Lecture 30 Elastic Flexural Analysis for Serviceability

1
Lecture 30 - Elastic Flexural Analysis for
Serviceability

• April 3, 2001
• CVEN 444

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Lecture Goals

• Serviceability

3
Introduction
Recall
Ultimate Limit States Lead to
collapse Serviceability Limit States Disrupt
use of Structures but do not cause
collapse
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Introduction
Types of Serviceability Limit States - Excessive
crack width - Excessive deflection -
Undesirable vibrations - Fatigue (ULS)
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Crack Width Control
Cracks are caused by tensile stresses due to
loads moments, shears, etc..
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Crack Width Control
Cracks are caused by tensile stresses due to
loads moments, shears, etc..
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Crack Width Control
Bar crack development.
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Crack Width Control
Temperature crack development
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Crack Width Control
Reasons for crack width control?

• Appearance (smooth surface gt 0.01 to 0.013
  public concern)
• Leakage (Liquid-retaining structures)
• Corrosion (cracks can speed up occurrence
  of corrosion)

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Crack Width Control
Corrosion more apt to occur if (steel oxidizes
rust )

• Chlorides ( other corrosive substances) present
• Relative Humidity gt 60
• High Ambient Temperatures (accelerates chemical
  reactions)
• Wetting and drying cycles
• Stray electrical currents occur in the bars.

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Limits on Crack Width
ACI Codes Basis
0.016 in. for interior exposure 0.013 in.
for exterior exposure
max.. crack width
Cracking controlled in ACI code by regulating the
distribution of reinforcement in beams/slabs.
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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. Service load stress in
reinforcement 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 (2dc
b)/n
w
b
fs
dc
A
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Limits on Crack Width
ACI Code Eqn 10-5 ( limits magnitude of z term )
Note w 0.076b z (b 1.2)
Interior exposure critical crack width 0.016
in. ( w 16 ) z 175k/in Exterior
exposure critical crack width 0.013 in. (
w 13 ) z 145k/in
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Limits on Crack Width
Thin one-way slabs Use b 1.35
z 155 k/in (Interior Exposure) z 130 k/in
(Exterior Exposure)
fs service load stress may be taken as
1.55 - average load factor f - strength
reduction factor for flexure
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Example
Given A beam with bw 14 in. Gr 60 steel 4 8
with 2 6 in the second layer with a 4 stirrup.
Determine the crack width limit, z for exterior
and interior limits (145 k/in and 175 k/in.).