92. Duhamel made some experiments on oak where the scantlings were as large as they are generally used in buildings; and as the results of experiments on large pieces will be more highly valued by the generality of readers, as many of them as are applicable to the present purpose will be described.

A piece of oak 9.6 inches deep and 10.66 inches in breadth, was placed upon two supports 24.5 feet apart, and a weight of 8198 lbs. was suspended to the middle, which bent it 3.73 inches. The piece broke with 9613 lbs., but it was found to have been faulty. Here the value of a for a deflection of 1/40 of an inch per foot in length is 0.0114.

Another piece or oak, which was very sound and straight grained, the depth 12.2 inches, the breadth 10.66 inches, and the bearing 24.5 feet, with a weight of 8198 lbs. bent 2.65 inches. Whence for a deflection of 1/40 of an inch per foot in length, a = 0.0157. The piece broke with a weight equivalent to 19,666 lbs. applied to the middle.

A third piece of oak, that was sound and straight grained, was tried; the depth was 13.83 inches, the breadth 12.8 inches, and the length 24.5 feet; and with a weight of 8198 lbs. it bent an inch in the middle.* Therefore for a deflection of 1/40 of an inch per foot a = 0.011.

' Memoires de l'Academie des Sciences,' Paris, 1768, pp. 585-537.

93. Table VI. - Experiments On The Stiffness Of Oak Supported At The Ends

Kind of Oak.

Spec, grav.

Length in feet.

Breadth in inches.

Depth in inches.

Deflection in inches.

Weight producing the deflection in lbs.

Values of a.

Authorities

Old ship timber

.872

2.5

1

1

0.5

127

.00998

Tredgold.

Oak from young tree, King's Langley, Herts

.863

2

1

1

0.5

237

.0105

"

Oak from Beau lieu, Hants .....

.616

2.5

1

1

0.5

78

.0164

"

Ditto, another specimen .........

.736

2.5

1

1

0.5

65

.0197

"

Oak from old tree

.625

2

1

1

0.5

103

.024

"

Oak from Riga.

.688

2

1

1

0.5

233

.0107

"

English oak ..

.960

7

2

2

1.275

200

.0119

Barlow.

Canadian oak..

.867

7

2

2

1.07

225

.009

"

Dantzic oak ..

.787

7

2

2

1.26

200

.0105

"

Adriatic oak ..

.948

7

2

2

1.55

150

.0193

"

English oak ..

.748

2.5

1

1

0.5

137

.00934

Ebbels.

Ditto, green ..

.763

2.5

1

1

0.5

96

.0133

"

Dantzic oak, sea soned .. ..

.755

2.5

1

1

0.5

148

.0087

Tredgold.

Oak, seasoned..

....

12.8

3.19

3.19

1.06

268

.088

Aubry.

4.25

803

.0105

Oak, green ....

...

6.87

5.3

5.3

.433

7587

.005

Buffon.

Oak, green.....

...

23.58

5.3

53

2.7

706

.0095

"

Oak......

...

8.52

5.06

6.22

0.709

4146

.0133

Girard.

Oak (bois du brin*) .. ..

...

16.86

10.66

11.73

0.67

4559

.0213

"

Oak (quercus sessiliflora) ..

..

2

1

1

0.35

149

.0117

Tredgold.

Oak (quercus robur†).. ..

..

2

1

1

0.35

167

.0104

"

* " Bois du brin," timber the whole size of the tree, excepting that which was taken off to render it square.

† See Section on " Nature of Timber," where the characters of these species are described.

94. Table VII. - Experiments On The Stiffness Of Fib Supported At The Ends

Kind of Fir.

Spec, grav.

Length in feet.

Breadth in inches.

Depth in inches.

Deflection in inches.

Weight producing the deflection in lbs.

Values of a.

Authorities.

Riga yellow fir, medium ..

...

18

2

7

0.25

103

.0115

Tredgold.

Yellow fir, from Long Sound, Norway ..

.6398

2

1

1

0.5

261

.00957

"

Yellow fir, Riga

.480

2.5

1

1

0.5

123

.0102

"

.404

2.5

1

1

0.5

116

.011

Ebbels.

Ditto, Memel. medium ..

.553

2.5

1

1

0.5

143

.0089

Tredgold.

.544

2.5

1

1

0.5

145

.0088

American pine, supposed to be the Wey mouth pine ..

.460

2

1

1

0.5

237

.0105

.407

3

1

1

0.5

69

.0112

"

White spruce, Christiana ..

.512

2

1

1

0.5

261

.00957

' '

White spruce, Quebec ..

.4650

2

1

1

0.5

180

.0138

"

Pitch pine ........

.712

7

2

2

1.33

150

.0166

Barlow.

New England fir

.560

7

2

2

.970

150

.0121

"

Riga fir ..

.765

7

2

2

.912

150

.01137

"

Scotch fir, Marl Forest .. ..

.715

7

2

2

1.560

125

.0233

"

Larch, Blair, Scotland, dry

.622

2.5

1

1

0.5

93

.0137

Tredgold.

