Analysis OneWay Joist
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Transcript of Analysis OneWay Joist
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Lecture 8 - Flexure
June 18, 2003
CVEN 444
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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
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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 theserequirements are designed as slabs andbeams. **
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Pan Joist Floor Systems
Slab Thickness
(ACI Sec. 8.11.6.1)
t 2 in. for joints formed with 20 in. widepans
t 2.5 in. for joints formed with 30 in. widepans (1/12 distance)
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Pan Joist Floor Systems
Slab Thickness (cont.)
Building codes give minimum fire resistancerating:
1-hour fire rating: in. cover, 3-3.5 slabthickness
2-hour fire rating: 1 in. cover, 4.5 slabthickness
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Pan Joist FloorSystems
StandardRemovable FormDimensions
Note the shapes
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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 or20 in.
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Pan Joist Floor Systems
Standard Removable Form Dimensions(cont.)
End Forms: one end is closed (built-in) toform the supporting beam
Tapered End Forms: provide additional shearcapacity at ends of joists by tapering ends toincrease rib width.
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Pan JoistSlabs
Standard Pan Joist
Form Dimensions
Ref. CECO Concrete
Construction Catalog
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Pan Joist
Slabs
Standard Pan Joist
Form DimensionsRef. CECO Concrete Construction
Catalog
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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
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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)
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Pan Joist Floor Systems
Distribution Ribs
Placed perpendicular to joists*
Spans < 20 ft.: None
Spans 20-30 ft.: Provided a midspan
Spans > 30 ft.: Provided at third-points
At least one continuous #4 bar is provided at topand bottom of distribution rib.
*Note: not required by ACI Code, but typically usedin construction
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Member DepthACI provides minimum member depth andslab thickness requirements that can be usedwithout a deflection calculation (Sec. 9.5 ACI318)
Useful for selecting preliminary membersizes
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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 fordesign, but should be checked as a minimum.
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MemberDepth
ACI 318-99: Table 9.5a
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Member Depth
Rule of Thumb:
hb (in.) ~ L (ft.)
Ex.) 30 ft. span -> hb ~ 30 in.
May be a little large, but okay as a start tocalc. DL
Another Rule of Thumb:
wDL (web below slab) ~ 15% (wSDL+ wLL)
Note: For design, start with maximummoment for beam to finalize depth.
Select b as a function of d
b ~ (0.45 to 0.65) (d)
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Approximate Analysis of ContinuousBeam and One-Way Slab Systems
ACI Moment and Shear Coefficients
Approximate moments and shearspermitted for design of continuousbeams and one-way slabs
Section 8.3.3 of ACI Code
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Approximate Analysis of ContinuousBeam and One-Way Slab Systems
ACI Moment and Shear Coefficients -Requirements:
Two or more spans
Approximately Equal Spans Larger of 2 adjacent spans not greater than
shorter by > 20%
Uniform Loads
LL/DL 3 (unfactored)
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Approximate Analysis of ContinuousBeam and One-Way Slab Systems
ACI Moment and Shear Coefficients -Requirements: ( cont.)
Prismatic members
Same A, I, E throughout member lengthBeams must be in braced frame withoutsignificant moments due to lateral forces
Not state in Code, but necessary for
coefficients to apply.
** All these requirements must be met to use thecoefficients!**
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Approximate Analysis of ContinuousBeam and One-Way Slab Systems
2
)(2
nu
vu
numu
lw
CV
lwCMwu = Total factored dead and live
load per unit length
Cm = Moment coefficientCv = Shear coefficient
ln = Clear span length for span inquestion forMu at interior
face of exterior support, +Muand Vuln = Average of clear span length
for adjacent spans forMu atinterior supports
ACI Moment and Shear Coefficients Methodology:
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Approximate Analysis of ContinuousBeam and One-Way Slab Systems
ACI Moment andShearCoefficients
See Section8.3.3 of ACICode
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Example
Design the eight-span east west
in figure. A typical 1-ft wide
design strip is shaded. A
partial section through this
strip is shown. The beams areassumed to be 14 in. wide.
The concrete strength is 3750
psi and the reinforcement
strength is 60 ksi. The liveload is 100 psf and dead load
of 50 psf.
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ExampleOne-way Slab
Use table 9.5(a) to determine the minimum
thickness of the slab. 12 in15 ft 180 in
ftl
180 in.
min. h = 7.5 in.24 24
l End bay:
180 in.min h = 6.43 in.28 28
l
Interior bays:
Use 7.5 in.
