MB Structural Design Compendium May16

Structural Design of Concrete and Masonry: A compendium of technical papers

Structural Design of Concrete and Masonry

Contents 4

How to calculate anchorage and lap lengths to Eurocode 2

12

Deflection – the span-to-effective-depth method and Eurocode 2

17

Fire Design of concrete columns and walls to Eurocode 2

23

Eurocode 6: Design of masonry structures for vertical loads

29

Eurocode 6: Design of masonry structures for lateral loads and other factors

34

Design of post-tensioned slabs

40

Guidance on the design of liquid-retaining structures

45

An introduction to strut-and-tie modelling

About The Concrete Centre The Concrete Centre provides material, design and construction guidance with the aim of enabling those involved in the design, use and performance of concrete and masonry to realise the potential of the material. Through funding from the cement, aggregates, ready-mixed and precast concrete sectors, The Concrete Centre is able to invest in the development of services and resources that support the design and construction of robust, sustainable, cost-effective structures throughout the built environment. Resources available for structural engineers are highlighted on the inside back cover of this document (page 51) and there is a wealth of material available at www.concretecentre.com.

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Structural Design of Concrete and Masonry

Structural Design of Concrete and Masonry This compendium includes articles that were first published in the renowned journal ‘The Structural Engineer’ following its invitation to The Concrete Centre to write a series of technical papers on structural design in concrete. The series includes topics chosen represent topical issues and respond to frequently asked questions that we receive from designers, such as guidance on anchorage and lap lengths, post-tensioning and column fire design. The compendium also includes papers on deflections, Eurocode 6, liquid retaining structures and strut-and-tie.

Acknowledgements The Concrete Centre would like to thank the authors and peer reviewers for their contribution to these technical papers including: John Roberts; RS Narayanan; Robert Vollum, Imperial College.

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Structural Design of Concrete and Masonry

How to calculate anchorage and lap lengths to Eurocode 2

This article provides guidance on how to calculate anchorage and lap lengths to Eurocode 2.

Introduction EC2 provides information about reinforcement detailing in Sections 8 and 9 of Part 1-1 (BS EN 1992-1-1)1. Section 8 provides information on the general aspects of detailing and this is where the rules for anchorage and lap lengths are given. Section 9 sets out the rules for detailing different types of elements, such as beams, slabs and columns.

In EC2, anchorage and lap lengths are proportional to the stress in the bar at the start of the anchorage or lap. Therefore, if the bar is stressed to only half its ultimate capacity, the lap or anchorage length will be half what it would have needed to be if the bar were fully stressed.

The calculation for anchorage and lap lengths is as described in EC2 and is fairly extensive. There are shortcuts to the process, the first being to use one of the tables produced by others2–4. These are based on the bar being fully stressed and the cover being 25mm or ‘normal’. These assumptions are conservative, particularly the assumption that the bar is fully stressed, as bars are normally anchored or lapped away from the points of high stress. Engineering judgement should be used when applying any of the tables to ensure that the assumptions are reasonable and not overly conservative. This article discusses how to calculate an anchorage and lap length for steel ribbed reinforcement subjected to predominantly static loading using the information in Section 8. Coated steel bars (e.g. coated with paint, epoxy or zinc) are not considered. The rules are applicable to normal buildings and bridges. An anchorage length is the length of bar required to transfer the force in the bar into the concrete. A lap length is the length required to transfer the force in one bar to another bar. Anchorage and lap lengths are both calculated slightly differently depending on whether the bar is in compression or tension. For bars in tension, the anchorage length is measured along the centreline of the bar. Figure 1 shows a tension anchorage for a bar in a pad base. The anchorage length for bars in tension can include bends and hooks (Figure 2), but bends and hooks do not contribute to compression anchorages. For a foundation, such as a pile cap or pad base, this can affect the depth of concrete that has to be provided. Most tables that have been produced in the UK for anchorage and lap lengths have been based on the assumption that the bar is fully stressed at the start of the anchorage or at the lap length. This is rarely the case, as good detailing principles put laps at locations of low stress and the area of steel provided tends to be greater than the area of steel required.

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Figure 1 Tension Anchorage

Ultimate bond stress Both anchorage and lap lengths are determined by the ultimate bond stress fbd which depends on the concrete strength and whether the anchorage or lap length is in a ‘good’ or ‘poor’ bond condition. ƒbd = 2.25η1η2ƒctd (Expression 8.2 from BS EN 1992-1-1) where: is the design tensile strength of concrete, ƒctd = αctƒctk,0,05/γC ƒctd ƒctk,0,05 is the characteristic tensile strength of concrete, ƒctk,0,05 = 0.7 × ƒctm ƒctm is the mean tensile strength of concrete, ƒctm = 0.3 × ƒck (2/3) is the characteristic cylinder strength of concrete ƒck γC is the partial safety factor for concrete (γC = 1.5 in UK National Annex5) αct is a coefficient taking account of long-term effects on the tensile strength and of unfavourable effects resulting from the way the load is applied (αct = 1.0 in UK National Annex)

Structural Design of Concrete and Masonry

≥5Ø ≥5Ø ≥5Ø ≥5Ø

≥150 ≥150 a a

90° 90° ≤ ≤a a< < 150° 150° a) Bend Bend or or ‘L’ ‘L’ bar bar a)

b) Hook Hook b)

c) Loop Loop or or ‘U’ ‘U’ bar bar c)

Source: EC2-1-1 Figure 8.1, b, c and d. Figure 2 Typical bends and hooks bent through 90o or more

Direction of concreting

Confinement of concrete results in the characteristic compression strength being greater than ƒck and is known as ƒck.c. If the concrete surrounding a steel reinforcing bar is confined, the characteristic strength of the concrete is increased and so will be the ultimate bond stress between the bar and the concrete. Increasing the ultimate bond stress will reduce the anchorage length. Concrete can be confined by external pressure, internal stresses or reinforcement.

Direction of concreting

a

250 c) h > 250 mm

a) 45º < a < 90º

Anchorage lengths

Direction of concreting Direction of concreting ≥ 300 h

h

b) h < 250 mm

d) h > 600 mm

Key ‘Good’ bond conditions

‘Poor’ bond conditions

Figure 3 ‘Good’ and ‘Poor’ bond conditions

Table 1 gives the design tensile strengths for structural concretes up to C50/60. is the coefficient relating to the bond condition and η1 η1 = 1 when the bond condition is ‘good’ and η1 = 0.7 when the bond condition is ‘poor’ It has been found by experiment that the top section of a concrete pour provides less bond capacity than the rest of the concrete and therefore the coefficient reduces in the top of a section. Figure 8.2 in BS EN 19921-1 gives the locations where the bond condition can be considered ‘poor’ (Figure 3). Any reinforcement that is vertical or in the bottom of a section can be considered to be in ‘good’ bond condition. Any horizontal reinforcement in a slab 275mm thick or thinner can be considered to be in ‘good’ bond condition. Any horizontal reinforcement in the top of a thicker slab or beam should be considered as being in ‘poor’ bond condition. η2 η2 ø

Figure 4 gives the basic design procedure for calculating the anchorage length for a bar. There are various shortcuts, such as making all α coefficients = 1, that can be made to this procedure in order to ease the design process, although this will result in a more conservative answer. Both anchorage and lap lengths are determined from the ultimate bond strength ƒbd. The basic required anchorage length lb,rqd can be calculated from: lb,rqd = (ø/4) (σsd/ƒbd) where σsd is the design stress in the bar at the position from where the anchorage is measured. If the design stress σsd is taken as the maximum allowable design stress: σsd = ƒyd = ƒyk/γs = 500/1.15 = 435MPa This number is used for most of the published anchorage and lap length tables, but the design stress in the bar is seldom the maximum allowable design stress, as bars are normally anchored and lapped away from positions of maximum stress and the As,prov is normally greater than As,req. The design anchorage length lbd is taken from the basic required anchorage length lb,rqd multiplied by up to five coefficients, α1 to α5. lbd = α1 α2 α3 α4 α5 lb,rqd ≥ lb,min where the coefficients α1 to α5 are influenced by: α1 – shape of the bar

= 1.0 for bar diameters ø ≤ 32mm = (132–ø)/100 for ø > 32mm (η2 = 0.92 for 40mm bars) is the diameter of the bar

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Structural Design of Concrete and Masonry

Figure 4: flow chart for anchorage lengths.

α1, α2, α3 and α5=1.0

Start

Determine fctd from Table 1

Is the bar in ‘good’ position?

Yes

No

No

Is the bar in compression?

η1= 0.7 α4 = 0.7

Yes

α4 = 1.0 No

η1 = 1.0 Yes Is bar diameter ø ≤ 32mm

No

Does the bar have transverse reinforcement welded to it?

η2 = (132‐ø)/100 Take lbd = lb,rqd

Yes

Determine the coefficients α1 to α5 (see Table 2)

η2 = 1.0

No Determine ultimate bond stress fbd = 2.25 η1 η2 fctd

Yes

Can lb,rqd be used as the design anchorage length lbd?

