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Lecture_20 - 4.5 Cracking 4.5.1 Methods for crack control...

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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 3.12.11.2.1 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 further cracking. 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 existing cracks. 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 reinforcement. 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 ...
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