Ditto, seasoned, medium ..

.644

2.5

1

1

0.5

101

.0126

"

.554

2.5

1

1

0.5

112

.0111

Ebbels.

Ditto, very young wood

.396

2.5

1

1

0.5

45

.0284

Tredgold.

Scotch, fir * ..

.529

2.5

1

1

0.5

89

.01437

"

Spruce fir, Bri tish .. ..

.555

2.5

1

1

0.5

103

.0124

Ebbels.

Fir(boisdubrin)

...

21.3

10.48

10.4

1.02

4389

.0115

Girard.

Fir(bois du brin)

...

10.65

10.48

10.48

0.2245

4122

.022

"

* The tree from which this specimen was taken was grown in Buckingham-chire.

95. Table VIII. - Experiments On The Stiffness Of Various Woods Supported At The Ends

Kind of Wood.

Spec grav.

Length in feet.

Breadth in inches.

Depth in inches.

Deflection in inches.

Weight producing the deflection in lbs.

Values of a.

Authorities.

Ash from young tree, white co. loured .. ..

.811

2.5

1

1

0.5

141

.009

Tredgold.

Ash from old tree, red co loured .. .

.753

2.5

1

1

0.5

113

.0113

"

Ash, medium quality ..

.690

2.5

1

1

0.5

78.5

.0163

Ebbels.

Ash......

.760

7

2

2

1.27

225

.0105

Barlow.

Beech...............

.688

7

2

2

1.025

150

.01277

"

Teak.................

.744

7

2

2

1.276

300

.0076

"

Elm......

.540

7

2

2

1.42

125

.0212

"

.544

2.5

1

1

0.5

99.5

.0128

Ebbels.

Cedar of Leba. non .. ..

.486

2.5

1

1

0.5

36

.0355

Tredgo

Maple, common

.625

2.5

1

1

0.5

65

.0197

"

Abele.................

.511

2.5

1

1

0.5

84

.0152

"

Willow .. ..

.405

2.5

1

1

0.5

41

.031

"

Horse chestnut

.4838

2.5

1

1

0.5

79

.0162

"

Lime-tree...........

.483

2.5

1

1

0.5

84

.0152

"

Walnut, green

.920

2.5

1

1

0.5

62

.020

Ebbsls.

Spanish chest. nut, green ..

.895

2.5

1

1

0.5

68.5

.0187

' '

Acacia, green..

.820

2.5

1

1

0.5

125

.0102

"

Plane, dry...........

.648

2.5

1

1

0.5

99.5

.0128

"

Alder, ditto ..

.555

2.5

1

1

0.5

80.5

.0159

"

Birch, ditto ..

.720

2.5

1

1

0.5

90.5

.0141

"

Beech, ditto ..

.690

2.5

1

1

0.5

97.5

.0131

"

Wychelm, green

.763

2.5

1

1

0.5

92

.014

"

Lombardy pop. lar, dry ..

.374

2.5

1

1

0.5

56.5

.0224

"

Honduras ma. hogany ..

.560

2.5

1

1

0.5

118

.0109

Tredgold.

Spanish ditto ..

.853

2.5

1

1

0.5

93

.0137

"

Sycamore..........

.590

2.5

1

1

0.5

76

.0168

Ebbels.

Pear-tree, green

.792

2.5

1

1

0.5

59.5

.0215

"

Cherry . tree, green .. ..

.690

2.5

1

1

0.5

92.5

.0138

"

96. The experiments in the following Tables were made by Mr. Fincham, to ascertain the relative qualities of timber used for the masts of ships. They were made with great care *

97. Table IX. - Pieces Supported At Both Ends And Loaded At The Middle. (Green.)

Length = 4 feet between Supports. Scantling = 3 in. x 3 in.

Description of Timber.

Spec, grav.

Deflection with 1680 lbs.

What it recovered after removal of Weight.

Deflection with 2520 lbs.

What it recovered after removal of Weight.

Deflection with 2520 lbs. left on for one hour.

What it recovered after removal of Weight.

Weight that broke the

Piece.

Values of a.

in.

in.

in.

in.

in.

in.

lbs.

Riga fir

Top

.664

.31

.29

.62

.59

.97

.91

3654

.0093

"

Butt

.720

.25

.22

.53

.50

.85

.73

3958

.0075

Red pine

Top

.627

.81

.68

1.37

1.13

1.40

1.10

2630

.0241

"

Butt

.712

.63

.59

.95

.91

1.20

1.05

3244†

.0190

American spruce

(Top

.598

.37

.36

.62

.60

1.87

.95

2406†

.0111

(Butt

.643

.31

.29

.63

.61

1.07

.95

2646†

.0093

Norway fir

(Top

.572

.57

.50

.82

.80

1.37

.93

2408†

.0172

(Butt

.595

.58

.56

.84

.82

1.37

.95

2618†

.0175

Adriatic

Top

.532

.30

.29

.42

.40

. .

...

