# Principles of Masonry Design

### Principles of Masonry Design.

Introduction

This page includes some notes on the design of masonry walls based on the principles as specified in BS EN 1996 part 1 2005.     The notes allow initial estimates of the design requirements sufficient for initial studies to be completed .    For detail design the relevant standards must be used.

The notes below include a large number of safety margins, design factors and tables and very few actual design equations.    In principle a simple masonry built construction is based on a number of walls supporting floors and roof constructions. The walls are transferring the structure loads to the foundations and are primarily under compression.    Masonry walls have poor strength is bending shear and torsion.    To increase the resistance of the walls to bending, shear and torsion, support is provided by piers , intersecting walls and intersecting floors.    Masonry walls are also strengthened using reinforcement.

Strictly for each masonry element it is necessary to calculate

Axial loads resulting from vertical and horizontal actions
Shear loads resulting from vertical and/or horizontal actions
Bending moments due to vertical and/or lateral actions
Torsional moments.

For each wall the design strength values for the material shall be obtained by dividing the characteristic values by the appropriate safety margin γ m.     These design value shall be used to obtain the Ultimate Limit design and serviceability limit for the building elements for operation and serviceability.

The design should ensure that under all operating conditions the stress conditions cannot exceed the Ultimate limit and Serviceability limit .

Relevant Standards

BS EN 1996-1-2 : 2005 .. Eurocode 6. Design of masonry structures. General rules. Structural fire design and structures..
BS EN 1996-2 : 2006... Eurocode 6. Design of masonry structures. Design considerations, selection of materials and execution of masonry
BS EN 1996-3 : 2006... Eurocode 6. Design of masonry structures. Simplified calculation methods for unreinforced masonry structures

Symbols
 t = Actual wall thickness (mm) t 1= Actual wall thickness one leaf of cavity wall (mm) t 2= Actual wall thickness second leaf of cavity wall (mm) tef = Effective wall thickness (mm) A' s = Area of Compression reinforcement b = width or effective width of section b w = average width of web. α =the bending moment coefficient. μ = the orthogonal ratio; γ f = Partial safety factor for load γ m = Partial safety factor for material strength σd = design compressive stresses E n = Characteristic Earth Load G k = Characteristic dead Load Q k = Characteristic imposed Load W k = Characteristic Wind Load f b = Normalised compressive strength of masonry units f k = Characteristic strength of masonry f m = Compressive strength of mortar fd = design compressive strength of masonry f cu = Characteristic strength of concrete f y = Characteristic strength of reinforcement Wk =is the characteristic wind load per unit area.

Category of masonry units

The design shall include the categorisation of the masonry units into category I or category II. A category I unit is a higher quality unit with guaranteed properties defined BS EN 771 1-6, and requires third party certification and monitoring of the production control system.    A category II unit is simply one that is not a category I grade.

Grouping of masonry units

The relevant standard includes a table grouping masonry units on the basis of volumes of holes as a percentage of the gross volume and the thickness of the webs and shells.    There are four groups . Group 1 has the lowest % of holes and lowest shell/web thickness and group 4 the highest.   Information on the group 1 values are provided below

Group 1
Volume of all holes =< 25%
Volume of any hole =< 12,5%
Value of thickness of webs/shells (mm) no requirement
Value of thickness of webs/shells (% of o/all thickness) -no requirement

Group 2

 Criteria Clay Calcium Silicate Concrete Volume of all holes (%of gross) > 25:=< 55 > 25:=< 55 > 25:=< 60 Volume of any hole (%of gross) Each of multiple holes = < 2 grip holes up to a total of 12,5 Each of multiple holes = < 15 grip holes up to a total of 30 Each of multiple holes = < 30 grip holes up to a total of 30 Declared value of thickness of webs and shells (mm) web >= 5 shell > = 8 web >= 5 shell > = 10 web >=15 shell > = 18 Declared value of combined thickness of webs and shells (% of overall width) > = 16 > = 20 > = 18

