How To Design Masonry Structures Using EC6 - Part 2 - Vertical Resistance
How To Design Masonry Structures Using EC6 - Part 2 - Vertical Resistance
How To Design Masonry Structures Using EC6 - Part 2 - Vertical Resistance
Eur Ing, Prof. J J Roberts BSc(Eng), PhD, CEng, FIStructE, FICE, FIMS, FCMI, MICT O Brooker BEng, CEng, MICE, MIStructE
Introduction
This publication is part of a series of three This guide is the second in a series of three giving guidance on the design of
guides entitled How to design masonry structures masonry structures to Eurocode 61. The first guide, Introduction to Eurocode 62
using Eurocode 6. The aim is to make the use of gives an introduction to design and assessment of actions using Eurocode 6 and
Eurocode 6, Design of masonry structures as easy also covers the specification and execution (workmanship) of masonry. This guide
as possible by drawing together in one place key explains how to design for vertical actions and determine vertical resistance. The
information and commentary required for the third guide in the series3 covers the design of laterally loaded masonry panels.
design of typical masonry elements. Throughout this guide the Nationally Determined Parameters (NDPs) from the UK
National Annexes (NAs) have been used. These enable Eurocode 6 to be applied in
The Concrete Centre (and, originally, The Modern the UK.
Masonry Alliance) recognised that effective
guidance was required to ensure that the UK
design profession was able to use Eurocode 6 Design procedure
quickly, effectively, efficiently and with confidence.
Therefore a steering group, with members from This guide explains how to determine the design resistance for a vertically loaded
across the masonry industry (see back cover for a wall. The first guide in the series, Introduction to Eurocode 6, should be referred to
list of members), was established to oversee the so that the design load can be determined. In essence, when using the Eurocodes
development and publication of the original guides. the designer should check that the resistance is greater than or equal to the
effect of the actions. A flow chart for the design of masonry walls to resist vertical
This second revision addresses the publication of actions is shown as Figure 1.
PD6697 in 2010 and revised National Annex to
BS EN 1996-1-1 in 2013. It was overseen by a
reconstituted steering group from industry (see
Compressive strength
back cover).
Eurocode 6 introduces some new concepts when dealing with the design of
masonry for vertical loads. The first of these relates to the way the compressive
strength of the masonry units is expressed. For design purposes the normalized
compressive strength, fb, of the masonry units is used. This is the compressive
strength of the units converted to the air-dried compressive strength of an
equivalent 100 mm wide by 100 mm high masonry unit. The detail is contained
in Part 1 of BS EN 772, Methods of test for masonry units4. The advantage to the
designer is that the normalized strength is independent of the size and shape of
the units used in the final construction.
The characteristic For blocks laid flat, Table 8 of the National Annex to Eurocode 6,
Part 1–1 contains a specific value for K to be used in Equation (3.1)
shell bedded masonry) is determined from the results of tests in in general purpose mortar and 50 N/mm2 when laid in thin layer
accordance with BS EN 1052–15. The tests are carried out on small mortar (fb is determined in the normal direction of loading).
wallette specimens rather than the storey-height panels used in the past. ¢¢ fm is taken to be not greater than fb nor greater than 12 N/mm2
The designer has the option of either testing the units intended to be when units are laid in general purpose mortar or 10 N/mm2 when
used in a project or using the values determined from a database. Values units are laid in lightweight mortar.
from a large database are provided in the UK NA to Eurocode 6, Part 1–1 ¢¢ The coefficient of variation of the strength of the masonry unit is
in the form of the constants to be used in the following equation: not more than 25%.
fk = K fba fmb [Equation (3.1) of Eurocode 6, Part 1–1] For masonry made with general purpose mortar, adjustments are
where made to the value of K as shown in Figure 2.
fk = characteristic compressive strength of the masonry, in N/mm2
K = constant – see Table 1 and Figure 2 In addition the following points should be noted:
¢¢ For masonry made of general purpose mortar where Group 2
a, b = constants – see Table 2
fb = normalized mean compressive strength of the units, in the and Group 3 aggregate concrete units are used with the vertical
direction of the applied action effect, in N/mm2 cavities filled completely with concrete, the value of fb should
fm = compressive strength of the mortar, in N/mm2 be obtained by considering the units to be Group 1 having a
compressive strength corresponding to the compressive strength of
the units or of the concrete infill, whichever is the lesser.
