Mechanics of Aircraft Structures C. T. Sun Second Edition P144 *************4.2*
ID: 1816583 • Letter: M
Question
Mechanics of Aircraft Structures C. T. Sun Second Edition P144
*************4.2**********
A uniform beam of a this Walter angle section as shown in Fig. 4.19 is objected in the heading M2(M1 = 0) Find the neutral axis and heading stress distribution over the terms section Figure 4.19 This walled angle section Because the angle section of Fig. 4.19 counterclockwise for 49degree. Find the neutral acts and the maximum bending stress. Compare the lead capacity with that of the original section given by Fig. 4.19Explanation / Answer
z 2h t ( h/ 22 ) c ??
????
??
--- ANS
(a) Moment of inertia
12
)
2
(
12
2 2
3
I t h 3 th y ?? ?? ??
3
)
2
(
3
2 2
3
I t h 3 th z ?? ?? ??
?? I ???? yzdA 0 xy (this is always true for symmetric sections)
(b) Set up a new coordinate system (y, z). Using equation (4.25) in the textbook,
4.2.1
Name:Abdur Rahman Hilal Email:arhilal@gmail.com (nabiya.h6@hotmail.com) Work Phone:971506573490
Address:P O Box 51784, A:1-503, Khalifa Complex,Tourist Club Area, Opp Abu Dhabi Mall,ae (United Arab Emirates),Zip Code:51784
Mechanics of Aircraft structures
C.T. Sun
' ' 2 2 z
II I
M I M I
y
II I
I MI M
y z yz
z y yz z
y z yz
y z yz y
xx ??
??
??
??
??
?? ??
and substituting the values of moments of inertia in the equation above, we obtain
z
th
M
z 12
I
M
3
y
y
y
xx ???? ??
--- ANS
Maximum positive stress is at
22
z ?? h , => 2
23
th
My
xx ?? ??
Maximum negative stress is at
22
?? ??z h , => 2
23
th
My
xx ???? ??
The absolute maximum stress is 2
23
th
My
xx ?? ??
(c) The neutral axis (plane) is located along ?? 0 xx ?? ,
0z
th
M
12 3
y
?? ?? xx ?? z =0> ??
So the neutral axis coincides with the centroidal axis.
Note that this section in this particular position is symmetric with respect to the
y-z coordinate system. For symmetric sections the neutral axis always coincides
with the location of the centroid.
--- ANS
(d) The load capacity with the original section
For the same maximum bending stress in both beams,
2
,
2
,
4
3 2 27
th
M
th
M y rotate y origin
xx ?? ?? ??
=> 1.59
12 2
27
M
M
y ,origin
??y ,rotate