Beam PropertiesConvenient ValuesLoads, Moments and StressesStress RatiosMargin of Safety

frontdotardUrban and Civil

Nov 15, 2013 (3 years and 11 months ago)

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The loads input to the spread sheet are the compressive load and the lateral load. The lateral load
is input in the form of a distributed load, which for the 47.25" strut is,


936/47.25 = 19.8 lbs/in


The input loads were rounded up from the calculated values of 1375.4 lbs and 19.8 lbs/in to,
1400
lbs

and
20 lbs/in

respectively, for simplicity and to be conservative.


The fixity coefficient is dependent on the conditions at the end of the column, which
for the pinned
ends of the aft strut is c =
1.0
.


The cross sectional dimensions taken from Data Block 3 and input for the spread sheet are the
outside diameter OD =
1.66"

and the thickness t =
0.144"
.


The material properties used are those for AISI 321 S
tainless Steel. The bending modulus of
rupture, F
b
, was extrapolated from Fig. 2.8.1.1 in Ref. 6.


The cross sectional properties of the tube were derived from the equations indicated in the spread
sheet and verified by comparison to Data Block 3.


As ind
icated in the heading of the spread sheet, the beam
-
column equations are taken from Ref. 7,
and include the Intermediate Results under the headings,
Beam Properties
,
Convenient Values
,
Loads, Moments and Stresses
, as well as the Outputs,
Stress Ratios

and
Margin of Safety
.


The Margin of Safety for the Aft Strut, when subjected to the maximum occurring compressive
and lateral stresses is calculated in Data Block 9 as,


MS = 2.28




Aft Strut End Fittings


The ends of the
aft struts are attached to the wing at one end and the rest of the assembly at the
other end via specially manufactured end fittings as described earlier. The end fittings are
attached with 4, #10 screws each, however the compressive loads on the struts a
re transferred to
the tubing via the mating surfaces between the tubing and the end fitting, not the fasteners.


The surface area of the tubing is shown in Data Block 3 as 0.67 in
2
. The axial stresses on the
bearing surface of the fitting is found from th
e 1376 lbs maximum strut load as, 1376/0.67 =
2054
psi
. For the AISI 321 Stainless Steel, that the fitting is made of, the internal stresses are,


OK by Inspection








Attachments


Main Attachment Plate


Probe Support Beam Fasteners

The Probe Support Beam is attached to the assembly via the Main Interface Plate with 16 Hi
-
Lok
fasteners. The 7.1g Down loading condition will subject the fasteners to
the largest loads. The
forces on the beam, probe canisters and probes during this condition are taken from Table 1 and
added to get
1420 lbs
. The load per fastener is 1420/16 =
89 lbs
. The HL18
-
8 fastener ultimate
strength in aluminum sheet, as taken from Ref. 6 is 4063 lbs. The resulting Margin of Safety for
the fasteners is,


MS = 4063/(89)(1.15)
-

1 = High




Forward Strut Tab Stress

The forwa
rd strut tabs on top of the main plate must react the bending, tensile and shear loads
imparted to them from the support beam, canisters and probes. The total bending on the tabs will
be highest for the case that has the c.g. of all the probes 2" forward
of the main plate, for the 7.1g
Down loading condition. The drag on the probes and support beam will add to the bending load.


If the weight of the support beam is conservatively assumed to act at the same location as the c.g.
of the probes, the total mom
ent from the inertial loads about the center of the plate is,


M
in
lbs
Plate
Center
Inertial
Loads








3
2
426
2
142
2840


Assuming the vertical center of the drag load that is acting on the support beam and the two end
probes, is 1.5" down from the bottom of the forward strut

tabs and the drag load acting on the
center probe is 9" down from the tabs, the total moment from the drag loads about the center of the
tabs is,


M
in
lbs
Tab
Center
Drag
Loads










2
40
1
5
70
5
1
5
40
9
585
75
.
.
.
.


The resulting total moment from all loads is,


M
in
lbs
Tab
Base
All
Loads





2840
586
3426


A diagram of the loads with respect to forward strut tabs is shown in Fig. 23.






















