Approximate Rules and Tables for the Depth of Arches and Thickness of Abutments.

= D. C representing coefficient, r radius of arch at crown, t thickness of abutment, h height of abutment to spring, and D depth of crown in feet.

In single arches, Stone C = .3, Brick .4, and Rubble .45.

Depths required for the Crowns of Arches.

Radius of Carre.

Stone.

Brick.

Feet.

Feet.

Feet.

2

•42

•56

2½

•47

.63

3

•52

•69

3½

•56

•75

4

•6

•8

4½

•64

•85

6

•67

•9

5½

•71

•94

6

•74

•98

7

•8

1.06

8

•85

113

9

•9

1.2

Radius of Curve.

Stone.

Brick.

Feet.

Feet.

Feet.

10

.95

1.26

11

1.

1.33

12

1.04

1.38

13

1.08

144

14

112

1.5

15

116

1.55

16

1.2

1.6

17

1.23

165

18

1'27

1.7

19

1.31

1 74

20

1.34

1 79

22

1.41

1.88

Radius of

Curve.

Stone.

Brick.

Feet.

Feet.

Feet.

24

1 47

1.96

25

15

2.

30

1.64

2.19

35

1.78

2.37

40

1.9

2.53

45

2.01

268

60

•2 12

283

55

2.22

2.97

60

2.33

3.1

65

2.42

3.22

70

2.51

3.35

75

26

3.46 |

Radius of Curve.

Stone.

Brick.

Feet.

Feet.

Feet.

80

2.68

3.58

85

2.77

3.69

90

2.85

38

95

2-92

3.9

100

3.

4.

110

315

4.2

120

329

4.38

130

3.42

456

140

3.55

473

150

3.67

4.9

160

38

506

170

413

5.22

Minimum Thickness of Abutments for Arches of 120°, where their Depth does not exceed 3 Feet.

Computed from the formula -

√ 6r + (3r/ 2h)2 3r/2h = t.

Radilus of Arch.

Height of Abutment to Spring in Feet,

5

7.5

10

90

80

Feet.

Feet.

Feet.

Feet.

Feet.

Feet.

4.

3.7

4.2

4.3

4.6

4.7

45

3.9

4.4

4.6

4.9

5.

5.

4.2

4.9

4.8

5.1

5.2

6.

4.5

4.7

5.2

5.6

5.7

7.

4.7

5.2

5.5

6.

6.1

8.

4.9

5.5

5.8

6.4

6.5

9.

5.1

6.8

6.1

6.7

6.9

10.

5.3

6.

6.4

7.1

7.3

11.

5.5

6.2

6.6

7.3

7.6

Radius of

Area.

Height of Abutment to Spring in Feet.

5

7.5

10

20

80

Feet.

Feet.

Feet.

Feet.

Feet.

Feet.

12.

6.6

6.4

6.9

7.6

7.9

15.

6.

7.

75

8.4

8.8

20.

6.5

7.7

84

9.6

10.

25.

6.9

8.2

91

10.5

11.1

30.

7.2

9.7

9.7

11.1

12.

35.

7.4

9.1

10.2

11.8

12.9

40.

7.6

9.4

10.6

12.8

13.6

45.

7.8

9.7

11.

13.4

14.3

50.

7.9

10.

11.4

14.

15.

Note

The abutments are assumed to be without counterforts or wing walls.

Keystones

2b Compute the Depth of Key atones for Segmental Arches of Stone.

(Trautwine.)

First Class of Arch. .36 √ of the radius at the crown. Second Class of Arch. .4 √ of the radius at the crown. Brick or Rubble. .45 √ of the radius at the crown. In Viaducts of several Arches. Increase the above units to .42, .46, and.51.