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Lecture 7 Flexure

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Floor systems with slabs and beams are placed in monolithic pour. ... Pouring a Pan Joist Slab. Walter P. Moore & Assoc. Pan Joist Floor Systems ... – PowerPoint PPT presentation

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Title: Lecture 7 Flexure


1
Lecture 7 - Flexure
  • June 16, 2003
  • CVEN 444

2
Lecture Goals
  • Doubly Reinforced beams
  • T Beams and L Beams
  • Pan Joist

3
Analysis of Flanged Section
  • Floor systems with slabs and beams are placed in
    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 8.10.2 T Beam Flange
9
ACI Code Provisions for Estimating beff
From ACI 318, Section 8.10.3 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 Assume steel yields
The flanges are considered to be equivalent
compression steel.
18
Analysis of T-Beam
Case 2 Equilibrium
19
Analysis of T-Beam
Case 2 Confirm
20
Analysis of T-Beam
Case 2 Confirm
21
Analysis of T-Beam
Case 2 Calculate nominal moments
22
Analysis of T-Beams
The definition of Mn1 and Mn2 for the T-Beam are
given as
23
Analysis of T-Beams
The ultimate moment Mu for the T-Beam are given
as
For a T-Beam with the tension steel yielded using
a function c/d
24
Limitations on Reinforcement for Flange Beams
  • Lower Limits
  • Flange in compression

25
Limitations on Reinforcement for Flange Beams
  • Lower Limits
  • Flange in tension

26
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

27
Example - T-Beam
Find Mn and Mu for T-Beam. beff 54 in. hf 3
in. b 7 ft. d 16.5 in. As 8.5 in2 fy
50 ksi fc 3 ksi bw 12 in L 18 ft
28
Example of L-Beam
Confirm beff
29
Example - T-Beam
Compute the equivalent c value and check the
strain in the steel, es
Steel will yield in the tension zone.
30
Example - T-Beam
Compute the reinforcement r and check to make
sure it is greater than rmin
Section works for minimum reinforcement.
31
Example - T-Beam
Compute w and check that the c value is greater
than hf
Analysis the beam as a T-beam.
32
Example - T-Beam
Compute w and check that the c value is greater
than hf
Compute a
33
Example - T-Beam
Compute nominal moment components
34
Example - T-Beam
Compute nominal moment
Compute ultimate moment
35
Example of L-Beam
Determine the effective b for the spandrel beam
and do the analysis. Use 4 9 bars and find the
ultimate moment capacity. fy50 ksi, fc 3 ksi
36
Example of L-Beam
Compute beff
37
Example of L-Beam
Compute beff
38
Example of L-Beam
The value beff and As
39
Example - L-Beam
Compute the equivalent c value and check the
strain in the steel, es
Steel will yield in the tension zone.
40
Example - L-Beam
Compute the reinforcement r and check to make
sure it is greater than rmin
Section works for minimum reinforcement.
41
Example - L-Beam
Compute w and check that the c value is greater
than hf
False!
Analysis the beam as a Singly reinforced beam.
42
Example - L-Beam
Compute a
43
Example - L-Beam
Compute nominal moment
44
Example - L-Beam
Compute ultimate moment
45
Pan Joist Floor Systems
View of Pan Joist Slab from Below
Walter P. Moore Assoc.
46
Pan Joist Floor Systems
Walter P. Moore Assoc.
View of Double Skip Joist Slab from Below
47
Pan Joist Floor Systems
Placing Reinforcement for a Pan Joist Slab
Walter P. Moore Assoc.
48
Pan Joist Floor Systems
General framing layout of the pan joist system.
49
Pan Joist Floor Systems
Pouring a Pan Joist Slab
Walter P. Moore Assoc.
50
Pan Joist Floor Systems
  • Definition The type of slab is also called a
    ribbed slab. It consists of a floor slab,
    usually 2-4 in. thick, supported by reinforced
    concrete ribs. The ribs are usually tapered and
    uniformly spaced at distances that do not exceed
    30 in. The ribs are supported on girders that
    rest on columns. In some ribbed slabs, the
    space between ribs may be filled with permanent
    fillers to provide a horizontal slab soffit.