The total tensile

load acting at the base of the tabs is the sum of all the down inertial loads used to
find the moments. The total shear acting on the tabs is the sum of all the drag loads used to find
the moments. The tensile and shear loads are found as,


P
Tensile

= 3


426 +142 = 1420 lbs

P
Shear

= 3


40 + 70.5 = 190.5 lbs


Figure
0
. Maximum Loading on Main Attachment
Plate Forward Strut Tabs














The two forward tabs react the total loads together. The cross sectional properties for a
single
forward strut tab was given earlier in Data Block 4. Considering two tabs as one unit, the normal
stress profile for an equivalent cross section can be found.


The MDSolids software is used to determine the stresses developed in the forward strut t
abs. A
profile of the normal stresses is shown in Fig. 24.


The largest normal stress developed can be seen in Fig 24 to be 18904 psi. For 0.25" thick,
2024
-
T3 plate, the ultimate tensile stress is taken from Ref. 6 to be 65 ksi. The Margin of Safety
f
or the Forward Strut Tabs is found as,


MS = 65000/18904
-

1 = 2.43




Forward Strut Fasteners

The two
forward struts
are attached
to the main
plate with 6
NAS 1304
bolts each. The maximum tensile load per strut was
found previously to be 2042 lbs. The shear
load per fastener then is 2042/6 = 341 lbs. From Ref. 6, the ultimate single shear for threaded
steel fasteners with a material strength of 156 ksi (NAS 1304 specifications indicate material
properties of 160
-
18
0 ksi) is 7660 lbs. The resulting margin of safety is,


MS = 7660/(341)(1.15)
-

1 = High




Center Probe Tab

Figure
0
. Normal Stress at Base of Forward Strut Tabs

The center canister and probe are attached to the tab at the bottom center of the plate. A lighter
weight clip is u
sed 4" aft of the tab to relieve bending loads on the tab, however this clip is ignored
for this analysis (conservative). The tab is assumed to support the entire inertial and
aerodynamic loads on the center canister and probe. Using the combination of
the 7.1g Down,
with the probe c.g. 2" forward of the main plate, in combination with the drag will result in the
maximum bending on the tab. Assuming the drag load is centered 6.25" down from the base of
the tab, the total moment around the base of the ta
b will be,


M
in
lbs
Tab
Base
All
Loads







2
5
426
6
25
40
1315
.
.


The cross sectional properties of the center tab are the same as those presented for the support
beam end fittings in Data Block 5. Using those properties, the bending moment just calculated
and a tensile

and shear load of 426 lbs and 40 lbs, respectively, the MDSolids software is again
employed to determine the maximum tensile stresses. A profile of the normal stresses is shown in
Fig 25.




Figure
0
. Normal Stress Profile for

Main Attach Plate Center Tab

The largest tensile stress in the tab can be seen in Fig. 25 to be 13648 psi. The resulting Margin of
Safety for the tab is,


MS = 65000/13648
-

1 = 3.76





End Fittings


Bending Stress

The Probe Support Beam End Fittings are used to attach the canisters and probes at each end of the
beam. Lighter weight clips are used aft of the end fittings in order to relieve the bending on the
fittings, however those clips ar
e ignored for this analysis (conservative) with regard to the bending.


The cross sectional properties of the fittings are given in Data Block 5. Assuming each fitting
must react the full drag and inertial loads from the canister/probe combination, a comb
ination of
bending moments are applied. Twisting of the fitting do to the offset of the canister/probe center
of gravity, is ignored for simplicity (this is considered valid in as much as the presence of the rear
clip will prevent the twisting load from o
ccurring).


The lateral distance from the canister/probe c.g. to the base of the end fitting is 6.25". The
moment due to the inertial load during the 7.1g Down condition is (6.25)(426) = 2662.5 in
-
lbs. The
moment due to drag on the canister/probe is
(6.25)(40) = 250 in
-
lbs. These moments are about
different axes. The MDSolids software is utilized to compute the maximum normal stress that
occurs for a simultaneous application of these loads. A snapshot of the screen, showing the
results is presente
d in Fig. 26.


As seen in the figure, the maximum tensile stress is calculated to be 8190.6 psi. The resulting
Margin of Safety for the end fitting in bending is,


MS = 65000/8190.6
-

1 = 6.93










Figure
0
. Maximum Tensile Str
ess on End Fitting








End Fitting Fasteners

The end fittings are fastened to the support beam using 4, HL18
-
8, Hi
-
Loks. They must react the
down inertial loads from the canister/probe. Loads in other direction
s are reacted by the surfaces
of the end fitting and the support beam bearing on one another. Those loads are accounted for in
the FEA analysis of the support beam presented earlier.


