Part
Summary of Critical Detail Parts Fasteners Material Stress M.S. Page Part Used (max psi) Name AD 6 - 1 0 NAS341-8 9076 0.102 Front Spar cap Front Spar A1 2024-T4 9310 0.074 AD6-10 web 0.040" Rear Spar NAS341-14 42176 0.043 cap Rear Spar A1 2024-T4 web 0.040" Aileron Spar A1 2024-T4 1167 0.29 Cap Aileron Spar A1 2024-T4 665 3.0 web AD6-12 NAS344-69 i0000 0 14 Front carrythrough cap 2024-T4 7076.5 0 0.196 Front carrythrough web ADS-7 NAS341-6 9900 0 12 Front carrythrough stiffeners AD6-9 NAS344-51 i0000 0 16 Rear carrythrough cap 2024-T4 3042.4 0 016 Rear carrythrough web AD4-8 NAS341-3 10880 0 178 Rear carrythrough stiffeners Skin 2024-T4 11770 0.25 D6-16 Carrythrough attachments • Description of Design 2.1 Front Spar The front spar was designed to make use of the maximum height available in the wing. It was placed at 25% of the chord line, which allowed it to be 9.5 inches _high at the root and 4.5 inches high at the tip.
The front spar was designed to be able to handle all of the lift loads present on the aircraft. The initial sizing was done using the dimensions at the root and the maximum theoretical loadings at the center line of the aircraft. This gave an overly conservative design.
A solid web with no lightening holes was used outboard until the 30% span mark. This allows for an integral fuel tank and provides extra strength for handling the landing gear loads which occur at 30% span.
From the 30% span mark outboard, lightening holes were sized using the maximum loadings at 30%, 60%, and 90%. These calculations yielded 3 inch diameter lightening holes until 75% span, where the holes were reduced to 2 inches. This is based on a stiffener spacing of 7 inches, which was chosen arbitrarily as suggested rib locations and is the same as the stiffener spacing on the rear spar for uniformity.
Due to the height of the spar and the loadings present, the NAS341-8 extrusion was found to be more than adequate as a spar cap.
The spar caps are attached to the web using AD6-10 rivets in a double row with 0.75 inch horizontal spacing between the rivets.
The vertical stiffeners are attached to the spar cap using AD6-12 rivets, and are attached to the web using ADS-7 rivets.
2.2 Rear Spar The rear spar was designed s_milarly to the front spar. It was placed at the 75% chord point to allow the flap and aileron loads to be transfered directly to it and to provide the largest moment armpossible between it and the front spar.
The first bay, outboard to 30% span, was kept solid for the same reasons as the front spar, except for access holes for the flap linkage.
This rear spar had to be designed to carry part of the lift loads, as well as the shear, bending, and torsional loads induced by aileron and flap deflection.
Since the height of the rear spar is smaller than that of the front spar, larger spar caps were needed to provide the required moment of inertia. In this case, NAS341-14 extrusions were chosen as the spar caps, attached to the web using MS20430Db rivets spaced 0.8 inches apart, with a total of 400 rivets.
As with the front spar, stiffeners were placed every 7 inches, and the lightening holes were sized to be 1.5 inches in diameter based on this and the 0.040 inch web thickness.
2.3 Carrythrough Structure The carrythrough structure was designed as a continuation of the front and rear spars. The carrythrough structure had to be designed to carry twice as much loading as the front and rear spar.
The carrythrough structure was designed similarly to both the front and rear spars. The structures maintained the same height as each of the spars but were o[ different web thickness and stiffener
spacing. Also, the structure had to account for the mounting of the
engine and the attachment to the fuselage. Finally, the structure
had to provide a 1.6 _ dihedral the wing.
Large width spar caps were chosen to facilitate the mounting
of the engine bracket. To attach the structure to the fuselage, a
series of AN3 bolts were used in the front and rear spar. These
bolts were attached through the four longerons on the bottom of the
aircraft and to the bottom spar caps of the front and rear spars.
