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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

  • The design compressive strength

αcc

  • The coefficient taking account of long term effects on the compressive strength

fck

  • The characteristic compressive cylinder strength of concrete at 28 days

γc

  • The partial safety factor for concrete

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

  • The maximum stress which can be applied at the edges of the node

k1

  • The coefficient for CCC joints

k2

  • The coefficient for CCT joints

k3

  • The coefficient for CTT joints

ν'

  • The coefficient

fcd

  • The design compressive strength

The reduction coefficient ν' is calculated in accordance with the chapter 6.5.2 (2):

Where is:

fck

  • The characteristic compressive cylinder strength of concrete at 28 days

Strut and tie model

The width (horizontal projection) of the compressive zone in the node is given by the expression:

Where is:

x1

  • The width of the compressive zone

FEd

  • The design value of vertical force

b

  • The corbel width

σRd,max

  • The design value for the compressive stress in node

The outer lever arm is calculated using formula:

Where is:

a

  • The outer lever arm

ac

  • The eccentricity of the vertical force

x1

  • The width of the compressive zone

HEd

  • The design value of horizontal force

FEd

  • The design value of vertical force

d'

  • The difference between the corbel height and the effective height

Δh

  • The height of slide plate

The width (vertical projection) of the compressive zone in the node is given by the expression:

Where is:

a

  • The outer lever arm

d

  • The effective height of the cross-section

x1

  • The width of the compressive zone

The inner lever arm is given by the expression:

The tensile force in the main reinforcement is given by the expression:

Where is:

FEd

  • The design value of vertical force

a

  • The outer lever arm

z

  • The inner lever arm

HEd

  • The design value of horizontal force

d'

  • The difference between the corbel height and the effective height

The force in the compression strut is given by the expression:

Where is:

Θ

  • The angle between the concrete compression strut and the beam axis perpendicular to the shear force

FEd

  • The design value of vertical force

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

  • The design yield strength of reinforcement

fck

  • The characteristic yield strength of reinforcement

γs

  • The partial safety factor for reinforcement steel

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

  • The vertical component of the tensile force

Thorz

  • The horizontal component of the tensile force

T

  • The transverse force in the compression strut

θ

  • The angle between the concrete compression strut and the beam axis perpendicular to the shear force

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

  • The required area of shear reinforcement

β

  • The coefficient

FEd

  • The design value of the force in compression strut

fyd

  • The design yield strength of reinforcement

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

  • The loaded area

Ac1

  • The maximum design distribution area with a similar shape to Ac0

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.

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