The shear loads on the end fitting fasteners are calculated using the V
irtual DER software. The
four fasteners are spaced 1.25" apart laterally and 1" apart vertically. The center of gravity of the
canister/probe combination is located 7.375" from the centroid of the fasteners. The resulting
shear loads are shown in Data B
lock 10.



Results:


Fastener Group Centroid:


Xcg = 0.625 in


Ycg = 0.500 in


Fastener Load:


R_x R_y
R

Fastener (lbs) (lbs)
(lb)



#1
-
613.02 659.78 900.62

#2 613.02 659.78

900.62


#3
-
613.02
-
872.78 1,066.56

#4 613.02
-
872.78 1,066.56


----------------------------------------------



















The largest fastener load is found to be
1067 lbs. The resulting Margin of Safety for the HL18
-
8
Data Block 10.

End Fi t t i ng Fas t e ner She ar Loads

fastener is,


MS = 4063/(1067)(1.15)
-

1 = 2.31




Probe Canister Attachments


Canister Interface Plate

The probe caniste
rs each interface to the support beam via an interface plate as shown in Fig. 7.
The internal loads on the plate are considered negligible and are,


OK by Inspection




Canister Interface Plate Fasteners

The

canister is
secured to
the plate with 12, AN507
-
8
-
32 screws. The Virtual DER software is again employed to
determine the maximum shear and tension in any one fastener. The loads on each fastener are
dependent upon the probe c.g. After checking the full

range of allowable c.g.’s, the maximum
shear load for any one fastener was found to result when the c.g. was assumed to be 2" forward of
the attach plate. The results are shown in Data Block 11.

The maximum shear load is seen in fastener #1 at 92.32 lbs
and the maximum tension load is seen
in fastener #5 at 102.69 lbs. The minimum ultimate shear strength of a #8 fastener as provided by
the AN507 specifications is 396 lbs. The minimum ultimate tensile strength provided is 660 lbs.



Results, Shear:



Fastener Group Centroid:


Xcg = 3.636 in


Ycg = 0.000 in



Fastener Load:


R_x R_y R


Fastener (lbs) (lbs) (lb)


==========================


#1
-
19.40
-
90.26
92.32


#2 12.74
-
90.26
91.16


#3
-
27.81
-
69.93
75.25


#4 21.14
-
69.93
73.06


#5
-
29.69
-
47.34
55.88


#6 23.02
-
47.34
52.64


#7
-
29.31

-
24.37
38.12


#8 22.64
-
24.37
33.27


#9
-
24.98
-
1.78
25.05


#10 18.32
-
1.78
18.40


#11
-
18.39 20.69
27.68


#12 11.73 20.69
23.78


----------------------------------------------





Results, Tension:



Fastener Group Centroid:


Xcg = 3.636 in


Ycg = 0.000 in




Reaction


Fastener (lb)


=======================


# 1 68.34


# 2
-
55.14


# 3 98.18


# 4
-
89.88


# 5 102.69


# 6
-
99.83


# 7 98.47


# 8
-
101.16


# 9 79.11


# 10
-
87.25


# 11 51.09


# 12

-
64.64


-----------------------



Data Block 11.

Shear and Tension in Probe Interface Plate Fasteners


-
9
-





















The resulting Margins of
Safety for shear and tension
are,


MS
Shear

= 396/(93)(1.15)
-

1 =
2.70



MS
Tension

= 660/(103)(1.15)
-

1 = 4.57




To calculate a Margin of
Safety for the shear and
tension interaction, the largest
values of shear and tension
will be used for simplicity
(conservative because they
occur at different fasteners).






MS
Interactio
n




1
93
1
15
396
103
1
15
660
1
8
51
2
2
(
)(
.
)
/
(
)(
.
)
/
.




Canister/Probe Clips

The canister interface plate is
attached to the probe support
beam end fitting via two,
back
-
to
-
back clips as shown
in Fig. 8. The stresses in the
¼" thick clips themselves are
considered negligible and are,


OK by Inspection



Canister/Probe Clips, HL21
-
8
Fasteners

The clips are attached to the
canister interface plate with 6,
HL21
-
6, Hi
-
Loks. These
fasteners must react shear

and
tension loads from the
probe/canister combination.
The maximum loading was
obtained for the end probes,
under the 7.1g Down loading
condition in combination with
the probe/canister drag loads.
Using the Virtual DER
software to resolve the
fastener l
oads, the results
presented in Data Block 12
were obtained.


