48 6
HISTOllY OF ENGINEERING.
Book I.
and more light and open as in the design, so as to bring the loading in those parts as nearto the equilibrium weight as the strength and stability of the iron frames will permit.
Mr. J. Rennie observed, that different methods may be adopted of rendering the archequally strong throughout. It may be balanced by the weight of the frames and loadingcharged on them towards the extremities so as to counterbalance that at the crown of thearch, or it may partly be done by weight, and partly by longitudinal braces placed in sucha direction as to answer the same purpose. The latter method will be found very usefulin this arch, particularly if put in addition to the weight which forms the equilibrio, for, asI apprehend, it will be impossible to prevent the iron from yielding in some degree; thisyielding will be greatest where the depths of the materials are least, which is at the crownof the arch, in which cases the braces will act in opposition to it, with more effect than thesimple gravity of whatever load may be placed upon it.
Mr. Attwood stated that the distribution of weight among the sections, so as to form anarch of equilibration, depends on the angles of the sections which form the entire arch. Ifthe angles should be equal, and of the magnitude stated, the weight of each section and thepressure on it appears from calculation to be as set forth in the table which follows. Thedimensions of the proposed bridge being
Height of the middle arch - - - - 65 feet.
Span ------- GOO
Radius - - - 724*8
Number of wedges which form the arch - - 63
Angle of each wedge or section - 46' 34"*314.
The inclination of the successive abutments to the vertical line is calculated from theangle of each section, 4G'34' / *314, a degree of exactness not necessary, except to prevent thesmall errors from accumulating. The angles of the abutments, entered in the second columnof the table, are expressed to the nearest minute of a degree. The weight of the highest ormiddle section, denoted by the letter A, is assumed equal to unity, the weight of all theother sections being in proportion to it.
Sections.
Angular Distances ofthe Abutments fromthe Vertical Line.
Wcightsofthe Sections.
Pressure on the Sec-tions next following.
Sums of the Weights ofthe Sections, deductingthe Weight of half thefirst Section.
A
0*23'
1*000
73*82
*500
B
1*10
] *000
73*83
1*500
C
1*56
1*001
73*86
2*501
D
2*43
1*002
73-90
3*503
E
3*30
1*003
73-95
4*506
F
416
1*005
74-02
5-510
G
5*3
1*007
74-10
6-517
H
5-49
1 *009
74-20
7-526
I
6*36
1*012
74*31
8-538
K
7*22
1*015
74 *43
9*553
L
8*9
1-019
74*57
10*57
M
8*56
1*023
74*72
11*59
N
9*42
1 027
74-89
12*62
O
10-29
1*032
75-07
13-65
P
11-15
1*037
75-26
14-69
Q
12*2
1*043
75-47
15-73
II
12-48
1 *049
75-70
16*78
s
13-35
1-055
75-94
17-84
T
14*22
1*062
76*20
18*90
U
15*8
1*069
76-47
19-97
V
15*55
1*077
76*76
21*04
W
16-41
1*086 *
77-06
22*13
X
17*28
1*094
77-38
23*22
Y
18*14
1*104
77*72
24*33
Z
19*1
1*114
78-08
25*44
A
19*48
1*124
78*45
26*57
B
20*34
1*135
78-84
27*70
C
21*21
1-147
79*25
28-85
D
22*7
1*159
79*68
30*01
E
22-54
1*172
80*13
31-18
F
23*40
1-185
80*60
32-36
G
24*29
1*199
81-09
33-56