????? Applied Statistics

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?????Applied Statistics
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• ?Modern Engineering Statistics?Lawrencel. Lapin?

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METHOD OF DESIGN

• Working Stress Design /
• Allowable Stress Design - ASD

• Ultimate Strength Design /
• Load Resistance Factor Design - LRFD

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??? ASD ? LRFD

• ASD (Allowable Steel Design)
• ???????????,??????????????????,??????????,????
  AISC 9th Edition ???,???????,??????????????? 60,
  ???????????,???????????
• LRFD (Load and Resistance Factor Design)
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  ?????????????,??????????????

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DIFFERENCES BETWEEN PBI '71 AND SNI
? PBI 1971 ? SNI Allowable Stress Load
Resistance Design (ASD) Factor Design
(LRFD) Ultimate Strength Design
? Q ? ? R
Where Q load ? load factor R
nominal strength of material ? reduction
factor SF safety factor
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ALLOWABLE STRESS DESIGN (ASD)
Where Q load R nominal strength of
material SF safety factor
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ASD?????

• ASDFb0.66Fy

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LOAD RESISTANCE FACTOR DESIGN (LRFD)
Where ? load factor ? reduction
factor Q load Rn nominal strength of material
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• ??????????????????????????????????????????????Q?R?
  ??,?RltQ?,????????
• ????????????????????????????,Q?R???????????,??????
  ?Qm?Rm,?????dQ?dR??????

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?????ß???

• ????,??????????????????,??????????ln(R/Q),?ln(R/Q)
  ? 0?,???????,???????????????????????Rm?Qm?dR?dQ??
  ?,?ßsln(R/Q) ln(R/Q)m,???ln(R/Q) ?
  0??????????ß????,ß??????????
• ??
• VRdR/Rm???? VQdQ/Qm?????? ß??????

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Load and Resistance Factor Calibration Concepts
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SAFETY PROVISIONS

• 1. Overloaded probability ? covered by Load
  Factor
• U 1.2 D 1.6 L
• 1.05 (D LR ? E)
• 0.9 D ? E
• 0.75 (1.2 D1.6 L1.6 W) etc.
• 2. Understrength probability ? covered by
  Reduction Factor
• Bending without axial load ? 0.80
• Axial Tension ? 0.80
• Axial Compression
• conventional stirrup ? 0.65
• spiral stirrup ? 0.70
• Shear and Torsion ? 0.60

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• 3. Reasons for Safety Factor Necessity
• Variability in Strength
• a. Variability of concrete strength steel
  reinforcement
• b. Actual dimension ? design dimension
• c. Simplification of Assumptions
• Variability in Loading
• Consequences of Collapse
• a. Loss of human life
• b. Loss of material, time, ......
• c. Cost of renovation and re-built

