & J N Tull. Handbook to BS5628 :Part 2:Section 1:Background an dMaterials. 1991. BOA.

(18) B A Haseltine & J N Tull . Handbook to BS5628:Part 2:Section 2:Reinforced MasonryDesign. 1992. BOA.

The following two references may be of interest and


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First p ublishe d Fe b r u ar y 1983Revised a n d r e p ri n te d F e br u ar y 1984(see Editor's Note opposite)Edited by J.Morton liSe PhD CEng M ICE l\lInstM

Design offl'ee slandingwallsJ. o. A. KORFF BSc CEng FIStructE MICEDeputy Structural Engineer. OLC Department of Architecture an d Civic Design


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INTRODUCTION I

This document. which has been prepared for the guidance of civil and structuralengineers. architects andbuilders. deals with the design and use of plain and reinforced free-standing brick walls not forming partof a building.Free-stand ing brick walls are widely used for bou nda ry demarcation. landscaping. screening. security.and noise barriers. When properly constructed . free-standing br ick walls have proved to be extremelydurable a nd pleasing in appearance. There are many examples of brick walls. hundreds of yea rs old.which apart from occasional pointing and a ttention to coping require no other maintenance. Bymodern standards. most of these old walls. bu ilt by rule of thumb. a re clearly over-designed.However. since the turn of the century. and particularly after the Second World War. financialconstraints and the phenomenal growth ofmass housing estates produced some very unsat isfactoryexamples offree-standing walling. Strange as it may seem. walls are not subjected to statutory control.except in the Inner London Area where approval is required when the height exceeds 1.83 m (6 ft )above ground level. It is. therefore. not surprising that in the majority ofcases walls a re put up ratherthan designed. and all too frequently prematurely deteriorate or blow over.In most cases. a durable and stable wall will cost little more than a sub-standard one. All that isrequired is the selection of suitable materials combined with an efficient arrangement of brickwork.I & 2 Free-standing wall screening a small mews development and reducing noise from a )ery husy trunk road.


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FACTORS AFFECTING DESIGN ANDCONSTRUCTION

EXPOSUREMore often than not . free-standing walls are exposed to the full effects of the weather. The action ofwind. as a lateral force. iscatered for by the strength design. But. the combined effect of rain anddr iving wind requ ires the use of suitable materials and correct const ructiona l det ails.Figure I shows the driving rai n index map of the United Kingdom which . at present . is the best publi shedguide to the severity of weather conditions. In general. bricks for free-standing walls in the moderate andsheltered zones should comply with the frost resistance requirement s (but not necessarily the otherrequirements) for special quality brick s. However. where the wall is properly weathered (ie provided withan overhanging coping) ordinary quality brick s may be used if recommended by the manufacturers for theparticular circumsta nces. In areas of severe exposure. special quality bricks to BS3921 ( n . or other brickshaving a high frost resistance, are recommended. Calcium silicate bricks Class 3 or stronger. inaccordance with BS 187.'" are suitable for all degrees ofexposure.These are very general guidelines which may be mod ified in the light oflocal conditions. Users shouldcontact the manufacturers to confirm tha t thei r bricks are suitable for the intended degree of exposure.It is also well worth while to examine existing walls in the neighbourhood and note the performance ofparticular bricks after a few winters' service . The exposure of saturated bricks to frost or. even moreimportantly. to the freeze/th aw cycle ove r severa l winters gives a very useful guide to durabil ity.Some of the more econom ical walls recommended in this guide incorpo rate half-brick pan els. Thesewalls a re particularly vulnerable to saturation in the winter months. but should perform satisfactorilyprovided they are constructed in accordance with the advice given in this guide and under competentsupervision.


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1Driving rain index

4

3

2

NF

NB

HY

TG


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may be used to prevent movements of end units, Figure 2n. For best results an overhang such as shownin Figure 2 (f- i) should be provided.MORTARSFree-stand ingwalls derive part of their resistance to lateral forces from their flexural strength. Whereadhesion between bricks and mortar is not achieved, or is lost due to deterioration of the mortar , thestrength maybe reduced by as much as 50%. It is therefore imperativeto ensure permanent flexuraltensile adhesion between the bricks and the mortar.There is some evidence that the presence of entrained air bubbles, due to the use of plasticisers, resultsin an inferior adhesion. Experience shows that plasticised or masonry cement mortars may be perfectlyworkable when the cement content is as low as a ha lfor a third of that specified. Thus, a visual checkon mortar workability cannot indicate whether it has been correctly gauged.The following recommendations should ensure adeq uate and durable adhesion between bricksandmortar :(1) Cement /lime/sand or cement/sand mortars should be used. Plasticised or masonry cement mortarsare not recommended, but may be used with the permission of the engineer and under closesupervision aimed at ensuring that:(a) the mortar is correctly gauged with adequate water content(b) mixing is strictly controlled to prevent excessive air entrainment(c) part ially set mortar (normally after two hours) is discarded and not reconst ituted(d) the suction rate of unit s is adjusted by controlled wetting.In general, air-entrained mortars are much more prone to site abuse, and circumstances may arisewhere adequate adhesion is not achieved.(2) In dry, hot weather, bricks should be wetted by lightly spraying stacks or docking individual units.Alternatively, a wetter mortar may be used.(3) Where bricks contain sulphates in excess of 0.5% (ie, where bricks do not conform to the maximumallowable soluble sulphate content for special quality bricks to BS3921) sulphate resisting Portland

2a 2bcastconcrete a stone copingStoas3798. copingswitharrinirnm",..;g,lof 1.5kNJm' are ~ r e d


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dpc toformdrip

---- 2c 2dd P t o f o r i " 7 5 = 7 5 = 9 ! " ' "drip

2e 21 2g

(j .," .copingb -ees 10854729

dpc toformdrip ~ ~

., ...',"iiEO.'; '9'q,:..'n,:;;. ; , , ~ " ..attemative sectorcioorsectco petered

2h brick on edge in1:l4;3 mortar.and 2 cou rse stile creasilg

2i 2 courses tilecreasingwit hcross joints ardridge tile in1:4 :3 mortar

dPC

2n 215x215x102.5soc erd peterednon-ferrousorgalvarised (without c. . < " ", ,: ._ .."..",-,brickonedge

capping2cocrsesp o o r m d r i - - ~ ~ l ! o ; ~ ! " : # t - - . . . t . . r r i n r r o n

2jaJtemati've shape


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TaM. 1 Brick and mortar requirements and associated materialsPosition inwall Bricks Mortar OPC RemarksFoundations 10 Clay to 1:1 :3 SRPC ifsulphates No t esse ntial with No otherformof150mm above BS3921 in brick or soil, low abso rption dpc should be used.ground level ( fro st ot herwise 1:1:3 PC bricks, but if unless allowed for inresistant), Where indoubt desired provide two structural design.

