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Reinforced Concrete to BS EN 1992-2 & UK National Annex Index 1.Introduction 2.Serviceability Limit State 3.Ultimate Limit State 4.Shear 1. Introduction Both the Serviceability and Ultimate Limit States need to be considered. Serviceability Limit State ensures that crack widths do not exceed specified values, and also ensures that concrete and reinforcement stresses are maintained below a safe limit. Ultimate Limit State ensures that the structure will not collapse. 2. Serviceability Limit State i) Crack Control Cracks in concrete can be caused by : y corrosion of the reinforcement which causes the concrete to spall y thermal movements, particularly cooling from heat of hydration (called early thermal cracking) y structural actions such as bending, shear or torsion Corrosion of reinforcement is controlled by use of suitable concrete grades and providing adequate cover to the reinforcement. Cracks due to thermal movements are controlled by providing minimum nominal steel area and restricting the maximum bar spacing. Ciria Publication C660 is used to calculate the minimum steel area and bar spacing to control early thermal cracking. The width of shear cracks is controlled by ultimate strength calculations. Crack widths caused by bending and tension may be calculated using Clause 7.3.4, alternatively Clause 7.3.3 may be used to limit the stress in the bar for a given bar diameter, or a given bar spacing, from Tables 7.2N & 7.3N. For calculating the crack width only the quasi-permanent load combination is used. 2 = 0 for traffic actions and 2 = 0.5 for thermal actions consequently only thermal actions (variable action) are considered in combination with the permanent actions. However only secondary effects of the temperature difference need to be considered; the primary self-equilibrating stresses may be ignored. Crack widths may be calculated using Clause 7.3.4. The crack width (wk) is a function of the spacing between the cracks (s r,max) and the strain in the reinforcement ( sm) and concrete (cm): wk = sr,max(sm - cm) ................ ............... .................... .............. ............... Equation (7.8) where sr,max = k3c + k1k2k4/p,eff ............................................................Equation (7.11) and (sm - cm) = {s - [ktf ct,eff (1 + ep,eff )/p,eff ]}/Es 0.6s /Es ................Equation (7.9) Using a rectangular section as an example: We first need to determine the position of the neutral axis: Es = 200kN/mm 2 (clause 3.2.7(4)) The short-term value of Ec,eff is obtained from the value of Ecm in Table 3.1 which is appropriate to the live load portion of the moment (Mst). The permanent load portion of the moment (M qp) has a long-term value of Ec,eff to take account of the effects of creep. The modified value of E c,eff used for the crack width calculation is an intermediate value between the short and long term values. Modified Ec,eff = Ecm(Mst + Mqp) / [Mst + Mqp(1 + )] where i s the val ue of the creep coefficient (,t 0). eff = Modular ratio = Es / Ec,eff . p,eff = As / bd and ' p,eff = A' s / bd Then x/d = ¥{[eff p,eff +(eff -1)' p,eff ] 2 +2[eff p,eff +(eff -1)'p,eff d'/d]}-[eff p,eff +(eff -1)'p,eff ] Second Moment of Area of Cracked Section I c = bx 3 /3 + (eff -1)As'(x-d') 2 + eff As(d-x) 2 Hence reinforcement stress s = eff MEd(d-x)/I c where MEd = Mqp+Mst kt is obtained by interpolation between 0.4 for long-term and 0.6 for short-term loadings:
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