In attaching the carrythrough structures to the wing spars, an
attachment bracket had to be designed. In providing for the
dihedral, the lower attachment bracket was designed to be (.25 in
for the front and .ii in. for the rear spar) longer than the top
attachment bracket. These brackets were machined out of 2024-T4
aluminum. The brackets were then attached to the spars and
carrythrough structures using D6 rivets.
2.4 Aileron Structure
The aileron design consists of a built up C channel for the
spar of the aileron made of 2024-T3 Aluminum. The aileron is
supported by two hinges which connect to the rear spar of the wing
and the spar of the aileron at the upper surface. Two end ribs are
used as well as three interior ribs to support the hinges and give
the aileron skin its aerodynamic shape. The web is 0.02 in thick 2024-T3 aluminum which geometrically fits the shape of the aileron.
Extruded caps are used as the caps to the spar and are connected to the web by rivets. The aileron actuator was placed on the aileron spar according to a lightening hole in the rear spar.
2.5 Wing Skin
3. Loads and Loadings
The external loadings on the wing structure were determined
using the stripwise estimation method outlined in Chapter 3 of the
Niu text.
This method yielded a non-dimensional lift distribution over half of the planform, which was multiplied by n*(W/2) to determine the actual loads present.
A curve was faired through the points determined by this estimation, and the lift force at 10% span increments was found from this graph.
This lift distribution is shown in the accompanying graph.
From this, the maximum lift force at the centerline of the aircraft, due to the lift on each half-span, was found to be 3538 ibs., and the maximum bending moment was determined to be 1485 ft.- Ibs.
At high angles of attack, these loads were assumed to act at 25% of the wing chord, and at low angles of attack these forces were assumed to move to the 33% chord point.
The front spar was assumed to carry this entire load at high alphas, and 2/3 of this load at low alphas.
At high angles of attack, the rear spar carries none of the primary lift loads, and carries 1/3 of these loads at low angles of attack.
The rear spar also carries the lift loads from the flaps and ailerons, which are transmitted to it at their respective hinge points.
The ailerons exert a maximum force of 181 ibs. on the rear
spar, and the flaps exert a maximum force of 261 ibs. This results
in a total force at the rear spar attachment of 1521 ibs. This
doesn't account for landing gear loads.
4. Structural Substantiation
4.1 Front Spar The front spar was designed to handle all of the aerodynamic loads exerted upon the wing. It was initially designed using the dimensions and loadings of the root, and stiffeners and lightening holes were sized from there.
at the root: stress=My/I I(req)= M*y/(allowable stress) =(1485)(12)(4.75)/10000 I(req)=8.46 i_ using NAS341-8 extrusions as the spar caps, the i(actual) becomes I(actual)= 9.33 i_ M.S.=0.1 with these extrusions, the shear flow is found by q= VQ/I = (3538)(4.75-0.356)(0.4808)/(9.33) =801 Ib/in by chosing AD6 rivets, the required rivet spacing is spacing= (862)/(801)= 1.08 in.
using a rivet spacing of 0.75 in yields M.S.= (1.08)/(0.75)-I =0.44 The shear flow in the web is given by q=V/h = (3538)/(9.5)= 372 ib/in t= (372)/(10000) = 0.0372 t= 0.040 Similar calculations were performed at 30% span and at 60% span to ensure the feasibility of these initial choices.
At 30%: M=630.5 ft.-lb.
V=2177 lb.
I(req)= 3.026 in 4 I(actual)= 7.74 in 4 q(cap)=492.7 Ib/in q(web)= 272 1b/in At 60%: M=161.6 ft-lb V=984 Ib I(req)= 0.636 in 4 i(actual)=4.07 in 4 q(cap)=336.5 Ib/in q(web)= 151 ib/in Lightening holes and stiffeners were used from 30% span outboard. Stiffeners were placed arbitrarily at 7 in. intervals.