Calcium sulphate resisti ng coursesof bricksSilicate cement should be having absorptionClass 3 10 used of not more than 7%BSI87 or two courseso f slatesto BS743 fully half-lapped and bedded inmortar

From 150mm Clay to M inimum 1:1 :6or I :1:3and I :1:41 areaboveground BS3921 1:1:4 ISRPCif more durablelevel to u/s sulphates in bricks inof coping excess ero.s%otherwise 1:1:6 or1:1:41 PCCalcium l: l :6PCSilicateClass 310BSI87

Coping or Clay Special 1:1:3 PCCapping Quality toBS3921 Flexible dpc to BS473 To improve water-below coping or proofingof copingCalcium 1:1:4 IPC capping. Preferably aluminium stearateSilicate Permagrip additivemay beusedClass 4 10BSI87

cement (SRPC) sho uld be specifi ed and the mortar strength mu st not be weaker than I : I :6. In cases ornear maximum permitted sulphate conten t and/o r severe exposure I :! :4!, or even 1:1:3 SRPC, ispreferable - see Table I.DAMP PROOF COURSESThe strength of unreinforced free-stand ing walls described in thi s guide is dependent on their flexuralten sile stress. Consequently, the use or any dpc near gro und level incapable or providing the necessaryadhesion across the joint is not permitted unless the ' No Tension -method or design is used, as explainedin 'Methods or Design' (page 20).In practice. the only dpcs which meet thi s requiremenl are :(a) two courses or (engineering) brick s to BS3921 or BS 743"! For free -standing walls. special qualitybricks with a water ab sorption or not more than 7% are considered to be adequate;(b) two courses or slat es fully half lapped and bedded in mortar to BS743.


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j--_.. ~ :...:--


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full height of the wall , including the dpc and cop ing or capping but not the foundations. Detailedrecommendations for the design ofmovement joints a re given in Section 3.FOUNDATIONSThe foundat ion requirements for free- standing walls may be less onerous than th ose for buildings.It is suggested that , for free-standing walls not fo rming part of a build ing and not exceeding . m inheight, a foundation depth 01'0.5 rn, on a sufficiently firm bottom in any type of so il, provides areasonable compromise between cost conside rations an d stability. For higher walls in cohesive soils, aminimum 01'0.75 m is recommended . Where mixed made-up ground is pre sent, it would be reasonableto assume an allowable net bearing pressure of 50 kN /m ' , provided no organic so il is pre sent and areasonable degree of con solidation has been attained over the yea rs.Fresh fill is not suitable for an y foundation s unle ss mech anically compacted in thin layers. In suchconditions, the allowable net bearing pre ssure should, however, be limited to 25 kN /m ' and the footingsshould be rein forced.For reasons explained on page 17 , the depth of brickwork below ground ought not to exceed 200 mm .Detailed recommendations in respect of founda tions for various walls, and worked examples, a reprovided in Section 3.

WIND LOADSThe design wind speed V. is calculated on the basis ofCP 3, Chapter V, Par t 2' ' ' :V, =VS,S ,S 3whereV = ba sic wind speed in m/sec (see Figure 3)S , = topographic factor. normally taken as IS, = ground roughness. size of structure and height factor. 0.6 value a pplies to wall s of any length notexceeding 3 m height above ground level, located in the co untry with many wind breaks, smalltowns or ou tskirts of large citi es.S3 = statistica l factor taken as I in all circumstances.Th erefore,V. = 0.6V m/sec.Since the limit state approach is ado pted. the design wind speed is redesignated V" th e characteristicwind speed, bu t not e tha t V. = V, =0.6V. The design wind pressure ca n now be ca lculated :p =KV. 'C,y, N/m 'wherep = design wind pressure, N/m'K = 0.613 universal coefficient from the wind codeC, =force coefficient , assumed 1.2Yr = partial safety factor for laterally loaded free-stand ing walls = 1.2.Therefore,p = 0.613 x (0.6V) , x 1.2 x 1.2= 0.318V' N/m 'For other S, and S, factors, the formula may be written in a more general form :


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3Basicw ind speeds inm/s

HY J.

NF I ~ 1 f


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open country with only scattered wind breaks (Category 2), equ ation p = 0.396V' should be used. Wherethere a re no windbreaks at all in open country (Category I), p = 0.537V' applies.The relevant values ofdesign wind pressure are given in Table 2. It should be noted that the correctassessment of gro und roughness ca tegory is important because it makes an app reciable difference to thedesign pressure. When in doubt, a higher category should be used. In unusua l circumstances, when wallsare constructed on very exposed hill slopes and crests where aoceleration ofwind is known to occur, or invalleys shaped to produce funnelling effects, the values of pre ssure given in Table 2, should be increasedby 20%.The existence of these unusual local effects should be checked with the nearest meteorologicaloffice.TaM, 2 Design wind pressure for walls o fany Im /(th not exceeding J m in height" (abov ground 1. .,0Basic Ground roughness Categor) 3 Category 2 Open country Category 1 Open countryWind Country with many windbreaks, with scattered windbreaks with no obstructionsspeed small towns, outskirts of large cities p N/m' pN/m'V mrsec p N/m'

38 459 572 77540 509 634 85942 561 699 94744 616 767 104046 673 838 113648 733 912 123750 795 990 134352 860 1071 145254 927 1155 156656 997 1242 1684

