Serviceability limit state - Eurocodes

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Influence of tension stiffening of concrete on stresses in reinforcement G. Hanswille Univ.-Prof. Dr.-Ing. Institute for Steel and Composite Structures University of Wuppertal-Germany ε sm N s equilibrium: z s M s ≈0 M Ma = M−Ns a a M a ε a -κ N = − a N s z a N a compatibility: mean strain in the concrete slab: ε sm = ε a + κa ε sm N + s E A a a N + E s a a A 2 a = M a E a J a ε s,2 ε s,m Δε s =βΔε s,r mean strain in the concrete slab: ε c ε s ε sm = ε s2 −βΔε sr N = s E A s s f −β ρ ct,eff s E s 14
Redistribution of sectional forces due to tension stiffening G. Hanswille Univ.-Prof. Dr.-Ing. Institute for Steel and Composite Structures University of Wuppertal-Germany fully cracked section tension stiffening z 2 =z st -z st,s z st,a a N s,2 -M s,2 ΔN ts -M a,2 + = ΔN ts a -M s N s -M a -M Ed -N a,2 -ΔN ts -N a N s α N sε st A = A N s st a J J st a ΔN ts = β ΔN ts N s,2 M Ed f ct,eff ρ M s α A st s N Sectional forces: N a s = N M = M M s = N a a2 s2 = M Ed + ΔN − ΔN a2 J J s st ts ts + ΔN = M = M ts a Ed Ed A A a = M s J J z Ed st z st st,s st,a J st = J 2 J J a st + ΔN − ΔN ts + ΔN ts ts a 15
Page 1 and 2: G. Hanswille Univ.-Prof. Dr.-Ing. I
Page 3 and 4: Serviceability limit states G. Hans
Page 7 and 8: Shear lag- effective width G. Hansw
Page 9 and 10: Effects of creep of concrete G. Han
Page 11 and 12: Modular ratios taking into account
Page 13: Effects of cracking of concrete and
Page 19 and 20: Effects of cracking of concrete - s
Page 21 and 22: Control of cracking G. Hanswille Un
Page 23 and 24: Exposure classes according to EN 19
Page 25 and 26: N s ε Cracking of concrete - intro
Page 27 and 28: N s Determination of initial crack
Page 29 and 30: Crack width for stabilised crack fo
Page 31 and 32: Crack width and crack spacing accor
Page 33 and 34: Simplified solution for the crackin
Page 35 and 36: Control of cracking due to direct l
Page 37 and 38: Direct calculation of crack width w
Page 39 and 40: Stresses in reinforcement for final
Page 43 and 44: Deformations and pre-cambering G. H
Page 45 and 46: More accurate method for the determ
Page 47 and 48: Differential equations in case of i
Page 49 and 50: Mean values of stiffness of headed
Page 51 and 52: Comparison of the exact method with
Page 53 and 54: Deflection in case of incomplete in
Page 55 and 56: Limitation of Stresses G. Hanswille
Page 57 and 58: Local effects of concentrated longi
Page 59 and 60: Serviceability limit state - longit
Page 61 and 62: Vibration- General G. Hanswille Uni
Page 63 and 64: Vibration - Example vertical vibrat
Page 65 and 66:
Vibration - vertical vibrations due
Page 67 and 68:
Vibration -vertical vibrations due
Page 69 and 70:
G. Hanswille Univ.-Prof. Dr.-Ing. I
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Serviceability limit state - Eurocodes

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