Normal Rules

The incidence of cracking is generally controlled by imposing a minimum area of steel criterion. The minimum reinforcement area A_s,minis given by

As,min¼ kck fct,effAct

_s ð5:35Þ

where A_ctis the area of the concrete in tension just before the concrete cracks, _sis the maximum permitted stress in the reinforcement which may be taken as f_yk, f_ct,eff is the effective tensile strength in the concrete based on the strength of the concrete at which cracks are expected and can generally be taken as f_ctmunless cracking is expected before 28 days, k_cis a coefficient allowing for the stress distribution due to loading and imposed deformations immediately prior to cracking and for reinforced

h d

x ε₂ = O

Least of 2,5(h−d), h−x/3, h/2 ε1

A_c,eff h_c,ef F^IGURE5.7 Definition of Ac,eff

and hc,ef

concrete takes values of 1,0 for pure tension and for bending and axial forces, the following may be used

 Rectangular sections webs of box sections and T sections

kc¼0,4 1  c

k1f_ct,eff ^h

h^

" #

1,0 ð5:36Þ

 Flanges of box and T sections

kc¼0,9 Fcr

A_ctf_ct,eff 0,5 ð5:37Þ

where _c is the mean stress in the concrete (¼ N_Ed/bh), h^*¼h for h  1,0 m or 1,0 m for h 4 1,0 m, k₁¼1,5 if N_Edis compressive or 2h^*/3h if N_Edis tensile, and F_ct is the absolute value of the force in tension flange at incipient cracking.

The parameter k takes a value of 1,0 for members less than 300 mm thick and 0,65 for greater than 800 mm (with linear interpolation). The minimum reinforcement level determined from Eq. (5.35) is further subject to the limit of the greater of 0,26 ( f_ctm/f_yk)b_td or 0,0013b_td, where b_t is the mean width of the tension zone (cl 9.2.1.1).

For additional design rules for slabs, see Section 10.5.3.

For beams, cracking will be kept below the design values for the minimum steel areas given by Eq. (5.35) if EITHER the bar diameter or spacing given in Table 5.4 (from Tables 4.11 and 4.12 from EN 1992-1-1) are complied with. The required spacings or diameters are controlled by the stress in the reinforcement under loads which can be considered quasi-permanent. Thus the variable actions should be multiplied by the factor ₂(from Table A1.1 of EN 1990)

TABLE5.4 Bar detailing data (from Tables 4.11 and 4.12 EN 1992-1-1).

Crack width wk

Steel stress (MPa) Maximum bar size (mm) Maximum bar spacing (mm)

0,4 0,3 0,2 0,4 0,3 0,2

160 40 32 25 300 300 200

200 32 25 16 300 250 150

240 20 16 12 250 200 100

280 16 12 8 150 75 50

320 16 12 8 150 100

--360 10 8 5 100 50

--400 8 6 4 -- --

--450 6 5 -- -- --

--90
Chapter 5 / Durability, Serviceability and Fire

In reinforced concrete the maximum bar diameter may be modified as follows:

Bending (at least part of the section in compression) s¼^_sf_ct,eff

2,9 k_ch_cr

2ðh  dÞ ð5:38Þ

tension,

s¼^_sfct,eff

2,9 hcr

24ðh  dÞ ð5:39Þ

where ^_s is the maximum bar diameter from Table 5.4, _sis the adjusted value, h is the depth of the section, h_cr is the depth of the tensile zone immediately prior to cracking under quasi-permanent load combinations and k_cis given by Eq. (5.36) or Eq. (5.37). For beams of depth greater than 1 m, additional reinforcement must be provided in the tensile zone. It should have a minimum value obtained from Eq. (5.35) with k ¼ 0,5 and _s¼f_yk. The spacing and size of such bars may be obtained from Table 5.4 assuming pure tension and a steel stress half of that used in the assessment of the main tensile reinforcement.

E

^XAMPLE

5.3

Crack width calculations. Check design crack width for the beam of Examples 5.1 and 5.2

The critical zone is at the support.

Determine the clear spacing between bars:

s ¼ ð370  2  45  4  40Þ=3 ¼ 40 mm

Limiting spacing for closely spaced bars is 5(c þ /2) ¼ 5(45 þ 40/2) ¼ 325 mm.