For walls between 3 & 4 m in height the values of the design wind pressure given in Table I should be increased by 5)00and for walls between 4 & .'5 m the values in Table 2 should be increased by 20%9


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10

9, 10 & 11 Sa tisfac torily designed wall, with adequate movement jo ints, suitable overhang and drip 01/ tile-creased capping(/0 ), and two- layer slate dpc ( I I ) .TYPE OF WALLThe ideal characteristics of free-standing walls are :(1) Strength and durability(2) Economy(3) Pleasing appea rance(4) SimplicityThe wall configurations shown in Tables 3 and 4 conform to these criteria. Tradit ionall y, the type ofwall frequently used by bu ilders and architects compr ises a 103*mm leaf with 215 mm square piersat 2 m spacing. Such a wall is at risk, even in a sheltered environment, and its strength is virtually thesame as that of a 103 mm wall without piers when the direction of the wind is on the face conta ining thepiers. Piers arc effective when the wind blows on the plain face but , clearly, there is no way of ensuringthis permanently.In general, 103 mm cantilever walls - plain or with small piers - should never be more than 0.9 m high,and should be restricted to parts of the country where the design wind pressure does not exceedapproximately 500 Nfm' .An imp roved type of 103 mm wall with a sma ll stagge r is shown in Figure 4. This may be used where the


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For walls higher than 5 m, diaphragm wall construction may be more economical. Thi s is dealt with inother BDA pub lication s'" 9} .Table 3 shows walls of the same order of strength as a 215 mm solid wall. The efficiency number is. b 100 x section modulus m' d i d d . di h i ' I hgiven y . an IS mten e to in reate t e re anon between f1exura strengtcross-sectional area m 2

and the volume ofmaterials used. The higher the number, the more efficient the configu ration.Table 4 shows walls of the same order of strength as a 328 mm solid wall which can be used for a heightof about 3 m. Above this height consideration should be given to the use of reinforced masonry, which islikely to be more economical.However, if an unreinforced wall is preferred , the configuration shown in Figure 5, which has an averageZ value of 3.0 x IO-'m ' per m run , is suitable for heights 3.5 to 4.5 m.

It is not recommended that walls above 3 m high should be constructed without advice from anengineer or other appropriately qualified person. Many factors vitally affecting the strength may be quiteinadvertently overlooked by the architect or the contractor, and the consequences of a failure ofa highwall could be very serious to life and property. When dealing with high ,expensive walls, the selection ofa suitable configuration should be the subject of a close consultation between the architect, the quantitysurveyor, and the engineer to arrive at an optimum solut ion. In the area covered by the GLC By-Laws,any free-standing walls in excess of 1.83m in height (from ground level) must be approved by the DistrictSurveyor.Table 3 Walls which can be used f or a height of up to 1.15 m (depending on location and subject todesign procedure)

Type of wall

Solid 215 mm , either bonded o rcollar jo inted.

Average cross-sectionalarea inm permrun

0.215

Average sectionpropertyper m run of wallZ mS I m'0.77 x 10- ' 0 .83 x 10- '

Efficiency rating[the higher the better)

3.6


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Table 4 Walls which can be used for height of up to 3.25 m (depending on location and subject todesign procedure)Type of wall

4 Solid 328 mm

Average cross-sectlonatarea in mI permrun

0.328

Average section propertyper m run of wall "

1.79 x 10- ' 2.94 x 10- '

Efficiency ratingthe higher the better

5.5

5 Staggered - GLC pat tern

6 Staggered - G LC patt ern

0.143

0.156

1.33 x 10- ' 2.93 x 10-'' See wall type 6 below.

1.93 x 10- ' 5_33 x 10- '

9.3

12.3215mrnr--~

*Forwalls type 5 & 6, the values forZ & I arecalculated on the basis of a restricted Flangewidth inaccordance with as 5628 : Part 1( 101: clause 36 .4 .3.

18m

7 With piersPiers need not besymmetricallydisposed in relation to wall.Zand I valuesare basedonpiers alone.328mmr-

ss \ \ ~ ~ m f l . 147mI 1 8manycnreoson between 0 and562mm

0.206 1.34 x 10- ' 4.47 x 10-' 6.5

12 A very old and tal l wall at BSI Conference Centre.


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DESIGN OF UNREINFORCED BRICKWALLS

Empirical selection procedureWhilst this guide deals in full with the theoreti cal aspects of the subject, an d th us will allow professiona lengineers to use its recommendations for other wall configuration s, it is recognised that a rchitects,surveyors and builde rs may wish to use it withou t havin g to produce lengthy calculations. To this end,th e guide provides tables an d diagrams which will allow a suitable wall to be selected by adopting theprocedure illustrated in the following exa mple.

Fr om Table 2. outskirts o f cities. gr o und roughnessCa tego ry 3.Design wind pressure, p = 561 N/m ' .2.2 m wall is required. Therefor e, with 0.2 m of wall belowgr ound (see note (a) below) . the effecti ve height is 2 .4 m.Locate point on Figure 7 corresponding to wind pressure560 n 'rn ' an d effective height. 2.4 01 curves to the right o fthis point ind icate satisfacto ry wall types. O r. from Table 6.select nea rest grea ter height (2.5 01 ) . All wall types capableo f resis ting pressures greater than 560 N/m ' are suitable.Therefore, wallstyp e 4 , 5, 6 & 7 (see Table4) a re a llsa t isfacto ry.\Vall type 7 isselec ted . ot e th at. in this example. only

EXAMPLEDesign a brick wall in the suburbs of Northampton, 2.2 111 high above ground level,Procedure ExampleI. Locat e the site o f the proposed wall on the map , No rthampton. fro m Figure 3. V = 42 m/sec.Figure 3, an d ob tain the approp riate bas ic wind speed.V (wind contour) .2. F rom Table 2. select the ground roughnesscategorywhich best fits theenvironment of thewal l ,and determinethe design wind pressure from the app ropriat e basic windspeed (wind co ntour)3. Determine the effective heigh t of wall required (secF igure 6).4. From the graphs in Figure7, or Table6. select type ofwall fo r the design wind pressure an d the effective height.