Figure 1
Flow chart for the design of masonry walls to resist vertical actions
Determine requirements
for mortar strength and
durability. See tables 5
Determine normalized
& 6 of Introduction to
compressive strength, fb.
Eurocode 6
Determine design value of
vertical actions (per unit
length), Ed, using Expression
(6.10), (6.10a) or (6.10b) of
Determine characteristic compressive strength of masonry,
Eurocode (see Introduction to
fk, from Equation (3.1) of Eurocode 6 and Tables 1 & 2
Eurocode 6)
Determine effective height, hef, Determine effective thickness, tef, Where cross-sectional area,
of the wall (see page 4) . of the wall (see page 4) A < 0.1 m2, factor fk by (0.7 + 3A)
2
2. Vertical resistance
¢¢ For collar jointed aggregate concrete masonry made with general ¢¢ When the perpendicular joints are unfilled, Equation (3.1) may be
purpose mortar, with or without the collar filled with mortar, the unit used, with consideration of any horizontal actions that might be
shape factor correction to obtain the normalized strength should use the applied to, or be transmitted by, the masonry. (See also CI. 3.6.2(4)
width of the wall as the unit width and the height of the masonry units. of BS EN 1996–1–1.)
¢¢ Where action effects are parallel to the direction of the bed joints, the
characteristic compressive strength may be determined from
Equation (3.1) with fb derived from BS EN 772–1, where the direction
of application of the load to the test specimens is in the same
The characteristic
direction as the direction of the action effect in the masonry, but with
compressive strength of
Licensed copy from CIS: univulster, University of Ulster, 18/11/2016, Uncontrolled Copy.
Table 2 Figure 3
Values to be used in Equation (3.1) Shell bedding
3
How to design masonry
masonrystructures
structuresusing
usingEurocode
Eurocode66
provided that: and have a thickness of at least 0.3 times the effective thickness of
¢¢ The width of each strip of mortar is at least 30 mm. the wall to be stiffened. When the stiffening wall contains openings,
¢¢ The thickness of the masonry wall is equal to the width or length the minimum length of wall should be as shown in Figure 4 and the
of the masonry units so that there is no longitudinal mortar joint stiffening wall should extend a distance of at least 1/5 of the storey
through all or part of the length of the wall. height beyond each opening.
¢¢ The ratio g/t is not less than 0.4
Where a wall is restrained at the top and bottom by reinforced
where
concrete floors or roofs spanning from both sides at the same level or
g = total width of the mortar strips
Licensed copy from CIS: univulster, University of Ulster, 18/11/2016, Uncontrolled Copy.
by a reinforced concrete floor spanning from one side only and having
t = the thickness of the wall.
a bearing of at least 2/3 of the thickness of the wall then:
¢¢ K is taken as above when g/t = 1.0 or half this value when g/t = 0.4.
Linear interpolation may be used for intermediate values. r2 = 0.75
Groups 2 and 3 may be designed as non-shell bedded masonry unless the eccentricity of the load at the top of the wall is greater
provided that the normalized mean compressive strength of the units than 0.25 times the thickness of the wall, in which case r2 = 1.0.
used in Equation (3.1) is obtained from tests carried out in accordance
with BS EN 772–14 for shell bedded units. Where the wall is restrained by timber floors or roofs spanning from
both sides at the same level or by a timber floor spanning from one
side having a bearing of at least 2/3 the thickness of the wall but not
Effective height less than 85 mm, then:
r2 = 1.0.
