This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 4.5 Cracking 4.5.1 Methods for crack control
• Excessive cracking and wide deep cracks will
o affect durability; and
o lead to corrosion of reinforcement although strength may not be affected.
• BS 8110: Part 1, clause 18.104.22.168.1 and Part 2, clauses 3.2.4 state that the maximum acceptable value of surface crack widths is 0.3
mm in normal environments.
• The actual width of cracks will vary between wide limits, and cannot precisely be estimated. Two methods are given in BS 8110
for checking that deflection is not excessive:
1. Limiting the maximum bar spacing in the tension zone of members – This method is used for all normal cases to
comply with the 0.3 mm crack-width limit (BS 8110: Part 1).
2. Calculation of crack width using the formula given in BS 8110: Part 2, Section 3.8 for special cases.
In day-to-day practical design, crack widths are controlled by
simply limiting the maximum bar spacing in tension in the
tension zone. 178 4.5.2 Mechanisms of crack development*
(1) Development of cracks due to axial loading
An axially loaded RC member is shown in Fig. 4.5-1(a). F F
Axially loaded member ′
f ct f ct Cracked axially loaded member. Fig. 4.5-1 Crack development of axially loaded member
• The axially loaded member initially behaves elastically
throughout the length as the applied axial force F is increased.
Bond builds up the stress in the concrete. * Optional course materials for CIVL 232 179 • The first crack will form when the tensile stress fct in the
concrete (represented by the shaded area) reaches the tensile
strength f c′t of the concrete (represented by the outer envelop)
at some section of the member shown in Fig. Fig. 4.5-1(b). At
the crack, the entire axial force is carried by the steel. • Further loading will cause bond to build up gradually the stress
in the concrete on side of the crack until the stress reaches the
tensile strength at some other section, as shown in Fig. 4.5-1(c).
This in turn causes the second crack to from. • With increasing loading, this process continues until the
distance between cracks is not long enough for the tensile stress
in the concrete to develop to cause further cracking (Fig. 4.5-1d
and e). • Once this stage is reached, the crack pattern has stabilised, and
further loading merely widens the existing cracks. • A stabilised crack pattern and stresses in the steel and concrete
along the member are shown in Fig. 4.5-2. These initial and
stabilised cracks are referred to as ‘primary cracks’, and the
spacing is a function of the overall member thickness, the cover,
the efficiency of the bond, and etc., largely independent of
reinforcement detailing. 180 F F Fig. 4.5-2 Stabilised cracks and stresses in concrete and steel (2) Development of cracks due to bending Fig. 4.5-3 Member subjected to a uniform moment
• Primary cracks
o When the tensile strain for concrete is reached, the first crack will form;
the adjacent tensile zone will then no longer be acted
upon by direct tension forces; bond gradually builds up
the stress in the concrete.
181 o The curvature of the beam causes further direct tensile stresses to develop at some distance from the first crack to
maintain internal equilibrium. This in turn causes further
cracks to form.
o The process continues until the distance between cracks does not permit sufficient tensile stresses to develop to cause
o The average spacing of the primary cracks in a region of constant moment has shown experimentally to be approximately 1.67(h – x).
o The spacing will be largely independent of steel detailing.
• Further development of cracks
o As the applied moment is increased beyond this point (development of the primary cracks), the development of
cracks is governed to a large extent by reinforcement.
o Tensile stresses in the concrete increase with distance from the primary cracks and may eventually cause further cracks
to form approximately midway between the primary cracks.
o This action may continue until the bond between concrete and steel is incapable of developing sufficient tension in the
concrete to cause further cracking in the length between
182 • Average crack spacing
o Since the development of the tensile stresses in the concrete is caused directly by the presence of the steel bars, the
spacing of cracks will be influenced by the spacings of steel
o It has experimentally been confirmed that the average spacing of cracks along a line parallel to, and at a distance acr
shown in Fig. 4.5-4 from, a main reinforcing bar depends on
the efficiency of bond, and may be taken as
1.67 acr for deformed bars; and
2.0 acr for plain bars
where acr is the distance of the point considered from a
point of zero crack width. Points of zero crack width are
the neutral axis and the surface of longitudinal bars.
The larger the value of acr is, the larger the crack width
will be. Fig. 4.5-4 Crack locations
183 4.5.3 Crack control by limiting reinforcing bar spacing
• In practical design, it is usual to comply with the 0.3 mm crack- width limit by a straightforward procedure of limiting the
maximum distance between bars in tension, as recommended by
BS 8110: Part 1, clause 3.4.7.
• BS 8110’s detailing rules for crack control are conveniently summarised in Fig. 4.5-5. 4.3-5 Fig. 4.5-5 Reinforcement spacing rules for crack control
o Table 4.3-1 is presented in page 161 of this Notes.
o In measuring the values of the clear distance ab between two bars and the clear distance ac to the corner, ignore any bars with
a size smaller than 0.45 times that of the largest bars.
(Note: 0.45, but not 0.5, is adopted so that, say, size 12 bars
may be used with size 25 bars). 184 o The detailing requirements for side bars are presented in Section 4.3.5 (Notes p. 163). For the maximum permissible centre-tocentre side bar spacing sb = 250 mm (Fig. 4.5-5), the minimum
sizes of the side bars are
0.75√b for high-yield steel; and
1.00√b for mild steel. 4.5.4† Calculation of crack widths (BS 8110: Part 2, Section 3.8)
(1) Crack locations
o The crack width at a point on the surface is affected by the surface strain; and
the distance of the point considered from a point of zero
crack width − Points of zero crack width are the neutral axis
and the surface of longitudinal bars (see Fig. 4.5-4). The
larger the distance, the large the crack width will be.
o Critical locations for cracking on the beam surface (Fig. 4.5-4) at A: equidistant between N.A. and the bar surface
at B: equidistant between the bars
at C: on the corner of the beam
(2) Crack width (BS 8110: Part 2, Clause 3.8.3)
o The maximum surface crack width (design surface crack width)
† Optional course materials for CIVL 232 185 wmax = 3a cr ε m
⎛ a − c min ⎞
1 + 2⎜ cr
⎝ h−x ⎠ (4.20) where
acr – the distance from the point considered to the surface of
the nearest longitudinal bar (Fig. 4.5-4)
cmin – the minimum cover to the tension steel
h– the overall depth of the member x– the neutral axis depth calculated on the assumption of a
cracked section εm – the average strain at the level where the cracking is being
considered, calculated allowed for the concrete stiffening
effect in the tension zone. ε m = ε1 − ε 2 (4.21) where ε1 is the strain at the level considered Fig. 4.5-6. ε1 εs Fig. 4.5-6 Concrete bending strains ε1 = y fs
d − x Es (4.22) and
186 ε2 = bt ( h − x ) ( a′ − x )
3Es As ( d − x ) (4.23) where bt − the width of the section at centroid of tensile steel.
a' − the distance from the compression face to the point
at which the crack width is being calculated.
o In Eq. (4.21), a negative value of εm indicates that the section is uncracked.
(3) Examples of calculations for crack width
i. Example 6.4 “Calculation of flexural crack widths”, the Text by
Mosley et al., pp. 129-130. the figure For fcu = 30 N/mm2 the 187 = 394 mm 188 ii. Example 6.3 “Crack width calculation for T-beam”, Reference
by MacGinley & Choo, pp. 129-130.
iii. Example 5.6-1 – calculation of the design surface crack width,
pp. 188-190, and Example 5.7-1 – Design and detailing, pp.
191-194, Reference by Kong & Evans. 189 ...
View Full Document
- Spring '06