Group 3

 Criteria Clay Calcium Silicate Concrete Volume of all holes (%of gross) > 25:=< 70 not used > 25:=< 70 Volume of any hole (%of gross) Each of multiple holes = < 2 grip holes up to a total of 12,5 not used Each of multiple holes = < 30 grip holes up to a total of 30 Declared value of thickness of webs and shells (mm) web >= 3 shell > = 6 not used web >=15 shell > = 15 Declared value of combined thickness of webs and shells (% of overall width) > = 12 > Not used > = 15

Group 4

 Criteria Clay Calcium Silicate Concrete Volume of all holes (%of gross) > 25:=< 70 not used > 25:=< 50 Volume of any hole (%of gross) Each of multiple holes = < 30 not used Each of multiple holes = < 25 Declared value of thickness of webs and shells (mm) web >= 5 shell > = 6 not used web >=20 shell > = 20 Declared value of combined thickness of webs and shells (% of overall width) > = 12 > Not used > = 45

Notes:
1. Holes may consist of formed vertical holes through the unit or frogs or recesses.
2. If there is national experience, based on tests, that confirms that the safety of the masonry is not reduced unacceptably when a higher proportion of holes is incorporated, the limit of 55% for clay units and 60% for concrete aggregate units may be increased for masonry units that are used in the country with national experience.
3.The combined thickness is the thickness of webs and shells, measured horizontally across the unit at right angles to the face of the wall

Characteristic strength of masonry

When test data for obtaining the characteristic strength fk is not available, then the approximate characteristic strength of plain masonry made with general purpose mortar may be calculated using the equation

fk = K *( fb 0.70 )*( f m0.30 ) [MPa]

when f m less than 20 MPa or 2.f b, whichever is the smaller and f b is less than 75 MPa

The value of constant K depends on the classification of masonry units into groups.    Following is a basic list providing a extract of table in the relevant standard listing K values against mortar type and masonry group. The list below simply provides the values of K related to group 1 and for general purpose mortar.

Clay bricks 1 K = 0,55
Calcium Silicate bricks K =0,55
Aggregate concrete blocks K = 0,55
Autoclaved Aerated concrete K= 0,55
Manufactured stone K= 0,45
Dimensioned natural stone K= 0,45

Note: The equations above provide an edited extract of the range of groups and relationships listed in the relevant code BS EN 1996. For other grades of mortar the indices in the equation are different

Table of characteristic compressive strength of masonry, fk, in N/mm2

 Constructed with standard format bricks of clay and calcium silicate having no more than 25% of formed voids, or 20% frogs Mortar strengthClass/Designation Compressive strength of unit (N/mm2) 5 10 15 20 30 40 50 75 100 125 150 M12 / (i) 2.5 4.0 5.3 6.4 8.3 10.0 11.6 15.2 18.3 21.2 23.9 M6 / (ii) 2.5 3.8 4.8 5.6 7.1 8.4 9.5 12.0 14.2 16.1 17.9 M4 / (iii) 2.5 3.4 4.3 5.0 6.3 7.4 8.4 10.5 12.3 14.0 15.4 M2 / (iv) 2.2 2.8 3.6 4.1 5.1 6.1 7.1 9.0 10.5 11.6 12.7

Modulus of Elasticity of masonry

The short term modulus of elasticity E, is properly obtained my tests in accordance with the relevant code BS EN 1052-1.

In absence of this information E can be taken as 1000. fk unless the local national codes provides other recommendations.     The long term E value is affected by creep such that Elt = E / (1+ φinf ).    φinf being the creep coefficient (This can vary from 0,5 to 2 ).

Partial Safety margins related to Ultimate limit state design

When using the design relationship for the ultimate limit the design load is taken as the sum of the products of the component characteristic loads multiplied by the most severe of the relevant partial safety factor.