Results, Shear:



Fastener Group Centroid:


Xcg = 0.000 in


Ycg = 0.000 in



Fastener Load:


R_x R_y R


Fastener (lbs) (lbs) (lb)


===========================


#1
-
105.07
-
184.54
212.36


#2
-
6.67
-
184.54
184.66


#3 91.74
-
184
.54
206.09


#4
-
105.07 42.54
113.36


#5
-
6.67 42.54
43.06


#6 91.74 42.54
101.12


----------------------------------------------




-
10
-

Results, Tension:



Fastener Group Centroid:


Xcg = 0.938 in


Ycg = 0.000 in




Reaction


Fastener (lb)


=======================


# 1 464.87


# 2
-
26.67


# 3
-
518.21


# 4 518.21


# 5 26.67


# 6

-
464.87


-----------------------



















The maximum shear and
tension allowable for the
HL21
-
6 as obtained from the
Hi
-
Lok specifications are
5380 lbs and 3180 lbs,
respectively. Using the
maximum loads obtained for
any given fastener, the
following Margins of Safety
are obtained for shear and
tension of the Hi
-
Loks.

MS
Shear

= 5380/(213)(1.15)
-

1 = High



MS
Tension

= 3180/(519)(1.15)
-

1 = 4.32




To calculate a Margin of
Safety for the shear and
tension interaction, the largest
values of shear and tension
will be used for simplicity
(conservat
ive because they
occur at different fasteners).






MS
High
Interactio
n




1
213
1
15
5380
519
1
15
3180
1
2
2
(
)(
.
)
/
(
)(
.
)
/





Canister/Probe Clips, AN3
Fasteners

The clips attach to the support
beam end fittings using 3,
AN3, bolts. The
bolts must
react the shear loads resulting
from the inertial loading
conditions on the
probe/canister. The largest
values of shear are obtained
for the end canisters during a
7.1g Down loading condition.
The resulting shear loads
were obtained using the
Virtual DER software and are
presented in Data Block 13.

Results:



Fastener Group Centroid:


Xcg = 0.396 in


Ycg = 0.688 in



Fastener Load:


R_x R_y
R


Fastener (lbs) (lbs) (lb)


=================
==========


#1 0.00 636.30
636.30


#2
-
1,351.78
-
531.15
1,452.39


#3 1,351.78
-
531.15
1,452.39


----------------------------------------------

Data Block 12.

Shear and Tension in Canister/Probe Clip Hi
-
Loks


-
11
-
















The largest allowable shear
stress for an AN3 is obtained
from the AN specifications as
2125 lbs. The largest resulting
shear value is used to
determine the Margin of
Safety for the AN3 bolts in
shear.


MS = 2125/(1453)(1.15)
-

1 =
0.27





Aft

Strut Linkage


Each aft strut is linked to the
assembly via the linkage
shown in Fig. 6. The
maximum load applied to a
single linkage from an aft
strut is found in Data Block 7
as 1376 lbs. The
load is
applied at an angle, with
respect to the linkage
fasteners, dependant on the
relative geometry of the
forward and aft struts. The
angles each strut makes with
the horizontal is shown in Fig.
27. The angle of the
aft strut w.r.t. the
forward strut

is 59


-

37


=
22

. Therefore, the
components of the maximum
load as applied at an angle of
22


are,


1376 Cos 22 = 1276 lbs

1376 Sin 22 = 516 lbs


relative to the horizontal
center of the strut linkage.












Aft Strut Linkage, Clevis
Stresses

The aft strut connects to the
linkage via a specially made
clevis, a photograph of which
is shown in Fig. 28. The
stresses in the clevis ar
e
determined for the smallest
cross section along its length.
The load components are
shown being applied to the
clevis in Fig. 28.


Data Block 13.

Shear Load on AN3 Bolts

Figure
0
. Strut
Angles With Horizontal


-
12
-













The dashed line in Fig 28
shows the location where the
cross section of the clevis is
the smallest. In this area, the
cross section is equivalent to
a 1" x 0.2" rectangle. The
normal stresses at the
narrowest cross section are
resolved using MDSolids.
T
he results are shown below
in Fig. 29.
















