90 
Mii. L. N. C4. FILOX OX AX APPFUXLMATE SOLUTIOX FOR BEXDIXO A 
P = - 
AV sinli — t( cosh u •. 7 
-COS — cosh c(u 
ttIi Jo siiih 2tc + 2tc 0 0 
V. siiili n, «.'■ 
W?/ r V. SI 
irW- J 0 >smh 2 
A\ 
7rfe 
0 
r /.oo 
- cos siiili 
n. + 2/( 0 0 
cosh a — a siuh u U '- . , uy 
— cos y smli 
r” [ cosh u — ii SI 
Jot siiih 2/(-— 
3 y 
^ hte 
_ AVv/ r 
Trlfi Jo 
K cosh u 
lu: 
COS - cosh / — 
sinh 2ii — 2u h h 4zr 
AV r siiih H + to cosh k o.f , uij , 
--cos cosli f du 
irh Jo siuh 2/' + 2;^. l> 0 
t( sinh ti. 
u.r . . uy 
COS ; Slllll - 7 du 
siuh 2ic 2a h 0 
w. r 
^ -rrl/ Jo 
AA'’ r"” [ cosh u + a sinh u 
nrh Jo [ 
-ITT «C< 
AA // 1 
+ 
Trlr 
siuh 2 to — 2to 
to cosh to 
COS — sinh ~r — 
0 0 
oiJL 
tu: , tty o 
. ■— -, COS -r cosh --0, 
siuh 2a — 2to h h ■Jta- 
hto- 
dot 
H = 
sill ' r siiiP 
h 0 
a.i: T vy 
«// 
du 
AV r a cosh to 
Trh Jo siuh 2a + 2 
'Wt/ to siiiu ((' . i'-'- I ‘>,7 7 
_ -A -- sm * cosh 7 dot 
Trlr J 0 siuh 2 ;( + 2 ;i h h 
AV a siuh to . -a-x , ay , 
+ ■ , , -^ Sill 7 - cosh -7 du 
tt/^ Jo siuh 2/', — h 0 
A\h/ r* to cosh a . ax . , ay , 
— " -— sill 7 Slllll 7 - du 
7r/r. Jo siuh 2 m — 2(6 b b 
1 
du 
d u 
J 
(72). 
§ IG. Consideration of the Stresses in the Neighbourhood of 
Concentrated' Load is Applied. 
the Point ivhere the 
The integrals in the expressions (7 i) and (72) are finite, one-valued and continuous 
at every point (cc, y) inside the heain, such that y is numerically less than b by a 
finite (piantity. For in tliis case, for large values of u, the integrand is comparable 
with where lyj stands for the numerical value of y. If, however, i^; = b, 
or the point in (piestion lies on the edges of the beam, the integrals are no longei 
necessarily convergent. In this case the expressions (71) and (/2) haAe to be 
transformed. 
Let us start with the stresses P, Q, S, as in their case the transformation is 
somewhat simpler. Further, let us consider instead of P and Q the somewhat more 
compactly expressed quantities 
