Title: Lecture 11 Flexure
1Lecture 11 - Flexure
- February 8, 2002
- CVEN 444
2Lecture Goals
3Analysis 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.
4Analysis of Flanged Sections
Positive and Negative Moment Regions in a T-beam
5Analysis of Flanged Sections
If the neutral axis falls within the slab depth
analyze the beam as a rectangular beam, otherwise
as a T-beam.
6Analysis of Flanged Sections
Effective Flange Width Portions near the webs are
more highly stressed than areas away from the web.
7Analysis 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)
8ACI Code Provisions for Estimating beff
From ACI 318, Section 8.10 T Beam Flange
9ACI Code Provisions for Estimating beff
From ACI 318, Section 8.10 Inverted L Shape Flange
10ACI Code Provisions for Estimating beff
From ACI 318, Section 8.10 Isolated T-Beams
11Various Possible Geometries of T-Beams
Single Tee Twin Tee Box
12Analysis of T-Beam
Case 1 Same as rectangular
section Steel is yielding
under reinforced Check
13Analysis of T-Beam
Case 1 Equilibrium
14Analysis of T-Beam
Case 1 Confirm
15Analysis of T-Beam
Case 1 Calculate Mn
16Analysis of T-Beam
Case 2 Assume steel yields
17Analysis of T-Beam
Case 2 Equilibrium
18Analysis of T-Beam
Case 2 Confirm
19Analysis of T-Beam
Case 2 Calculate
20Analysis of T-Beams
The definition of Cc and Cf for the T-Beam are
given as
21Analysis of T-Beams
The definition of Cc and Cf for the T-Beam are
given as
22Limitations on Reinforcement for Flange Beams
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)
23Limitations on Reinforcement for Flange Beams
- Lower Limits
- Flange in compression
24Limitations on Reinforcement for Flange Beams
- Lower Limits
- Flange in tension
25Limitations 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
26Example - 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