Normalised mean compressive strength of masonry unit fb, in N/mm2

The mean value determined by testing of at least ten equivalent, air dried, 100 mm by 100 mm specimens cut from the masonry unit.    In the case where the strength is obtained by testing full sized units, the mean value of strength is multiplied by the shape factor d, which takes into account the actual dimensions of the unit. In case the compressive strength of masonry is specified as characteristic strength, it should be first converted to the mean equivalent using a conversion factor based on the coefficient of variation, and than multiplied by the shape factor d.

In the relevant European standards (BS EN 771-1-6) are given minimum value of normalised mean compressive strength of masonry units to be used for masonry walls:

Clay units: min fb =2.5 MPa
Calcium silicate units: min fb =5.0 MPa
Concrete units: min fb=1.8 MPa
Autoclaved aerated concrete units: min fb=1.8 MPa

Characteristic flexural strength of masonry, fkx, in N/mm2

Based on BS EN 1996

 Masonry Unit Failure plane parallel to bed Failure plane perpendicular to bed Gen Pur Mortar fm < 5N/mm 2 Gen Pur Mortar fm >= 5N/mm 2< Thin Layer mortar Lightweight mortar Gen Pur Mortar fm < 5N/mm 2 Gen Pur Mortar fm >= 5N/mm 2< Thin Layer mortar Lightweight mortar fxk1 N/mm2 fxk2 N/mm2 Clay 0,1 0,1 0,15 0,10 0,2 0,40 0,15 0,10 Calcium Silicate 0,05 0,1 0,2 not used 0,20 0,40 0,30 not used Aggregate concrete 0,05 0,1 0,2 not used 0,20 0,40 0,30 not used Autoclaved Aerated concrete den <400 kg/mm2 0,05 0,1 0,15 0,10 0,20 0,20 0,20 0,15 Autoclaved Aerated concrete den >= 400 kg/mm2 0,05 0,1 0,15 0,10 0,20 0,40 0,30 0,15 Manufactured stone 0,05 0,1 not used not used 0,20 0,40 not used not used Dimension Natural stone 0,05 0,1 0,15 not used 0,20 0,40 0,15 not used

Characteristic initial shear strength , fvko, in N/mm2

Based on BS EN 1926

 Masonry unit fvko General Purpose Mortar of strength class given Thin Layer mortar Lightweight mortar Clay Mortar class M10-M20 0,3 0,3 0,15 Clay Mortar class M2,5-M9 0,2 0,3 0,15 Clay Mortar class M1,5-M1 0,1 0,3 0,15 Calcium silicate Mortar class M10-M20 0,2 0,4 0,15 Calcium silicate Mortar class M2,5-M9 0,15 0,4 0,15 Calcium silicate Mortar class M1,5-M1 0,1 0,4 0,15 Aggregate concrete blocks 0,20 0,3 0,15 Autoclaved Aerated concrete 0,15 0,3 0,15 Manufactured stone and dimensioned natural stone 0,1 0,3 0,15

Characteristic shear strength of masonry

The characteristic shear strength of masonry fvk is determined for tests.   However it is allowable to use the following equation if the mortar is general purpose mortar or designated thin layer mortar.

fvk = fvko +0,4.σd

Partial safety margins for materials

The design value of a material is simply obtained by dividing its characteristic value by the relevant partial factor for the material.    The partial safety margin for the compressive strength of masonry construction (general) (γ mc ) is taken as 3,5 and the partial safety margin for the flexural strength of masonry (γ mf ) is 3,0 ( From BS 5628).    These margins are based on normal methods of construction.

table showing values of γM (From BS EN 1996)

 Material γ M Class 1 2 3 4 5 Masonry units of cat I,designed mortar 1,5 1,7 2,0 2,2 2,5 Masonry units of cat I,prescribed mortar 1,7 2,0 2,2 2,5 2,7 Masonry units of cat II, any mortar 2,0 2,2 2,5 2,7 3,0 Anchorage of reinforcing steel 1,7 2,0 2,2 2,5 2,7 Reinforcement steel and prestressing steel 1,15 Ancillary components 1,7 2,0 2,2 2,5 2,7 Lintels 1,5 to 2,5

Preliminary sizing of masonry walls.