The effective height of a masonry wall is obtained by applying a factor
to the clear height of the wall such that: For walls restrained at the top and bottom and stiffened on one
hef = rn h vertical edge, use rn = the value r3 from Figure 5 and where both
where vertical edges are stiffened, use rn = the value r4 from Figure 6. Note
hef = effective height of the wall that Equations (5.6), (5.7) and (5.8) in Eurocode 6, Part 1–1 may be
h = clear storey height of the wall used as an alternative to the use of the graphs.
rn = reduction factor, where n = 2, 3 or 4, depending upon the
edge restraint or stiffening of the wall
Figure 4 Figure 5
Minimum length of stiffening wall with openings Graph showing values of r3
1.0
Stiffened wall Stiffening wall r2 = 1.0
0.9
0.8
t
Reduction factor, r3
0.7
r2 = 0.75
0.6
h h2 (window)
>h/5 h1
h2(door) 0.5
0.4
0.3
0.2
0 1 2 3 4 5
1 (h1+ h2) Ratio hef /tef
>t
5 2
4
2. Vertical resistance
of the wall (t), provided this is greater than the minimum thickness,
tmin. The value of tmin for a loadbearing wall should be taken as 90 mm Assessment of eccentricity
for a single-leaf wall and 75 mm for the leaves of a cavity wall.
When a wall is subjected to actions that result in an eccentricity at
For a cavity wall the effective thickness is determined using the right angles to the wall, Eurocode 6 requires the resistance of the wall
following equation: to be checked at the top, mid-height and bottom. The eccentricity at
top or bottom of the wall is:
tef = 3R t13 + t23 ≥ t2 Mid
ei = + ehe + einit ≥ 0.05t
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where Nid
t1 = actual thickness of the outer or unloaded leaf
where
t2 = actual thickness of the inner or loaded leaf
Mid = design value of the bending moment at the top or the
bottom of the wall resulting from eccentricity of the floor
Note that the effective thickness of the unloaded leaf should not be
load at the support
taken to be greater than the thickness of the loaded leaf and that ties
Nid = design value of the vertical load at the top or the bottom of
should be provided at a density of 2.5 per m2 or greater.
the wall
When a wall is stiffened by piers the effective thickness is enhanced by ehe = the eccentricity at the top or bottom of the wall resulting
using the following equation: from the horizontal loads
einit = initial eccentricity for construction imperfections, which
tef = rtt
may be taken as hef/450, with a sign that increases the
where absolute value of ei and em as appropriate
tef = effective thickness t = thickness of the wall
rt = coefficient obtained from Table 3
The mid-height eccentricity, emk, is:
t = thickness of the wall
emk = em + ek ≥ 0.05t
0.7
0.6
r2 = 0.75 Table 3
Stiffness coefficient, rt, for walls stiffened by piers
0.5
Ratio of pier spacing Ratio of pier thickness to actual
(centre to centre) to pier thickness of wall to which it is bonded
0.4 width 1 2 3
5
How to design masonry
masonrystructures
structuresusing
usingEurocode
Eurocode66
At the top or bottom of the wall, the reduction factor for slenderness For sections of small plan area, less than 0.1 m2, fd should be
and eccentricity is given by: multiplied by (0.7 + 3A)
e
Fi = 1 – 2 i where
t
A = loadbearing horizontal cross-sectional area of the wall in m2
where
Licensed copy from CIS: univulster, University of Ulster, 18/11/2016, Uncontrolled Copy.
Fi = reduction factor at the top or bottom of the wall In the case of a faced wall, the wall may be designed as a single-leaf
ei = eccentricity at the top or bottom of the wall wall constructed entirely of the weaker material with a longitudinal
t = thickness of the wall joint between leaves.
A method for calculating a capacity reduction factor at the mid-height A double-leaf (collar-jointed) wall may also be designed as for a
of the wall, Fm, is given in Annex G of Eurocode 6, Part 1–1, which single-leaf wall provided that the leaves are tied together adequately
simplifies the principles given in Cl. 6.1.1. This is shown graphically in and both leaves carry similar loads and the cavity does not exceed
Figure 8, which shows the corresponding capacity reduction factors for 25 mm, or it may be designed as a cavity wall with one leaf loaded.
different values of slenderness and eccentricity for an elastic modulus
1000 fk , which is the value recommended in the UK NA. In the case of cavity walls, check each leaf separately using a
slenderness ratio based on the effective thickness of the wall.