The allowable hole size using 0.040 in. thick sheet for the web worked out to be 4 in. However, due to geometric constraints, this
was reduced to 3 in., with a further reduction to 2 in. at spar
station 122.
Composite analysis on web
N_= 3538 ib GT=600000 ib/in ET= 1.5"106 ib/in Using data from p. 519 of the Niu text, the size of the web is dependant upon the stiffness requirements, which yields 24 plies, 0.005 in thick each, 0.12 in. total thickness 4.2 Rear Spar f=My/I = (12834.2)(2)/(0.1443) = 42176 psi M.S.= (44000)/(42176)-I = 0.043 This moment of inertia was obtained using NAS341-14 extrusions.
At 40% outboard, the loads were rechecked and the spar cap changed to a NAS341-13.
M=5208 in.-ib. I=0.1248 in. 4 M.S.= 0.27 At 60% outboard, the spar caps were changed again, this time to NAS341-7.
I=0.0348 in 4 M=1939.2 in. -ib M.S.= 0.2 Using D5 rivets, the rivet spacing is (755) / (943)=0.8 M.S. = (943)/(681) = 0.39 This requires 400 rivets.
Web thickness
t=0.040
M.S..now = 8284/8224 -i = 0.007 M.S.ul _ = 60000/(8225"1.5) -I = 3.86 M.S.y_.id = 45000/8225 = 5.47 Fatigue analysis n/N # cycles f=f1_t*n1±m±_ N 0.011 I0000 13500 9"10' 0.0167 55 3000 16500 18"105 I000 19500 3.5"104 0.0286 300 22500 1.8"104 0.0167 200 25500 1"104 0.02 30 28500 5"10' 0.006 I0 31500 4"10' 0.0025 3 34500 3"10' 0.001 0.0008 2 37500 2.5"10' D= 0.10037 safe life=(1/D)*(1000)/(scattor) =(1/0.10037)*(1000)/(3) = 3321 flight hours.
4.3 Carrythrough Structure 4.3.1 Front Spar Shear Calculation V = 3538.2 ib (from wing loading) h = 9.5 in.
V_o_ = 7076.4 lb.
q = V_o_/h = 7076.4/9.5 = 744.9 Ib/in = q * use 2024-T4 A1 *assumed h = 9.5 in. D = 4.0 in. b_ = i0 in.
I0
Table 4.1.1
t b_/t F< K: F_ f_
.05 200 6800 1.38 9384 14898
.063 159 8100 1.19 9639 11824
.071 141 9000 1.08 9720 10492
.08 125 9500 0.98 9310 9311
.09 iii ii000 0.9 9900 8278
From Niu text pg. 169)
Fig. 4.1.1
t = 0.09 in.
M.S. = 9900/8278 - 1 = 0.196 = M.S.
Stiffener Area
These equations are taken fron the Niu text ex.#2
pg. 169 & 170.
Ao = b=(t) {.385 - 0.08(b_/h) _]
Ac, = -
* This equation provided a negative area.
A_ let to = t = .09 bu1/t _ = 9 bo2/t o : 12 b_ = 9(.09) = 0.81 bo2 = 12(.09) = 1.08 Ao:_q = (.81+1.08) (.09) = 0.1701 = Aor.q Inertia of Stiffeners ii
i<_ = F_ t b_ h: / 10t(h-D)
= 9900(.09) (I0) (9.5):/i0_(9.5 - 4.0) I_ = 0.00139 in. _ This is the minimum moment of inertia required for the stiffeners.
Actual Io : t o b02 _ (4b0: + b_)/!2(b_ + b_i) Io_c _ = 0.0216 in. 4 > minimum inertia.