S. From Tab les 3 & 4, select the type of wall you prefer.


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(a) Flexural strength(b) Notional rotation about one of the faces at the base, section virtually fully cracked(c) Section under compression throughoutThese methods are illustrated in relation to a s olid wall, but are equally applicable to staggered wallsand walls with piers.6

I I O-2mreco i i let idedmax.00

Hm

(a) Design based on flexural strengtb (see Figure 6)The flexural strengths of a wall is assessed in accordance with the masonry code, BS 5628"0 , (see Table15). In the guide, for simplicity, the characteristic flexural strength ofmasonry is taken asf = 0.3 Njmrn' . This represents the minimum value which applies to all clay and calcium silicate brickslaid in a I : I :6mortar, or stronger, see Table 15 (page 33).In order to derive a simple relation between H (effective height) and p (design pressure), it is assumed thatthe critical section occurs at foundation level. Whilst, in some instances, the wall may have significantlateral support from any well-compacted soil over the base, such resistance is not always present , andqui te difficult to quantify. For economical design, it is best to keep the depth ofwall in the ground to aminimum. Plant ing ofgrass or flowers will require a dept h of soil over the foundations of some 150mmbut, in any case, the soil cover should not exceed 200 mm.Design parameters and procedureThe self weight ofa masonry wall assists in its stability.Weight of masonry, Wm = 21000 N/m ' is assumed.Where low den sity bricks are used, the weight of masonry may be as low as 18000 N/m ' . However , this


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19000HH '- 1-.547 -x- Ic:O-_-=-= 0, for Ym = 3.1

96800pH ' - 293H - 1490Similarly,pH' - 293H - 1320 = 0, for Ym = 3.5These expressions may also be assumed to apply to walls types 2 and 3 which have a higher Z value.The quadratic equation can be solved with respect to H for different values of the design wind pressure,p , obtained from Table 2. Similar quadratic equationscan be derived for the wall s shown in Table 4from the general expression , substituting app ropriat e values of Z.Table 5 Formulae for different types of wallType ofwall Quadratic equation applicable(seetables3&4) Ym = 3.t QuadraticequationapplicableYm = 3.51, 2. 35.74. 6

pH ' - 293H - 1490 0pH ' - 503H - 2580 0pH' - 677H - 3470 0pH ' - 293H - 1320 0pH ' - 50m - 2280 = 0pH ' - 677H - 307P = 0

The solutions to th ese equations a re plot ted in Figure 7 f o r values of the design wind pressure between400 and 1500 N/m . Example: a wall is required near Lincoln - basi c wind speed 44 ra]- in th e opencountry with sca ttered windbreaks. From Table 2. the design wind pressure is 767 N/m ' , and from thegraph in Figure 7 we read offth e limiting heights ofdifferent types ofwall for Ym = 3. 1:1.6 m for types 1,2 & 32.2 m for types 5 & 72.6 m for types 4 & 6(b) Design based on notional rotation about one of the faces at base levelDesign parameters andprocedure:Design wind pre ssure p N/m ' (va lues from Table 2)Weight of masonry, Wm = 21 kN /m'Y, for dead load = 0.9Assume width of stress block at po int X = see Figure 8.(Thisassumption is valid for all strengths of brickwork)t = thic kness of wall in mMomen t at base, M pH '= - - Nm27 E \ 1 I I I:

W325 \ , I I"3 \ \'\ 4 -1" ..\ ,\\ -...- IDs: 3 4 - !> -\ \ -,1-


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8 --Hm.-.----

x0 .0.0 0 00.0 . 0 D 0

The wall is assumed to be rotating about the centre of a very narrow stress block at X, with a tensilecrack extending over almost the full width of the wall. In th is condition the use ofYmis inappropriateand a general factor of safety YG = 1.2 is introduced which, together with partial factors for live anddead loads, give a global factor of safety YGl related to the stability limit state:YGl = Y f ( d ~ a d ) x y,(wind)

I= 1.2 x 0.9 x 1.2 = 1.6Consider rotation of the wall about the mid-point of the stress block at X, then,overturning moment x general facto r = righting moment:pH '- 2- x YG = 0.45t x H x t x Wm x Y,where the distance between the centre of the stress block and the centre of the wall is :t t2 200.6pH

= 0.45t= 0.45t ' x 21000 x 0.9

Therefore,H = 1 where H and t are in metres and p in Nlm ' .pEXAMPLEConsider 328 mm 11'011 (type 4),fronl the expression above:


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(c) Design based on section under compression tbrougbout (no tension method)In thi s approach, it is assumed that flexural tension is not allowed. Thu s, the compression due to selfweight, reduced by Yr, must equal the flexural tension due to the design wind load. Consider a I m runofwall H m high :pH ' 6H X Wm X Yr = -2 x -

t 't 'H = 6300 -pBy comparing this with design method (a) or even (b), it is clear that extremely con servative results wouldbe obtained. For example, if the wall is 215 mm and the design wind pressure 420 N/m ', thenH = 0.7m.Thi s design approach should never be used because it leads to over-conservative results. It is mentionedhere because some designers have been known, qui te wrongly, to attempt to apply it to masonry walls,and because it may be legitimately used in the design ofdry masonry walls.RECOMMENDED DESIGNComparison of the th ree method s ofdesign, clearly indicate that an economical solution should bebased on method (a) - flexural strength. Walls must, therefore, be built to ensure tensile resistance, seeTable I and section on mortars.The three sets of quadratic equations given in Table 5 can be solved for a given magnitude ofp (fromTable 2) thus obtaining the appropriate value of height ; but a s impler way is to substitute values ofH at0.25 m intervals and obtain the corresponding values of p. In general, p = bHH; c where band carethe coefficients of the appropriate quadratic equation from Table 5.For example, if a wall type 4 or 6 is chosen and a height, H, of 3 m is required, the allowable designwind pressure is given by:_ 677 X 3 + 3473 _ 612 N/ 'h - 3 Ip - 9 - m , w en Ym - .