The least favourable value of Fi and Fm should be used to calculate NRd.
The design resistance of a single-leaf wall per unit length, NRd, is given where a1 Ab
by the following: b = 1 + 0.3 1.5 – 1.1
hc Aef
NRd = F tfd = e nhancement factor for load that should not be less
than 1.0 nor taken to be greater than:
where a
1.25 + 1 or 1.5, whichever is the lesser
F = capacity reduction factor allowing for the effects of 2hc
slenderness and eccentricity of loading Figure 8
Capacity reduction factor, Fm at the mid-height of the wall
Figure 7
Moments from calculation of eccentricities
Eccentricity =
1.0
0.05t
0.9
M1d 0.10t
0.8
N1d (at underside
of floor) 0.15t
Capacity reduction factor, Fm
0.7
0.20t
0.6
0.25t
h2 0.5
Nmd Mmd 0.4
0.30t
h (at mid-height
0.35t
of wall) 0.3
h2 0.40t
0.2
a) Section b) Bending moment diagram Values of Fm at the mid-height of the wall against slenderness ratio for different
eccentricities, based on E =1000 fk
6
2. Vertical resistance
VRd = f vd tl c
The enhancement factor, b, is shown graphically in Figure 9.
where
For walls built with Groups 2, 3 and 4 masonry units and when shell VRd = the design value of shear resistance of the wall
bedding is used, it is necessary to check that, locally under the bearing fvd = the design value of the shear strength of the masonry (the
of a concentrated load, the design compressive stress does not exceed characteristic shear strength divided by the partial factor
the design compressive strength of the masonry, fd (i.e. b is taken to for masonry, gM) based on the average vertical stresses over
be 1.0). the compressed part of the wall that is providing the shear
resistance
In any case, the eccentricity of the load from the centre line of the t = the thickness of the wall resisting the shear
wall should not be greater than t/4 as shown in Figure 10. lc = the length of the compressed part of the wall, ignoring any
part of the wall that is in tension
In all cases where a concentrated load is applied, the requirements
for vertical load design should be met at the mid-height of the wall
In calculating lc assume a linear distribution of the compressive stress,
below the bearings. Account should be taken of the effects of any
take into account openings, etc. and do not include any area of the
other superimposed vertical loading, particularly where concentrated
wall subjected to vertical tensile stresses.
loads are sufficiently close together for their effective lengths
to overlap.
The concentrated load needs to bear on a Group 1 unit or other solid Effect of chases
material. The length of this unit or bearing should equal the required
Eurocode 6 recognises that chases and recesses should not impair
bearing length plus a length on each side of the bearing based on
the stability of a wall and provides appropriate guidance. Further
a 60° spread of load to the base of the solid material. For an end
explanation is given in the third guide in this series, Lateral resistance3.
bearing the extra length is required on one side only.
Figure 9 Figure 10
Enhancement factor, b, concentrated load under bearings Walls subjected to concentrated load
h
1.4
2a1 = 1 + + lefm + +
hc lefm lefm
1.3
a1 = 0
a) Elevation
1.2
NEdc a NEdc
1
1.1 Ab
60o ≤ t /4
1.0 hc t
0 0.1 0.2 0.3 0.4 0.45 0.5 lefm
Ratio, Ab / Aef
t
7
2. Vertical resistance
Selected symbols
Symbol Definition Symbol Definition
A Loadbearing horizontal cross-sectional area of the wall in m2 lefm Effective length of the bearing as determined at the mid-height of the
a1 Distance from the end of the wall to the nearer edge of the loaded area wall or pier
Ab Loaded area Mid Design value of the bending moment at the top or the bottom of the
wall resulting from eccentricity of the floor load at the support
Aef Effective area of the bearing
Mmd Design value of the greatest moment at the mid-height of the wall
ehe Eccentricity of the top or bottom of the wall resulting from horizontal resulting from the moments at the top and bottom of the wall,
loads including any load applied eccentrically to the face of the wall
Licensed copy from CIS: univulster, University of Ulster, 18/11/2016, Uncontrolled Copy.
