Shear

Design aids for shear reinforcement

Slabs: this extract is from How to Design Concrete Structures using Eurocode 2 (page 23)

It is not usual for a slab to contain shear reinforcement, therefore it is only necessary to ensure that the concrete shear stress capacity without shear reinforcement (vRd,c – see Table 7A below) is more than applied shear stress (vEd = VEd /(bd)). Where shear reinforcement is required, e.g. for ribs in a ribbed slab, refer to Beams below.

Table 7A vRd,c resistance of members without shear reinforcement, MPa

r I =

As/(bd)

 

Effective depth, d (mm)

 

≤200

225

250

275

300

350

400

450

500

600

750

0.25%

 

0.54

0.52

0.50

0.48

0.47

0.45

0.43

0.41

0.40

0.38

0.36

0.50%

 

0.59

0.57

0.56

0.55

0.54

0.52

0.51

0.49

0.48

0.47

0.45

0.75%

 

0.68

0.66

0.64

0.63

0.62

0.59

0.58

0.56

0.55

0.53

0.51

1.00%

 

0.75

0.72

0.71

0.69

0.68

0.65

0.64

0.62

0.61

0.59

0.57

1.25%

 

0.80

0.78

0.76

0.74

0.73

0.71

0.69

0.67

0.66

0.63

0.61

1.50%

 

0.85

0.83

0.81

0.79

0.78

0.75

0.73

0.71

0.70

0.67

0.65

1.75%

 

0.90

0.87

0.85

0.83

0.82

0.79

0.77

0.75

0.73

0.71

0.68

≥2.00%

 

0.94

0.91

0.89

0.87

0.85

0.82

0.80

0.78

0.77

0.74

0.71

k

 

2.000

1.943

1.894

1.853

1.816

1.756

1.707

1.667

1.632

1.577

1.516

 

Table derived from: vRd,c = 0.12 k (100rI fck)1/3 ≥ 0.035 k1.5 f0.5

ck

where k = 1 + R(200/d) ≤ 2 and rI = As /(bd) ≤ 0.02

 

Note

  1. This table has been prepared for fck = 30.
  2. Where rI exceeds 0.40% the following factors may be used:

fck

 

25

28

32

35

40

45

50

Factor

 

0.94

0.98

1.02

1.05

1.10

1.14

1.19

                                       

Note: Extract from How to Design Concrete Structures using Eurocode 2 (page 27, Table 7)

Beams

Procedure for determining vertical shear reinforcement in beams is shown in the following flow chart

Shear theory

Note: Extract from How to Design Concrete Structures using Eurocode 2: Beams (page 34, Figure 5)

Table 7: Minimum and maximum concrete strut capacity in terms of stress

fck

vRd, max (cot Θ = 2.5), MPa

vRd, max (cot Θ = 1.0) MPa

25

3.10

4.50

28

3.43

4.97

30

3.64

5.28

32

3.84

5.58

35

4.15

6.02

40

4.63

6.72

45

5.08

7.38

50

5.51

8.00

Note: Extract from How to Design Concrete Structures using Eurocode 2 (page 34, Table 7)