PracUse_EC2.pdf

The practical use of Eurocode 2

1 Introduction

When or before Eurocode 2 is introduced in early 2003, most engineers will need to be

assured that it can be used as a practical concrete design tool, as well as producing

economic results. If they are not assured of this, practices will continue to use BS 8110 in

preference to adopting the new code.

Necessary guidance in the form of explanatory literature, process flowcharts, spreadsheets

and other software etcetera is in preparation. This brief report will attempt to summarise the

principal design procedures required by EC2, compare them with their BS 8110

counterparts, and demonstrate that the transition to EC2 need not be a difficult process.

2 Comparisons with BS 8110

2.1 Loading

EC2

BS 8110

Loaded spans:

Worst of γ G = 1.35, γ Q = 1.05

and γ G = 1.15, γ Q = 1.5

γ G = 1.4, γ Q = 1.6

Unloaded spans:

γ G = as above

γ G = 1.0

Loading pattern:

All + adjacent + alternate spans All spans + alternate spans

For the sake of simplicity, γ G = 1.35 and γ Q = 1. 5 may be used for loaded spans ( with γ G =

1.35 on unloaded spans ), although this would be very conservative. Both γ G and γ Q are

marginally lower than in BS 8110, but for unloaded spans γ G is higher, reflecting a lower

probability of variation in dead loads. For a typical member with Q k = 0.5 G k , maximum

ULS loading would be 13.6% lower than for BS 8110. The use of the same value for γ G

throughout also reduces the effect of pattern loading, thus marginally reducing span

moments.

The loading code, EN 1991-1-1, stipulates values of imposed loads that vary only

marginally from current UK practice ( e.g. 3 kN/m 2 for offices ). This code stipulates weights

for both construction materials and stored materials, and it should be noted that the density

of normal weight reinforced concrete should be taken as 25 kN/m 2 .

2.2 Cover

Nominal covers required for durability and bond are fairly similar to BS 8110. However,

nominal cover to EC2 is in two parts, C nom = C min + ∆ c , where ∆ c is a design tolerance

varying from 0 to 10mm, depending upon quality assurance level. This can have the effect

of increasing cover to slabs when larger diameter bars are used, as C min ≥ bar φ and ∆c must

be added.

2.3 Materials

EC2

BS 8110

Partial factor, concrete:

γ c = 1.5

Partial factor, steel:

γ s = 1.15

γ s = 1.05

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The practical use of Eurocode 2

At first inspection, the higher γ s factor in EC2 would appear disadvantageous. However, this

difference is almost exactly neutralised by the introduction of reinforcing steel with f yk =

500 N/mm 2 .

2.4 Stress block – flexure

Eurocode 2

ε c

f =

ηα γ

cc ck

f /

d 2

ε sc

As 2

F c

λ x

F sc

neutral axis

ε s

F st

Section

Strain

Stress

f ck = characteristic concrete cylinder strength ( equivalent to 80% cube strength ).

For f ck ≤ 50 N/mm 2 , η = 1, ε c = 0.0035, α cc = 1.0 and λ = 0.8. As γ c is the same for both

codes, this results in concrete design strengths being 19.4% higher than in BS 8110 below.

This difference gives advantage in terms of reinforcement areas because of the resulting

increase in the lever arm, z.

ε c = 0.0035

f = 0.67 f /

d’

ε sc

F c

As’

0.9x

F sc

neutral axis

ε s

F st

Section

Strain

Stress

BS 8110

2.5 Stress block – columns

In BS 8110, an identical stress block is used for both pure flexure and bending with axial

load. In EC2 however, ε c the limiting concrete compressive strain, starts to reduce when the

neutral axis x drops outside of the section height, h . This strain reaches a lower bound value

( 0.00175 for f ck ≤ 50 N/mm 2 ) when the section is in pure compression.

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The practical use of Eurocode 2

The diagram below demonstrates this procedure. Effectively, the strain diagram has a

“hinge point”, which falls at h/2 for normal strength concretes. This process is easily

automated, but is not suited to hand calculation, so it is best accomplished by spreadsheet.

As few columns are very close to being in pure compression, this gradual reduction in

strain, and hence compressive stress, has less effect than one might imagine.

0.0035 max

0.001 75x /(x -h/2)

0.00175

h/2

hinge

point

ε s

0.00175 min

0.00175

General relationship

When x > h

Pure compression

EC2 strain relationship at ULS (f ck ≤ 50 N/mm 2 )

2.6 Redistribution

EC2

BS 8110

Neutral axis limit: x/d ≤ δ - 0.4

x/d ≤ β b - 0.4

Redistribution limit: 30% classes B & C

30% generally

20% for class A rebar

10% sway frames > 4 storeys

0% in coluns

0% in columns

Limitations:

Adjacent spans ratio ≤ 2

The EC2 x/d limit reduces for concrete with f ck > 50 N/mm 2 , otherwise both codes are very

similar.