* Use stiffener to fit required moment of inertia NAS341-6 Web-to-Flange Riveting Strength qr = 1.25 F_ t (h/h-d) = 1.25(9900) (.09) (9.5/9.5-4.0) = 1923.8 ib/in = qr * use AD6 rivets, double row, spaced 0.8 in.
q:_111 = 862(2)/0.8 = 2155 Ib/in M.S. = 2155/1923.8 - 1 = 0.1201 = M.S.
Web-to-Stiffener Rivet Strength P_ = .0024 Ao F o bs/t (h/h-D) P_t = .0024(.2003) (9900) (i0)(9.5/5.5)/.09 P,_ = 940.7 Ib * use AD5 rivets .75in. spacing P_ = 596(2) = 1192 ib M.S. = 1192/940.7 - 1 = 0.267 = M.S.
Equivalent-Weight Thickness (web) teq = t(l - 0.785 D2/b_h + Ao/b_t) t.q = 0.0987 in.2 Spar Caps Stress = M y / I = 1485.6(12)(2)(4.75)/I_ : i0 _ I = 16.94 in. 4 * using parallel axis theorem and assume a cap area and thickness.
use NAS 344-69 extrusion Note: this is very overdesigned, but the width of the extrusion provides attachment space for the fuselage and engine mountings.
4.3.2 Rear Spar Use the same analysis as the front spar...
V = 1521.2 ib t = 0.071 D = 1.0 in. h = 4.0 in. b, = 5 in.
M.S. (web) = 0.016 Stiffener area required = 0.1344 in. _ Actual inertia of stiffener = 0.0135 in. 2 use NAS341-3 spar caps !
t
, 7
....
FIG. 4.1.2 Web-to-Flange Rivet Strength Use AD6 double row spaced 1.25 in.
M.S. = 0.071 Web-to-Stiffener Rivet Strength use AD4 rivets 5/8 in. spacing M..S. = 0.178 Equivalent web thickness t_! = 0.095 in. 2 Spar Caps use NAS344-51 for caps 4.3.3 Attachment to Wing Spars use 2024-T4 A1 V = 3538.2 ib use AN8 bolts in double shear f_ = 11770.5 ib/in 2 f_c_,_tl = 14700 ib/in _ M.S. = 0.25 M.S. (tension) = 4.73 M.S. (bearing) = 3.29 M.S. (tear-out) = 4.27 M.S. (rivet) = 0.0355 Note: bottom attachment must be .25 longer on the front spar and .ii longer on the rear spar.
/,3/
÷ +
"7 4.3.4 Composite Analysis This is a copy of example of #2 pg. 519 in the Niu text.
Nx = 0 Ny : 0 Nxy = 744.9 GT = 600000 ib/in ET = 1.5 X l0 t ib/in Shear Requirement # of +/- 45 ° plies Nxy/(tF_) : 744.91b/in/(.005x38000) 4.3.5 Aileron Structure Web shear fs = V/ ht V = 90.5 ib h = 3.5 in f = 34000 psi t = 0.00076 inch
Use thickness skin : 0.02 in
= (3.1415): k_ E/ 12(1- v_) (t/b)_
buckling
from Bruhn
k,. = 4.0
v_ : 0.3
E = i0.6E6
f_i_ = 665.3 ib
Caps
compression f< = My/I
M = 778 inlb x 1.5
y = 2.4 in
f= = 38000 ib
I = 0.0737
use Cap with I = 0.0776
Skin
torque fs = T/2At
T = 4675.0 inlb
A = 21 in 2
f_ = 39000 ib
use 0.02 in thick skin
t = 0.00286
4.3.6 Composite Investigation
Composite investigation for the aileron skin
Fy = 13110 ib
Fx = 0.0 ib
Fxy = 5565 ib
for 45_' plies Nxy = n4s x t x F_2
5565 ib/ (0.005 (38000) = 29.8 plies
for 90_ plies Ny - F:_:_ x t_ / t x F_. = n _'c_
13110 - (15000) (0.005)(30) / (0.005) (98000) = 22.16 plies for 0 ° plies Fx : 0 therefore use 10% of total number for stability 45 ° plies = 30 plies 90 ° plies = 23 plies 0 ° plies = 5 plies o Manufacturing and Maintenance When assembling this wing, the wing structure alone should be the skin and ailerons, and then it assembled first, including should be attached to the carrythrough structure within the fuselage.