As shown in Fig. 29, the
maximum normal tensile
stress in the clevis is 35700
psi. The resulting Margin of
Safety
for the clevis stress is,


MS = 65000/35700
-

1 = 0.82




Aft Strut Linkage, Clevis
Fasteners

The clevis is fastened to the
linkage clip with 3,
NAS517
-
3, screws. The
maximum allowable shear
stress for #10,

threaded steel
fasteners, with a material
shear strength of 95 ksi, as
taken from Ref. 6, is 2694 lbs.
The resulting shear loads on
the clevis fasteners are
resolved using the Virtual
DER software. The results
are shown below in Data
Block 14.

Results:



Fastener Group Centroid:


Xcg = 0.950 in


Ycg = 0.000 in



Fastener Load:


R_x R_y R


Fastener (lbs) (lbs) (lb)


============================


#1
-
172.00 984.98
Figure
0
. Load Applied to Clevis

Figure
0
. Normal Stress Profile in Clevis Cross Section


-
13
-

999.89


#2
-
172.00
-
425.33
458.80


#3
-
172.00
-
1,835.65
1,843.69


----------------------------------------------
















As seen in Data Block 14 the

largest shear load on any one
fastener is 1844 lbs. The
resulting MS for the clevis
fasteners is


MS = 2694/(1844)(1.15)
-

1 =
0.27




Aft Strut Linkage, Clip Stress

The clip portion of the
linkage is made from

two
0.071", bent angles, back to
back, with a 0.125" spacer
between them. The base legs
of the clip are 1". The
stresses at the base are
obtained assuming the cross
section at the base is
equivalent to a rectangular
cross section, (2)(0.071)" by
3.35".

The
bending at
the base is
calculated from the loads
applied at the clevis, 6.25"
away. The MDSolids
software is used to resolve the
normal stresses. The results
are shown in Fig. 30.

















As can be seen in Fig. 30, the
largest tensile stress is found
to be 28942 psi. The
resulting Margin of Safety for
the bending of the clip is,


MS = 65000/28942
-

1 = 1.24



The forward strut must be
Data Block

0
. Shear on Clevis Fasteners

Figure
0
. Normal Tensile Stress at Bas
e of Clip


-
14
-

capable of locally carrying
the resulting bending
moment, transferred from the
aft strut linkage. The
moment the forward strut
must react locally is 6.25


1276 = 7975 in
-
lbs. For
simplicity, the strut is
modeled as 2 “C” channe
ls,
back
-
to
-
back
(conservative). The
bending stress is evaluated
using the MDSolids software.
The resulting tensile stresses
are shown in Fig. 31, below.


The resulting MS for the local
forward strut bending stresses
is,


MS =
65000/3701
4
-

1 = 0.75

















Aft Strut Linkage, Clip
Fasteners

The linkage is fastened to the
forward strut using 6, AN4,
bolts. The loads

on the bolts
are evaluated assuming the aft
strut loads are at a distance of
6.25", from the plane of the
bolts. The tension on the
bolts is resolved using the
Virtual DER Software. The
results are shown below in
Data Block 15.


Results:



Fastener G
roup Centroid:


Xcg = 0.000 in


Ycg = 0.000 in



Reaction


Fastener (lb)


=============


# 1 1,647.70


# 2
-
86.00


# 3
-
1,819.70


# 4 1,647.70


# 5
-
86.00


# 6
-
1,819.70


----------
-------------


















Figure
0
. Local Bending Stress Reacted by Forward Strut

Data Block

0
. Tension on Clip Bolts


-
15
-

The shear loads on the bolts is
simply 1276/6 = 213 lbs.
The largest tension on any
one bolt is seen in Data Block
15 as 1648 lbs. The
maximum allowable shear

and tension loads on AN4
bolts, as taken from the AN
specification is, 3680 lbs and
4080 lbs, respectively.


The resulting MS for shear
and tension of the bolts is,


MS
Shear

= 3680/(213)(1.15)
-

1 = High



MS
Tension

= 4080/(1648)(1.15)
-

1 = 1.15





The
MS for the interaction of
shear and tension loads on a
single bolt is,






MS
Interactio
n




1
213
1
15
3680
1648
1
15
4080
1
3
54
2
2
(
)(
.
)
/
(
)(
.
)
/
.