Determine As,req and As,prov where the anchorage starts

Determine ultimate design stress in bar σsd = 435 As,req / As,prov

Determine basic anchorage length lb,rqd = (ø/4) (σsd/fbd) (This can be conservatively used as the design anchorage length, lbd)

Figure 4 Flow chart for anchorage lengths

α2 – concrete cover α3 – confinement by transverse reinforcement α4 – confinement by welded transverse reinforcement α5 – confinement by transverse pressure The minimum anchorage length lb,min is: max {0.3lb,rqd; 10ø; 100mm} for a tension anchorage max {0.6lb,rqd; 10ø; 100mm} for a compression anchorage The maximum value of all the five alpha coefficients is 1.0. The minimum is never less than 0.7. The value to use is given in Table 8.2 of BS EN 19921-1. In this table there are different values for α1 and α2 for straight bars and bars called other than straight. The other shapes are bars with a bend of 90° or more in the anchorage length. Any benefit in the α coefficients from the bent bars is often negated by the effects of cover. Note that the product of α2 α3 and α5 has to be ≥ 0.7.

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To calculate the values of α1 and α2 the value of cd is needed. cd is obtained from Figure 8.3 in BS EN 1992-1-1 and shown here in Figure 5. cd is often the nominal cover to the bars. In any published anchorage tables, a conservative value for the nominal bar cover has to be assumed and 25mm is used in the Concrete Centre tables. If the cover is larger than 25mm, the anchorage length may be less than the value quoted in most published tables. For hooked or bent bars in wide elements, such as slabs or walls, cd is governed by the spacing between the bars. In Table 8.2 of BS EN 1992-1-1 anchorage length alpha coefficients are given for bars in tension and compression. The alpha values for a compression anchorage are all 1.0, the maximum value, except for α4 which is 0.7, the same as a tension anchorage. Hence, the anchorage length for a compression anchorage can always conservatively be used as the anchorage length for a bar in tension.

Structural Design of Concrete and Masonry

Yes

α1 = 1.0 α2 =1‐0.15(cd‐ø)/ø 0.7≤ α2 ≤1.0

Is the bar straight?

No

END

α1= 0.7 if cd > 3ø α1=1.0 if cd ≤ 3ø α2 =1 ‐ 0.15 (cd‐3ø)/ø 0.7≤ α2 ≤1.0

Check lbd > max{0.3lb,rqd;10ø;100mm}

lbd = α1∙α2·α3·α4∙α5·lb,rqd

Yes

α3 = 1 – Kλ 0.7≤ α3 ≤1.0

Does the bar have another bar between the surface of the concrete and itself?

Take α2·α3·α5 = 0.7 Yes

No

No Is α2∙α3∙α5 < 0.7

α3 = 1.0

Is the bar confined by transverse pressure? Yes

α5=1– 0.04p 0.7≤ α5 ≤1.0

α5=1.0

No

Alpha values for tension anchorage Alpha values for tension anchorage are provided in Table 8.2 of BS EN 1992-1-1. α1 – shape of the bar Straight bar, α1 = 1.0 There is no benefit for straight bars; α1 is the maximum value of 1.0.

Table 1: Design tensile strength, ƒctd C20/25

C25/30

C28/35

C30/37

C32/40

C35/45

C40/50

C50/60

ƒctm

2.21

2.56

2.77

2.90

3.02

3.21

3.51

4.07

ƒctk, 0.05

1.55

1.80

1.94

2.03

2.12

2.25

2.46

2.85

ƒctd

1.03

1.20

1.29

1.35

1.41

1.50

1.64

1.90

Bars other than straight, α1 = 0.7 if cd > 3ø; otherwise α1 = 1.0 If we assume that the value of cd is 25mm, then the only benefit for bars other than straight is for bars that are 8mm in diameter or less. For bars larger than 8mm, α1 = 1.0. However, for hooked or bobbed bars in wide elements, where cd is based on the spacing of the bars, α1 will be 0.7 if the spacing of the bars is equal to or greater than 7ø. α2 – concrete cover Straight bar, α2 = 1 – 0.15(cd – ø)/ø ≥ 0.7 ≤ 1.0 There is no benefit in the value of α2 for straight bars unless (cd – ø) is positive, which it will be for small diameter bars. If cd is 25mm, then there will be some benefit for bars less than 25mm in diameter, i.e. for 20mm diameter bars and smaller, α2 will be less than 1.0. Bars other than straight, α2 = 1 – 0.15(cd – 3ø)/ø ≥ 0.7 ≤ 1.0

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Structural Design of Concrete and Masonry

C1

a

a

C1

C

C

b) Bent or hooked bars cd = min (a/2, c1)

a) Straight bars cd = min (a/2, c1, c)

c) Looped bars cd = c Source: EC2-1-1, Figure 8.3.

Figure 5 Values of cd (c and c1 are taken to be cnom)

Øt,

As

Ast

As

K = 0.1

Øt,

Ast

As

K = 0.05

Øt,

Ast

K=0

Source: EC2-1-1, Figure 8.4. Figure 6 Values of K

Table 2: Anchorage and lap lengths for locations of maximum stress Reinforcement in tension, bar diameter, Ф (mm)

Bond Condition

Anchorage length, lbd

Lap length, lo

8

10

12

16

20

25

Reinforcement 32

40

in compression

Straight bars only

Good

230

320

410

600

780

1010

1300

1760

40Ф

Poor

330

450

580

850

1120

1450

1850

2510

58Ф

Other bars only

Good

320

410

490

650

810

1010

1300

1760

40Ф

Poor

460

580

700

930

1160

1450

1850

2510

58Ф

50% lapped in one location (a6=1.4)

Good

320

440

570

830

1090

1420

1810

2460

57Ф

Poor

460

630

820

1190

1560

2020

2590

3520

81Ф

Good

340

470

610

890

1170

1520

1940

2640

61Ф

Poor

490

680

870

1270

1670

2170

2770

3770

87Ф

100% lapped in one location (a6=1.5)

Notes 1) Nominal cover to all sides and distance between bars ≥2mm (i.e. α2 max{0.3α6∙lb,rqd; 15ø; 200mm}

η1 = 1.0

No

Is smaller bar diameter ø ≤ 32mm

η2 = (132-ø)/100 l0 = α1∙α2∙α3∙α5∙α6∙lb,rqd

Yes η2 = 1.0

Determine ultimate bond stress fbd = 2.25 η1 η2 fctd Take α2·α3∙α5 = 0.7

Determine As,req and As,prov where the lap starts

Yes

Determine ultimate design stress in bar σsd = 435 As,req / As,prov

Is α2·α3∙α5 < 0.7

No

Determine basic anchorage length lb,rqd = (ø/4) (σsd/fbd) α5 =1.0 Determine α6 α6 = 1.4 for 50% lapped at a section α6 = 1.5 for 100% lapped at a section

Is lb,rqd· α6 satisfactory as the lap length?

No

Is the bar confined by transverse pressure?

Yes

α5 = 1 – 0.04p 0.7≤α5≤1.0

Yes

Take l0 = lb,rqd·α6 No

α3 =1.0

Determine the coefficients α1, α2, α3 and α5 (see Table 2)

Is the bar in compression? No Yes

Is the bar straight?

α1 =1.0 α2 = 1-0.15(cd‐ø)/ø 0.7≤ α2 ≤1.0

No

Figure 9 Flow chart for lap lengths

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No

Yes

Does the bar have another bar between the surface of the concrete and itself?

α1, α2, α3 and α5=1.0 α1 = 0.7 if cd > 3ø α1 = 1.0 if cd ≤ 3ø α2 = 1‐ 0.15(cd‐3ø)/ø 0.7≤ α2 ≤1.0

α3 = 1 – Kλ 0.7≤ α3 ≤1.0 Yes

Structural Design of Concrete and Masonry

“The largest possible savings in lap and anchorage length can be obtained by considering the stress in the bar where it is lapped or anchored.” typical building structures, there is usually no need to lap bars where they are fully stressed, e.g lapping bars in the bottom of a beam or slab near mid-span. Examples where bars are fully stressed and laps are needed are in raft foundations and in long-span bridges. The wording of this clause regarding guidance on the provision of transverse reinforcement is that it should be followed rather than it must be followed. This may allow the designer some scope to use engineering judgement when detailing the transverse reinforcement, e.g increasing the lap length may reduce the amount of transverse reinforcement. All the bars in a section can be lapped at one location if the bars are in one layer. If more than one layer is required, then the laps should be staggered. A design procedure to determine a lap length is given in Figure 9 and, as can be seen in the flow chart, the initial steps are the same as for the calculation of an anchorage length. Design lap length, l0 = α1 α2 α3 α5 α6 lb,rqd ≥l0,min (Eq. 8.10 in BS EN 1992-1-1)

Recommendations The largest possible savings in lap and anchorage length can be obtained by considering the stress in the bar where it is lapped or anchored. For most locations, the old rule of thumb of lap lengths being equal to 40ø should be sufficient. For this to be the case, the engineer should use their judgement and should satisfy themselves that the lap and anchorage locations are away from locations of high stress for the bars being lapped or anchored. Where it is not possible to lap or anchor away from those areas of high stress, the lengths will need to be up to the values given in Table 2. This article presents the rules currently set out in EC2. However, there has been significant recent research which may find its way into the next revision of the Eurocode. For example, research into the effect of staggering on the strength of the lap (α6) was discussed by John Cairns in Structural Concrete (the fib journal) in 20146. In the review of the Eurocodes, the detailing rules have been the subject of 208 comments (18% of the total for EC2) and it is acknowledged that the rules need to be simplified in the next revision.