The front and rear spars are constructed of thin aluminum sheet with extrusions riveted to them. It is recomended that the web be cut to dimension first, including cutting lightening holes, and then the spar caps and stiffeners riveted to the web.
The spar assemblies can be covered with skin and the ailerons then attached to the rear spar.
Manufacturing of the ailerons begins with the making of the spar which is a built up C channel. A 0.02 inch thick sheet of 2024-T3 aluminum is cut to the proper dimensions to serve as the web of the spar. The extruded L sections used for the caps are then riveted to the sheet according to the design
drawings. Five ribs, which can be hydropressed, are connected
perpendicular to the spar to givethe skin of the aileron its
airfoil shape. For the skin two sheets of 2024-T3 aluminum is
again used at 0.02 inches thick for both the upper and lower half-
of the skin. Two hinges are used at 25 and 75% span of the aileron
to connect the aileron itself to the rear spar of the wing.
No access panels are incorporated into the aileron design
because interior parts do not need to be inspected on a regular
basis.
This manufacturing process seems to be the most reasonable.
A built up C channel is cheaper to make than an extruded C section
because of the changing height of the web. From the composites
calculation a composite structure could work for the skin but it
was felt that this would add to much cost to the aircraft and also
a primary trainer would be subjective to frequent inspections and
unusual loading. With these considerations aluminum pieced
together would be more logical.
From this, all that remains is bolting the wing structure to
the carrythrough.
6. Cost Analysis .
Weight summary Front spar- 221bs.
Rear Spar- Carrythrough- 16.37 Ibs Aileron- 5.60 ibs caps 2 at 2.8 ibs each web 1 at .1505 ibs 0.31 lbs ribs 5 at 0.0541 0.27 Ibs skin 2 at 1.86 3.72 ibs rivets 1 lb 1.00 ibs total aileron weight half span 10.90 Ibs Skin- Total half span weight = Total planform weight= 8. Conclusions Due to the time constraints, complete optimization analysis was not possible. This resulted in a structure that would be slightly over the minimum possible weight to carry the loadings present.
Also, many of the detail parts were chosen based on conservative assumptions, since this aircraft will be used as a trainer and is destined for abuse unknown to other types of aircraft. Again, this results in a conservative design which satisfies the FAR "fail-safe" requirement.
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L.t- I \'J ; _.E_. _ _-J L ........ l ..- l ..l............. I ......... Jl .... J c_ I I I AT]_t-_ _]l_ S'l'[:[l-__- DL:"I'_-[I. DESIg Report Additions: Wing Skin 421S93ADP02-2 4-19-93 AE421/04/TEAM #2 LEAD ENGINEER: Garrett Sager TEAM MEMBERS: Bob Mallon Mohamed Alameri Bill Steinbach Ronald Roberts SUBMITTED TO: Professor C.N. Eastlake 04/16/93
Table of Contents
Wing Skin Report Additions
C. Wing Torque vs. Span Graph ........ I0 D. FORTRAN program for wing torque ... II
2.5 Wing Skin
The wing skin caries the torque load created by the i) lift
distribution 2) moment about the mean aerodynamic chord and 3) flap
and aileron hinge forces. The center of torque was assumed to be at 40% of the chord by Niu (pg.85) suggestion. The torque loading varies parabollicaly from 0.0 at the wing tip to a maximum value at the root, the hinge reactions from the flaps and ailerons were modeled as point loads [see Appendix: graph 3).
