Punching shear

The design value of the punching shear force, Kd, will usually be the support reaction at the ultimate limit state. In principle the design for punching shear in Eurocode 2 and BS 8110 is similar. The main differences are as follows.

■ Standard factors for edge and corner columns that allow for moment transfer (B) are greater in Eurocode 2. However, B can be calculated directly from Expressions (6.38) to (6.46) of the Eurocode to give more efficient designs.

Figure 4

Basic span-to-effective-depth ratios for flat slabs

Figure 4

Basic span-to-effective-depth ratios for flat slabs

Flat Slabs Supported Columns

0.40% 0.60% 0.80% 1.00% 1.20% 1.40% 1.60% 1.80% 2.00% Percentage of tension reinforcement (>4 s/bd)

39 37 35

t 33

H 29

0.40% 0.60% 0.80% 1.00% 1.20% 1.40% 1.60% 1.80% 2.00% Percentage of tension reinforcement (>4 s/bd)

Notes

1 This graph assumes a simply supporteS flat slab (K = 1.2).

2 Compression reinforcement, r', has been taken as 0.

3 Curves based oathefgllowing expressions:

6 [i 1 + Uffc + 3.2 f ( R0 - i)1 5 ] where p , p o and

■ In Eurocode 2 the maximum value of shear at the column face is not limited to 5 MPa, and depends on the concrete strength used.

■ With Eurocode 2 the permissible shear resistance when using shear links is higher, although such designs may not be economic or desirable.

As an alternative to using shear links, proprietary shear stud rails may be used. Eurocode 2 (Figure 6.22) allows them to be laid out in a radial or cruciform pattern and gives spacing requirements for both. Other techniques are available for increasing punching shear resistance and these are covered in a best practice guide10.

■ The control perimeters for rectangular columns in Eurocode 2 have rounded corners.

■ Where shear reinforcement is required the procedure in Eurocode 2 is simpler; the point at which no shear reinforcement is required can be calculated directly and then used to determine the extent of the area over which shear reinforcement is required.

■ It is assumed that the reinforcement will be in a radial arrangement. However, the reinforcement can be laid on a grid provided the spacing rules are followed.

The procedure for determining the punching shear requirements is shown in Figure 6.

Figure 5

Determination of steel stress

rf 280

E 220

1/' 1

1

Ratio Gk/Qk

C2 = 0.6, gc = 1.25 C2 = 0.3, gc = 1.25 C2 = 0.2, gc = 1.25

To determine stress in the reinforcement (as), calculate the ratio G^/Qk, read up the graph to the appropriate curve and read across to determine aSu.

as can be calculated from the expression: as = asu

C is the factor for quasi-permanent value of a variable action. For further explanation refer to How to design concrete structures using Eurocode 2: Introduction to Eurocodes3.

Figure 6

Procedure for determining punching shear capacity

START

Determine value of factor ß (refer to Figure 7 or Expressions (6.38) to (6.46) of the Eurocode)

Determine value of vEd,max (design shear stress at face of column) from:

VEd max = &Vid /(Ui df where u is perimeter of column deff = (dy + dz)/2 (dy and dz are the effective depths in orthogonal directions)

Determine value of vRd,max from Table 7

Determine value of vEd, (design shear stress) from:

where u is length of control perimeter (see Figure 8)

Determine concrete punching shear capacity (without shear reinforcement), vrd,c from Table 8 where pl = (ply plz)05 (ply, plz are the reinforcement ratios in two orthogonal directions for fully bonded tension steel, taken over a width equal to column width plus 3d each side.)

Punching shear reinforcement not required

Determine area of punching shear reinforcement per perimeter from:

Sr is the radial spacing of shear reinforcement (see Figure 9) fywdef = 250 + 0.25 d6ff < fywd (see Table 9)

Determine the length of the outer perimeter where shear reinforcement not required from:

Determine layout of punching shear reinforcement (see 'Spacing of punching shear reinforcement' Section and Figure 9).

Table 7 Values for m

Table 9 Values for /ywd,ef

fck

Vd, max

■ de«

^ywd,ef

20

3.31

150

288

25

4.05

175

294

28

4.48

200

300

30

4.75

225

306

32

5.02

250

313

35

5.42

275

319

40

6.05

300

325

45

6.64

325

331

50

7.20

350

Recommended standard values for p

Figure 7

Recommended standard values for p

Table 8

vRd,c resistance of members without shear reinforcement, MPa

Table 8

vRd,c resistance of members without shear reinforcement, MPa

Ri

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

Notes

1 Table derived from: vRd,c = 0.12 k (100p fck)1/3 a 0.035 k15 /ck0 5 where k = 1 + R(200/d) < 2 and pt = R(ply + plz) < 0.02, p,y = As,/(bd) and plz = Asz/(bd)

2 This table has been prepared forfck = 30;

Where p ( exceeds 0.40% the following factors may be used:

fk

25

28

32

35

40

45

50

Factor

0.94

0.98

1.02

1.05

1.10

1.14

Typical basic control perimeters around loaded areas l2d

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Responses

  • Michelle
    How to check punching shear in concrete slab to eurocode?
    6 years ago
  • jannette gallagher
    How to calculate punching shear using eurocode?
    5 months ago

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