Calculation of shear connection reinforcement

Concrete characteristic strength

f_ck

MPa

e.g. 30 MPa for concrete class C30/37. For a list of concrete classes see Table of Concrete Design Properties

Steel characteristic yield strength

f_yk

MPa

Type of interface between old and new concrete

See table below for interface classification

Classification of interface according to EN1992-1-1 §6.2.5(2)
Very smooth	A surface cast against steel, plastic or specially prepared wooden moulds (c = 0.025 to 0.10, μ = 0.5)
Smooth	A slipformed or extruded surface, or a free surface left without further treatment after vibration (c = 0.20, μ = 0.6)
Rough	A surface with at least 3 mm roughness at about 40 mm spacing, achieved by raking, exposing of aggregate or other methods giving an equivalent behaviour (c = 0.40, μ = 0.7)
Indented	A surface with indentations complying with EN1992-1-1 Figure 6.9 (c = 0.50, μ = 0.9)

Adjustment factor for concrete bond coefficient c

The provided value is applied as a multiplier for the concrete bond coefficient c. A value of 1.0 leads to no adjustment. According to EN1992-1-1 §6.2.5(5) under fatigue and dynamic loads a value of 0.5 should be considered. For bridges according to EN1992-2 §6.2.5(105) under fatigue and dynamic loads a value of 0.0 should be considered.

Normal stress on the interface (compression positive)

σ_n

MPa

Stress per unit area caused by the minimum external normal force across the interface that can act simultaneously with the shear force (positive when compressive)

Design value of the transverse shear force

V_Ed

Transverse shear force acting on the composite cross-section (see figure below)

Lever arm of internal forces for composite section

In the shear analysis of reinforced concrete with small axial force, the approximate value z = 0.9d may normally be used, according to EN1992-1-1 §6.2.3(1) where d is the effective depth of the cross-section to the centroid of tensile reinforcement

Width of the interface

b_i

Width of the interface where shear forces are transferred between old and new concrete. See figure below for typical cases.

Part of the compressive or tensile longitudinal force in the new concrete area

Ratio of the longitudinal force in the new concrete area to the total compressive or tensile longitudinal force for the section considered. When the longitudinal force in the new concrete is compressive the total compression force of the cross-section is considered. When the longitudinal force in the new concrete is tensile the total tension force of the cross-section is considered, resulting from the tension forces of the longitudinal reinforcement. A value of β=1 is always conservative.

Angle between reinforcement and interface (45°≤α≤90°)

An angle of 90° corresponds to the bars being perpendicular to the plane of the interface. Values less than 90° mean that the bars are in tension due to the shearing action on the interface.

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Eurocode 2 Design of shear connection at the interface between concrete cast at different times

Examples of shear interfaces between concrete cast at different times (reproduced from EN1992-1-1 Figure 6.8)