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Lecture 11 Flexure

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Floor systems with slabs and beams are placed n monolithic pour. Slab acts as a top flange to the beam; T-beams,and Inverted L(Spandrel) Beams. ... – PowerPoint PPT presentation

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Title: Lecture 11 Flexure


1
Lecture 11 - Flexure
  • February 8, 2002
  • CVEN 444

2
Lecture Goals
  • Basic Concepts
  • T Beams

3
Analysis of Flanged Section
  • Floor systems with slabs and beams are placed n
    monolithic pour.
  • Slab acts as a top flange to the beam
    T-beams,and Inverted L(Spandrel) Beams.

4
Analysis of Flanged Sections
Positive and Negative Moment Regions in a T-beam
5
Analysis of Flanged Sections
If the neutral axis falls within the slab depth
analyze the beam as a rectangular beam, otherwise
as a T-beam.
6
Analysis of Flanged Sections
Effective Flange Width Portions near the webs are
more highly stressed than areas away from the web.
7
Analysis of Flanged Sections
Effective width (beff) beff is width
that is stressed uniformly to give the same
compression force actually developed in
compression zone of width b(actual)
8
ACI Code Provisions for Estimating beff
From ACI 318, Section 8.10 T Beam Flange
9
ACI Code Provisions for Estimating beff
From ACI 318, Section 8.10 Inverted L Shape Flange
10
ACI Code Provisions for Estimating beff
From ACI 318, Section 8.10 Isolated T-Beams
11
Various Possible Geometries of T-Beams
Single Tee Twin Tee Box
12
Analysis of T-Beam
Case 1 Same as rectangular
section Steel is yielding
under reinforced Check
13
Analysis of T-Beam
Case 1 Equilibrium
14
Analysis of T-Beam
Case 1 Confirm
15
Analysis of T-Beam
Case 1 Calculate Mn
16
Analysis of T-Beam
Case 2 Assume steel yields
17
Analysis of T-Beam
Case 2 Equilibrium
18
Analysis of T-Beam
Case 2 Confirm
19
Analysis of T-Beam
Case 2 Calculate
20
Analysis of T-Beams
The definition of Cc and Cf for the T-Beam are
given as
21
Analysis of T-Beams
The definition of Cc and Cf for the T-Beam are
given as
22
Limitations on Reinforcement for Flange Beams
  • Upper Limits

From balanced strain condition
Note For flange in compression and when balanced
neutral axis depth, cbal, is below flange Cc(bal)
Cf(bal) Cw(bal)
23
Limitations on Reinforcement for Flange Beams
  • Lower Limits
  • Flange in compression

24
Limitations on Reinforcement for Flange Beams
  • Lower Limits
  • Flange in tension

25
Limitations on Reinforcement for Flange Beams
  • Lower Limits
  • If As(provided) 4/3 As(reqd) based on
    analysis then As(min) is not required
    (i.e.) fMn 4/3Mu for As(provided)
    See ACI 10.5.3

26
Example - T-Beam
Find Mn As(max), As(min) for T-Beam. beff 54
in. hf 3 in. d 16.5 in. As 8.5 in2 fy
50 ksi fc 3 ksi bw 12 in L 18 ft
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