Effective height

The effective height of a load bearing wall is assessed based on the relative stiffness of the elements of the structure connected to the wall together with the efficiency of the connection.    A wall is stiffened by floors , or roofs , suitable cross walls or any similar construction element.

Walls are considered stiffened by a vertical edge of a stiffening wall if both walls are made of materials of similar mechanical properties, are evenly loaded, are erected together and are bonded together. alternatively the walls are stiffened if the connection between the walls can resist tension and compressive forces by anchors, ties or similar suitable methods.

A stiffening wall should have a length of at least 20% of the clear height and a thickness of at least 30% of the effective thickness of the stiffened wall.

Walls stiffened on two vertical edges with l >= 30t or walls stiffened on one vertical edge with l >= 15t should be treated as walls restrained only at the top and bottom.

A stiffened wall is weakened by vertical chases and/or recesses and the reduced value of wall thickness should be used for t.     If the thickness remaining after the vertical chase or recess in less than t/2 then a free edge should be assumed.

Walls with opening having a clear height of more than 1/4 of the wall clear height or length of more than 1/4 the wall clear length or and area of more than 1/10 the total wall area should considered to have a free edge at the opening.

The minimum length of a stiffening wall with openings is shown in the sketch above.

The effective height of a wall including consideration of the above factors is

hef = ρn h ...n = 1.2. of 3 depending on the edge condition or stiffening.

For walls restrained and top and bottom by concrete floors spanning from both sides with bearing of at leas 2/3 t ..ρ2 =0,75
For walls restrained,as above but with timber flows or roofs ..ρ2 =1,00
For wall restrained at the top and bottom and stiffened by one vertical edge, with one free edge

For wall restrained at the top and bottom and stiffened by two vertical edges

Effective Thickness

The effective thickness tef of a single-leaf, double leaf , a shell bedded wall and a grouted cavity wall should be taken as the actual thickness t.

The effective thickness of wall stiffened by piers is obtained from equation

tef = ρt.t

table showing values of ρt

 Ratio of pier spacing Cen-Cen to pier widthSp/Wp Ratio of pier depth to thickness of wall ( tp/t ) 1 2 2 6 1,0 1,4 2,0 10 1,0 1,2 1,4 20 1,0 1,0 1,0

The effective thickness tef of a cavity wall with both leaves connected with wall ties is

kef is factor based on relative E values of leaves t1 and t2 (must be less than 2 )

The effective thickness tef of a cavity wall with only one leaf loaded can be based on the above equation provided the wall ties are flexible

Resistance to lateral movement

Slenderness ratio

The slenderness ratio ( He/te ) should not exceed 27.    For walls less than 90mm thick in two story building or more the slenderness ratio should not exceed 20

When analysing walls subject to vertical loading . The design should include for

Second order effects eg swaying
eccentricity resulting from construction deviations.

The bending moments should be considered and an initial eccentricity einit should be allowed for the full height of the wall allowing for construction imperfections. einit may be assumed to be hef /450

Ultimate Limit State design

In calculating the vertical resistance of masonry walls it is assumed that plane section remain plane and the tensile strength of the masonry perpendicular to the bed joints is zero.

At Ultimate limit design the vertical load NED shall be less , or equal to the design value of the vertical resistance of the wall NRD i.r

NED         NRD

The design value the vertical resistance of a single leaf wall per unit length =

NRD     =  φ.t.fd

Where φ is the capacity reduction factor at the top, bottom (φi) or middle (φm) as appropriate.
t = wall thickness
fd is the design compressive strength of the masonry eg fk / γ m

Mid = design value of bending moment at the top or bottom of wall.
Nid = design value of vertical load at the top of bottom of wall
ehe = eccentricity at the top or bottom of wall ,if any, from horizontal load
einit = initial eccentricity
t = wall thickness