Table 6 shows the compilation of these results for different types ofwalls. The requi red values can beobtained by interpolation, or from the graphs in Figure 7 .Table 6

Maximumallowable design wind pressure, p, in N /m'Hm Walls type 1,2,3 Wallstype 5, 7 Walls type 4, 6

Ym = 3.t Ym = 3.5 Y 3.t Y 3.5 Ym = 3.1 Ym = 3.53.25 399 371 537 4993.00 454 421 612 5672.75 524 484 705 6522.50 614 566 826 7622.25 425 733 674 987 907


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= 0.324pAssume maximum spanmoment, M = P I where from Tables 3 & 4 span Lis 1.8 m.

p x 1.8'10

z 0.103' x I6 = 1.77 x 10- ' m' per metreI- x f.,'Ym

M= zI x 0.9 x 10'3.1 0.324p1.77 x 10- 'p = 1.77 x 0.9 x 10' = 1586 N/m ' , say 1600 N/m '3.1 x 0.324Thus the wall is safe in allcases when p " 1600 N/m ' .Shear strength of piersConsider wall type 6, which gives the lowest shear resistance (seeTable 4).When p = 2000 N/m 'Shear force on pier = 1.8 x 2000 x (1.5 - 0.2) = 4680N (see Table 6)

where 1.5 - 0.2 is the height of wall above ground.4680Average shear stress = 552 x 215 = 0.039 N/mm '

which is well below the minimum allowable value of . ~ = 0. 14 N/mm 2where 0.35 N/mm' is the characteristic shear strength of masonry la id in I : I :6 mortar and 2.5 is 'Ymvthepartial safety factor in shear.End ConditionWalls type I and 4 can be stopped at any point, and walls type 3 and 7 will clearly terminate at a pier.But, in the case ofwalls type 2, 5 & 6 which derive their strength from the Z configuration , the end pierhas to be considerably enlarged. In some instances, a gate one metre wide may be attached to the pierand thu s the total length of the wind face supported by the pier is + 0.5 = 1.4m.The requi red section modulus of the end pier, Z. = : : : x sectionmodulus of 1.8m run of staggered wall.In the case of wall type 2, for example, where the section modulus of 1.8 m run = 0.79 x 10- ' x 1.8= 1.42 x IO- 'm ' :Z. = ::: x 1.42 x 10-' = 1.1 x IO- 'm '


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End conditions for other staggered walls are shown in Table 7. In all cases a metre wide gate wasass umed attached to the end pier.Table 7Wall type

2

5

6

Sect ion modulusof end pierrequiredin maJ.1 x 10- '

1.87 x 10- '

2.1 x 10- '

or

End condition

Design of movement jointsAs has already been said, masonry materials are subject to dimensional changes for a varie ty ofcauses,the most important ofwhich relate to variations in moisture content and temperature.The effect of mois ture expansion of clay bricks will be reduced by using mature bricks. Clay brickmasonry is hardly affected by drying shrinkage. It also has a low coefficient of thermal expansion.To accommodate movement in free-standing walls of clay brick s, it is recommended that , in the case ofstaggered brick walls types 2,5 & 6,10 mm open joints should be provided in the middle of every sixthbay (see Figure 10), and for straight walls type s I & 4, suchjoints should occur at about 10m centres.10

joints at 10 4m centreslOnmmovement roint \ I&:::S0l , \;


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Table 8 gives the order of free movement that might be expected in a 10m length ofwall.Table 8

Cause of movement

Moisture expansionThermal expansionor contractionDry ing shrinkage

Movement (mm)in a to m length . fwall+ J.5 to 5.5 (clay)2.5 (clay) } . 50' C . .4.5 (calcium silicate) assummg a varration- 2.5 (calcium silicate)

Where the provision of a movement joint cuts the leafbetween piers, its strength when acting as acantilever should be checked. Figure I I (a) shows such a movementjoint i n a wall type 7. Alt ernat ively,in wall s type 3 & 7 only, a movement joint may be incorporated at a pier as shown in Figure II (b).11a r movemen tpm& ~ : 15mm ., O79m

I. 18m ctrs.11b

, -movement joint l Qmm&' ' ] ~ i1-.11..-.1215 1 rrm rrm

12 ~ - - - - - e r t e n bead ofacrylic mastic

' " " " ' ' ' ' ' t r ' ' ' ' - ' ' \ f l d e d neoprene bailieapproximately2mmthick

Qmm

To check the strength of cantilever in Fig II (a) : M = O.7;'P = O.3lp N/m .This is, in fact , a smallermoment than in the case of a con tinuous span (see page 21) and the cantilever is clearly adequate for thedesign wind pre ssure, p, of up to 1600N/m ' .Movement joints may be left open or, where pri vacy is required, pointed with acry lic mastic of suitablecolour. Another usefu l detail , shown in Fig 12, incorporates a folded neoprene baffle lightly tacked to themasonry by a suitablema stic such as acrylic.For neat appearance, and to facilitate sealing,movement jo ints should be formed using a sliding boardof appropriate thickness. For reinforced brickwork, movement joints may be located and constructed asrecommended for unreinforced brickwork.Design of foundationsSuitable foundations for walls up to 3 m high may, in general, be selected on the basis of Tables 9 & 10,together with information from a tria l hole inspection carried out by a competent per son . It is stronglyrecommended, however, that for higher walls, advice should be ob tained from an engineer. In certaincases, the engineer may recommend a full ground inve stigation to establish the soil properties, and toconfirm the ab sence of faults (eg, layers of organic soil or swallow holes) lower down and the stability of


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Wind pressure for foundation design = ~ ~ = 690 N/m' (seeTable 6)Assume that, in this case, the suitable formation level is0.7 m below the surface.Allowable bearing pressure (soft clay)= 50 x 1.25+ 17 x 0.7 = 75kN/m 'Allowable bearing pressure (loose sand)= 100 x 1.25+ 17 x 0.7 = l37kN/m '(a) Consider I m run ofwalland assume 0.75mwidth of foundations.Weight of stem = 2.5 x 0.328 x 21 = 17.2kNWeight of base = 0.75 x 0.5 x 23 = 8.6 kNWeight ofsoil = 0.75 x 0.2 x 17 = 2.5 kNTotal 28.3 kN

3.02 x 60.75'

Wind moment at formation level= 2.5 x 690 x (1.25 + 0.5)3020e = 28300

28.3Ground pressure = 0.75

= 3020Nm= 0.107m

= 38 32= 70or 6 kN/m ' (see Figure 13)Foundation is suitable for soft clay.

