Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

310 CHAPTER 9 Thin Plates

Fig.9.12

Beam of Example 9.1.

thatis,

FT=17.7kN

Hence,thedirectstressinthetopflangeproducedbytheexternallyappliedbendingmomentandthe
diagonaltensionis17.7× 103 / 350 =50.7N/mm^2 .Inadditiontothisuniformcompressivestress,local
bendingofthetypeshowninFig.9.11occurs.Thelocalbendingmomentinthetopflangeatthebuilt-in
endisfoundusingEq.(9.25),thatis,

Mmax=

5 × 103 × 3002 tan42.6◦

12 × 400

=8.6× 104 Nmm

Themaximumcompressivestresscorrespondingtothisbendingmomentoccursatthelowerextrem-
ity of the flange and is 8.6× 104 / 750 =114.9N/mm^2. Thus, the maximum stress in a flange occurs
on the inside of the top flange at the built-in end of the beam, is compressive, and is equal to
114.9+50.7=165.6N/mm^2.
ThecompressiveloadinastiffenerisobtainedusingEq.(9.23),thatis,

P=

5 ×300tan42.6◦

400

=3.4kN

Since, in this case,b<1.5d, the equivalent length of a stiffener as a column is given by the first of
Eqs.(9.24),thatis,

le= 400 /

√

4 − 2 × 300 / 400 =253mm

FromEq.(8.7),thebucklingloadofastiffeneristhen

PCR=

π^2 × 70000 × 2000

2532

=22.0kN

Clearly,thestiffenerwillnotbuckle.