Corbel
The analysis in the software "Corbel" is done according to the following procedures:
Design value of the stress in joint
The value of the design compressive strength is defined as
Where is: | fcd |
|
αcc |
| |
fck |
| |
γc |
|
The design values for the compressive stresses in nodes where no ties are anchored at the node (type CCC) is given by the following expression according to the chapter 6.5.4. (4):
The design values for the compressive stresses in compression - tension nodes with anchored ties provided in one direction (type CCT) is given by the following expression according to the chapter 6.5.4. (4):
The design values for the compressive stresses in compression - tension nodes with anchored ties provided in more than one direction (type CTT) is given by the following expression according to the chapter 6.5.4. (4):
Where is: | σRd,max |
|
k1 |
| |
k2 |
| |
k3 |
| |
ν' |
| |
fcd |
|
The reduction coefficient ν' is calculated in accordance with the chapter 6.5.2 (2):
Where is: | fck |
|
Strut and tie model
The width (horizontal projection) of the compressive zone in the node is given by the expression:
Where is: | x1 |
|
FEd |
| |
b |
| |
σRd,max |
|
The outer lever arm is calculated using formula:
Where is: | a |
|
ac |
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x1 |
| |
HEd |
| |
FEd |
| |
d' |
| |
Δh |
|
The width (vertical projection) of the compressive zone in the node is given by the expression:
Where is: | a |
|
d |
| |
x1 |
|
The inner lever arm is given by the expression:
The tensile force in the main reinforcement is given by the expression:
Where is: | FEd |
|
a |
| |
z |
| |
HEd |
| |
d' |
|
The force in the compression strut is given by the expression:
Where is: | Θ |
|
FEd |
|
The shear resistance without transverse reinforcement
The shear resistance of the cross-section without stirrups is verified according to the chapter 6.2.2(1) of EN 1992-1-1.
Reinforcement design
The value of the design compressive strength is defined as
Where is: | fyd |
|
fck |
| |
γs |
|
The required area of the main reinforcement is given by the formula:
The transverse tensile force for the calculation of vertical and horizontal stirrups is given by the chapter 6.5.3(3).
Vertical and horizontal components of the tensile force are calculated using following formulas:
Where is: | Tvert |
|
Thorz |
| |
T |
| |
θ |
|
The vertical and horizontal components of the tensile force are increased by 20% due to different direction of the force and reinforcement.
The minimum shear reinforcement for long corbels is calculated according to the chapter 6.2 of EN 1992-1-1
Where is: | Asv,req |
|
β |
| |
FEd |
| |
fyd |
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This reinforcement should be placed in the middle three quarters of the distance between the clumn and slide plate.
Minimum vertical and horizontal reinforcement are given by the expression
Stress under slide plate
The stress under slide plate is verified in accordance with the chapter 6.7 of EN 1992-1-1:
Where is: | Ac0 |
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Ac1 |
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The area Ac1 is calculated according to the chapter 6.7(3) using the maximum angle of 26.56° provided that design distribution area can't overlap the edge of corbel.