Rod Ends


The rod ends used for
attaching the struts to the
wing hard point bolts and the
aft struts to the rest of the
assembly, are subjected to the
maximum loads that the struts
experience. The maximum
load for either strut, is the
2042 lbs of tension that the
forward strut experiences
during the 7.1g Down
condition. The MS21242
-
5
rod end has a ultimate load of
7180 lb
s as taken from the
MS specification. The
resulting Margin of Safety for
the rod end is,


MS = 7180/(2042)(1.15)
-

1 =
2.05




The “pin” used to join each
rod end with its respective
clevis/fork is a AN5 bolt.
The shear on
these bolts is
maximum for the forward
strut tension of 2042 lbs.
The AN5 allowable shear
load is taken from the AN
specifications as 5750 lbs.
The Margin of Safety for the
rod end pins is,


MS = 5750/(2042)(1.15)
-

1 =
1.44





Wing Hard Point Bolts


The wing bolts must react the
maximum loading that either
strut experiences. In order to
determine the stresses in the
specially designed bolts, an
Algor FEA model was
created. The model was
subjected to two load cases,
o
ne representing the
maximum load from the
forward strut and the other
representing the maximum
load from the aft strut. A
snapshot of the results screen,
showing the maximum Von
Mises stress in the bolt for
each load case, is shown in
Fig. 32.



-
16
-

The maximu
m value of 34602
psi can be seen in Fig. 32, for
load case 2. Load case 2
represents the bolt subjected
to the maximum tension load
reacted by the forward strut.



















The bolt was made from AISI
416 Stainless Steel and heat
treated to a Rockwell
Hardness of C41. The yield
strength for 416 at C41, as
taken from Ref. 8, is 145 ksi.
Again, comparison to the
yield strength, for stresses
obtained from the ultimate
loads
, is very conservative,
however the linear FEA
analysis is only valid for the
linear range of the material,
therefore comparison is made
to the allowable yield stress.


The resulting Margin of
Safety for the bolt is,


MS = 145000/34602
-

1 =
3.19





Figure
0
. Maximum Von Mises Stress in Wing Bolt


-
17
-

C
ONC
LUSION


The new PMS Probe Support
Structure has been
substantiated for the ultimate
static flight loads of the
WP
-
3D aircraft. The
structure will support up to
three PMS probe/canisters.
Unless further analyses shows
otherwise, no single

probe/canister combination
may exceed 60 lbs. Also,
unless further analyses show
otherwise, the center of
gravity of any probe/canister
combination must lie in a
fore
-
aft range from 2" aft of
the Main Interface Plate/End
Fittings to 2" forward of the
Mai
n Interface Plate/End
Fittings. The limitations are
depicted in the figure below.



Figure
0
. Range of Allowable Probe/Canister Center of Gravity


-
18
-

R
EFERENCES


1.)

Structural
Subtantiation of Wing
Pylon Frame

Structure For P
-
3
Aircraft
, Report No.
R
-
111582, K.W.
Thomson, Nov. 15
1982.


2.)

NOAA Stress Analysis
Worksheets
,
Lockheed California
Company, C. L.
Crockett, G. L. Smith,
Apr. 29, 1975.


3.)

Effect of Nose Shape
on Subsonic
Aerodynamic
Characteristics

of a
Body of Revolution
Having a Fineness
Ratio of 10.94
, NACA
RM L57F25, Langley
Aeronautical
Laboratory, Edward
C. Polhamus, Aug. 12,
1957.


4.)

Tests of the NACA
0025 and 0035
Airfoils In the
Full
-
Scale Wind
Tunnel
, NACA
Report No. 708,
Langley Memoria
l
Aeronautical
Laboratory, W.
Kenneth Bullivant,
Sept. 25, 1940.


5.)

Aerodynamic Data for
Loads Analysis
,
Report No. 13134,
Lockheed Aircraft
Corporation, J.E.
Meyer, J.E. Torrillo,
T.W. Feistel, Feb. 22,
1960.


6.)

Metallic Materials
and Elements for
Aer
ospace Vehicle
Structures
,
Mil
-
Hdbk
-
5E,
Department of
Defense, June 1,
1987.


7.)

Analysis & Design of
Flight Vehicle
Structures
, Jacobs
Publishing, Inc., E. F.
Bruhn, 1973.


8.)

Mark’s Standard
Handbook for
Mechanical
Engineers
,
McGraw
-
Hill, Inc., E.
Aval
lone, T.
Baumeister, 1987.