\fdO'^ - Old Forge Coal Mines

STRENGTH OF MATERIALS. 2-25
c d f. To draw the shear diagram, project the point 1
across the vertical through F^^ and draw O s. Next project
the point 2 across to /, and 3 across to u, and draw / ?/.
O s t 71 ft 111 is the shear diagram. The maximum moment
is seen to be at the support, and is equal to a hx P w/. To
the scale of distances, a /; = 58.8 in.,
1,400 lb. to the scale of forces. Hence,
ing moment is 58.8 X 1,400 = 82,320 in. -lb. Ans.
{b) From formula 74,
i^=§i- = 82,320. 5, = 12,500;/= 8.
_ , I 82,320X8 _.y.
^ ^,^,^— = 52. G8.
Therefore, - = —'
c 12,500
while Pm = H =
the maximum bend-
But, - = -^^y- = -7:-, and d= 2^ b, or /; = -— .
Hence, L^^L^1. = ^1 = 52,68. rt^' = 52.68 X 15 = 790.2.
c lo
^ = -^'79(h2 = 9.245". b = ^^- =3.7", nearly. Ans.
(598) Referring to the table of Moments of Inertia,
{bd'- b^d;y -4rbdb^d^{d- d^y _
U{bd-b^d^)
[8 X 10' - 6 X {S^yy - 4 X 8 X 10 X G X 8i (10 - 8^)' ^
12 (8 X 10 - 6 X 8i)
280.466.
d b,d/ d-d, \
" "^
2 2 \bd-bjj~
10 6 X 8^
2 "^
2 (.x^l^f^^)---
{a) From the table of Bending Moments, the maximum
. Wl
bending moment is — 7—.
4
5, = 120,000; /= 7; /= 35 X 12 = 420 in.
Using formula 74, M = —r- = —~-^ or
„. ^SJ 4 X 120,000 X 280.466 .
' „ ^ _ ,,
W— = ,
,^r. m = jTrrrr: 7.246 lb. Ans.
Ifc 420 X 7 X G.319