Bars are thus closely spaced, thus s_r,maxis given by Eq. (5.31), sr,max¼3,4c þ 0,425k1k2= p,eff

k₁¼0,8 (high bond ribbed bars) k₂¼0,5 (flexure)

Effective loading:

Permanent: 30 kN/m

Quasi-permanent: 0,340 ¼ 12 kN/m (assuming ₂¼0,3) M_Sd¼42  4²=2 ¼ 336 kNm,

From Example 5.2:

I_cr¼11,46  10⁹mm4; x ¼ 298 mm

s¼
eM_sdðd  xÞ=I_cr¼12,5  366  10⁶ ð635  298Þ=11,46  10⁹¼135 MPa:

A_c,eff¼2,5 ðh  dÞb ¼ 2,5ð700  635Þ370 ¼ 60125 mm²:

subject to the limits:

bðh  xÞ=3 ¼ 370ð700  298Þ=3 ¼ 49580 mm² bh=2 ¼ 370  700=2 ¼ 129500 mm²

Thus A_c,eff should be taken as 49580 mm² As¼5026 mm²;

r¼As=Ac,eff ¼5026=49580 ¼ 0,101  ¼40 mm, c ¼ 45 mm

Thus from Eq. (5.31),

sr,max¼3,4  45 þ 0,425  0,8  0,5  40=0,101 ¼ 220 mm Determination of "_sm"_cm(from Eq. (5.32)):

f_ct,effmay be taken as f_ctm¼0,3  f_ck^(2/3)¼2,56 MPa Duration factor k₁:

Conservatively assume long term loading, i.e. k_t¼0,4, so from Eq. (5.32)

"_sm"_cm¼_s ktðf_ct,eff= _p,effÞ1 þ
_{e p,eff} E_s

¼135  0,4ð2,56=0,101Þ 1 þ 12,5  0,101ð Þ

200  10³ ¼653  10^6

Limiting value is given by 0,6_s/E_s¼0,6135/20010³¼40510^6 Thus, the value of "_sm"_cmto be used is 65310^6.

Determine w_kfrom Eq. (5.31)

wk ¼sr,maxð "sm "cmÞ¼220  653  10^6

¼0,144 mm

This is below the limit of 0,3 mm, and therefore acceptable.

If the whole of the transient load is considered as permanent, then M_Sd¼560 kNm;

_s¼206 MPa; "_sm"_cm¼1008 mstrain; w_k¼0,22 mm (this is still satisfactory).

E

^XAMPLE

5.4

Bar spacing rules. The data are as before.

Determination of reinforcement stress _s: Effective loading:

Permanent: 30 kN/m

Quasi-permanent: 0,340 ¼ 12 kN/m (assuming ₂¼0,3) MSd¼42  42=2 ¼ 336 kNm,

92
Chapter 5 / Durability, Serviceability and Fire

From Example 5.2:

Icr¼11,46  10⁹mm⁴; x ¼ 298 mm

s¼
eMsdðd  xÞ=Icr¼12,5  366  10⁶ ð635  298Þ=11,46  10⁹¼135 MPa:

Using the lowest value in Table 5.4 of _s¼160 MPa, the maximum bar spacing for w_k¼0,3 is 300 mm. This is clearly satisfied as there are four bars in a total width of 370 mm.

The maximum bar size allowed (before modification) is 32 mm.

Use Eq. (5.38) for sections in flexure to determine the modified bar diameter:

^_s¼32 (from Table 5.4) f_ct,eff:

This may be taken as f_ctm¼0,3  f_ck²⁼³¼2,56 MPa The depth of the tensile zone at incipient cracking, h_cr:

From Example 5.2, The depth of the uncracked neutral axis is 385 mm, so, h_cr¼h  x ¼ 700  385 ¼ 315 mm.

Use Eq. (5.36) to determine k_c:

As there is no applied axial force, _c¼0, thus k_creduces to a value of 0,4.

So using (5.38)

s¼^_sf_ct,eff 2,9

kchcr

2ðh  dÞ

¼322,56 2,9

0,4  315

2ð700  635Þ¼27,4 mm

Note in this case the modification factor produces a reduced bar diameter.

Interpolating between values of _sof 200 and 240 from Table 5.4 gives a bar spacing of around 240 mm. The actual is well below this. However, as EITHER the bar diameter rules OR bar spacing rules need be satisfied, the design is satisfactory.

Note, a further example on crack width calculations is given in Example 11.5.

5.3 F IRE

Design for fire is required, where applicable, in order to ensure any structure is capable of withstanding the accidental effects of exposure from high temperatures caused by the occurrence of fire. Although all multi-storey structures are required to be checked for such effects, single storey structures may only need evaluating to ensure the structure does not collapse outside its effective boundary. All building structures need to be designed to ensure that evacuation of persons can be carried out safely and that the fire can be fought with no ill-effects to the fire fighters

(Purkiss, 1996). It should also be noted that for other structures such as bridges the risk of fire exposure is generally very low and therefore can be ignored.

The England and Wales Building Regulations, Approved Document B (Department of the Environment, 2000) allows either the use of a full fire engineering approach to the evaluation of structures exposed to the accidental effects of fire, or an approach using tabulated data where the structure is considered to be exposed to the standard furnace test temperature–time curve. It should be noted that the fire endurance periods in the current version of Approved Document B are being revised (Kirby et al., 2004).

In document Concrete Design to en 1992, Second Edition (2006)-Lawrence Martin, John a Purkiss- (Page 107-112)