540 CHAPTER 19 Structural Idealization
TheidealizedsectionisshowninFig.19.4(b),inwhich,fromsymmetry,B 1 =B 6 ,B 2 =B 5 ,B 3 =B 4.
Sincethesectionisrequiredtoresistbendingmomentsinaverticalplane,thedirectstressatanypoint
intheactualwingsectionisdirectlyproportionaltoitsdistancefromthehorizontalaxisofsymmetry.
Further,thedistributionofdirectstressinallthepanelswillbelinearsothateitherofEq.(19.1)orof
Eq.(19.2)maybeused.Wenotethatinadditiontocontributionsfromadjacentpanels,theboomareas
includetheexistingsparflanges.Hence,
B 1 = 300 +
3.0× 400
6
(
2 +
σ 6
σ 1)
+
2.0× 600
6
(
2 +
σ 2
σ 1)
or
B 1 = 300 +
3.0× 400
6
( 2 − 1 )+
2.0× 600
6
(
2 +
150
200
)
whichgives
B 1 (=B 6 )=1050mm^2Also,
B 2 = 2 × 300 +
2.0× 600
6
(
2 +
σ 1
σ 2)
+
2.5× 300
6
(
2 +
σ 5
σ 2)
+
1.5× 600
6
(
2 +
σ 3
σ 2)
thatis,
B 2 = 2 × 300 +
2.0× 600
6
(
2 +
200
150
)
+
2.5× 300
6
( 2 − 1 )+
1.5× 600
6
(
2 +
100
150
)
fromwhich
B 2 (=B 5 )=1791.7mm^2Finally,
B 3 = 300 +
1.5× 600
6
(
2 +
σ 2
σ 3)
+
2.0× 200
6
(
2 +
σ 4
σ 3)
thatis,
B 3 = 300 +
1.5× 600
6
(
2 +
150
100
)
+
2.0× 200
6
( 2 − 1 )
sothat
B 3 (=B 4 )=891.7mm^2