2.7 Beamshear

A strut-and-tie model is used for shear reinforcement to EC2, which can have a varying

angle θ between the compressive struts and main tension chord. Cot θ is normally taken as

the maximum value of 2.5, but may be as low as 1.0 if required for high shear forces.

For UD loading, 2

BS 8110

Shear resistance: ν = 0.7 – f ck /200 ≥ 0.5

k = 1 + √(200/d) ≤ 2

v c = from Table 3.8

ρ 1 = A sl /b w d ≤ 0.02

At support face:

Rd,max = 0.9b w d.f cd /(cot θ + tan θ )

V max = 0.8√f cu ≤ 5

At d from support: V Rd,ct = 0.12k(100 ρ 1 f ck ) 1/3

V c = v c .b v d

If V Rd,ct ≥ V Ed nominal links

If Vc ct ≥ V, nominal links

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The practical use of Eurocode 2

Links:

A sw /s = V Ed /(0.9d. ν. f cd cot θ )

A sv /s v =1.05 b v (v-v c ) /f yv

Nominal links:

A sw /s ≥ 0.5 ν. f cd b w /f ywd

A sv /s v ≥ 0.42b v /f yv

Understandably, these approaches are somewhat different although both methods are simple

enough to apply. One can see from the above formulae that when more than nominal links

are required, EC2 ignores any contribution from the concrete. The strut-and-tie method

produces an additional tension in the main steel where the compression strut meets this

steel. This effect is catered for by applying the “shift rule” when detailing ( see Section 3 ).

2.8 Punchingshear

The calculation of punching shear is basically similar to BS 8110, except that the control

perimeter is at 2d , rather than 1.5d from the column face, and follows a locus from the

column face, rather than being rectangular in shape.

1.5d

EC2

BS 8110

Basic control perimeter:

At 2d

at 1.5d

Control perimeter shape:

Rounded corners

Rectangular

Flat slab shear enhancement factors

Internal:

1.15

Edges:

1.4

1.4 or 1.25

orners:

1.5

1.25

When links are required, EC2 allows a contribution of 75% of the concrete shear resistance

( unlike beam shear ), and a radial distribution of links is assumed. An outer perimeter, at

which no further links are required, is based upon the link arrangement rather than the basic

control perimeter.

The much higher enhancement factor of 1.5 for corner columns may prove critical in some

circumstances, when sizing flat slabs for shear. However, the method as a whole seems very

logical and may result in fewer links and be simpler to detail than the BS8110 method.

Rod Webster Concrete Innovation & Design Page

The practical use of Eurocode 2

2.9 Span to depth ratios

EC2

BS 8110

Basic L/d ratios:

K factors from Table 7.4 used in

equations 7.14a & b

From Table 3.9

Tension steel

modifier:

In equations

From Table 3.10

Compression steel

modifier:

In equations

From Table 3.11

Flanged sections:

1 ≥ 1 – 0.2b w /b f /3 ≥ 0.8

Interpolated between Table

3.9 values

Only used if there are brittle partitions

Flat slabs: 8.5 /L ≤ 1

Otherwise: 7 /L ≤ 1

Long span modifier:

10 /L ≤ 1

Service stress

modifier:

310 / σ s (steel service stress)

Formulae included in Table

3.10

These two methods are very similar, but in practice, Eurocode 2 effectively allows

marginally shallower members than BS 8110. This is likely to be because the EC2 ratios

have made no allowance for early age overloading during construction, which can increase

the degree of cracking, particularly in slabs.

2.10 Maximum bar spacing

For normal internal exposure, EC2 recommends a maximum crack width of 0.4mm

compared to 0.3mm in BS 8110. However, the maximum bar spacings in Table 7.3 are

somewhat less than those now commonly used in the UK. This will tend towards the use of

slightly smaller diameter bars in slabs. The actual calculation of crack widths to clause 7.3.4

allows more flexibility.

2.11 Beam flange widths

To both codes, effective flange widths may be calculated directly from the distances

between points of contraflexure, but the default values below give an indication of

comparative values.

EC2

BS 8110

Effective span, spans:

Simple supports, L

End span, 0.85L

Internal span, 0.7L

Simple supports, L

End span, 0.85L

Internal span, 0.7L

Effective span, supports:

Cantilever, L.

Others, 0.15L either side of support.

Not applicable

[b 1 /5+L eff /10]≤L eff /5

plus [b 2 /5+L eff /10]≤L eff /5

≤ b w +b 1 +b 2

Effective b f , T-beam:

b w +L eff /5 ≤ b w +b 1+ b 2

Effective b f , L-beam: b w +{[b 1 /5+L eff /10]≤L eff /5} ≤ b w +b 1 b w +L eff /10 ≤ b w +b 1

b 1 and b 2 are the actual flange outstands on either side of the web

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