Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

15.4 Calculation of Section Properties 465

FromEq.(15.19),

σz=

Mx(Iyyy−Ixyx)

IxxIyy−Ixy^2

(i)

Thesectionpropertiesarecalculatedasfollows

Ixx= 2

ht

2

(

h

2

) 2

+

th^3

12

=

h^3 t

3

Iyy= 2

t

3

(

h

2

) 3

=

h^3 t

12

Ixy=

ht

2

(

h

4

)(

h

2

)

+

ht

2

(

−

h

4

)(

−

h

2

)

=

h^3 t

8

SubstitutingthesevaluesinEq.(i)

σz=

Mx

h^3 t

(6.86y−10.30x) (ii)

Onthetopflangey=h/2,0≤x≤h/2,andthedistributionofdirectstressisgivenby

σz=

Mx

h^3 t

(3.43h−10.30x) (iii)

whichislinear.Hence,

σz,1=−

1.72Mx

h^3 t

(compressive)

σz,2=+

3.43Mx

h^3 t

(tensile)

In the web,h/2≤y≤−h/2 andx=0. Again the distribution is of linear form and is given by the
equation

σz=

Mx

h^3 t

6.86y

fromwhich

σz,2=+

3.43Mx

h^3 t

(tensile)

and

σz,3=−

3.43Mx

h^3 t

(compressive)