The coefficients α1, α2, and α5 are calculated in the same way as for anchorage lengths and, again, all the coefficients can be taken as = 1.0 as a simplification.

References:

α3 is calculated slightly differently. When calculating α3 for a lap length ΣAst,min = As(σsd /fyd), with As = area of one lapped bar.

1) British Standards Institution (2004) BS EN 1992-1-1:2004 Design of concrete structures. General rules and rules for buildings, London, UK: BSI

The design lap length can therefore be determined by multiplying the design anchorage length by one more alpha coefficient α6, provided α3 has been calculated for a lap rather than an anchorage.

2) Bond A. J., Brooker O., Harris A. J. et al. (2011) How to Design Concrete Structures using Eurocode 2, Camberley, UK: MPA The Concrete Centre

Minimum anchorage length, l0,min = max {0.3 α6 lb,rqd; 15ø; 200mm}

3) The Institution of Structural Engineers and the Concrete Society (2006) Standard method of detailing structural concrete: A manual for best practice. (3rd ed.), London, UK: The Institution of Structural Engineers

α6 – coefficient based on the percentage of lapped bars in one lapped section, ρ1 α6 = (ρ1/25)0.5 ≥ 1.0 ≤ 1.5

4) The Institution of Structural Engineers (2006) Manual for the design of concrete building structures to Eurocode 2, London, UK: The Institution of Structural Engineers

Design lap length, l0 = α6 lbd ≥ l0,min

where: ρ1

is the percentage of reinforcement lapped within 0.65l0 from the centre of the lap length considered

In most cases either the laps will all occur at the same location, which is 100% lapped and where α6 = 1.5, or the laps will be staggered, which is 50% lapped and where α6 = 1.4.

5) British Standards Institution (2005) NA to BS EN 1992-1-1:2004 UK National Annex to Eurocode 2. Design of concrete structures. General rules and rules for buildings, London, UK: BSI 6) Cairns J. (2014) ‘Staggered lap joints for tension reinforcement’, Structural Concrete, 15 (1), pp 45–54

For vertically cast columns, good bond conditions exist at laps.

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Deflection – the span-to-effective-depth method and EC2

The span-to-effective-depth (L/d) method is a very popular way of verifying the limit state of deformation (i.e. deflection) of concrete slabs and beams.

Introduction Essentially, the span-to-effective-depth method is a hand method based on experience, justified by various reports1,2. The L/d method also serves as a very useful and valuable hand check on computer outputs. According to Section 7.4.2 of BS EN 1992-1-13 (Eurocode 2) and fib Model Code 20104, its use “will be adequate for avoiding deflection problems in normal circumstances”. The main attraction of the method is that it avoids the need to undertake laborious calculations. While according to Eurocode 05, deflection limits should be agreed with clients, generally the limits implicit in the L/d verification of deflection of concrete structures are L/250 overall and L/500 post partitions (i.e. for deflection affecting partitions, brittle finishes, etc.). The current L/d method In simple terms, the current BS EN 1992 L/d method means verifying that: Allowable L/d = N x K x F1 x F2 x F3 ≥ actual L/d (1) where: N = basic span-to-effective-depth ratio derived for K = 1.0 from the formulae: if ρ ≤ ρ0

F1 = factor to account for flanged sections. When beff/bw = 1.0, factor F1 = 1.0. When beff/bw > 3.0, factor F1 = 0.80. For values of beff/bw between 1.0 and 3.0, interpolation may be used F2 = factor to account for brittle partitions in association with long spans. Generally F2 = 1.0 but if brittle partitions are liable to be damaged by excessive deflection, F2 should be determined as follows: a) in flat slabs in which the longer span is greater than 8.5m, F2 = 8.5/leff b) in beams and other slabs with spans in excess of 7.0m, F2 = 7.0/leff F3 = factor to account for service stress in tensile reinforcement = 310/σs. It is considered conservative to assume that 310/σs = 500As,prov/(ƒykAs,req) where: σs = tensile stress in reinforcement at mid-span (at support for cantilevers) under design load at serviceability limit state (SLS) calculated using the characteristic value of serviceability load6 F3 is restricted to ≤1.56 Notes

or if ρ > ρ0

Factors F1, F2 and F3 have been used here for convenience, they are not symbols used in BS EN 1992-1-1. According to the notes to Table NA.5 of the UK National Annex (NA)6 warnings are given that the values of K may not be appropriate when formwork is struck at an early age. L/d may not exceed 40K

N = L/d = K[11 + 1.5ƒck0.5 ρ0/(ρ – ρ’) + ƒck0.5 (ρ’ / ρ0)0.5 /12] (2b)

Basis and current issues

N = L/d = K[11 + 1.5ƒck0.5 ρ0/ρ + 3.2ƒck0.5 (ρ0 / ρ – 1)1.5] (2a)

for ρ’ = 0, N may be determined from Figure 1 where: L = span d = effective depth ƒck = characteristic compressive cylinder strength of concrete at 28 days ρ0 = fck0.5/1000 ρ = As,req/bd ρ’ = As2req/bd K = factor to account for structural system (Table 1)

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The L/d method is outlined in Eurocode 2 Commentary7. The method is based on parametric studies by Corres et al.2, rather than theory. There have been many comments relating to the soundness of the method, which is now acknowledged to have some limitations and deficiencies8,9: •

The expressions (7.16a) and (7.16b) in BS EN 1992-1-1 (Equations 2a and 2b) assume a certain ratio between total load and dead load, superimposed dead load (SDL) and imposed load (IL). It would be desirable to introduce different possibilities for these ratios in order to widen the application field of these formulae

Structural Design of Concrete and Masonry

Notes 1 For two-way spanning slabs, the check should be carried out on the basis of the shorter span. 2 This graph assumes simply supported span condition (K = 1.0). K = 1.5 for interior span condition K = 1.3 for end span condition K = 0.4 for cantilevers 3 Compression reinforcement, r’, has been taken as 0. 4 Curves based on the following expressions:

[

l 1.5 fck r 0 + 3.2 = K 11 + r d

fck

( )] 1.5 r0 –1 r

where r ≤ r 0 and

[

l 1.5 fck r 0 + = K 11 + d ( r – r ’)

fck 12

r’ r0

]

where r > r 0 .

Percentage of tension reinforcement (As,req/bd)

Figure 1 Basic span-to-effective-depth ratios, N, for K = 1, ρ’ = 0

Figure 2 Typical loading and deflection history for slab in multistorey building

Figure 3 L/d for simply supported slabs

Figure 4 L/d for simply supported slabs supporting imposed load of 2.5kN/m2

•

The expressions do not account for excess reinforcement in tension or compression. (UK practice allowed up to 100% additional reinforcement.) This parameter should be included

•

The analysis of the section to determine whether the section was cracked or not looked at the “centre span of the beam only”, and conservatively used those properties throughout

•

The expressions do not account for peak loading during construction and the cracking induced during that process (Figure 2). This parameter should also be introduced

•

The assessment of Ec,eff (effective modulus) was questionable

•

The relative humidity (RH) was taken as 70%. In the UK, RH is often taken as being 50% internally and 80% or 85% externally

•

The effects of ƒctm,ƒl (mean flexural tensile strength of concrete) were ignored in the background document, whereas the effects are very noticeable for sections with 1.5b, but to limit b’ in this expression. If h > 1.5b then b’ should be limited to 2b × 1.5b/(b + 1.5b) = 1.2b. This will give a conservative answer for the fire resistance. Example: Blade column design Assume a 600 × 200 column, fully loaded in the normal temperature design condition, designed in the UK (αcc = 0.85) with an effective length in fire of 2m (4m floor-to-floor height). μfi = 0.7 as the column is fully loaded ➝ Rηfi = 83(1–μfi) = 24.9 Axis distance a = 25mm cover + 10mm link + 8mm (H16 bar) = 43mm ➝ Ra = 1.6(a–30) = 20.8 l0,fi = 2m ➝ Rl = 9.6(5–l0,fi) = 28.8 b’ is kept to 1.2b = 240mm ➝ Rb = 0.09b’ = 21.6 Rn = 12 as there are more than four bars in the column R = 120 ((Rηfi + Ra + Rl + Rb + Rn)/120)1.8 R = 120((24.9 + 20.8 + 28.8 + 21.6 + 12)/120)1.8 = 99min Columns: Method B Method B provides a more comprehensive method for the design of columns in that the restrictions on eccentricity of the first order moments are less onerous. For most columns Table 5.2b willJenny be Burridge adequate, but there are tables in Annex C of EC2 which give Concrete more & Fire Version 1 options where the limitations of Table 5.2b are exceeded. Chap 7 Fig 7.8

x

x

xbfifcd,fi (20)

Fs = As fscd,fi (

m

)

As’ z

dfi

z

z

As

As1fsd,fi (

m)

Fs = As2fsd,fi (

m)

bfi

Mu = Mu1 + Mu2 As = As1 + As2

Figure 3 Stress distribution at ultimate limit state for rectangular concrete cross-section with compression reinforcement