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LOAD REDUCTION FACTOR
Pf 460 e-4.3?
? 3.5 Pf 1.1 x 10 -4 ? 4 Pf
3.2 x 10 -5 ? 4.5 Pf 3 x 10 -6 ?
?R e -??VR ?R R/RN ? ?U e ??VU
??y
Frequency
0
Y R - Q Safety margin
P (R - Q) lt 0 shaded area Pf
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Risk of Various Activities
10-3 Motorcycle racing Avoidable risks
connected Mining with daring people 10-3
per year Automobile travel 10-4
Swimming Avoidable risk connected Airplane
travel with careful people 10-4 per year
Fire in Building 10-5 Poisoning Unavoidable
risk Structural collapse 10-5 per
year 10-6 Lightning 10-7
10-8 Vaccinations
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VARIABILITY IN STRENGTH
Distribution of steel yield stress for grade 60
reinforcement (Allen 1972)
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VARIABILITY IN STRENGTH
- Contd.
Variation in mill test yield strength with bar
size grade 60 reinforcement (Grant 1976)
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- Contd.
VARIABILITY IN STRENGTH
Difference between actual widths of columns and
the sizes shown on drawings. (Tso and Zelman 1970)
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- Contd.
VARIABILITY IN STRENGTH
Ratio of actual bar area to nominal area (Allen
1972)
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- Contd.
VARIABILITY IN STRENGTH
Comparison of strengths calculated using
rectangular stress block to strength measured in
laboratory tests. (Mattock et al.1961)
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- Contd.
VARIABILITY IN STRENGTH
Dispersion of strengths of eccentrically loaded
columns in a randomly generated sample of 1000
columns (Grant 1976).
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SUBSTANTIAL PARAMETERS CAUSE DEVIATION IN
CONCRETE STRUCTURE DESIGN
BENDING fy 63 BEAMS As 24
BENDING d 56 SLABS fy 31 As
12 COLUMNS fc 89.9 fy
9.8 SHEARS s 70 fy 16
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DEAD LOADS
1. Mass unit of building material
Steel 7850 kg/m3 Un-reinforced concrete 2200
kg/m3 Reinforced concrete 2400
kg/m3 Wood/timber 1000 kg/m3 Glass 2500
kg/m3 Sand 1800 kg/m3 Soil 2000 kg/m3 Water
1000 kg/m3
2. Dead load of building component
Cement specimen with 10 mm thick 0.21
kPa Aspalt with 10 mm thick 0.14 kPa Brick wall
(one brick thick) 4.50 kPa Brick wall (½ brick
thick) 2.50 kPa Batako wall with 200 mm thick
2.00 kPa Batako wall with 120 mm thick 1.20
kPa Ceiling with AC ducting 0.30 kPa Granite
floor 0.26 kPa Floor specimen with 10 mm
thick 0.22 kPa Precast panel granite 4.50
kPa
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LIVE LOADS - for several analysis
Live Loads Analysis of Analysis
of Analysis of Slab and Frame Earthquake Room
Secondary Beam (kN/m2) (kN/m2) (kN/m2
) 1. Office 2.50 - 4.00 1.50 - 2.40 0.75 -
1.20 2. Hotel, hospital, 2.50 1.875 0.75
Apartment 3. School 2.50 2.25 1.25 4. Market,
Dept.store 2.50 2.00 2.00 5. Parking Area
- single floor 0.80 7.20 4.00 -
others 4.00 3.60 2.00 6. Multifunction
Hall 5.00 4.50 2.50 7. Library, storage
4.00 - 5.00 3.20 - 4.00 3.20 - 4.00 8.
Stair - Office 3.00 2.25 1.50 -
Hotel 3.00 2.25 0.90 - Others 3.00 2.70 1.50
Reduced Live Load (LR)
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LIVE LOADS - for Axial Load in Columns
Number of storey Live Load Reduction Coefficient
multiplied with supported by column sum of axial
live load supported by columns
1 1.0 2 1.0 3 0.9 4 0.8 5 0.7 6 0
.6 7 0.5 more than 7 0.4
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Variability of Strength
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VARIABILITY

• measured properties not exact
• always variability
• material
• sampling
• testing
• probability of failure
• mean, standard deviation (s), coefficient of
  variation (COV)

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DESIGN / SAFETY FACTORS

• design strength f(material, construction
  variables)
• working stress f(sy)
• N 1.2 to 4 f(economics, experience,
  variability in inputs, consequences of failure)

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?????LOADS ON BRIDGES

• Permanent Loads remain on the bridge for an
• extended period of time (self weight of the
  bridge)
• Transient Loads loads which are not permanent
• - gravity loads due to vehicular, railway and
• pedestrian traffic
• - lateral loads due to water and wind, ice
  floes??(?),
• ship collision, earthquake, etc.

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?? ???kg/m3
? 7850
?? 7210
??? 2800
?? 800
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???????????? 1900
??????? 1600
???????? 2250
?? 2400
??? 2700
?? 300
???25mm? 44
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Statistical Methods
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• ?????( Descriptive Statistics )
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• ?????( Inferential Statistics )
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Descriptive Statistics

• Involves
• Collecting data
• Presenting data
• Characterizing data
• Purpose
• Describe data

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Descriptive Statistics

• Involves
• Collecting data
• Presenting data
• Characterizing data
• Purpose
• Describe data

X 30.5 S2 113
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Inferential Statistics

• Involves
• Estimation
• Hypothesis testing
• Purpose
• Make decisions about population characteristics

Population?
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Key Terms

• Population (universe)
• All items of interest
• Sample
• Portion of population
• Parameter
• Summary measure about population
• Statistic
• Summary measure about sample

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Key Terms

• P in Population Parameter
• S in Sample Statistic

• Population (universe)
• All items of interest
• Sample
• Portion of population
• Parameter
• Summary measure about population
• Statistic
• Summary measure about sample

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• Descriptive statistics
• - Describe data by numbers
• average of proportion
• measure of variability
• divide the range of data into parts with equal
  frequency
• - Describe data by graphs (histograms).

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