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ExampleOne-way Slab
Compute the trial factored loads based on thickness.
D 3 2
1 ft lb lb7.5 in 150 93.75
12 in ft ft
w
u D L1.2 1.6 1.2 50 psf + 93.75 psf 1.6 100 psf
332.5 psf
w w w
Factored load
L D3w wCheck ratio for 8.3.3
OK!
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ExampleOne-way Slab
Compute factored external moment.
22
UU
332.5 psf 15 ft6801. lb-ft/ft
C 1181.61 k-in/ft
w LM
UN
81.61 k-in/ft 90.68k-in/ft0.9
MM
Nominal moment
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ExampleOne-way Slab
The thickness is 7.5 in. so we will assume that the bar
is located d = 7.5in1.0 in. = 6.5 in. (From 3.3.2 ACI
318 0.75 in + ~0.25 in( 0.5*diameter of bar) = 1.0 in
N s y
2Ns
y
0.92
90.68 k-in/ft0.258 in /ft0.9 60 ksi 0.9 6.5 in
aM T d A f d
MA f d
Assume that the
moment arm is 0.9d
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ExampleOne-way Slab
Recalculate using As = 0.2 in2
s y
c
NN s y s
y
s
2
0.258 in. 60 ksi0.405 in.
0.85 0.85 3.75 ksi 12 in
2
2
90.68 k-in/ft0.405 in.
60 ksi 6.5 in.2
0.240 in /ft
A fa
f b
MaM A f d A
af d
A
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ExampleOne-way Slab
Check the yield of the steel
1
t cu
0.405 in.0.476 in.
0.85
6.5 in. 0.476 in.0.003
0.476 in.
0.038 0.005
ac
d c
c
Steel has yielded so
we can use = 0.9
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ExampleOne-way Slab
Check to minimum requirement for every foot
s
y
min min
c
y
0.24 in.0.00301
12 in. 6.5 in.
200 200 0.0033360000
0.003333 3 3750
0.003160000
A
bd
f
f
f
Problem!
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ExampleOne-way Slab
What we can do is rework the spacing between the bars
by change b Use a #4 bar As = 0.2 in2
2
s s 0.2 in 9.23 in.0.00333 6.5 in.
Use b = 9 in.
A Ab
bd d
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ExampleOne-way Slab
Check for shrinkage and temperature reinforcement for
min = 0.0018 As = minbh from 7.12.2.1 ACI
2s min
2
2
0.0018 12 in. 7.5 in. 0.162 in /ft
0.2 inspacing = 12 in. =14.8 in.
0.162 in
A bd
Use 1 # 4 bar every 9 in.
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Pattern Loads
Using influence lines to determine patternloads
Largest moments in a continuous beam orframe occur when some spans are loadedand others are not.
Influence lines are used to determine whichspans to load and which spans not to load.
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Pattern Loads
Influence Line: graph of variation ofshear, moment, or other effect at one
particular point in a structure due to a unitload moving across the structure.
P tt
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PatternLoads
QuantitativeInfluenceLines
Ordinate arecalculated(exact)
MacGregor (1997)
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Pattern Loads
Qualitative Influence Lines
Mueller-Breslau Principle
Used to provide a qualitative guide tothe shape of the influence line
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Pattern Loads
Qualitative Influence Lines (cont.)
For moments
Insert pin at location of interest
Twist beam on either side of pinOther supports are unyielding, so
distorted shape may be easily drawn.
For frames, joints are assumed free to
rotate, assume members are rigidlyconnected (angle between membersdoes not change)
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Qualitative Influence LinesThe Mueller-Breslau principle
can be stated as follows:
I f a function at a point on a
structure, such as reaction, or
shear, or moment is allowed to
act without restraint, the
deflected shape of the structure,
to some scale, represents the
inf luence line of the function.
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Pattern LoadsFrame Example:
Maximize +M at point B.
Draw qualitative
influence lines.
Resulting pattern load:
checkerboard pattern
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Pattern Loads
Arrangement of Live Loads (ACI 318-02, Sec. 8.9.1)
It shall be permitted to assume that:
The live load is applied only to the flooror roof under consideration, and
The far ends of columns built integrally
with the structure are considered to befixed.
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Pattern Loads
Arrangement of Live Loads ACI 318-99, Sec. 8.9.2:
It shall be permitted to assume that the
arrangement of live load is limited tocombinations of:
Factored dead load on all spans with full
factored live load on two adjacentspans.
Factored dead load on all spans with fullfactored live load on alternate spans.