Table 9 Allowable net bearing pressure and other recommendationsGroup Type Minimum allowable NET Remarksbearingpressure kN/rn ' Cohesive Stiff clay ISO Bottoms of trenches must besoils protected.

Fi rm clay 100 Concretingor blinding should becarried out within2 or 3 days afterSoft clay SO excavation

Non Loose gravel or ISOto 200 Waterlevel at least0.5 m belowcohesive loose sand and bottom of foundationsoils gravelLoose sand 100Rocks Soft chalk 100tolSO Bottoms of trenches must be(puttychalk) protected by early concreting orOtherrocks SOO blinding to prevent formation

of slurryMade up Mature SO Local soft spots. pocketsof organicsoils (undisturbed soiletc shouldberemovedand backfor several filledin leanconcrete. Stripsshouldyears)mixed preferably be reinforcedfill of cohesiveandgranular

(b) Now consider foundations in loose sand and assume a width of0.5m.


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= 130kN/m ' (see Figure 14)= 0.123 rn, which is outside the middle third of a 0.5 m strip

To tal weight is now 24.6 kN because the strip is narrower.Wind moment is unchanged at 3020 N/m3020e = 24600

G d 24.6roun pressure = 0.5 x 0.38Foundation is suitable for loose sand.

O ' I14 750mrn

13

o .0 0

14

,3QkN,m

e0 -127 0 -123 0-5m

0o.

o . o. 0 . . g00 - - .0 0 .:> .0 . o o _. l/VV ixO-27 - 0 -38mTable 10 Recommended f oundations

Type Foundations Max. bt. of Width of hase(m) Allowahle NET Minimum l\linimumof wall measured bearing pressure fromTable 9 thickness depth ofwall from top of (m) embedment (m)base (m) 50 100 150

I f i } 2.25 0.5 0.5 0.5 0.3 0.52

t I I i 2.25 0.5 0.5 0.5 0.3 0.53

: : ~ ~ 0 . 5 a - 0.52.25 b =0.5 b -0 .5 b =0.5 0.3 0.5a _ 1 c = 1.0 c = 0.75 c =0.75J.- b-eJ


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REINFORCED BRICKWORK 4

a - Iever arm coefficientPmb-permissible bending stress in masonryPOl - permissible tensile stress in reinforcement:140N /mm' for mild steel210 N/mm' for high yield steel

METHODS OF DESIGNTwo methods of design of reinforced brickwork are currently in use:(I) Permissible stress method, as given in CPI I I, Part 2, 1970(amended June 1971 )1111(2) Limit state method, for which there is as yet no British Standard Code ofPractice, but which iscovered by SP 91n i l ,PERMISSIBLE STRESS DESIGNMETHODFigure 15shows a reinforcedbrickwork section in bending,Where:d ,,-effective depthz -lever armb -width of sectionn -cornpression stress block coefficient

15

Assume the stress ratio POI = r, and the modular ratio EEs = m, then from similar triangles the followingPmb b

the applied moment and Q is given in Table I I or in Fig 16.


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The area of reinforcement isA .. = -;-Pita erDesign parameters for the working stress method are given inTable 11.Table / ICrushing strengthorbricks in :"ljmml io.s 20.5 27.5 .34.5 52 69CP I t I, Table 3.mortar 1:1:3PmbNjmm' 1.4 2.2 2.73 3.33 4.67 4.67limit limitp" ( H Y ) Nlmm' 210.0 210.0 210.0 210.0 210.0 210.0m (table 6a of (heE. 33.0 27.0 24.0 21.0 15.0 12.0mendment) -

p" 150.0 95.0 76.9 63.1 45.0 45.0~ Pm.r- 4.55 3.52 3.20 3.0 3.0 3.75mn 0. 18 0.22 0.24 0.25 0.25 0.21a, lever arm factor 0.940 0.927 0.920 0.917 0.917 0.930Q Nlmm' (max .) 0.118 0.224 0.301 0.382 0.535 0.456

. E Iro HYsteel1:1 :3mortar"1llk

0 95 .- -> .....---../'94


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r

m

are 50-100mm wide.No additives should be used in mortar, grout or concrete, but carefully controlled amounts of co lour ingagents may be used.Minimum area of reinforcementAlthough the Code (CPIII , Part 2) does not specify the minimum percentage of reinforcement inflexura lmembers, the au thor considers that 0.1%of the gross cross-sectional area of the membershould be provided .Reinforced Quetta bond, pocket & grouted cavity wallsEXAMPLE, PERMISSIBLE STRESS DESIGN METHODDesign a free standing wall 3 m high, using three different types of construction: Quetta bond, pocket andgrouted cavity. Basic wind speed is 50mis, ground roughness Category I. Bricks with a crushing strengthof34.5 N/mm' in l : j:3 mortar are specified in all cases.Pm. = 3.33 N/mm ' (see Tab le I I ) .