ehm Eccentricity at the middle of a wall, resulting from horizontal loads Nid Design value of the vertical load at the top or the bottom of the wall
ei Eccentricity of the wall Nmd Design value of the vertical load at the mid-height of the wall,
including any load applied eccentrically to the face of the wall.
einit Initial eccentricity
NRd Design resistance of a single-leaf wall per unit length
em Load eccentricity
NRdc Design vertical load resistance to a concentrated load
emk Eccentricity at the mid-height of the wall
t Thickness of the wall
fb Normalized mean compressive strength of a masonry unit
t1 Effective thickness of the outer or unloaded leaf
fd Design compressive strength of the masonry in the direction being
considered t2 Effective thickness of the of the inner or loaded leaf
fm Compressive strength of the mortar tef Effective thickness
fk Characteristic compressive strength of the masonry, in N/mm2 tmin Minimum thickness of loadbearing wall
fvk Characteristic shear strength of masonry VRd Design value of shear resistance of the wall
fvd Design value of the shear strength of the masonry v Notional inclination angle to the vertical
g Total of the widths of the mortar strips a and b Constants to be used with Equation (3.1) of Eurocode 6, Part 1–1
h Clear storey height of the wall b An enhancement factor for concentrated load
hc Height of the wall to the level of the load F Capacity reduction factor allowing for the effects of slenderness and
eccentricity of loading
hef Effective height of the wall
gM Partial factor for a material property
htot Total height of the structure
rn Reduction factor (depending upon the edge restraint or stiffening of
K Constant to be used with Equation (3.1) of Eurocode 6, Part 1–1 the wall, h/l and floor restraint)
lc Length of the compressed part of the wall, ignoring any part of the rt Stiffness coefficient
wall that is in tension.
References
1 BRITISH STANDARDS INSTITUTION. BS EN 1996: Eurocode 6 – Design of masonry structures. BSI (4 parts). Including their NAs.
2 ROBERTS, JJ & Brooker, O. How to design masonry structures to Eurocode 6: Introduction to Eurocode 6. The Concrete Centre, 2013.
3 ROBERTS, JJ & Brooker, O. How to design masonry structures to Eurocode 6: Lateral resistance. The Concrete Centre. 2013.
4 BRITISH STANDARDS INSTITUTION. BS EN 772–1: Methods of test for masonry units – Determination of compressive strength. BSI, 2011.
5 BRITISH STANDARDS INSTITUTION. BS EN 1052–1: Methods of test for masonry – Determination of compressive strength. BSI, 1999.
Members of the steering group for 2nd revision ¢¢ Concrete Block Association - www.cba-blocks.org.uk
Cliff Fudge, Aircrete Products Association; Charles Goodchild, The ¢¢ MPA - Mortar Industry Association - www.mortar.org.uk
Concrete Centre; Simon Hay, Brick Development Association; Andy
¢¢ MPA - The Concrete Centre - www.concretecentre.com
Littler, Concrete Block Association; John Roberts, Consultant; Guy
Thompson, The Concrete Centre.
For more information on Eurocode 6 and other questions Published by The Concrete Centre
relating to the design, use and performance of concrete units, Gillingham House, 38-44 Gillingham Street, London, SW1V 1HU
visit www.eurocode6.org Tel: +44 (0)207 963 8000 | www.concretecentre.com
Ref: TCC/03/36. ISBN 978-1-904818-57-1 All advice or information from MPA The Concrete Centre (TCC) et al is intended only for use in the UK by those who will evaluate the
significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for
First published December 2007
any loss resulting from such advice or information is accepted by TCC or their subcontractors, suppliers or advisors. Readers should note that
(in partnership with the Modern Masonry Alliance) the publications from TCC et al are subject to revision from time to time and should therefore ensure that they are in possession of the
revised January 2009 and June 2013 latest version.
8
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