The reduction factor φm within the middle of the wall can be determined using the eccentricity at the middle of the wall emk which is calculated using

values of φm are obtained by using the table below and interpolating as necessary.
Note: the table has been developed using the graph in the relevant standard. The values are based on E = 1000.fk.

table showing values of φm

 emk/t hef/tef 0 5 10 15 20 25 30 0,05 0,9 0,88 0,84 0,75 0,62 0,5 0,38 0,1 0,8 0,78 0,74 0,64 0,52 0,39 0,28 0,15 0,7 0,68 0,63 0,54 0,4 0,29 0,2 0,2 0,6 0,58 0,52 0,43 0,3 0,2 0,12 0,25 0,5 0,48 0,42 0,32 0,2 0,12 0,07 0,3 0,4 0,38 0,32 0,22 0,12 0,05 0,02 0,35 0,3 0,28 0,22 0,12 0,05 0,01 0,0 0,4 0,2 0,18 0,12 0,05 0,01 0,0 0,0

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Calculation of design moments in laterly supported wall panels

An approximate method of obtaining the design moments in a wall under lateral loading is to use the following simple equations

When failure plane is perpendicular to bed joint
M = α.W k.γ f.L2 per unit height,

When failure plane is parallel to bed joint
M = μ.α.W k.γ f.L2 per unit height

 Wall arrangement μ α h/L 0,3 0,5 0,75 1,00 1,25 1,5 1,75 1,00 0,031 0,045 0,059 0,071 0,079 0,085 0,090 0,90 0,032 0,047 0,061 0,073 0,081 0,087 0,092 0,80 0,034 0,049 0,064 0,075 0,083 0,089 0,093 0,70 0,035 0,051 0,066 0,077 0,085 0,091 0,095 0,60 0,038 0,053 0,069 0,080 0,088 0,093 0,097 0,50 0,040 0,056 0,073 0,083 0,090 0,095 0,099 0,40 0,043 0,061 0,077 0,087 0,093 0,098 0,101 0,35 0,045 0,064 0,080 0,089 0,095 0,100 0,103 0,30 0,048 0,067 0,082 0,091 0,097 0,101 0,104 1,00 0,024 0,035 0,046 0,053 0,059 0,062 0,065 0,90 0,025 0,036 0,047 0,055 0,060 0,063 0,066 0,80 0,027 0,037 0,049 0,056 0,061 0,065 0,067 0,70 0,028 0,039 0,051 0,058 0,062 0,066 0,068 0,60 0,030 0,042 0,053 0,059 0,064 0,067 0,069 0,50 0,031 0,044 0,055 0,061 0,066 0,069 0,071 0,40 0,034 0,047 0,057 0,063 0,067 0,070 0,072 0,35 0,035 0,049 0,059 0,065 0,068 0,071 0,073 0,30 0,037 0,051 0,061 0,066 0,070 0,072 0,074 1,00 0,020 0,028 0,037 0,042 0,045 0,048 0,050 0,90 0,021 0,029 0,038 0,043 0,046 0,048 0,050 0,80 0,022 0,031 0,039 0,043 0,047 0,049 0,051 0,70 0,023 0,032 0,040 0,044 0,048 0,050 0,051 0,60 0,024 0,034 0,041 0,046 0,049 0,051 0,052 0,50 0,025 0,035 0,043 0,047 0,050 0,052 0,053 0,40 0,027 0,038 0,044 0,048 0,051 0,053 0,054 0,35 0,029 0,039 0,045 0,049 0,052 0,053 0,054 0,30 0,030 0,040 0,046 0,050 0,052 0,054 0,055 1,00 0,013 0,021 0,029 0,035 0,040 0,043 0,045 0,90 0,014 0,022 0,031 0,036 0,040 0,043 0,046 0,80 0,015 0,023 0,032 0,038 0,041 0,044 0,047 0,70 0,016 0,025 0,033 0,039 0,043 0,045 0,047 0,60 0,017 0,026 0,035 0,040 0,044 0,046 0,048 0,50 0,018 0,028 0,037 0,042 0,045 0,048 0,050 0,40 0,020 0,031 0,039 0,043 0,047 0,049 0,051 0,35 0,022 0,032 0,040 0,044 0,048 0,050 0,051 0,30 0,023 0,034 0,041 0,046 0,049 0,051 0,052