= 21 from Table 6a, CPl lI, Pa rt 2 (Amendment )P.. = 210 N/mm ' for high tensile steel (CPIII, Part 2)

= 210 = 633.33In = 0

1+ 21a = 0.917Q = 3.; 3 x 0.917 x 0.25 = 0.38 N/mm 'M, = 0.38bd,, 'Alternati vely, Q, may be obtained from the graph in Fig . 16, or Tab le I I.From Ta ble 2, for basic wind speed 50 mis, ground roughness Category I , we have:Design wind pressure fo r limit state de signDesign pressure for permissible stress de sign

= 1343 N/m '= 1343 = 1120 1m'1.2

D be di pH 'esign n mg moment, M = 2M = 1120t 3 ' = 5040 Nm = 5.04 x 10' mmThe minimum required effective depth, d , ca n now be calculated :

19


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1m 1m

w a l l t i e s

Pocket wall (Figs, 18 & 19)Use 21 5 mm overall thickness collar jointed wall with 200 x 110mm staggered pockets at about 2 m elcon both sides of the wall. Bend ing moment is as in the previous example.Q M 5.04 x 10' 02 h r d h f . I= bd ,,' = 10' x 160' = . , t ere,ore propose strengt 0 masonry IS amp e.z = 0.917 x I6O = 147 mm

5.04 x 10' x 2 _ 327 ' 2A.. - 0.917 x 160 x 210 - mm per m runor,O. I%ofg rossa rea = 2000 x 215 x 10- ' = 430mm ' .Provide two 16 mm HY bars in each pocket, A.. = 402 mm '.. 402 x 100percentage of remforcement = 1000 x 215 = 0.18Shear stress = 1120 x 3

= 10' x 160 x 0.917= 0.023 Njrnrn", is satisfactory.A suitable arrangement of staggered pockets at 2 m spacing, on alternate sides of the wall , is shownin Fig. 18.Th e appearance of the wall will be considerably improved if the pocke ts are faced with brickwork,attached to the concrete by suitable ties, as shown in Fig. 19.Grouted cavity wall (Fig. 20)The wall consists of two half-brick leaves with a 100 mm grouted cavity.Moment of resistance,M, 0.38 x 1000 x 153' = 8.9 x 10' Nmm. But, since the applied moment is5.04 x 10' Nmm (see Quetta bond example) the wall is adequate.

5.04 x 10' _ 7 'A.. 0.917 x 153 x 210 - I I mmor, 0.1% of gross area = 306 x 10 ' x 10- ' = 306 mm ' .

MYmsAs =---zr;-


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M = applied design momentM, = design moment of resistanceb = width of sectiond, = effective depth of sectionf, = characteristic tensile strength of the reinforcement, given in Table 14f. = characteristic compressive st rengt h of brickwor k, given in Tab le 12a = lever a rm coefficient (see a lso page 34 )z = lever armYmm = partial safety factor for brickwor k strength, given in Table 13Yms = partial safety factor for reinforcement strength which should be taken as 1.15Table 11 Characteristic compressive strength ofbrickwork.A , normal to bed joints (Nlmm ') fo r thedesign of reinforced masonry to limit state

Mortargrade and mix(i) I :1:3(ii) 1:1:41

Compressive strength of brick (N /mm l )15 20 35 50 70 1006.0 7.4 11.4 15.0 19.2 24.05.3 6.4 9.4 12.2 15.1 18.2

Table IJ Partial safe ty factors (y m) * forstrength of brickwork in compression and flexureapplicable to reinforced and unreirforced masonrydesigned to limit state

Category ofconstruction control

Catego ry o f Normalmanufacturing controlo f structural uni ts Special

Normal3.53.1

Special2.82.5

For reinforced masonry this fa ctor is designatedYmmTable 14 Characteristic strength of reinforcementfor limit s tate design

Nominal sizes CharacteristicDesignation (mm) strength f r(N/mm' )HOI-rolled mild steel A ll sizes 250(BS 4449)HOI-rolled high yield All sizes 410(BS 4449)Co ld-worked high yield Up 10 and inc!. 16 460

Slenderness limits for reinforced cantilever walls


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The ratio of spa n to effective depth ofa cantilever wall, with up to 0.5 % reinforcement based on grosscross-sect ional area , should no t normally exceed 18. However, where the load is transient (wind) , andthere is no danger of damage to finishes, the slenderness ratio limit may be increased by 30% to 23.4.Reinforced Quet ta bond wallEXA M PLEDesign a reinforced free standing wall 3 m high const ruc ted in Quet ta bond, using limit sta te design method.Basic wind speed is 56mls, and ground roughness Ca tego ry 1 are assumed.Design moment M = p = 1684 x = 7578 Nm . Thickness of wall in th is case is governed by theslenderness lim it. Minimum d" = = 130 mm . Use 328 mm wall as shown in Figure 21. Theeffective depth of 164 mm is satisfacto ry.

21 JOD ODnC 1- 'It:fJ 0 TIJEjU- .t 1328mmr\\ " , d" = 1164,-,pockets at 17Qrrm St

Assume 20 Nlmm' bricks in l : j :3 mortar. fo= 7.4 Nlmm ' = 7.4 x 10' kN lm ' (see Table 12) and Ymm= 3. 1 (see Tabl e 13).Th e maximum de sign moment of resistance can now be calculated := 0.3 x 10' x 164' x 1.5 x 7.4 = 28900 NmM, 3. 1 x 10' .which is ample in relation to the app lied moment.

"Assuming MS reinforcement (f, = 250 N /mm ' . see Table 14), and z = 0.9 x 164 mm:_ 7.58 x 10 ' x 1.15 _ 236 sA, - 250 x 164 x 0.9 - mm

or. 0.1% of gross cross-sectional area = 328 x 10' x 10-'= 328 mm 'Provide 12 mm MS in a lterna te pockets. Since thc minimum a rea of reinforcement governs. theassumption of th e a pproximate lever arm as 164 x 0.90 has no practical significance.

Shear stress = 1684 x 3 = 0.03 Nlmm ' . Th is is less than the design shear strength10' x 164which is 0.35 = 0.14 N/mm ' .2.5'ote: The minimum percentage ofreinforcement recommendedby ref erence CI ZI is 0.2%of the gross

cross-sectional area. The authorfe e ls that this perc entage is rather highfo r simple boundar y walls and,consequently, 0.1%has been adopted throughout these examples .

20 N/mm ' bricks in I :1 :3mortar are specified (as in the previous example),


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Ymm is taken as 3.1 (see Table 13).Maximum design moment of resistanceM 0.3 x 10' x 160' x 1.5 x 7.4d 3.1 x 10'= 27500 Nm, which is ample.