2386

.0090

"

Butt

.582

.29

.27

.43

.41

.65

.45

2592

.0087

Yellow pine

Top

.553

.89

.77

1.48

1.10

..

..

2408

.0268

"

Butt

.661

.73

.60

1.00

.90

. .

. .

2686

.0220

Scotch spruce

(Top

.478

.84

.83

. .

. .

. .

. .

2072

.0253

(Butt

.542

.72

.70

..

..

..

..

2190

.0217

Kowrie

Top

.626

.31

.30

.43

.41

.62

.54

3983

.0093

"

Butt

.643

.31

.30

.43

.41

.62

.54

4032

.0093

* Papers on Naval Architecture, vol. i., pp. 53-4.

† Broke off after the pressure had continued about 5 minutes.

98. Table X. - Pieces Supported At Both Ends And Loaded At The Middle. (Dry.)

Length = 4 feet between Supports. Scantling = 3 in. X 3 in.

Description of Timber.

Spec, grav.

Deflection with 1680 lbs.

What it recovered after removal of Weight

Deflection with 2520 lbs.

What it recovered after removal of Weight

Deflection after one hour's pressure with 2520 lbs.

What it recovered after removal of Weight

Weight that broke the Piece.

Values of a.

in.

in.

in.

in.

in.

in.

lbs.

Riga fir

Top

.516

.50

.48

.93

.87

1.01

.97

3616

.0151

"

Butt

.633

.31

.30

.62

.56

.97

.85

3850

.0093

Bed pine

Top

.514

.56

.51

1.25

1.13

137

1.20

2576

.0169

"

Butt

.644

.42

.50

.62

.56

.69

.60

2800

.0127

American spruce

Top

.488

.47

.38

.91

.87

1.08

.97

2546

.0142

Butt

.546

.47

.35

.82

.78

1.06

.94

2549

.0142

Norway fir

Top

.464

.51

.49

.83

.81

...

...

2366*

.0154

"

Butt

.506

.57

.56

.84

.80

1.00

.81

2590*

.0172

Adriatio

Top

.443

.27

.25

..

..

..

..

2378

.0081

"

Butt

.462

.25

.23

..

..

...

...

2515

.0075

Yellow pine

Top

.395

.60

.48

..

..

..

..

2380

.0181

"

Butt

.442

.66

.50

99

.67

1.60

1.21

2632

.0199

Scotch spruce

Top

.348

.75

.72

...

..

..

..

1750

.0226

Butt

.442

.62

.61

..

. .

...

...

1848

.0187

Kowrie

Top

.560

.56

.56

.68

.64

.75

.67

3612

.0169

"

Butt

.582

.27

.27

.43

.43

.50

.48

3948

.0081

Poona

Top

.632

.32

.32

.61

.60

.64

.62

3990

.0096

"

Butt

.658

.25

.25

.56

.56

.62

.61

4180

.0075

99. Table XI. - Pieces Supported At Both Ends And Loaded At The Middle. (Very Dry And Particularly Good.)

Length = 4 feet between Supports. Scantling = 3 in. X 3 in.

Description of Timber.

Spec grav.

Deflection with 1680 lbs.

What it recovered after removal of Weight

Deflection with 2520 lbs.

What it recovered after removal of Weight

Deflection after one hour's pressure with 2520 lbs.

What it recovered after removal of Weight

Weight that broke the Piece.

Values of a.

in.

in.

in.

in.

in.

in.

lbs.

Riga fir ...........

.610

.25

.25

.37

.33

.40

.33

4530

.0075

Red pine .........

.544

.36

.35

.68

.62

.86

.78

3780

.0108

Yellow pine ...........

.439

.37

.30

.78

.72

1.00

.82

2756

.0111

Norway fir ....

.517

.31

.30

.61

.60

86

.63

3292

.0093

Scotch pine ...........

.453

.62

.60

.93

.90

...

....

2520

.0187

Kowrie ...........

.579

.29

.29

.46

.44

.50

.45

4110†

.0087

* Very good specimens. + Broke after pressure had continued 15 minutes.

100. By means of equation [4] the following rules have been obtained. In that equation 40 x99 Table XI Pieces Supported At Both Ends And Load 51 equals L, and if L bo substituted the equation becomes -

LxBxD3/L3xW = a; [7] or in its simplest form,

BxD3/L2xw =a [8]

101. The constant number a is calculated on the supposition that the deflection is equal to 1/40 of an inch for each foot in length: that is, when the length is 1 foot the weight will produce a deflection of 1/40 of an inch; when the length is 20 feet, the deflection will be 20/40, or half an inch, and so on. When the deflection is required to be less than here assumed, multiply the constant number a by some number that will reduce the deflection to the proposed degree; for instance, if the deflection should be only half of 1/40 multiply a by 2; if one-third of 1/40, multiply a by 3, etc. Also, if the deflection may be greater than 1/40 per foot, divide a by 2, 3, or any number of times that the proposed deflection may exceed 1/40 of an inch per foot.