The restrictions on the use of Table 5.2b are that: • the slenderness of the column under fire conditions should be λfi = l0,fi / i ≤ 30, where i is the minimum radius of inertia • the first order eccentricity under fire conditions should satisfy the limit: e = M0Ed,fi / N0Ed,fi ≤ emax, where emax = 100mm, e/b ≤ 0.25 and b = minimum column dimension The load level at normal temperature conditions, n, is used in the determination of the minimum values (Table 3). n = N0Ed,fi / [0.7(Ac ƒcd + As ƒyd)] Note that in the table the mechanical reinforcement ratio, ω, is one of the required parameters: ω = ASƒyd / Ac ƒcd In BS EN 1992-1-1, a conservative value in the determination of limiting slenderness for the column takes ω = 0.1. For a class C30/37 concrete, this represents approximately 0.4% reinforcement, whereas when ω = 1.0, the column would require approximately 4% reinforcement. Walls Tabulated data for load-bearing walls are given in Table 5.4 of BS EN 1992-1-2 (Table 4). The degree of utilisation μfi is the same as that for Method A for columns. Another restriction is that: clear wall height

wall thickness Amendments 24.02.09, 26.02.09, 29.06.09, 13.11.09

≤ 40

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Structural Design of Concrete and Masonry

Simplified calculation methods 500°C isotherm method In the isotherm method, concrete at a temperature above 500°C is neglected in the calculation of section resistance, while concrete at or below 500°C is assumed to retain its full, ambient temperature strength. In BS EN 1992-1-2 the method is illustrated with reference to rectangular sections. Thus, the calculation process is to first check that the section meets the minimum cross-sectional width requirements in Table 5.

Wall

kc (

The rounded corners of the residual section reflect the real profile of the isotherm and may be approximated to a rectangle (Figure 2); some interpretation may be required.

m1)

a z1

a z1

a z1 a z1 a z1

W1

If the minimum requirements are met, the area not damaged by heat, i.e. within the 500°C isotherm, is determined to give a reduced section size (bfi, dfi) where the concrete retains its original properties. All the reinforcement can be taken as acting with the section, including the reinforcement in the zone outside the 500°C isotherm, but the strength of the bars is reduced. The strength can be taken from Figure 4.2a of BS EN 1992-1-2. While the temperature gradient through a section denoted by isotherms may be determined from testing, BS EN 1992-1-2 provides temperature profiles for a number of typical member types and cross-sections in Annex A.

Wall end

M1

W1

W1

W1

Column kc (

m1)

a z1 a z1

a z1 W1

W1

Figure 4 Reduction of cross-section when using zone method

The section resistance may then be determined using conventional calculation methods (Figure 3) and compared against the design load in the fire situation in this figure, where:

Table 2: Minimum column dimensions and axis distances for square and circular columns Load level at normal temperature conditions (n) 0.15

0.3

0.5

0.7

Reinforcement ratio

Fire resistance period (minutes) R 30

R 60

R 90

R 120

R 180

R 240

0.1%

150/25

150/30 200/25

200/40 250/25

250/50 350/25

400/50 500/25

500/60 550/25

0.5%

150/25

150/25

150/35 200/25

200/45 300/25

300/45 450/25

450/45 500/25

1.0%

150/25

150/25

200/25

200/40 250/25

300/35 400/25

400/45 500/25

0.1%

150/25

200/40 300/25

300/40 400/25

400/50 550/25

500/60 550/25

550/40 600/25

0.5%

150/25

150/35 200/25

200/45 300/25

300/45 550/25

450/50 600/25

550/55 600/25

1.0%

150/25

150/30 200/25

200/40 300/25

250/50 400/25

450/50 550/25

500/40 600/30

0.1%

200/30 250/25

300/40 500/25

500/50 550/25

550/25

550/60 600/30

600/75

0.5%

150/25

250/35 350/25

300/45 550/25

450/50 600/25

500/60 600/50

600/70

1.0%

150/25

250/40 400/25

250/40 550/25

450/45 600/30

500/60 600/45

600/60

0.1%

300/30 350/25

500/25

550/40 600/25

550/60 600/45

>600

>600

0.5%

200/30 250/25

350/40 550/25

500/50 600/40

500/60 600/50

600/75

>600

1.0%

200/30 300/25

300/50 600/30

500/50 600/45

600/60

>600

>600

20 I www.concretecentre.com

Jenny Burridge Concrete & Fire Version 1 Chap 7 Fig 7.9 05.09.08 Amendments

ge ire

.12

Structural Design of Concrete and Masonry

80 70

1.0

FRR

60

240 min

0.8

50

FRR 30 min

120 min 30

90 min

k c ( m )

az

180 min 40

0.6

0.4 20 10 0 0

90 min 120 min

60 min 30 min

60 min

0.2 180 min 240 min

50

100

150 w (mm)

200

250

300

0 0

50

100

150

200

250

w (mm)

Figure 5 Fire damaged zone az

Figure 6 Reduction of compression strength

Table 4: Tabulated data for load-bearing walls Exposed condition

One side exposed

Both sides exposed

Load level μfi

Fire resistance period (minutes) REI 30

REI 60

REI 90

REI 120

REI 180

0.35

100/10*

110/10*

120/20*

150/25

180/40

REI 240 230/55

0.7

120/10*

130/10*

140/25

160/35

210/50

270/60

0.35

120/10*

120/10*

140/10*

160/25

200/45

250/55

0.7

120/10*

140/10*

170/25

220/35

270/55

350/60

Note * Normally the cover required by BE EN 1992-1-1 will control Design notes according to 5.4.2 of BS EN 1992-1-2: A. The tabular data can be used for plain concrete walls B. For calcareous aggregates, the minimum wall thickness can be reduced by 10% C. To prevent excessive thermal deformation and subsequent integrity failure between wall and slab, the ratio of clear wall height to wall thickness should not exceed 40

bfi =

width of reduced cross-section

dfi =

effective depth of reduced cross-section

z=

lever arm between tension reinforcement and concrete

z’ =

lever arm between tension and compression reinforcement

As =

area of tension reinforcement

As1 =

part of tension reinforcement in equilibrium with concrete compression block

As2 =

part of tension reinforcement in equilibrium with compression reinforcement

As’ =

area of compression reinforcement

ƒscd,fi(θm) = design value of compression reinforcement strength in the fire situation at mean temperature θm in that layer

Jenny Burridge

ƒcd,fi(20) = design value of compression strength concrete Concretein&the Firefire situation at normal temperature = ƒck/γc,fi Version 1 Chap 7 Fig 7.11 08.09.08

ƒsd,fi(θm) = design value of tension reinforcement strength in the fire Amendments situation at mean temperature θm in that 09.02.09, layer 24.02.09

total force in compression reinforcement in the fire situation, Fs = and is equal to part of the total force in the tension reinforcement For UK design: λ = 0.8 for fck ≤ 50MPa, or λ = 0.8 – (fck – 50)/400 for 50 < fck ≤ 90MPa, η = 1.0 for fck ≤ 50MPa, or η = 1.0 – (fck – 50)/200 for 50 < fck ≤ 90MPa, x is as defined for normal temperature design and γc,fi = 1.0. Zone method In the zone method, the cross-section is divided up into several zones which are ascribed different temperatures. The strength of each zone is assessed and the strengths are aggregated to give an assessment of the strength of the whole section. The zone method is more accurate than the 500°C isotherm method, but is more complicated. The design procedure for the zone method can be summarised as follows:

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Structural Design of Concrete and Masonry

Table 5: Minimum cross-sectional width of columns or walls Fire resistance

R 60

R 90

R 120

R 180

R 240

Minimum width of crosssection (mm)

90

120

160

200

280

References: 1) British Standards Institution (2010) BS EN 1992-1-2:2004 Eurocode 2. Design of concrete structures. General rules. Structural fire design, London, UK: BSI

1. The cross-section is divided into three or more parallel zones of equal thickness.

2) British Standards Institution (2014) BS EN 1992-1-1:2004 Eurocode 2: Design of concrete structures. General rules and rules for buildings, London, UK: BSI

2. The corresponding mean temperature of each of the zones is checked, using the temperature graphs in BS EN 1992-1-2 AnnexA, and the corresponding concrete compressive strength fcd(θ) and elastic modulus (if applicable) of each zone is calculated.

3) British Standards Institution (2010) PD 6687-1:2010 Background paper to the National Annexes to BS EN 1992-1 and BS EN 1992-3, London, UK: BSI

3. The fire-damaged zone az (Figures 4 and 5) is calculated; this will be ignored in the strength and stiff ness calculation. When calculating the fire-damaged zone, the width w is taken as either the thickness of a wall or column that is exposed on one side, half the thickness of a two-sided exposed wall or column, or half the smallest dimension of a four-sided exposed column. 4. All the reinforcement, including that in the fire-damaged zone, can be taken into account in the analysis of the section, but with a reduced strength calculated using Figure 4.2a of BS EN 1992-1-2. 5. The load-bearing capacity and stiffness are determined based on the reduced cross-section and strength (Figure 6), using normal temperature design procedures.