 Wall arrangement μ α h/L 0,3 0,5 0,75 1,00 1,25 1,5 1,75 1.00 0.008 0.018 0.030 0.042 0.051 0.059 0.066 0.90 0.009 0.019 0.032 0.044 0.054 0.062 0.068 0.80 0.010 0.021 0.035 0.046 0.056 0.064 0.071 0.70 0.011 0.023 0.037 0.049 0.059 0.067 0.073 0.60 0.012 0.025 0.040 0.053 0.062 0.070 0.076 0.50 0.014 0.028 0.044 0.057 0.066 0.074 0.080 0.40 0.017 0.032 0.049 0.062 0.071 0.078 0.084 0.35 0.018 0.035 0.052 0.064 0.074 0.081 0.086 0.30 0.020 0.038 0.055 0.068 0.077 0.083 0.089 1.00 0.008 0.016 0.026 0.034 0.041 0.046 0.051 0.90 0.008 0.017 0.027 0.036 0.042 0.048 0.052 0.80 0.009 0.018 0.029 0.037 0.044 0.049 0.054 0.70 0.010 0.020 0.031 0.039 0.046 0.051 0.055 0.60 0.011 0.022 0.033 0.042 0.048 0.053 0.057 0.50 0.013 0.024 0.036 0.044 0.051 0.056 0.059 0.40 0.015 0.027 0.039 0.048 0.054 0.058 0.062 0.35 0.016 0.029 0.041 0.050 0.055 0.060 0.063 0.30 0.018 0.031 0.044 0.052 0.057 0.062 0.065 1.00 0.007 0.014 0.022 0.028 0.033 0.037 0.040 0.90 0.008 0.015 0.023 0.029 0.034 0.038 0.041 0.80 0.008 0.016 0.024 0.031 0.035 0.039 0.042 0.70 0.009 0.017 0.026 0.032 0.037 0.040 0.043 0.60 0.010 0.019 0.028 0.034 0.038 0.042 0.044 0.50 0.011 0.021 0.030 0.036 0.040 0.043 0.046 0.40 0.013 0.023 0.032 0.038 0.042 0.045 0.047 0.35 0.014 0.025 0.033 0.039 0.043 0.046 0.048 0.30 0.016 0.026 0.035 0.041 0.044 0.047 0.049 1.00 0.005 0.011 0.018 0.024 0.029 0.033 0.036 0.90 0.006 0.012 0.019 0.025 0.030 0.034 0.037 0.80 0.006 0.013 0.020 0.027 0.032 0.035 0.038 0.70 0.007 0.014 0.022 0.028 0.033 0.037 0.040 0.60 0.008 0.015 0.024 0.030 0.035 0.038 0.041 0.50 0.009 0.017 0.025 0.032 0.036 0.040 0.043 0.40 0.010 0.019 0.028 0.034 0.039 0.042 0.045 0.35 0.011 0.021 0.029 0.036 0.040 0.043 0.046 0.30 0.013 0.022 0.031 0.037 0.041 0.044 0.047 1.00 0.004 0.009 0.015 0.021 0.026 0.030 0.033 0.90 0.004 0.010 0.016 0.022 0.027 0.031 0.034 0.80 0.005 0.010 0.017 0.023 0.028 0.032 0.035 0.70 0.005 0.011 0.019 0.025 0.030 0.033 0.037 0.60 0.006 0.013 0.020 0.026 0.031 0.035 0.038 0.50 0.007 0.014 0.022 0.028 0.033 0.037 0.040 0.40 0.008 0.016 0.024 0.031 0.035 0.039 0.042 0.35 0.009 0.017 0.026 0.032 0.037 0.040 0.043 0.30 0.010 0.019 0.028 0.034 0.038 0.042 0.044