lecture27 - Elastic Flexural Analysis for Elastic Flexural...

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Unformatted text preview: Elastic Flexural Analysis for Elastic Flexural Analysis for Serviceability Serviceability August 11, 2003 August 11, 2003 CVEN444 CVEN444 Lecture Goals Lecture Goals Serviceability Crack width Moments of inertia Introduction Introduction Ultimate Limit States Lead to collapse Serviceability Limit States Disrupt use of Structures but do not cause collapse Recall: Introduction Introduction Types of Serviceability Limit States- Excessive crack width- Excessive deflection- Undesirable vibrations- Fatigue (ULS) Crack Width Control Crack Width Control Cracks are caused by tensile stresses due to loads moments, shears, etc. . Crack Width Control Crack Width Control Cracks are caused by tensile stresses due to loads moments, shears, etc. . Crack Width Control Crack Width Control Bar crack development. Crack Width Control Crack Width Control Temperature crack development 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? 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 ) Limits on Crack Width Limits on Crack Width 0.016 in. for interior exposure 0.013 in. for exterior exposure max. . crack width = ACI Codes Basis Cracking controlled in ACI code by regulating the distribution of reinforcement in beams/slabs. 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 = = f s 3 c s 076 . A d f = 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 . A d f = Limits on Crack Width Limits on Crack Width ACI Code Eqn 10-5 ( limits magnitude of z term ) Note: = 0 .0 7 6 z ( = 1 .2 for beams 29 Interior exposure: critical crack width = 0.016 in. ( = 1 6 29 z = 175k/in Exterior exposure: critical crack width = 0.013 in....
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lecture27 - Elastic Flexural Analysis for Elastic Flexural...

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