4) British Standards Institution (2010) BS EN 1990:2002+A1:2005 Eurocode. Basis of structural design, London, UK: BSI 5) British Standards Institution (2009) NA to BS EN 1992-1-1:2004 UK National Annex to Eurocode 2. Design of concrete structures. General rules and rules for buildings, London, UK, BSI Further reading The Concrete Centre (2011) How to design concrete structures using Eurocode 2, Camberley, UK: MPA The Concrete Centre Bailey C. G. and Khoury G. A. (2011) Performance of concrete structures in fire, Camberley, UK: MPA The Concrete Centre

The impact of a major fire at Tytherington County High School, Cheshire was limited due to the fire resistance of the concrete structure.

22 I www.concretecentre.com

Concrete Design Guide

Structural Design of Concrete and Masonry

No. Eurocode 2: Eurocode6:6:Design Design of ofmasonry masonry structures for vertical loads

structures for vertical loads

This series is produced by The Concrete Centre to enable designers to realise the potential of concrete. The Concrete Centre, part of the Mineral Products Association (MPA), is a team of qualified professionals with expertise in concrete construction, engineering and architecture. www.concretecentre.com

roduction

BS EN 1996-2 and encompasses usefulof masonry, associated test methods. ight seem strange that a series on Thethe design whether blockwork or brickwork, design information previously contained The standards supporting EC6 were crete design should include articles is coveredinin Eurocode 6. BS 562810–12, which does not conflict with the developed within a common framework but it out masonry design. However, much did not prove possible to standardise all the sonry design in the UK uses concrete principles contained in EC6. test methods used by the different materials EC6 has been developed to enable cks, made by members of the Concrete from whichand masonry units are made.from Words the designer to use the following types ck Association, which is affiliated to the Introduction units are made. Words like ‘brick’ ‘block’ have disappeared the and ‘block’ have disappeared of masonry unit: clay, calcium silicate, eral Products Association. European vocabularylike and‘brick’ they are all referred to as masonry units. from BS(Eurocode EN 1996 (Eurocode 6) covers of masonryconcrete, for buildings and the European vocabulary and they are all aggregate autoclaved aerated BS EN 1996 6) covers the the design civil engineering worksand andcivil is organised into four parts. In common with Newstone methods were introduced foras determining compressive referred to masonry the units. concrete (aircrete), manufactured ign of masonry for buildings 1 the other material Eurocodes, Part 1-1 covers the structural design rules strength of masonry units and the method of determining New methods were introducedthe for and natural stone. European Standards for gineering works and is organised into four and Part 1-2the covers structural fire design2.these Thereafter, there ishave somebeen published characteristic strengththe of masonry changed from testing determining compressive strength materials by thecompressive ts. In common with other material divergence fromthe other Eurocodes in that Part covers aspects to masonry much smaller masonry wallette specimens. units and the method of BSI 2and form part of ofdesign, an array ofstorey-height standards panelsof ocodes, Part 1-1 covers structural 3 materials while Part 3 relating looks after German need determining the characteristic compressive tothe masonry-related products and the ign rules1 and Partand 1-2workmanship covers structural for simplifiedthere calculation methods4. Masonry bridges are not covered design2. Thereafter, is some by EC6. Each part has a corresponding UK national annex5–8. ergence from other Eurocodes in that

t 2 coversBS aspects of design, EN 1996-1-1 was firstmaterials published in 2005 along with BS EN 1996-1-2. 3 workmanship while Part 3 looks after BS EN 1996-2 and 1996-3 were published in 2006. The corresponding Figure 1 German need for simplifi ed calculation National Annexes bear the same dates. Corrigenda were issued Modifi cations to K for units 4 thods . Masonry bridges covered with generalwas purpose mortar to Part 1-1 in 2006are andnot 2009, and in 2012 laid a new version published EC6. Eachincorporating part has a corresponding UK the 2012 changes to BS EN 1996Amendment 1. While 5–8 onal annex . relatively small, the opportunity was taken to update the 1-1 are BS EN 1996-1-1 was firstUK published in corresponding National Annex based on feedback from use and 05 along with BS EN 1996-1-2. recalibration of some ofBS the EN outcomes. The discussion and observations 6-2 and 1996-3 were in 2006. that follow arepublished therefore related to the 2012 version of the UK National e corresponding National Annexes Annex to BS EN 1996-1-1. bear same dates. Corrigenda were issued A further Standards Institution (BSI) publication, PD 66979, Part 1-1 in 2006 andBritish 2009, and in 2012 published in 2010. This covers recommendations for the design ew versionwas was published incorporating masonry to BS EN 1996-1-1 and BS EN 1996-2 and endment 1.ofWhile thestructures 2012 changes encompasses the useful design information previously contained BS EN 1996-1-1 are relatively small, 10–12 in BS 5628 , which does opportunity was taken to updatenot theconflict with the principles contained in UK EC6.National Annex based responding

E

feedback from use and recalibration EC6 has been developed to enable the designer to use the following ome of the outcomes. The discussion types of masonry unit: clay, calcium silicate, aggregate concrete, observations that follow therefore autoclaved aeratedare concrete (aircrete), manufactured stone and natural ted to thestone. 2012European version of the UKfor these materials have been published Standards ional Annex to BS by the BSI EN and 1996-1-1. form part of an array of standards relating to masonryA further British Standards Institution (BSI)test methods. related products and the associated blication, PD 66979, was published in 2010. The standards supporting EC6design were developed within a common s covers recommendations for the framework to butBS it did prove possible masonry structures ENnot 1996-1-1 and to standardise all the test methods used by the different materials from which masonry

Concrete v3.indd 38

Figure 1 Modifications to K for units laid with general purpose mortar

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Structural Design of Concrete and Masonry

Ancillary components are dealt with in a coherent way within the standards and in BS EN 1996-1-1 suitable values of partial factors have been introduced. The partial factors for use with masonry are given in National Annex Table NA.1 and shown here in Table 1. Two levels of attestation of conformity are recognised: Category I and Category II. This forms part of the declaration made by the manufacturer of the masonry units. Two classes of execution control are also recognised: 1 and 2. Vertical load design Strength During the drafting of EC6, a way had to be found to deal with the wide range of masonry units used across Europe. This range not only includes different materials such as clay, concrete and stone, but also a variety of configurations based upon the proportion and direction of any holes or perforations, web thickness etc. This has resulted in four groupings of masonry units according to the percentage size and orientation of holes in the units when laid. The UK only has experience of Group 1 and Group 2 masonry units, but no doubt Group 3 and Group 4 units will find their way to the UK. In the UK National Annex, information is only provided for Group 1 and Group 2 units because of this lack of a UK national database for Groups 3 and 4. Properties for Groups 3 and 4 would normally be established by testing. Two levels of quality assurance for the manufacture of masonry units are specified:

Table 1: Value of partial factors for materials for ultimate limit states Material

When in a state of direct of flexural compression Unreinforced masonry made with: Units of category I

2.3†

2.7†

Units of category II

2.6†

3.0†

Reinforced masonry made with mortar M6 or M12: Units of category I

2.0†

_‡

Units of category II

2.3†

_‡

2.3†

2.7†

2.0†

2.4†

2.5†

2.5†

When in a state of flexural tension Units of category I and II but in laterally loaded wall panels when removal of the panel would not affect the overall stability of the building When in a state of shear Unreinforced masonry made with: Units of category I and II

Reinforced masonry made with mortar M6 or M12:

Category I masonry units, which have a declared compressive strength with a probability of failure to reach it not exceeding 5%

Units of category I and II

•

Category II masonry units, which are not intended to comply with the level of confidence of Category I units

The characteristic compressive strength of masonry is presented in BS EN 1996-1-1 as Equation 3.1. This equation includes the normalised strength of the masonry unit ƒb and the strength of the mortar ƒm. The UK National Annex places limits on the use of this equation for general purpose mortar as follows: •

ƒb is not to be taken to be greater than 110N/mm2

•

ƒm is not to be taken to be greater than ƒb or 12N/mm2

•

the coefficient of variation of the strength of the masonry units is not more than 25%

2*

Masonry

•

In addition the UK National Annex requires that the coefficient of variation for the compressive strength of masonry units should not exceed 25%.

Class of execution control γM 1*

2.0†

_‡

Anchorage of reinforcing steel

1.5§

_‡

Reinforcing steel and prestressing steel

2.0§

_‡

Ancillary components – wall ties

3.0†

3.0†

Ancillary components – straps

1.5**

1.5**

See NA to BS EN 845-2

See NA to BS EN 845-2

Steel and other components

Lintels in accordance with EN 845-213

* Class 1 of execution control should be assumed whenever the work is carried out following the recommendations for workmanship in BS EN 1996–2, including appropriate supervision and inspection, and in addition: i) the specification, supervision and control ensure that the construction is compatible with the use of the appropriate partial safety factors given in BS EN 1996–1–1 ii) the mortar conforms to BS EN 998-2, if it is factory made mortar. If the mortar is site mixed, preliminary compressive strength tests, in accordance with BS EN 1015-2 and 1015-11, are carried on the mixture of sand, lime (if any) and cement that is intended to be used (the proportions given in Table NA.2 may be used initially for the tests) in order to confirm that the strength requirements of the specification can be met; the proportions may need to be changed to achieve the required strengths and the new proportions are then to be used for the work on site. Regular compressive strength testing is carried out on samples from the site mortar to check that the required strengths are being achieved.

