Shear

Design aids for shear reinforcement

Slabs: this extract is from 'How to Design Concrete Structures using Eurocode 2' (page 21)

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 21, 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 28, 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 21, table 7)