2. masonry design - compression

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2. MASONRY DESIGN

2.1 Structural design of masonry

The structural design of masonry is carried out in accordance with the guidance given in BS

5628 ‘Code of practice for use of masonry’. This is divided into the following three parts: BS 5628 Part 1 - Structural use of unreinforced masonry. BS 5628 Part 2 - Structural use of reinforced and prestressed masonry. BS 5628 Part 3 - Materials and components, design and workmanship.

The design of masonry dealt with in this manual is based on Part 1, which gives designrecommendations for unreinforced masonry constructed of bricks, concrete blocks or naturalstone.

2.2 Design Philosophy

The design approach employed in BS 5628 is based on limit state philosophy. In the context of

load bearing masonry its objective is to ensure an acceptable probability that the ultimate limitstate will not be exceeded. Thus for a masonry member, which will be either a wall or a column,

Ultimate design strength ≥ ultimate design load

Partial safety factors are applied separately to both the loads and the material stresses in limitstate design.

2.3 Loads

The basic or characteristic load is adjusted by a partial safety factor to arrive at the ultimate

design load acting on a wall.

Characteristic loads

The characteristic loads applicable to masonry design are the same as those defined for concretedesign:

Values of f are given in BS 5628 Part 1 for the following load combinations:(a) Dead and imposed load(b) Dead and wind load(c) Dead imposed and wind load

(d) Accidental damage.

Those for the dead and imposed load combination which would usually apply to verticallyloaded walls are as follows:

Design dead load: 1.4Gk Design imposed load: 1.6Qk


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2.4 Ultimate design load

The ultimate design load acting vertically on a wall will be the summation of the relevantcharacteristic load combinations multiplied by their respective partial safety factors. Thereforethe ultimate design load for the dead plus imposed load combination on a vertically loadedwall would be expressed as follows:

Ultimate design load dead + imposed = 1.4Gk + 1.6Qk

Ex 01:The characteristic loads (from BS 6399) for a floor used for offices are:(a) Characteristic dead load, Gk = 3.0 kN/m2 (b) Characteristic imposed load, Qk = 2.5 kN/m2 (offices for general use)Determine the design load.

2.5 Characteristic Compressive Strength of Masonry, f k

The characteristic compressive strength of masonry depends upon: the characteristic strength of the masonry unit mortar designation the shape of the unit whether the work is bonded or unbounded thickness of the mortar joints the standard of workmanship.


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BS 5628-1:2005 – Page 16


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Ex 02:Determine the characteristic compressive strength, f k, of a wall constructed in hollow blocks (asshown in Figure) of gross area compressive strength 7 N/mm2, if the blocks are filled withconcrete having a 28 day compressive strength equal to that of the blocks and a mortardesignation (iii) is used.


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2.6 Partial Safety Factors for Material Strength, m

The degree of care exercised in the control of the manufacture of the units and in the construction of themasonry affects the design strength of the wall, column, etc. The characteristic strength of masonry hasto be divided by a partial safety factor to obtain the design strength. The partial safety factor depends onthe degree of quality control on manufacture and construction. The factor also depends on whether the

masonry is subject to compression loading or lateral loading.

Manufacturing Control

(a) Category I: This category is used when suppliers can meet a specified strength limit (knownas the ‘acceptance limit’) when not more than 2.5% of the test results will fall below theacceptance limit, and also when the supplier’s quality control scheme can satisfy the buyer thatthe acceptance limit is consistently met.(b) Category II: This category is used when the supplier can meet the compressive strengthrequirements of the appropriate British Standard.

Construction Control

(a) Normal category: Normal category should be assumed whenever the work is carried outfollowing the recommendations for workmanship in Annex A of BS 5628-3:2001, or BS 8000-3including appropriate supervision and inspection. (b) Special Category

Design Strength = Characteristic compressive strength (fk)Partial safety factor for materials (m)

Ex 03:

1.

Determine the design strength of the brickwork in Example 2, if the manufacturingcontrol is category I and construction control is normal category.

2.

Determine the design strength of the brickwork in Example 2, the manufacturing controlis category I and the construction control is special category.


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2.7 Slenderness Ratio

Slender masonry walls and columns under compressive loading are likely to buckle in the sameway as concrete, steel or timber columns in compression. It is therefore, necessary to determinethe masonry wall’s or column’s slenderness ratio in order to relate a failure in buckling to thecompressive load-carrying capacity of a wall or column.

Slender ratio = effective height (or length) / effective thickness → hef (or lef) / tef

2.7.1 Effective height

The effective height hef depends on the degree of horizontal lateral support provided and maybe defined as follows for walls and columns.

For walls it should be taken as(a) 0.75 times the clear distance between lateral supports which provide enhanced resistance, or

(b) The clear distance between lateral supports which only provide simple resistance.