51
One-Way Joist Construction
Definition Pan joist floor systems are series
of closely spaced cast-in-place T-beams or joists
used for long-span floors with relatively light
loads. Typically removable metal forms (fillers
or pans) are used to form joists.
MacGregor, Fig. 10-28
52
One-Way Joist Construction
Details of ribbed floor with removable steel pans.
Ribbed-floor cross sections.
53
One-Way Joist Construction
The design of a ribbed floor with steel pan forms
and average weight of the floor.
54
One-Way Joist Construction
The design of a ribbed floor with steel pan forms
and average weight of the floor.
55
One-Way Joist Construction
56
Pan Joist Floor Systems
  • ACI Requirements for Joist Construction
  • (Sec. 8.11, ACI 318-02)
  • Slabs and ribs must be cast monolithically.
  • Ribs must be spaced consistently
  • Ribs may not be less than 4 inches in width

57
Pan Joist Floor Systems
  • ACI Requirements for Joist Construction (cont.)
  • (Sec. 8.11.2, ACI 318-02)
  • Depth of ribs may not be more than 3.5 times the
    minimum rib width
  • Clear spacing between ribs shall not exceed 30
    inches.
  • Ribbed slabs not meeting these requirements
    are designed as slabs and beams.

58
Pan Joist Floor Systems
  • Slab Thickness
  • (ACI Sec. 8.11.6.1)
  • t 2 in. for joints formed with 20 in. wide
    pans
  • t 2.5 in. for joints formed with 30 in. wide
    pans (1/12 distance)

59
Pan Joist Floor Systems
  • Slab Thickness (cont.)
  • Building codes give minimum fire resistance
    rating
  • 1-hour fire rating ¾ in. cover, 3-3.5 slab
    thickness
  • 2-hour fire rating 1 in. cover, 4.5 slab
    thickness

60
Pan Joist Floor Systems
  • Standard Removable Form Dimensions
  • Note the shapes

61
Pan Joist Floor Systems
  • Standard Removable Form Dimensions
  • Standard Widths 20 in. 30 in. (measured at
    bottom of ribs)
  • Standard Depths 6, 8, 10, 12, 14, 16 or 20 in.

62
Pan Joist Floor Systems
  • Standard Removable Form Dimensions (cont.)
  • End Forms one end is closed (built-in) to form
    the supporting beam
  • Tapered End Forms provide additional shear
    capacity at ends of joists by tapering ends to
    increase rib width.

63
Pan Joist Slabs
Standard Pan Joist Form Dimensions Ref. CECO
Concrete Construction Catalog
64
Pan Joist Slabs
Standard Pan Joist Form Dimensions Ref. CECO
Concrete Construction Catalog
65
Pan Joist Floor Systems
  • Laying Out Pan Joist Floors
  • Rib/slab thickness
  • Governed by strength, fire rating, available
    space
  • Overall depth and rib thickness
  • Governed by deflections and shear

66
Pan Joist Floor Systems
  • Laying Out Pan Joist Floors (cont.)
  • Typically no stirrups are used in joists
  • Reducing Forming Costs
  • Use constant joist depth for entire floor
  • Use same depth for joists and beams (not always
    possible)

67
Pan Joist Floor Systems
  • Distribution Ribs
  • Placed perpendicular to joists
  • Spans lt 20 ft. None
  • Spans 20-30 ft. Provided a midspan
  • Spans gt 30 ft. Provided at third-points
  • At least one continuous 4 bar is provided at top
    and bottom of distribution rib.
  • Note not required by ACI Code, but typically
    used in construction

68
Member Depth
  • ACI provides minimum member depth and slab
    thickness requirements that can be used without a
    deflection calculation (Sec. 9.5 ACI 318)
  • Useful for selecting preliminary member sizes

69
Member Depth
  • ACI 318 - Table 9.5a
  • Min. thickness, h (for beams or ribbed one-way
    slab)
  • For beams with one end continuous L/18.5
  • For beams with both ends continuous L/21
  • L is span length in inches
  • Table 9.5a usually gives a depth too shallow for
    design, but should be checked as a minimum.

70
Member Depth
ACI 318-99 Table 9.5a
71
Member Depth
  • Rule of Thumb
  • hb (in.) L (ft.)
  • Ex.) 30 ft. span -gt hb 30 in.
  • May be a little large, but okay as a start to
    calc. DL
  • Another Rule of Thumb
  • wDL (web below slab) 15 (wSDL wLL)
  • Note For design, start with maximum moment for
    beam to finalize depth.
  • Select b as a function of d
  • b (0.45 to 0.65) (d)
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