The shear flow calculations indicated that a very thin aluminum skin would provide the needed shear flow path. However a 0.02in. skin was selected to avoid wrinkling, meet environmental condition requirements, and aid in easy manufacturing and assembly.
4.5 Wing Skin The wing skin provides the reaction for the wing torque created by the aerodynamic loads which acts about the 40% chord.
The shear flow at l)the root 2) the midspan and 3) slightly in- board of the tip are the critical positions for determining skin thickness and rivet spacing.
In-board of TiD: q= T/2A (568 Ibs.)/2,(41.6) = 6.83 ibs./in.
Rivets=: MS20470AD-3 From MiI-HB5 f, = 2171bs.
Recommended Spacing: 2171b/6.831bs/in = 31 in.
This large calculated rivet spacing is due to the reduction of torsion to zero at the tip.
Selected Spacing: 4.0 in.
At midspan fSkin over-lap_: T = 10,260 in-lbs. Area = 108 in 2 Same rivet and math as above, q = 47.5 Ibs/in. Calculated spacing- 4.6in.
Selected spacing - 2.5 in.
Spacing M.S. - 2.5/4.6 - I = 0.45 At Wina Root: T - 28,061 in-lbs. Area - 208 in 2 Same rivet and math as above, q - 67.5 ibs/in. Calculated spacing- 3.2in.
Selected spacing - 2.0 in.
Spacing M.S. z 2.0/3.2 - I = 0.38 Skin Thickness Selection: Due to the low torsional load on the wing a very thin skin could be used however it would be extremely fragile. Therefore a thickness of 0.020in was selected.
This thickness provides 34x103psi. which greatly exceeds the maximum shear at the root of 2,700psi.
Weight Estimation: sheet Skin weight is determined from the volume of A1 plus the estimated weight of the rivets.
Volume of A1 skin matterial = 476 in 3 Weight =(volume),(density) =(473),(0.0984) Weight of skin = 46.8 Ibs.
Weight of rivits = 8.0 Ibs.
Total Weight - 54.8 Ibs.
Commosite Analysis 4.5 Wing Skin Composite Analysis This method of determining the type and number of plies of composite was determined by the method presented in Nui pg.519. To handle the shear load +/- 450 plies were used.
N x _ 0 Ny - 0 N_ - 67.51bs./in.
Number of +/- 45° plies = N_ / t, F,2
= 67.5/(.005)(3.8ksi) = 9 plies of +/- 45 ° The use of graphite composites for the wing skin would provide a weight reduction of 15%, however the cost of manufacturing would increase to an unacceptable level for the mission requirements of the PFT Viper.
5.5 Manufacturing and Maintenance of Wing Skin The wing skin consist of five separate panels that will be riveted to the spars, ribs and each other. The four panels the cover the upper and lower planform will be cut from 4'x8' A1 sheets, the outboard panel will be installed first so that the inboard panel over-laps the out-board panel by about 3.0inches. The final panel will be a 3'x16' sheet that will be hand formed around the leading edge. To avoid flow spoilage no rivets will be used on the nose of the airfoil and as few as possible in the region near the leading edge, approximately 2in. away.
The four wing skin panel will be riveted to the front and rear spar, the ribs spaced 7.0in. apart and at the over lap point. The rivet spacing determined near the root (high stress area) should be 2.0 in., near the midspan (panel over-lap) 2.5 in., and near the wing tip 4.0 inches. The skin will be fastened to the ribs by 425 MS2047AD-3 rivets and to the front and rear spar by 218 rivets; the rivet edge distance will be 0.25 in. Note the number of parts listed above is for a semi-span, multiply by 2 for the total number of parts for the entire wing.
The wing skin will be painted to protect the material and meet the environmental requirements set in the Statement of Work #2. , See Appendix for Environmental Conditions.
