A technique for preloading a deployable box truss beam by extension of one face diagonal per bay was studied to determine if it would result in uniform loading of truss joints without causing excessive truss deformations. Results indicate that it is possible to accomplish uniform loading in the beam region way from beam boundaries, whereas in the regions near boundaries the member loading becomes non-uniform with magnitudes greater than those in the uniform load region. Also, the type of deformation which results in the beam depends on the pattern of preloaded members

Lake, M. S.

Wu, K. C.

English

NASA Technical Reports Server

NASA Technical Memorandum 87673 
NASA-TM-87673 19860014152 
ANALYSIS OF A SINGLE-FOLD DEPLOYABLE TRUSS BEAM 
PRELOADED BY EXTENSION OF SELECTED FACE DIAGONAL 
r'1EMBERS 
K. Chauncey Wu and Mark S. Lake 
APRIL 1986 
NI\5I\ 
National Aeronautics and 
Space Administration 
Langley Research Center 
Hampton, Virginia 23665 
. " ,.. 
, ''*,'', .. 
111111111111111111111111111111111111111111111 
NF01253 
" ' 
--------------- - -----
https://ntrs.nasa.gov/search.jsp?R=19860014152 2020-03-20T15:46:23+00:00Z
ANALYSIS OF A SrnGIE-FOID DEPIDYABIE TRUSS BEAM PREIOADED 
BY IDcr'ENSION OF SEIECI'ED FACE DIAGONAL MEl-ffiERS 
K. Cllauncey Wu 
Mark S. lake 
NASA langley Research Center 
HaIrpton, VA 23665 
IN'ffiOIlJCI'ION 
A major concern in the design of large space structures is the loss 
of structural predictability due to non-linear joint stiffnesses. A 
primary cause of non-linear behavior in deployable truss joints is free 
play in pin connections. In this study, one technique for removing joint 
free play am inproving truss perfonnance is analyzed for an existing 
deployable truss concept. 
Box trusses which deploy in one direction (single-fold), much like 
an accordion, are being considered for future space structure 
applications. One single-fold truss concept is described in reference 1. 
'Ibis concept has fixed batten frames, folding longerons, am telescoping 
face diagonals (see figure 1a). A methcxl proposed for reducing possible 
non-linear behavior in this design is to induce a preload in the truss by 
adjusting the length of one face diagonal in each bay. 'Ibis preload is 
designed to eliminate joint free play and unifonnly load the joints into a 
linearly elastic region where their behavior is more predictable. To 
enhance predictability and avoid stress concentration areas within the 
structure, it is necessary to insure that all joints are preloaded 
unifonnly. 
2 
In this study, four preload cases were analyzed using linear finite 
element techniques to detennine the force distribution in the nenbers am 
truss defomations :resulting fran the applied preload. Each case involved 
the lengthening of a different pattern of face diagonal struts. Results 
from these analyses were c::arpared to detennine if a pattern existed that 
would irrluce a unifonn distribution of forces in the nenbers while causing 
:minimum truss defomations. 
mDEL DESCRIPl'ION 
Four bays of the aforementioned truss configuration are diagrammed 
in figure l(a). A finite element IOOdel was developed for a 21 bay truss 
beam of this configuration. '!he truss nenbers are represented by axial 
stiffness elements having properties of two inch diameter graphite/epoxy 
tubes with a cross sectional area of 0.3657 in2 , a Young's modulus of 
40xl06lbf"in2, and a coefficient of thennal e>q)aJlSion of 0.5xlO-6injin°F 
(reference 2). All truss joints are assumed to behave linearly. '!his 
assumption is based on the design criterion that the preload must load the 
joints into a linear stress-strain region. Also, the joints are assumed 
to have the same linear stiffness as the stnlts. 
A statically detenninant set of constraints are applied to three 
nodes at one ern of the truss beam to restrain rigid body Irotion without 
interfering with the defomation of the truss nenbers. '!he other ern of 
the truss beam is left free. Effects of. the preload are studied in three 
typical regions of the truss beam (figure l(b»: 1) the region near a 
fixed ern, 2) the region near a free ern, am 3) the region away fram any 
ern corrlitions where the stnlctural behavior approaches that of an 
infinite truss beam. Note that due to the choice of constraints at the 
fixed or "cantilevered" end, the member forces and local defonnations in 
this region should be the same as those for the free end. 
3 
To mathematically represent an extension, or a strain, in the face 
diagonal members, a unit thennal load was applied. The unit load chosen 
was a tenperature differential that would cause a 1 lbf corrpressive force 
in a diagonal if its ends were fixed (i.e. fully constrained). The 
equation which relates the member force (P) to the applied thennal loading 
(AT) is 
P = -FAa AT 
where E is the Young's modulus, A is the cross sectional area, and a is 
the coefficient of thennal expansion. 
Using this equation, the thennal load required to generate a 1.0 lbf 
corrpressive force in a fully constrained diagonal may be corrputed. This 
