Shear strength in concrete joints
EUROCODE-2

Shear strength in concrete joints

DATA
Type of joint (?)
  • Composite beam: for horizontal joints in beams and slabs composed of concrete cast at different times.
  • Construction joint: for joints between slabs, walls, beams or columns elements.
Close
Joint surface (?)
  • Very smooth: a surface cast against steel, plastic or specially prepared wooden moulds
  • Smooth: a slipformed or extruded surface, or a free surface left without further treatment after vibration
  • 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
  • Indented: a surface with indentations complying with Figure 6.9 of EC2
Close

composite concrete beam

Dimensions
bi(cm)   (?)   d(cm)
  • bi: width of the interface. Valid values from 10 to 150
  • d: effective depth. Valid values from 10 to 150
Close
Concrete strength (?)
fck (MPa)       γc       αct
  • fck: the characteristic compressive cylinder strength of concrete. Valid values from 20 to 90
  • γc: Partial factor for concrete for ultimate limit state. National choice 2.4.2.4(1). Valid values from 1 to 2
  • αct: National choice 3.1.6 (1)P: Coefficient of fatigue strength of the concrete. Recommended value is 1.0. Valid values from 0.5 to 1
Close
Loads and forces
VEd(Kn)   (?)   Dynamic
  • VEd: Design shear force in the section considered. Valid values from 0 to 0.5·fcd·bi·d
  • Dynamic: Under fatigue or dynamic loads, the values for c in 6.2.5 (1) is halved
    Close

REINFORCEMENT CROSSING THE INTERFACE
Reinforcement strength
fyk(MPa)   (?)   γs
  • fyk: the characteristic strength of reinforcement. Valid values from 400 to 600
  • γs: Partial factor for reinforcement for ultimate limit state. National choice 2.4.2.4(1). Valid values from 1 to 1.8
Close
Transverse reinforc. (?)
Asw(cm2)     s(cm)     α(osex)
  • Asw: Cross-sectional area of reinforcement crossing the interface. Valid values from Ast,min >0 to Asw,max (Φ32 bars in width section (bi) separated 5cm).
  • s: The spacing of the stirrups. Valid values from 5 to 60.
  • α: Angle between the reinforcements and the member′s axis. Valid values from 45 to 90.

You can enter the area directly or through the following data:

typeNum Φ
1
2
Intro

VALUES FOR USE IN A COUNTRY
Use values recommended
Value v (?)
·(1-fck/250)

v is a strength reduction factor (see clause 6.2.2(6)
The recommended value is 0.6·(1-fck/250). Valid values from (0.3 to 1.0)·(1-fck/250)

Close

 

RESULT

Design value shear stress Design shear resistance Requirement
vEdi (MPa) vRdi (MPa) vEdi ≤ vRdi
0.89 1.06 OK



DETAILS OF CALCULATION

Notation and methodology according to clause 6.2.5 of EC2

vEdi (design value of the shear stress) = 0.89 MPa

vEdi = VEd / (z·bi) = 70000 / (225·350) = 0.89 MPa
where:

  • z (inner lever arm) = 0.9 · d = 0.9 · 250 = 225 mm

vRdi (design shear resistance at the interface) = 1.06 MPa

vRdi = min [vRdi(1) ; vRdi(2)] = min[1.06 ; 4.5] MPa
where:

  • vRdi(1) = c·fctd + ρ·fyd·(μ·sinα + cosα)
    vRdi(1) = 0.4·1.2 + 0.0019·434.78·(0.7·sin90º+cos90º) = 1.06 MPa
    with:
    • fctd (design tensile strength) = αct · fctk,0.05 / γc
      fctd = 1 · 1.8 / 1.5 = 1.2 MPa
      with:
      fctk,0.05 = 0.7 · fctm = 0.7 · 2.56 = 1.8 MPa
      fctm = 0,30 × fck(2/3) = 0,30 × 25(2/3) = 2.56 MPa
    • ρ = Asw / (s·bi) = 1.01 / (15·35) = 0.0019
    • fyd = fyk / γs = 500 /1.15 = 434.78 MPa
    • c = 0.4 ; μ = 0.7 (interface Rough, No dynamic loads)
  • vRdi(2) = 0.5·v·fcd = 0.5 · 0.54 · 16.67 = 4.5 MPa
    with:
    • v = 0.6 ·(1-fck/250) = 0.54
    • fcd = αcc · fck / γc = 1 · 25 / 1.5 = 16.67 MPa