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Order of Play… Introduction What width is suitable for my project? Calculations to BS5400-4 Eurocode (Evan) Question Time
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Crack Width Calculations 4 Design: general 4.1 Limit state requirements 4.1.1 Serviceability limit states 4.1.1.1 Cracking. Cracking of concrete should not adversely affect the appearance or durability of the structure. The Engineer should satisfy himself that any cracking will not be excessive, having regard to the requirements of the particular structure and the conditions of exposure. In the absence of special investigations, the following limits should be adopted. a) Reinforced concrete . Design crack widths, as calculated in accordance with 5.8.8.2 , should not exceed the values given in Table 1 under the loading given in 4.2.2 . BS5400-4-1990 Introduction
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What width is suitable for my project? (Table 1 BS5400-4) http://www.avongard.co.uk/images/products_crack_width_gauge/Crack_Width_Gauge_Product.jpg viewed on 23/09/09 0.25 mm Environment: Severe – Concrete surfaces exposed to driving rain OR alternate wetting and drying. 0.25 mm Environment: Moderate – Concrete surfaces above the ground level and protected from the following: rain de-icing salts sea water spray 0.25 mm Environment: Moderate – Concrete surfacing permanently saturated in water with a pH > 4.5
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What width is suitable for my project? (Table 1 BS5400-4) http://www.avongard.co.uk/images/products_crack_width_gauge/Crack_Width_Gauge_Product.jpg viewed on 23/09/09 0.15 mm Environment: Very Severe – Concrete surfaces directly affected by de-icing salts or sea water spray. 0.10 mm Environment: Extreme – Concrete surfaces exposed to abrasive action by sea water or water with a pH < 4.5
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x x Where do we start!? ε s ε c σ c F c F S d dc Strain Stress
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σ c F c F S Calculations STEEL: Fs = A s * E s * ε s Going back to the previous slide, as the strain in the steel is a function of the strain in the concrete (it varies linearly) we can substitute for: ε s = ((d-dc)/dc)* ε c F s = A s * E s * ((d-dc)/dc) * ε c Where f s ≤ 0.75f y CONCRETE: Fc = f cu * b * dc * 0.5 As fcu is a stress we can substitute f cu = E c ε c Fc = 0.5 * E c ε c * b * dc For Equilibrium: F c = F s As… E = σ / ε and F = σ * Area using Table 2 … ε s ε c
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0.5 * E c ε c * b * dc A s * E s * ((d-dc)/dc) * ε c For Equilibrium: Fc = Fs = Calculations After cancelling ε c from both sides we now have a formula which can be rearranged to solve for the unknown dc by using quadratic formula… x x d dc ε s ε c σ c F c F S N.B. 4.3.2.1 Table 3 gives values for E c to use for the characteristic strength. b) Analysis of section. To determine crack widths and stresses due to the effects of permanent and short term loading and imposed deformations: an appropriate intermediate value between that given in Table 3 and half that value. creep Using the quadratic equation the end result will be: d c = - A s .E s + - √((A s .E s ) 2 – 2E c .b.A s .E s ) Ec.b
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Calculations The next step is to calculate the second moment of area I conc and I steel for the section using d c calculated. This is required to help us to find ε s . I total = I conc + I steel remembering to modify I conc by the modular ratio of the two different materials. σ / y = M / I and σ = M / Z and ε = σ / E Therefore… ε s = M / Z * 1 / Es (with Z calculated from I above) Using your applied moment the equation can be solved to find the strain in the steel bars
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Crack Width Equations (BS5400-4) Equation 24 where Equation 25 But ε m is not greater than ε 1 From previous slides we know h, d c , A s , b t , M q and M g Allows for stiffening effect of concrete in tension zone a) For solid rectangular sections, stems of T beams and other solid sections shaped without re-entrant angles, the design crack widths at the surface (or, where the cover to the outermost bar is greater than c nom, on a surface at a distance c nom from the outermost bar) should be calculated from the following equation:
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cL cL Level of Point Considered, strain at this point is ε m a cr a’ dc What is ε m ? ε m is the strain at the level at which the crack width is being considered allowing for the stiffening effect of the concrete in tension zone (negative value = uncracked). c nom ε 1 is the strain at the level at which the crack width is being considered ignoring the stiffening effect (this is calculated using earlier calculated value of ε s , as the strain varies linearly when ignoring the stiffening effect). a cr is the distance from the crack to the surface of the nearest bar which controls the crack width. h b t
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b) For flanges in overall tension, including tensile zones of box beams and voided slabs, the design crack width at the surface (or at a distance c nom from the outermost bar) should be calculated from the following equation: Design crack width = 3 a cr ε m Equation 26 where ε m is obtained from equation 25. Finally… compare design crack width to Table 2. Crack Width Equations (BS5400-4)
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