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lecture27 - Serviceability August11,2003 CVEN444...

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    Elastic Flexural Analysis for  Elastic Flexural Analysis for  Serviceability Serviceability August 11, 2003 August 11, 2003 CVEN444 CVEN444
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    Lecture Goals Lecture Goals Serviceability Crack width Moments of inertia
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    Introduction Introduction Ultimate Limit States Lead to collapse Serviceability Limit States Disrupt use of Structures but do not cause collapse Recall:
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    Introduction Introduction Types of Serviceability Limit States - Excessive crack width - Excessive deflection - Undesirable vibrations - Fatigue (ULS)
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    Crack Width Control Crack Width Control Cracks are caused by tensile stresses due to loads moments, shears, etc..
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    Crack Width Control Crack Width Control Cracks are caused by tensile stresses due to loads moments, shears, etc..
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    Crack Width Control Crack Width Control Bar crack development.
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    Crack Width Control Crack Width Control Temperature crack development
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    Crack Width Control Crack Width Control Appearance   (smooth surface > 0.01 to 0.013                   public concern) Leakage (Liquid-retaining structures) Corrosion      (cracks can speed up occurrence  of  corrosion) Reasons for crack width control?
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    Crack Width Control Crack Width Control Chlorides ( other corrosive substances)  present Relative Humidity > 60 % High Ambient Temperatures (accelerates  chemical reactions) Wetting and drying cycles Stray electrical currents occur in the bars . Corrosion more apt to occur if (steel oxidizes rust )
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    Limits on Crack Width Limits on Crack Width 0.016 in. for interior exposure 0.013 in. for exterior exposure max.. crack width = ACI Code’s Basis Cracking controlled in ACI code by regulating the distribution of reinforcement in beams/slabs.
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    Limits on Crack Width Limits on Crack Width Gergely-Lutz Equation Crack width in units of 0.001 in. Distance from NA to bottom (tension) fiber, divided by distance to reinforcement. =(h-c)/(d-c) Service load stress in reinforcement in ksi ϖ = β = f s = 3 c s 076 . 0 A d f β ϖ =
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    Limits on Crack Width Limits on Crack Width Gergely-Lutz Equation Distance from extreme tension fiber to center of reinforcement located closest to it, (in.) effective tension area of concrete surrounding tension bars (w/ same centroid) divided by # bars. (for 1 layer of bars A = (2d c b)/n d c = A = 3 c s 076 . 0 A d f β ϖ =
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    Limits on Crack Width Limits on Crack Width ACI Code Eqn 10-5 ( limits magnitude of z term ) Note: ϖ = 0.076β z ( β = 1.2 for beams 29 Interior exposure: critical crack width = 0.016 in. ( ϖ = 16 29 z = 175k/in Exterior exposure: critical crack width = 0.013 in. ( ϖ = 13 29 z = 145k/in 3 c s A d f z =
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    Limits on Crack Width Limits on Crack Width Tolerable Crack Widths Tolerable Crack Width Dry air or protective membrane - 0.016 in.
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