Class 2 of execution control should be assumed whenever the work is carried out following the recommendations for workmanship in BS EN 1996–2, including appropriate supervision. †

When considering the effects of misuse or accident these values may be halved.

Class 2 of execution control is not considered appropriate for reinforced masonry and should not be used. However, masonry wall panels reinforced with bed joint reinforcement used: i) to enhance the lateral strength of the masonry panel or ii) to limit or control shrinkage or expansion of the masonry can be considered to be unreinforced masonry for the purpose of class of execution control and the unreinforced masonry direct or flexural compression γM values are appropriate for use.

‡

§

When considering the effects of misuse or accident these values should be taken as 1.0.

For horizontal restraint straps, unless otherwise specified, the declared ultimate load capacity depends on there being a design compressive stress in the masonry of at least 0.4N/mm2. When a lower stress due to design loads may be acting, for example when autoclaved aerated concrete or lightweight aggregate concrete masonry is used, the manufacturer’s advice should be sought and a partial safety factor of 3 should be used. **

24 I www.concretecentre.com

Structural Design of Concrete and Masonry

› Number 2

40

TheStructuralEngineer February 2015

Technical Concrete design

E

Figure 2 Wall stiffened by piers

Figure 2 Wall stiffened by piers

Table 2: Values of K to be used with Equation 3.1 Masonry unit

General purpose mortar

Thin layer Lightweight mortar of density ρd (kg/m3) mortar (bed joint ≥0.5mm and Table 2: Values of K to be used with Equation 3.1 ≤3mm) Masonry unit

General purpose mortar

Clay Group 1

0.50

Thin layer 600≤ Lightweight of density ρd ρd ≤800 mortar800< ρd ≤1300 mortar (bed (kg/m3) joint ≥0.5mm 600≤ ρd ≤800 800< ρd ≤1300 and ≤3mm)

0.75

0.30

0.40

Clay

Group Group 2 1 Group 2

Group 3 and 4

0.40 –*

Group 3 and 4

0.50

0.70 0.75

0.25 0.30

0.40 0.30

0.40

0.70

0.25

0.30

–*

–*

–*

–*

–*

–*

–*

0.50

Group 2

Group 2

0.50

0.80 0.80

––†*

–*

0.40

0.70

–

–

0.40

0.70

Aggregate concrete

*

–†

*

–†

–†

Group 1

0.75

0.90

0.45

0.45

Group 1‡ (units

0.50§

0.70§

0.40§

0.40§

Aggregate concrete Group 1

laid flat)

0.75

Group 2

0.50§ Group 1‡ (units laid flat) Group 3 and 4

0.70

Group 1

–*

0.70§

–*

Group Autoclaved 2 0.70 aerated concrete Group 3 and 4

0.90

0.75

Manufactured stone

Group aerated 1 0.75 Autoclaved concrete Dimensioned natural stone

Group 1

Group 1

0.75

0.45

0.45

0.76

0.40§

0.45

0.45

–*

–*

–*

0.76 –*

0.45

0.40§

0.45

0.45

0.90

0.45

0.45

0.90

–*

–*

0.90

–*

0.45 –*

–*

of masonry (other than shell-bedded

the results of K ƒb α ƒm isβ determined [Equationfrom 3.1 of BS EN 151996-1-1] ƒk =masonry) The tests are carried out on small wallette where: specimens rather than the storey-height

used in BS 5628. compressive The designer has is the characteristic strength of the masonry, ƒk panels the option of2either having the units intended in N/mm to be used in a project tested or to use the K values is a constant determined from the UK national The latter values are provided α, βdatabase. are constants in the UK National Annex in the form of ƒb theisconstants the normalised mean compressive strength of the units, to be used in the following in the direction of the applied action effect, in N/mm2 equation: ƒm is the compressive strength of the mortar, in N/mm2 fk = K fbα fmβ [Equation 3.1 of BS EN Values of K to be used1996-1-1] with Equation 3.1 are provided in the UK National Annex Table NA.4 and are shown in Table 2. where:

–*

0.45 –*

* Manufactured stone Group 3 and 4 units have not traditionally been used in the UK, so no values are available.

and mortar combinations have not traditionally been used†in the UK, so no values are † – Group 1These masonry unit0.75 0.90 – †

available.

‡ If Group 1 aggregate concrete units contain formed vertical voids in the normal direction, Dimensioned stone multiply K natural by (100 - n)/100, where n is the percentage of voids, maximum 25%. § When aggregate concrete masonry units are to be used laid flat the normalised strength of the unit should be calculated using the width and height of the unit in the upright position along–† with the compressive strength†of – Group 1 0.45 –† the unit tested in the upright position. Note * Group 3Where and 4aunits have traditionally used in the UK, sobe nomodified values are available. mortar jointnot is parallel to thebeen face of the wall K should (Figure 1). † These masonry unit and mortar combinations have not traditionally been used in the UK, so no values are available. ‡ If Group 1 aggregate concrete units contain formed vertical voids in the normal direction, multiply K by (100 - n)/100, where n is the percentage of voids, maximum 25%. § When aggregate concrete masonry units are to be used laid flat the normalised strength of the unit should be calculated using the width and height of the unit in the upright position along with the compressive strength of the unit tested in the upright position. Note Where a mortar joint is parallel to the face of the wall K should be modified (Figure 1).

TSE38_38-43 Concrete v3.indd 40

dried compressive strength of an equivalent

wide by 100mm high masonry The100mm characteristic compressive strength of masonry (other than shellunit. The detail is contained in the test bedded masonry) is determined from the results of tests in accordance methods for masonry units in BS EN 772The are carried with114BS ENadvantage 1052-115. to . The thetests designer is that out on small wallette the normalised independent panels used in BS 5628. The specimens rather strength than theisstorey-height of the size of the units used in the final designer has the option of either having the units intended to be used construction thereby obviating the need in afor project tested or the values determined from the UK national recalculation if ato diffuse erent size of unit is selected. database. The latter values are provided in the UK National Annex in the The characteristic compressive strength form of the constants to be used in the following equation: tests in accordance with BS EN 1052-1 .

Calcium silicate Calcium silicate Group Group 1 1

The normalised strength is new to the UK and relates the compressive strength unit determined by test fb a standardised shape • fm is of notthe to be taken to be greater than to 12N/mm2content. The normalised compressive strength is the andormoisture • the coefficient of variation of the strength compressive strength of the units converted to the airdried compressive of the masonry units is not more than 25% strength of an equivalent 100mm wide by 100mm high masonry Thedetail normalised strength in is new to the UK unit. The is contained the test methods for masonry units in and772-1 relates 14 the compressive strength of the BS EN . The advantage to the designer is that the normalised unit determined by test to a standardised strength independent of theThe sizenormalised of the units used in the final shapeis and moisture content. construction thereby obviating the need for recalculation if a different compressive strength is the compressive the units converted to the airsizestrength of unit isofselected.

fk is the characteristic compressive The value of K is reduced by multiplying by 0.8 when a mortar joint runs strength of the masonry, in N/mm2 continuously intermittently through the masonry at right angles to K is a or constant α, βjoints, are constants the cross as shown in Figure 1. Note also that for blocks laid flat, fb contains is the normalised mean the table a specific value for K to be used in Equation 3.1. compressive strength of the units,

in the direction of the applied Values of α, β for use with Equation 3.1 are shown in Table 3 and are action effect, in N/mm2 takenffromisclause NA.2.4 ofstrength the UK National Annex to Part 1-1. the compressive of the m

mortar, in N/mm2

Values of K to be used with Equation 3.1 are provided in the UK National Annex Table NA.4 and are shown in Table 2. The value of K is reduced by multiplying by 0.8 when a mortar joint runs continuously or intermittently through the masonry at right angles to the cross joints, as shown in Figure 1. Note also that for blocks laid flat, the table contains a specific value for K to be used in Equation 3.1. Values of α, β for use with Equation 3.1 are shown in Table 3 and are taken from clause

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Structural Design of Concrete and Masonry

www.thestructuralengineer.org

41

�

Figure 3 Values of Φm against slenderness ratio for different eccentricities, based on E of 1000fk

1996-1-1 and depends on the ratio of the pier spacing to pier width and the ratio of the pier depth to the wall thickness. For awall cavity wall the effective thickness For a cavity the effective thickness in the UK is determined using the in the UK is determined using the following following equation: equation:

tef =

3

3

3

t 1 + t32 3 3 = 1 + 2 where: is the effective thickness of the 1 outer or unloaded leaf ist thethe effective thickness of the outer or unloaded leaf effective thickness of the inner 2 the effective thickness of the inner or loaded leaf or loaded leaf

where: t t1 t2

Note that the effective thickness of the leaf should not be Note that the effective thickness ofunloaded the leaf should taken to of bethe loaded leaf and that ties takenunloaded to be greater than not thebe thickness greater than the at thickness . loaded leaf should be provided 2.5 per of m2the and that ties should be provided at 2.5 per

m. The slenderness ratio of the wall is obtained by dividing the effective The slenderness ratio of the wall is height by the effective thickness and should not be greater than 27 for obtained by dividing the effective height by wallsthe subjected mainly vertical loading. effectiveto thickness and should not be 2

greater than 27 for walls subjected to mainly

Figure 3 Values of Φm against slenderness ratio for different eccentricities, based on E of 1000ƒk

