+ WNS/8D × L/B = + WLN²/8D (2)
_Verticals._--The maximum stress = -W. (3)
_Diagonals._--The maximum stress is
± w¹lS/16DB = ± w¹lN/16D (4)
These results show that the method generally adopted in the construction
of bowstring girders is erroneous; and one consequence of the method is
the observed looseness and rattling of the long embraced ties referred to
at the commencement of the article during the passage of the live load;
the fact being that they have at such times to sustain a compressive
stress, which slightly buckles them, and sets them vibrating when they
recover their original position.
Another necessity of the common method of construction is the use of an
unnecessary quantity of metal in the diagonals; for, by leaving them
unbraced, the set of diagonals which does act is subjected to exactly
twice the stress which would be caused in it if the bridge was properly
constructed. A comparison of the results of a set of calculations on the
common plan with those given in this paper, shows at once that this is
the case; for the ordinary system of calculation the stresses, in
addition to showing compression in the verticals, gives exactly twice the
amount of tension in the diagonals which they should have.
FIG. 1B.
________________________________________________________________________________
|
Top Flange Stresses. | Stresses in Diagonals.
Hor. Ver. |
|
C= 31.5 × 10/4.5 = +70.00 = 31.50 |a = 70 -65 =+5.00 = 2.25
|
15.75 × 10/4.5 = 35 |b = " " =-5.00 = 4.00
\ |
D > +65.00 = 22.75 |c = 65 -58.33-5 =+1.67 = 1.33
/ |
24 × 10/8 = 30 |d = " " " =-1.67 = 1.75
\ |
E > +58.33 = 14.58 |e = 58.33-55.83-1.67 =+ .83 = .88
/ |
29.75 × 10/10.5 = 28.33 |f = " " " =- .83 = 1.01
\ |
F > +55.83 = 8.37 |g = 55.83-54.50- .83 =+ .50 = .59
/ |
33 × 10/12 = 27.5 |h = " " " =- .50 = .61
\ |
G > +54.50 = 2.72 |i = 54.50-53.67- .50 =+ .33 = .43
/ |
33.75 × 10/12.5 = 27 |j = " " " =- .33 = .41
\ |
H > +53.67 = 2.68 |k = 53.67-53.09- .33 =+ .24 = .28
/ |
32 × 10/12 = 26.67 |l = " " " =- .24 = .24
\ |
I > +53.09 = 7.97 |m = 53.09-52.67- .24 =+ .18 = .20
/ |
27.75 × 10/10.5 = 26.42 |n = " " " =+ .18 = .16
\ |
J > +52.67 = 13.17 |o = 52.67-52.36- .18 =+ .13 = .11
/ |
21 × 10/8 = 26.25 |p = " " " =- .13 = .06
\ |
K > +52.36 = 18.33 |
/ |
11.75 × 10/4.5 = 26.11 |
|
L= 23.5 × 10/4.5 = +52.22 = 23.50 |
____________________________________________|___________________________________
|
_Bottom Flange Stresses._ | _Stresses in Verticals._
|
Hor. | Ver.
M same as C = 70.00 | r = 15 - 4 = - 11.00
N " D = 65.00 | s = 5 + 2.25 - 1.75 = - 5.50
O " E = 58.33 | t = 5 + 1.33 - 1.01 = - 5.32
P " F = 55.83 | u = 5 + .88 - .61 = - 5.27
Q " G = 54.50 | v = 5 + .59 - .41 = - 5.18
R " H = 53.67 | w = 5 + .43 - .24 = - 5.19
S " I = 53.09 | x = 5 + .28 - .16 = - 5.12
T " J = 52.67 | y = 5 + .20 - .06 = - 5.14
U " K = 52.36 | z = 5 + .11 = - 5.11
V " L = 52.22 |
____________________________________________|___________________________________
--_The Engineer._
* * * * *