124 
ME. L. N. (1. FILOX ON AN APPROXIMATE SOLUTION FOE BENDING 
wliere 
and 
^2^+1 
<-''2. 
c,, 
- 
^2i-+l - 
S_1 
- 0 
——;-— cos - au 
siiih 'lit + hi b 
a^<'+- Siiili u id. , 
-—- COS - du 
0 sinli 2u + 2u h 
“ siiih a . id I 
--— Sin -7 du 
0 snih 2u — 'hi 0 
■* id''+- c'oah H . id , 
• 1 o o 7 
11 aiiih All — Ate b 
V =■ 
V = 
0 , 1 , 2 , 
I, U, 1, 2, 
0, I, 2, 
0 , 1 , 2 , 
l'” 1 cosh ti sin ul’l 
' , 1 
Jo 1 siiih 'All — 'All 
4«“7j 
du. 
. (102). 
§ 30. Distortion of the Axis of the Beam. 
If in file expression for V we write ^ = 0 Ave obtain the equation of tlie distorted 
E)rni of the axis 
. ...... .. . 
/>/ ( 27 ^+ 1 ): 
7roLx+/7. /i-j n ! 
To the tirst approximation it is a semi-cnbical pandiola 
This bolds if x be small compared with h. If further Ave have I small compared AA'ith 
h, so that the tAvo concentrated loads are applied in near pai'allel lines {e.g., as in the 
case of material pressed betAA^een the edges of a pair of scissors), then Ave ha\'e, to the 
first approximation, 
U id coali n dll 
air Jo dull ‘Ai — 'Alld 
^ / ii cosh ii 3 \ ; 
f^-i = 7 • 1 .7 ^ “ I ^ 
^ /i Jo ■ siiili All — All 4/(.“/ 
= [ (see p. ‘jy). 
V- 
I d 
u _ A I 1(1 
'-u — ^■'.2 0 /,8 '-^1’ 
/ d 
= jfh- ii j', ^G- 
Tlie terms of order F'/h^ may be dropped in the coefficient of the latter 
quantity lieiiig already small, and A\'e have finally 
Lii 
1 u I n 