8.1 Wing Skin Conclusion
The low wing torque created by the i) lift distribution 2)
moment about the mean aerodynamic chord and 3) flap and aileron
hinge forces permits a very thin skin which is extremely difficult to work with, so a durable and standard size A1 sheets were used.
The protective coating (paint) on the skin will meet the environmental requirements set in the Statement of Work #2.
Unfortunately the target wing weight of 216 Ibs. was not achieved. Based on the findings in this report the wing designed by Team #2 is a suitably strong, rigid and light wing structure that is well suited for the Primary Flight Trainer Viper.
Appendix A
Appendix A
Envi r¢>_nta ]_ CQn¢_[.i. t J. ¢>ns I. Temperature All modes of operation and storage shall not be degraded for temperatures from -40_ to +122°F.
2. Atmospheric Pressure Operation to I0,000 feet (ICAO Std.) shall be possible.
3. Sand and Dust External surfaces, mechanisms and associated items shall endure up to 150 microns in size and combinations of sand and dust in concentrations up to 0.041 grams per cubic foot without degradation.
• . Rain All external surfaces, mechanisms and associated items shall endure and seal against water intrusion from rainfall at a rate up to 4.0 inches/hour with wind velocities up to 50 mph. Any cavities that could hold water shall be provided with a drain.
5. Humidity External surfaces, mechanisms and associated items shall endure up to I00 percent relative humidity at +95_ without degradation.
6. Ice
All external surface, mechanisms and associated items shall endure
ice at temperatures to -40_ and remain operational.
7. Snow
All horizontal external surface, mechanisms and associated items
shall endure accumulations for depths up to 8.0 inches of wet snow.
8. Salt/Fog Atmosphere
All external surface, mechanisms and associated items shall
withstand prolonged exposure to salt/fog atmosphere as encountered
in coastal areas without degradation in performance, there shall be
no binding of moving parts nor corrosion that obstructs operation.
9. Wind and Gust
Wind of 50 mph with gust in accordance with FAR23 shall not degrade
operation. Ground tie downs shall withstand loads associated with
a wind of 120 mph from any lateral direction and from
elevation/depression angles of up to I0 degrees.
10. Shock and Vibration
The airplane structure designed shall withstand shock vibration
loads associated with normal operation and storage in accordance
with FAR23 section 2.1
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:Jc,ipt started on Wed Aor 7 16:13:41 1993 a.outsun2X enter soail oositior,_ vertic._,] she.-:_r" force O. 3538.2 enter soan Position. vertical shear force • 1. 3074 enter span oosition., vertical shea force .2.2618.7 enter span oosition, vertical shear force .3.2176.7 enter soan oosition, vertical shear force • 4. 1754.3 enter soan oosition, ve',-tical shE,a; ,c, zue 0.5. 1354.8 enter soan oosition vertical _.,_,e_:,_ ....... force •6. 984.3 e..-,ter soan oosition vertJ.c_,l _ ........ " .... _llt_'cll I L I Lt .7. 650.2 enter soan osition, vertic_,i sl_ear !orce .8.360.3 _'nter sr, an oosition, verti,:_l __,,_t,_ i':_rce .9.125.9 er, ter s_an oosition, vertical shea_ _o,-,-e .%,.37.5 <<nter soan oosition, vertical shear fc, rce 1.0 i::,osition DeltaSz dr.w
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0.00 464.20 4829.5 0.10 455.30 4475.4 0. _0 / _ q -4&' 0.20 442.00 4B90.7 0.3_ 422.40 3666.6 O.OO z _._.; 2. g _. 40 399.50 3.,.o8, 3 0.50 370.5_ 2790.4 _.6_ 7,_4 10 o_oa 1 ,-J _,6. " _. 7_ 289.90 """:" ' _. 8_ 234.4_. .!7,61 ,. 4 _._r_, _ o,::.'-'' 40 ..,o_.' 6 sun2% exit _un2_, 7 Ic;io:'-7_. Irr_ ::..-.riot de.he on Wed A0r