Whenvertical a wallloading. is subjected to vertical loads which result in an eccentricity a wall is subjected vertical at rightWhen angles to the line of thetowall, EC6loads requires the resistance of the which result in an at right angles wall to be checked at eccentricity the top, mid-height and bottom. to the line of the wall, EC6 requires the

resistance ofof the wall to be checked at the The eccentricity the load at the top and bottom of the wall is given by:

designation mortars has1-1. also changed the need for a of the top, mid-height and bottom. NA.2.4 The of the UK Nationalof Annex to Part h iswith the clear storey height eccentricity of the load at the top and The designation mortars also rather than mix wall MThe declarationofbased onhas strength proportions. Thus, an id ehethe + ewall ≥ 0.05t changed with the need for a declaration ρn is a reduction factor, where n = 2, ei = bottom+of int is given by: M12 mortar may be expected to have a strength of 12N/mm2. Equivalent Nid based on strength rather than mix 3 or 4, depending upon the mixesThus, are shown National Table NA.2 andrestraint are shown inening Tableof4.the proportions. an M12in mortar may Annex be edge or stiff where: = id + i he + init ≥ 0.05 expected to have a strength of 12N/mm2. wall. The reduction factor to be Eccentricity id applied depends upon the restraint M is the design Equivalent mixes are shown in National value of the bending moment at the top or the id where: offered by adjoining elements Annex Table NA.2 and are shown in Table 4. A further area of change for vertical load relates to the treatment of bottom wallvalue resulting eccentricity of the floor load at Mid is of thethe design of thefrom bending eccentricity, where a frame analysis approach is implied than the tmin the support The value for the rather minimum thickness Eccentricity moment at the top or the bottom A further change forofvertical load that any of the wall resulting of eccentricity a load-bearing BSarea 5628ofapproach assuming atwall the should top of be thetaken as Nid is the design value of thefrom vertical load at the top or the bottom of relates to the treatment of eccentricity, eccentricity of the floor load at the 90mm for a single-leaf wall and 75mm for wall reduces to zero at the bottom of the wall. The use of a frame analysis the wall where a frame analysis approach is implied support the leaves of a cavity wall. For a single-leaf will not usually justifiedofgiven typical UKa construction practice eccentricity theof top bottom of the wall resulting from rather than the BS 5628be approach wall, double-leaf wall, a facedand wall,ita shell-ehe isNthe is the designat value theorvertical id assuming thatacceptable any eccentricity at the the BS top5628 approach. bedded wall and a grouted cavity wall the imposed load at the top loads or the bottom of the is still to use horizontal of the wall reduces to zero at the bottom effective thickness tef is taken as the actuale is the initial wall eccentricity resulting from construction imperfections init is used to allow for anyofinaccuracies An initial eccentricity of the wall. The use of a frame eanalysis thickness the wall t. in the ehe is the eccentricity at the top or init and may be taken as h /450 will notconstruction usually be justifi given typicaland is takenWhen a wall stiffened (Figure bottom of the wallefresulting from ofed the masonry as einit = hefis/450 wherebyhpiers is the ef UK construction practice and it is still 2), the effective thickness is given by the imposed horizontal loads effective height of the wall. The initial eccentricity is applied to the full acceptable to use the BS 5628 approach. coefficients contained in Table 5.1 of BS EN einit is the initial eccentricity resulting height of the wall to result in the greatest value of eccentricity. An initial eccentricity Table 3: Values of K to be used with Equation 3.1 einitsois as used to allow for any inaccuracies in the construction of Masonry unit Masonry unit is obtained applying The effective height a masonry wall hTable 3: Values by to be used inaEquation 3.1 the masonry and is taken as eof ef init = hef/450 factor toeff the clearheight height of the wall such that: where h ective of the wall. ef is the Type of mortar The initial eccentricity is applied to the h hef = full height ofρthe n wall so as to result in the General purpose mortar greatest value of eccentricity.

General purpose mortar Lightweight mortar

α = 0.7 and β = 0.3

Values to be used

α = 0.7 and β = 0.3

Thin layer mortar in bed jointsαof=thickness 0.7 and 0.5–3mm β = 0.3 (using

clay units of Group 1, calciumαsilicate where: The eff ective height of a masonry wall hef Lightweight mortar = 0.7units, and aggregate β = 0.3 concrete units and autoclaved aerated concrete units) is obtained by applying a factor to the clear Thin layer mortar in bed joints of thickness 0.5–3mm (using α = 0.85 and β = 0 h is the clear storey height of the wall height of the wall such that: Thin layer mortar in bed joints of thickness 0.5–3mm (using clay units of Group 1, calcium silicate units, aggregate 3 or 4, depending upon the aerated edge concrete ρn is a reduction factor, where n = 2,concrete units and autoclaved units) clay units of Group 2)

hef = ρnh restraint or stiffening of the wall. The reduction factor to be Thin layer mortar in bed joints of thickness 0.5–3mm (using adjoining elements clayoffered units ofby Group 2) where: applied depends upon the restraint and is given in BS EN 1996-1-1 clause 5.5.1.2 (11). The value for the minimum thickness tmin of a load-bearing wall should be taken as 90mm for a single-leaf wall and 75mm for the leaves TSE38_38-43 Concrete v3.indd 41 of a cavity wall. For a single-leaf wall, a double-leaf wall, a faced wall, a shellbedded wall and a grouted cavity wall the effective thickness tef is taken as the actual thickness of the wall t. When a wall is stiffened by piers (Figure 2), the effective thickness is given by the coefficients contained in Table 5.1 of BS EN 1996-1-1 and depends on the ratio of the pier spacing to pier width and the ratio of the pier depth to the wall thickness. 26 I www.concretecentre.com

α = 0.85 and β = 0

α = 0.7 and β = 0

α = 0.7 and β = 0

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Structural Design of Concrete and Masonry

Table 4: Acceptable assumed equivalent mixes for prescribed masonry mortars for Class 2 of execution control Compressive strength class*

Prescribed mortars (traditional proportion of materials by volume) (see Notes) Cement†: lime: condition sand with or without air entrainment

Cement†: sand with or without air entrainment

Masonry cement‡: sand

Masonry cement§: sand

Mortar designation

Suitable for use in environmental condition

Severe(S)

M12

1 : 0 to ¼ : 3

1:3

Not suitable

Not suitable

(i)

M6

1 : ½ : 4 to 4½

1 : 3 to 4

1 : 2½ to 3½

1:3

(ii)

Severe(S)

M4

1 : 1 : 5 to 6

1 : 5 to 6

1 : 4 to 5

1 : 3½ to 4

(iii)

Moderate(M)

M2

1 : 2 : 8 to 9

1 : 7 to 8

1 : 5½ to 6½

1 : 4½

(iv)

Passive(P)

The number following the M is the compressive strength for the class at 28 days in N/mm2 that may be assumed for the proportions given in columns 2 to 4; site compressive strength testing is not required for these traditional mixes. Checking of prescribed mortars should only be done by testing the proportions of the constituents. † Cement or combinations of cement (which include CEM I and many CEM IIs) in accordance with NA.2.3.2, except masonry cements ‡ Masonry cement in accordance with NA.2.3.2 (inorganic filler other than lime) § Masonry cement in accordance with NA.2.3.2 (lime) *

Notes When the sand portion is given as, for example, 5 to 6, the lower figure should be used with sands containing a higher proportion of fines whilst the higher figure should be used with sands containing a lower proportion of fines. For Class 2 of execution control site compressive strength testing is not required for these traditional mixes and checking of prescribed mortars should only be done by testing the proportions of the constituents.

Characteristic vertical actions

Masonry unit properties • Type and group • Dimensions • Strength Determine requirements for mortar strength and durability. See tables 5 & 6 of Introduction to Eurocode 6

Determine normalized compressive strength, fb.

Determine characteristic compressive strength of masonry, fk, from Equation (3.1) of Eurocode 6 and Tables 1 & 2

Determine effective height, hef, of the wall (see page 4) .

