# 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 This table has been prepared for fck = 30. 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)

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