IExample 1A Wing Rib is supported at the end by spar caps and resiststhe aDDlied load of 3000 lb. as shown below Show the loadsTra nsmitted by the Stiffener AB and the shear webs.

i i l i ) 11. r. l {} ' } l l . , rr

t i iur! ll.

t l- '1 . , , . - - --- t l r , , : r - l

.ttxl l-r

: i) ix: It i

lllr1 l l t

;1i, ]l l; -.n' ,r : ,l i l 'I I l ll l l lT,'I

] l rx) th

tf--lrr :_J),,r'ii,,,,

ri--lti l t l.-',,iL"

Example 2A fuselage frame shown below is subject to 1000 lb. verircal load.Ar = 0. 10 inZ, y,=34 tn, y2=24 in, y,=15 in, y4=6 in, y5=0 in.find the shear fo$s in the skins.

4Arr " l ' - l - J(4) " (st

y'Ar 2 yAr q, lbl in(7) (8) (e)

Stringer no.( l)

qa63.?

,Ar(6)

AJ Y(2) (3)

l

4

5

t

0.05 34.0

0.10 24.0

0.10 15.0

0.10 6.0

0.05 0.0

16.5 0.925

8.5 0.85

-0.5 -0.05

9.5 -0.95

15.5 0.' t75

0.925 10.20

L775 19.55

1.' t25 19.00

0.775 8.54

1 . 7

0.6

0.0

17.12

1.23

0.02

9.02

t2.0145.40

(19.55 tb/ in)

3

centroid t is determined from the summations of columns 4 and 2:

, . _ z A r y ' _ 9 ? _ , . . , -t - - 4 . - O A - ' ' ' ' " '

It is now necessary to obtain coordinates of the stringers with respect tothe centroidal axis. These values, y : y'- y-, obtained by subtracting 15.5from terms in column 3, are shown in column 5. The terms 1,4J. and y2 A, arecalculated in columns 6 and 7. The summation of column 7 yields themoment of inertia LU|lnE!-

D 500 -o = 1 l t A 1 - f t ^ l Y e t

The valuglof 4 are calculated in column 9

3

I I ( le.00lb/in)

t'//

4

(8.54 lb/in)

i l . i i f i

Example 4

Find the angle of tv/ist for the boxed beam with thedimensions and shear f lows shown below.Assume G=4x106 psi

, L - t20 /N.

l . . lutl l [. i l

5..4-

e -l-,/ -

q . A s L2 / + 6 2 A G

5 ?As-t

/ 2.. /4oo x /Oo - c 3 l

2oc 7- 4c - *Z :9= ri9O.o32-

b l =( z ) ( 4 a o 1 ( 4 r , t 4 S

9 = O-ezo 4 ,Au .

O . o + n

l{ll lb ,r I:Ul 'l r{

I

I /tt

Example 53. 1 ln the beam cross sectiolr shown below, each stringer has a cross-sectional area of 0.5 in.2The rnaterial used in all components is 2024-T3 aluminum, for which E: 10 x 10"psi, G:4 x106 psi , and S1 = 47,000 psi .(a) Find the shear flows that are produced in the webs by a 40,000-lb upward force applied at

stringer d.(b) Determine the minimum wall thicknesses t1 (the cun'ed web) and t: (the straight webs) for a

factor of safety of 1 .25 (based on yielding).(c) Assuming web thicknesses as found in (b), how much twist (in degrees) would be produced

by the 40,000-lb load in a beam length of20 ft?

a+opoo lLR = a in.---a

r Al-arr fLo,-' 4-,,r-u

dF_10 in__ l

v, -- +o'a-c,v--olf 4

T. 7 L,w+Z L

4t i^'c*,-'t--* "{-" t/ / / ^

A'.. ^F ft/"a ar/evvv\-AJ T-

l b - , ^ ,

F"

0oo t L ,U-S-ALr*-/,*\ v.,\-{'-.\^4

^ o ^ ( l ' +A Mu-- Vr nu

lrl.--""n J- r\-r--kr i w'v:-+- L-a'v't '

L9r-nrs r\n-ur -q ; a {-4-v';'^+t"'; Jq'k a's 4':o /

(af*)^ = o*vo =(+o'9oo'rk")=J6oa4oll'-^-, o ,\\,\ Cj-t "-t^+ ,' "

6 W =(ner)^An= $ ooooryfo's )= Lsoot" rL

V T / \I qr/-? /A tr,^.^ ,-1 rl-4,-- {lo,--.. 1) t - n* ;

e-

7r,':y''

.v2,9@Ar

Lb

a

A I/Yj /17\/.- ,- \(Z t-< l.e,)\ . - . ) A ; g t. - - - i t 'l - t v

J o , O O o l L - ; ^ ,

5 > , L b o n t- r 1 0 0 f ( ?

"/+q. I C.*,)Q p q-'zu l r - 1 6 . ' 1 - )

U '| ,.t -'t

&-ll L"U

Q z : - | l r , 3 CU

t l ll A 2 / t ^ ,

tL 1 . ,

l D l ^

1q-3,1cr tL/ , ^f E.+s,lbxn

I r = , t r " l L l w ,

Js zt ' tL / , ; .

1 t 5 . 1 ( , 1 b 1 , . .

-(; '''''LJ -{"" --.,.,',64 ..^sG, *r O7^. 6 ), (t),u- h)

1 " . ( , ) :O -o,- - # ( t , t ,s

j t r , - 1o o? ' - )QoD(n; '^ / * ) ; -ps rsO oL*z *J,{ , 3 1 '

dq t oE u7l too(f+7,n7 ' 4 - t t t , llL/-

----> '-'+ '-'-+

,011,,'^