Determine effective thickness, tef, of the wall (see page 4)

Check area ≥ 0.04 m2

Check slenderness ratio hef /tef ≤ 27

Фi = 1 – 2 Determine design value of vertical actions (per unit length), Ed, using Expression (6.10), (6.10a) or (6.10b) of Eurocode (see Introduction to Eurocode 6)

Obtain gM from table 1 of Introduction to Eurocode 6

Check complete

Figure4 Flow chart for design of masonry walls to resist vertical actions

The eccentricity at the mid-height of the wall emk includes the initial eccentricity einit, the horizontal load eccentricity ehm, and the load eccentricity em. The mid-height eccentricity emk is: emk = em + ek which must be greater than or equal to 0.05t em =

Mmd Nmd

t

where: Φi is the reduction factor at the top or bottom of the wall

t Check Ed ≤ NRd

Determine eccentricity (see page 5)

Determine capacity reduction factors, Fm and Fi from (see page 6)

ei

ei is the eccentricity at the top or bottom of the wall

Where cross-sectional area, A < 0.1 m2, factor fk by (0.7 + 3A)

Calculate design resistance (per unit length) from least favourable of: NRd = Fm t fk / gM and NRd = Fi t fk / gM

At the top or bottom of the wall, the reduction factor for slenderness and eccentricity is given by:

+ ehm + ei

where: Mmd is the design value of the greatest moment at the middle height of the wall resulting from the moments at the top and bottom of the wall, including any load applied eccentrically to the face of the wall

is the thickness of the wall

The capacity reduction factor in the middle of the wall Φm may be determined by using either the equation or the graph (Figure 3), which is given in Annex G of BS EN 1996-1-1. The value of the modulus of elasticity to be taken in the UK is 1000ƒk. The design resistance of a single-leaf wall per unit length NRd is given by: NRd = Фtƒd where: Ф is the capacity reduction factor allowing for the effects of slenderness and eccentricity of loading (the least favourable value obtained for the top, bottom and mid-height, Фi or Φm) t

is the thickness of the wall

ƒd is the design compressive strength of the masonry and is taken as ƒk/γM

Nmd is the design value of the vertical load at the middle height of the wall, including any load applied eccentrically to the face of the wall ehm is the eccentricity at the middle of the wall resulting from imposed horizontal loads ek is the creep eccentricity and, in the UK, can be ignored if the slenderness ratio is not greater than 27

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Structural Design of Concrete and Masonry

For sections of small plan area, less than 0.1m2, ƒd should be multiplied by (0.7 + 3A), where A is the loadbearing horizontal cross-sectional area of the wall in m2. A flow chart for vertical load design is provided in Figure 4.

References: 1) British Standards Institution (2013) BS EN 1996-1-1:2005+A1:2012 Eurocode 6. Design of masonry structures. General rules for reinforced and unreinforced masonry structures, London, UK: BSI

Concentrated loads Concentrated loads are dealt with by a calculation approach using a dispersion angle of 60°. Only Group 1 masonry units may be enhanced.

2) British Standards Institution (2005) BS EN 1996-1-2:2005 Eurocode 6. Design of masonry structures. General rules. Structural fire design, London, UK: BSI

For a Group 1 unit (not shell bedded) the vertical load resistance is given by:

3) British Standards Institution (2006) BS EN 1996-2:2006 Eurocode 6. Design of masonry structures. Design considerations, selection of materials and execution of masonry, London, UK: BSI

NRdc = β Abƒd (Ex. 6.10: EN 1996-1-1) where: β=

(

1 + 0.3

a1 hc

)(

1.5 – 1.1

Ab Aef

)

(where Ab/Aef is not to be taken as greater than 0.45) which should not be less than 1.0 nor taken to be greater than: 1.25 +

a1 2hc

or 1.5, whichever is the lesser

where: β is an enhancement factor for load a1 is the distance from the end of the wall to the nearer edge of the loaded area hc is the height of the wall to the level of the load Ab is the loaded area Aef is the effective area of the bearing lefm is the effective length of the bearing as determined at the midheight of the wall or pier t is the thickness of the wall, taking into account the depth of recesses in joints greater than 5mm For walls built with Groups 2, 3 and 4 masonry units, and when shell bedding is used, it is necessary to check that, locally under the bearing of a concentrated load, the design compressive stress does not exceed the design compressive strength of the masonry fd (i.e. β is taken to be 1.0). In any case, the eccentricity of the load from the centre line of the wall should not be greater than t/4.

Further Reading: 1) Roberts J. J. and Brooker O. (2013) How to design masonry structures using Eurocode 6. 1. Introduction to EC6, London, UK: MPA The Concrete Centre 2) Roberts J. J. and Brooker O. (2013) How to design masonry structures using Eurocode 6. 3. Vertical Resistance, London, UK: MPA The Concrete Centre 3) Roberts J. J. and Brooker O. (2013) How to design masonry structures using Eurocode 6. 3. Lateral resistance, London, UK: MPA The Concrete Centre

28 I www.concretecentre.com

4) British Standards Institution (2006) BS EN 1996-3:2006 Eurocode 6. Design of masonry structures. Simplified calculation methods for unreinforced masonry structures, London, UK: BSI 5) British Standards Institution (2013) NA to BS EN 1996-1 1:2005 +A1:2012 UK National Annex to Eurocode 6. Design of masonry structures. General rules for reinforced and unreinforced masonry structures, London, UK: BSI 6) British Standards Institution (2013) NA to BS EN 1996-1-2:2005 UK National Annex to Eurocode 6. Design of masonry structures. General rules. Structural fire design, London, UK: BSI 7) British Standards Institution (2007) NA to BS EN 1996-2:2006 UK National Annex to Eurocode 6. Design of masonry structures. Design considerations, selection of materials and execution of masonry, London, UK: BSI 8) British Standards Institution (2007) NA+A1:2014 to BS EN 19963:2006 UK National Annex to Eurocode 6. Design of masonry structures. Simplified calculation methods for unreinforced masonry structures, London, UK: BSI 9) British Standards Institution (2010) PD 6697:2010 Recommendations for the design of masonry structures to BS EN 1996-1-1 and BS EN 1996-2, London, UK: BSI 10) British Standards Institution (2005) BS 5628-1:2005 Code of practice for the use of masonry. Structural use of unreinforced masonry, London, UK: BSI 11) British Standards Institution (2005) BS 5628-2:2005 Code of practice for the use of masonry. Structural use of reinforced and prestressed masonry, London, UK: BSI 12) British Standards Institution (2005) BS 5628-3:2005 Code of practice for the use of masonry. Materials and components, design and workmanship, London, UK: BSI 13) British Standards Institution (2013) BS EN 845-2:2013 Specification for ancillary components for masonry. Lintels, London, UK: BSI 14) British Standards Institution (2000) BS EN 772-1:2000 Methods of test for masonry units. Determination of compressive strength, London, UK: BSI 15) British Standards Institution (1999) BS EN 1052-1:1999 Methods of test for masonry. Determination of compressive strength, London, UK: BSI

Structural Design of Concrete and Masonry

Eurocode 6: Design of masonry structures for lateral loads and other factors

The previous article in the series explained how to design masonry for vertical actions1.

Introduction Throughout this article the Nationally Determined Parameters (NDPs) from the UK National Annexes (NAs) have been used. These enable Eurocode 6 (BS EN 1996-1-1)2 to be applied in the UK. Lateral loads EC6 offers two approaches to the design of laterally loaded panels. The first method relies on the flexural strength of the masonry and makes use of yieldline analysis. The second method is an approach based on arching and the assumption of a three-pinned arch being formed within the wall. Figure 1 shows a flow chart for lateral load design. The flexural strength approach is the most widely used and does not depend upon rigid supports to resist arch thrust. Values of the characteristic flexural strength of masonry are provided in Table NA.6 of EC6 and are shown here in Table 1. The assessment of the edge conditions is a requirement for the flexural strength approach. A free edge is easily identified but some judgment on the part of the engineer is necessary in deciding between simply supported or fixed conditions. When considering the vertical support condition, attention also needs to be paid to the potential position of movement joints, and to the changes the provision of such joints makes to the panel size and restraint conditions. Where the walls are not rectangular (e.g. a trapezoidal-shaped wall to a mono-pitched structure), engineering judgement may be applied to determine the effective wall height. Wall panels with openings need to be treated with care and may typically be subdivided into smaller panels around the opening. It is beyond the scope of this article to deal with the topic in detail and reference should be made to suitable handbooks3. Alternatively, a yieldline analysis from first principles may be applied to wall panels4. If a damp-proof course (DPC) is present in a wall subjected to flexure, then the degree of fixity may be altered. The bending moment coefficient at a DPC may be taken as that for an edge over which full continuity exists, provided that there is sufficient vertical load on the DPC to ensure that the flexural strength capacity is not exceeded. Walls may be either horizontally or vertically spanning, or both, and the ultimate strength of the wall is governed by the capacity of the masonry to resist flexural tension. This capacity is enhanced by the presence of

vertical load, as the masonry can resist significantly more in compression than it can in tension. Clearly, the potential flexural strength is greater if the potential plane of failure is perpendicular rather than parallel to the bed joint, due to the interlocking of the masonry units. The designer needs to assess the panel support conditions (or assume a free edge) and decide whether these provide simple or continuous (fully restrained) support. Care also needs to be exercised in considering the effect of DPCs, movement joints, openings in walls etc.3 For panels without openings, the bending moments per unit length MEd are: MEd1 = a1 WEdl2 when the plane of failure is parallel to the bed joints MEd2 = a2 WEdl2 when the plane of failure is perpendicular to the bed joints where: a1 is the bending moment coefficient parallel to the bed joints (= μa2, Annex G of BS EN 1996-1-1) a2 is the bending moment coefficient perpendicular to the bed joints (Annex G of BS EN 1996-1-1) WEd is the design wind load per unit area γQ Wk l

is the length of panel between supports

μ is the orthogonal ratio ƒxk1/ƒxk2 The presence of a vertical load increases the flexural strength of a panel in the direction parallel to the bed joints. The design moment of resistance within the height of the wall is given by: MRd =

( ƒγ

xk1 M

)

+ σd Z

where: ƒxk1 is the characteristic flexural strength of masonry bending about an axis parallel to bed joints (Table 1) γM is the appropriate partial factor for materials σd is the design vertical load per unit area (