Giải thích hệ số PBN - Kennedy and Sennah

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Kennedy and Sennah
Steel Boxes
Possibly concrete with modifications
Similar to LRFD approach (authors claim
better accuracy)
Empirical
“Ugly” equations
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European Practice
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Examples
AASHTO LRFD
Henry (old method)
CSA
Sanders and Elleby
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Summary
Moment Shear Moment Shear Moment Shear Moment Shear
AASHTO LRFD 0.694 0.955 0.840 0.840 0.732 0.884 0.733 0.733
Canadian Bridge Design Code 0.895 0.895 1.034 1.034 0.783 0.783 0.930 0.930
Sanders and Elleby 0.710 0.710 0.710 0.710 0.946 0.946 0.946 0.946
Equal Distribution Factor Method 0.774 0.774 0.774 0.774 0.655 0.655 0.655 0.655
Interior Exterior
PCI Example 4
Interior Exterior
Method
AISI Example 2
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Task 2 – Range of structural forms, materials
and range of application

Range of application
 There is no reason at this point to limit range of
application (we can include range outside of
conventional practice and geometries)
 “All” parameters will be included in the
database
 A large amount of data is available from
several sources (see Task 6 tables)
 Additional data can be added
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Task 3 -- Analytical method
 Mathematical model
 Equilibrium,
compatibility, and
constitutive
relationships
 Beam theory
 Kirchhoff plate theory
 Results in governing
ODE or PDF


4
4
p x
d w
dx EI x

 
4

,p x y
w
D
 
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Task 3 -- Analytical method
Numerical methods
 Finite difference
 Finite element method (plate or shell elements)
 Grillage
 Finite Strip Method
 Harmonic analysis (Sanders and Elleby)
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Theorem Requirements
Calculated internal actions and applied
forces are in equilibrium
Materials and section/member behavior
must be ductile
Independent of the
modeling assumptions!
No instability or fracture
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The lower bound theorem is
one of the most important
theorems/concepts in
structural engineering.
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The lower bound theorem is
one of the most important
theorems/concepts in

structural engineering.
Offers wonderful assurance as the models
are often simple approximations to the
real world.