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Table B4

Limit stress resultants of continuous slab [*]NoteThis table also applies to continuous beams, although rarely met at earthquake resistant structures. as a function of the ratio gd/pd

gd/pd

gd=0

pd=qd

Two-span beam

gd=pd

qd=0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

m1

10.45

10.75

11.07

11.41

11.75

12.12

12.50

12.90

13.32

13.76

14.22

mB

-8.00

-8.00

-8.00

-8.00

-8.00

-8.00

-8.00

-8.00

-8.00

-8.00

-8.00

p1A

2.29

2.32

2.35

2.39

2.42

2.46

2.50

2.54

2.58

2.62

2.67

p1B

-1.60

-1.60

-1.60

-8.00

-1.60

-1.60

-1.60

-1.60

-1.60

-1.60

-1.60


gd/pd

gd=0

pd=qd

Three-span beam

gd=pd

qd=0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

m1

9.88

10.10

10.33

10.57

10.82

11.07

11.34

11.61

11.9

12.19

12.50

mB

-8.57

-8.70

-8.82

-8.96

-9.09

-9.23

-9.37

-9.52

-9.68

-9.84

-10.00

m2

13.33

14.29

15.38

16.67

18.18

20.00

22.22

25.00

28.57

33.33

40.00

p1A

2.22

2.25

2.27

2.30

2.33

2.35

2.38

2.41

2.44

2.47

2.50

p1B

-1.62

-1.63

-1.63

-1.63

-1.64

-1.64

-1.65

-1.65

-1.66

-1.66

-1.67

p2B

1.71

1.74

1.76

1.79

1.82

1.85

1.87

1.90

1.94

1.97

2.00


gd/pd

gd=0

pd=qd

Four-span beam

gd=pd

qd=0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

m1

10.04

10.28

10.53

10.80

11.07

11.36

11.65

11.96

12.28

12.61

12.96

mB

-8.30

-8.39

-8.48

-8.58

-8.68

-8.78

-8.89

-9.00

-9.11

-9.22

-9.33

m2

12.42

13.14

13.96

14.87

15.92

17.12

18.53

20.17

22.14

24.54

27.51

mC

-9.33

-9.66

-10.00

-10.37

-10.77

-11.20

-11.67

-12.17

-12.73

-13.33

-14.00

p1A

2.24

2.27

2.30

2.32

2.35

2.38

2.41

2.45

2.48

2.51

2.55

p1B

-1.61

-1.61

-1.62

-1.62

-1.63

-1.63

-1.63

-1.64

-1.64

-1.64

-1.65

p2B

1.66

1.68

1.70

1.72

1.74

1.76

1.78

1.80

1.82

1.84

1.87

p2C

-1.75

-1.78

-1.82

-1.85

-1.89

-1.93

-1.97

-2.01

-2.06

-2.11

-2.15


gd/pd

gd=0

pd=qd

Five-span beam

gd=pd

qd=0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

m1

9.99

10.23

10.48

10.74

11.00

11.28

11.57

11.87

12.18

12.5

12.84

mB

-8.36

-8.46

-8.57

-8.67

-8.78

-8. 89

-9.01

-9.13

-9.25

-9.37

-9.50

m2

12.65

13.43

14.31

15.32

16.48

17.82

19.40

21.29

23.59

26.45

30.08

mC

-8.99

-9.26

-9.54

-9.85

-10.17

-10.52

-10.89

-11.28

-11.71

-12.17

-12.67

m3

11.69

12.26

12.88

13.57

14.34

15.20

16.17

17.27

18.54

20.00

21.71

p1A

2.24

2.26

2.29

2.32

2.35

2.37

2.41

2.44

2.47

2.50

2.53

p1B

-1.61

-1.62

-1.62

-1.63

-1.63

-1.63

-1.64

-1.64

-1.64

-1.65

-1.65

p2B

1.67

1.69

1.71

1.73

1.76

1.78

1.80

1.83

1.85

1.87

1.90

p2C

-1.73

-1.77

-1.80

-1.83

-1.87

-1.90

-1.94

-1.98

-2.02

-2.07

-2.11

p3C

1.69

1.72

1.75

1.77

1.80

1.83

1.86

1.90

1.93

1.96

2.00


gd/pd

gd=0

pd=qd

-span beam

gd=pd

qd=0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

mF

9.99

10.23

10.48

10.74

11.00

11.28

11.57

11.87

12.18

12.50

12.84

mS

-8.36

-8.46

-8.57

-8.67

-8.78

-8.89

-9.01

-9.13

-9.25

-9.37

-9.50

pFS

12.65

13.43

14.31

15.32

16.48

17.82

19.4

21.29

23.59

26.45

30.08


Example:

Given: Three-span continuous slab with L=5.0 m, with nominal loads g=6.5 kN/m and q=5.0 kN/m

Question: Calculate the maximum absolute values of bending moments and shear forces for ULS, at supports and spans, forγg =1.35 and γq=1.50.

Solution:

The design loads for ULS are equal to:

gd=1.0×g, qd=(1.00-γg)×g + γq×q = 0.35×g + 1.35×q
and pd = gd + qd = γg×g + γq×q = 1.35×g + 1.50×q →

gd=1.0×6.5=6.5 kN/m, qd=0.35×6.5+1.5×5.0=9.775 kN/m pd=1.35g+1.50q=1.35×6.5+1.50×5.0=16.275 kN/m

Using the table for three-span slabs yields:

gd/pd=6.5/16.275=0.40 → m1=10.82, mB=-9.09, m2=18.18, p1A=2.33, p 1B=-1.64, p2B=1.82

V01,max=pd×L/p1A=16.275×5.0/2.33=34.9 kN

V10,min=pd×L/p1B=-16.275×5.0/1.64=-49.6 kN

V12,max=pd×L/p2B=16.275×5.0/1.82=44.7 kN

M01,max=pd×L2/m1=16.275×5.02/10.82=37.6 kNm

M1,min=pd×L2/m1=-16.275×5.02/9.09=-44.8 kNm

M12,max=pd×L2/m2=16.275×5.02/18.18=22.4 kNm

 


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