For columns it should be taken as(a) The distance between lateral supports in respect of the direction in which lateral support isprovided, shown as hef = h in Figure Case (a), or(b) Twice the height of the column in respect of a direction in which lateral support is notprovided, shown as hef = 2h in Figure Case (b).


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2.7.2 Effective Length

The effective length lef is a consideration that only applies to walls, and depends on the degreeof vertical lateral support provided. It may be taken asa) 0.75 times the clear distance between vertical lateral supports (case a) or twice the distancebetween a support and a free edge (case b), where lateral supports provides enhancedresistance to lateral movement;b) The clear distance between lateral supports (case c) or 2.5 times the distance between asupport and a free edge (case d), where lateral supports provide simple resistance to lateralmovement.

Ex 04: Determine the slenderness ratio for the wall as shown in Figure, assuming tef = 102.5 mm.


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2.7.3 Effective Thickness

Ex 05: Determine the effective thickness of the wall shown in Figure 1-4.

(1) (2)

(3) (4)


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Design summary for a vertically loaded wall or column

Requirement Page Table/Section(a) Calculate the slenderness ratio for the

wall or column under consideration.hef or lef

tef 23 Section 4 –

24.1(b) Obtain the capacity reduction factor β Slenderness ratio,

Eccentricity of loading30 Table 7

(c) Obtain the characteristic compressivestrength ƒ k of the masonry units

Brick/Block type,Shape factor,

Mortar designation

16 Table 2

(d) Material partial safety factor γm Manufacturing control,Construction control

22 Table 4(a)

(e) Calculate the vertical load resistance β , ƒ k ,γm , t, b 29,30 32.2

Ex 06: A wall has an effective height of 2.25 m and an effective thickness of 102.5 mm. The brick

strength is 15 N/mm2

and the mortar mix is 1 : 1 : 6.1.

The manufacturing control is category II and the construction controls are special.Determine:

(a)

The design strength of the wall,(b)

The loadbearing capacity of the wall.2.

Determine the loadbearing capacity of the wall, when both the manufacturing control iscategory II and construction controls is normal.

Ex 07: Determine the design compressive strength of a column, 440 mm × 440 mm, 4.4 m clearheight between concrete floors giving enhanced lateral restraint. The bricks have a compressivestrength of 35 N/mm2, and the mortar is designation (ii). The manufacturing control is category

II and construction controls is normal.

Ex 08: A 102.5 mm thick single skin brick wall, as shown in Figure, is built between the concretefloors of a multi-storey building. It supports an ultimate axial load, including an allowance forthe self-weight, of 250 kN per metre run. What brick and mortar strengths are required ifcategory II manufacturing and normal construction control apply and the wall is first 10 m longand secondly only 1 m long?


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Ex 09: The brick cavity wall shown in Figure supports an ultimate axial load of 150 kN/mshared equally by both leaves. Select suitable bricks and mortar if both the manufacturing andconstruction control are to be normal.

Ex 10: The wall shown in Figure is built of 50 N/mm2 clay bricks set in grade (i) mortar.Calculate the vertical design strength of the wall if it is 2.4 m high and is provided with simplelateral support at the top. The category of manufacturing control is to be category II and that forconstruction is special.


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2.10 Eccentric Loading

When considering a member subject to compressive loading, it is unlikely that the loading willever be truly applied concentrically. In most instances, the load will be applied at someeccentricity to the centroid of the member, whether due to construction tolerances, varyingimposed loads on adjacent floor spans or other causes.

Eccentricity of single slab bearing onto wall:The most common cause is bending in thebeam or floor or roof being supported. Thatis, as if a triangular stress distribution isassumed under the bearing

Eccentricity of continuous slab bearing ontowall:Where a uniform floor is continuous over awall, the Code recommends that each span ofthe floor should be taken as being supportedindividually, on half the total bearing area

Eccentricity of single timber joist supportedin joist holder:Where joist hangers are used, the load should

be assumed to be applied at the face of thewall.

Ex 11: The brick cavity wall shown in Figure supports an ultimateload on the inner leaf of 75 kN/m, the outer leaf being unloaded.Select suitable bricks and mortar if both the manufacturing and

construction control are to be normal.


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Additional eccentricity due to slenderness

The eccentricity is assumed to vary from the value ex at the top of the wall to zero at thebottom of the wall, subject to an additional eccentricity being considered to coverslenderness effects.

No slenderness effect need be considered for walls or columns where the slendernessratio is less than or equal to 6.

The additional eccentricity may be assumed to vary linearly from zero at top and bottomof the wall, to a value ea over the central fifth of the wall height where ea is given by:

t is the thickness of the wall (or depth of column);tef is the effective thickness of the wall or column;hef is the effective height of the wall or column.

ex Eccentricity is calculated as: max

0.6 ex + ea

2. masonry design - compression

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