A. 11 530 x 10' x 1.15assuming HY reinforcement and an approximate lever arm of 160 x 0.90.460 x 160 x 0.90A. = 2oomm 'or , 0.1% of the gross cro ss-sectional area= 215 mm ' (all per m run).Provide staggered pockets of 200 x 110mm approximately, at about 2 m cic on each face as shown inFigure 18. Area of reinforcement in each pocket = 400 mm', provide one 16 mm and two 12mm HYbars, A. = 427 mm ' . The concrete pockets can be faced with brickwork, as shown in Figure 19.For 215 mm bonded walls, use I brick wide pockets at 9 br ick centres.Half brick wall stiffened with reinforced piersEXAMPLEDesign a wall 4.25 m highwith reinforced piers at about 2.5 m cleo Design windspeed is 46mls, and gronndroughness Category 2.Design wind pressure from Table 2 is 838 N/m ' but. because the wall is just 4 m high above ground level.th is pressure should be increased by 9% (see footnote to Tab le 2). Designwind pressures =838 x 1.09 = 913N/m ' .Consider 103 mm unreinforced brickwork spanning continuously between piers.Clear span is 2.035m, see Figure 23, and the effective span = clear spa n + thickness of wall = 2.14m.23 cover10 main bars 20mm

44Qmm

ef 310mm'-;1 4 ~ o : : :m = m = ~ m ..

Clear span

Take:M WL 913 x 2.14 418 Nm10 10103' x 1000 .Z 6 = 1.77 x 10' mm ' for I m Widt h ofwall

Assume a lever arm coefficientof0.9.A = Mym _ 2.07 X 10' x 1.15 = 185mm'


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f, x Z 460 x 0.9 x 310Provide four 12mm HY bars, percentageof reinforcement = 4 5 O = 0.23.The lever ann coefficientcan now beverified using A. = 185mm'and f, = 460 N/mm ' :a = ( I _ 0.53 x 185 x 460 x 3.1 ) = (I _ 0.08) = 0.92.440 x 310 x 1.15 x 1.5 x 7ATherefore the lever ann coefficient of 0.9 is satisfactory.Check shear stress, v = 2::;} : ; ; ~ 5 = 0.07 N/mm '. Section safe since the maximumdesign shear strength = O ~ = 0.14 N/mm ' .Table IS Charact"isticjfexural(temile) strength o f mas onry , f . . . N l m m ' fo r the design ofunreinforced masonry to limit state

Mortar designationMortar proportion byvolumeClay bricks having a water absorptionless than 7 %between 7%and 12%over 12%Calcium silicate bricks

Plane of failureparalle l to bed joints(i) (ii) and (iii)1:1:41I :1:3 1:1:60.7 0.50.5 0.40.4 0.30.3

Plane of failureperpendicular to bed joints(i) (ii) and (iii)1:1:411:1:3 1:1:62.0 I.SI.S 1.11.1 0.90.9

Simplified method for derivinglever arm coefficient in limit state designThe expression for the lever ann coefficient in limit state design:a = ( I 0.53A.f, Ymm ) .. 0.95bd,rYmI .5fis rather cumbersome, and cannot be used directly to calculate the area of reinforcement from :A = MYm f,a d"It can be shown that the lever arm coefficient lies between 0.8 and 0.95 hence, in practice, the best

Design procedure(I) Obt ain Q design moment


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bd , r' f(2) Select f, and Y mm so that Q .; 0.45 - '-Ymm(3) Substitute the obtained value of Q from ( I) and the selected value f from (2) into

YmmQ =2 .834 a - and hence by solving a simple quad rat ic equation fi nd a.Y m mThe process is further simplified by plotting and tabulating a ll the var iables in their appropriate limit sas shown in Fig 24 and Table 16. Th is allows the value ofa to be obta ined directly.24 b

etM =Qbd ' I el fwhereQ =2 '834 a(1 ' a) X':"

a . O 5 b9 ' 0 9 0 00 083 0 " ha . / '" . / . / "/ / ./ V . / / 1 ,......-

/ V i> 1......- :.-' V V1 / V ././ / " " / V . /.// / / , , /V / 1,......-/ ./ , , / / " " V1 / 1 . / :::-:-:V/ 0 y

10

5

1.5

2 3 4 5Q Nmm '

Table /6 Vii/lie. of Q {unit s a. fo,.f, )< :: r 1.00 2.00 3.00 . O 5.00 6.00 7.00 H.OO 9.00 10.0

a0.95 0.135 0.269 0 . 4 0 ~ 0.538 0.673 0.808 O. 9 1.077 I 1 1 . . 1 ~

REFERENCES


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5

(I ) BS 392 I :1974. Clay Bricks and Blocks. British Standards Inst itution.(2) BS 187:1978. Ca lcium silicate (sandlime and f1intlime) bricks. British Standards Institution .(3) BS4729 : I97 I . Shapes and dimensions of special bricks. British Standards Institution.(4) BS3798: 1964. Coping units (of c1 ayware, unreinforced cas t concrete, unreinforced cas t stone, naturalsto ne and slate). Briti sh Standards Inst itut ion.(5) BS 743: 1970. Ma terials for damp proof courses. Briti sh Stan dar ds Institutio n.(6) CP3 : Chapter V : Par t 2 : 1972. Wind loads. Briti sh Stan d ar ds Inst itutio n.(7) C. W. Newberry & K. J. Ea ton . Wind loading handbook. Building Research Establishment Report,

HMSO .(8) W. G . Curtin & K. Al-H ash irni. Design ofhrickwork in industrial buildings. 1978. BrickDevelop m en t Association .(9) W. G . Curtin. G . Shaw, J. K. Beck & W. A. Bray. Design of brick diaphragm walls. 1982. BrickDevelopment Association .(10) BS 5628:1978. S tructural use of masonry. Par t 1: Unreinforced masonry. British StandardsInstitution.( I I) CPIII: I970. S tructural recommendations for loadbear ing walls. Brit ish Standards Institution.(12) SP9 I :1977. Design guide for reinforced and prestressed clay brickwork. British Ceramic ResearchAssociat ion .


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Design of Free Standing Walls Feb 1984

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