thennal load is 0.1367oF. since the face diagonals in the truss are not 
fully constrained, the actual corrpressive force in these members will be 
less than 1.0 lbf . 
STATIC ANALYSIS OF FOUR PREIOAD CASES 
Four preload cases are analyzed and corrpared in this study; each 
involves loading a different pattern of face diagonal members (figure 2). 
For each case, the unit thennal load is applied to one diagonal in each 
bay of the truss, and the resulting member forces and static defonnations 
in the truss are calculated. 
--------.--------.-----.-- .- -- --_._ .. _._---_._-
4 
Member Force Distribution 
For each of the preload cases described, the resulting member forces 
were calculated ani the ranges (maxinrums ani minimums) of these forces 
were noted for each member type (i. e. longerons, face diagonals, batten 
diagonals, ani battens). Despite the differences in the preload patterns 
all patterns give essentially the same ranges of forces for each member 
type although the distributions may differ slightly. Table 1 lists these 
ranges within the three characteristic regions of the truss beam (Le. 
near a fixed ern, near a free ern, ani away from any ern constraints). 
In the region away from ern constraints all of the members of a 
given type are loaded approximately the same, as imicated by maximums ani 
minimums that are about equal. '!his result in'plies that the truss joints 
in this region would be loaded tmifo:rmly, a con:tition which was described 
as a necessity. For the nDde1 being studied, this region starts four bays 
, 
in from each ern of the beam (see figure 1 (b) ) • 
'!here is, however, a spread in the forces for each member type in 
the ern regions as imicated by maxinrums ani minimums that are not equal. 
'Iherefore, the joints in the ern regions are not loaded unifo:rmly with the 
present preload scheme. F\1rther, it should be noted that as a result of 
this preload scheme the maximum forces that exist in an ern region are 
greater than the corresporrling member forces in the tmifonn load region of 
the beam. 
Tnlss Defonnations 
Although the four preload patterns considered all resulted in the 
same max.irnum ani minimum member forces, the static defonnations of the 
truss are different in each case. Figures 3 through 6 are plots of the 
5 
tnIss defonnations resulting from preload cases 1 through 4, respectively. 
'!hese plots are each scaled to their own maximum deflection and can, 
therefore, only be compared qualitatively. 
'!Wo types of defonnation result from preloading. '!he first is a 
shearing defonnation where adjacent batten frames move relative to each 
other in the y-z plane. '!he second is a twisting defonnation where 
adjacent batten frames rotate relative to one another about the x axis. 
As seen in figures 4 and 5, preload cases 2 and 3 result in similar 
twisting defonnations of the tnIss beam, whereas preload cases 1 and 4 
result in predominantly shearing defonnations (figures 3 and 6). However, 
the type of shearing present in preload case 1 is different than that of 
preload case 4. In preload case 1 (see figure 3a) adjacent bays are 
shearing in opposite directions as viewed in the x-z plane. In preload 
case 4 (figure 6a) all bays shear in the same direction. '!his result is 
justified by considering the preload patterns in figure 2 and noting that 
in both cases 1 and 4 all of the preload members are parallel to the x-z 
plane, lining up in the same direction in case 4 and in a "zig-zag" 
arrangement in case 1. 
To quantitatively compare the tnIss defonnations, the deflections at 
the free end of the tnIss are summarized in Table 2. '!hese deflections 
represent the average of the deflections at the four joints of the end 
batten frame. It should be noted that the y-z plane of the coordinate 
system is fixed to the three nodes constrained in the fixed end of the 
beam and therefore, warping of the fixed end batten frame will result in a 
rigid body rotation of the beam in the y or the z direction. 
6 
For all four preload cases the average x deflection (dX) is 
essentially the same. In all preload patterns only one diagonal per bay 
is being loaded and thus, the average longitudinal stretching (dX) should 
be the same. Also, the average y deflection (dY) is the same for all load 
cases. This is understood by recalling the constraint condition iInposed 
on the fixed end and noting that the same diagonal has been preloaded in 
the first bay (near the fixed end) for all load cases. This first preload 
diagonal causes warping in the fixed end batten frame which, consequently, 
causes a rigid body rotation of the beam due to the constraints on three 
of the four joints in that frame. The Z deflection (dZ) is also 
approximately the same for cases 1-3, due to this rigid body rotation, but 
is nearly 5 times larger for preload case 4 due to the fact that all 
preloaded diagonals in case 4 have the same oriention (see figure 2). As 
noted previously, in cases 2 and 3 the preloaded diagonals fonn spiral 
patterns causing the truss to undergo a c::onprratively large twist, as 
shown by the large ex rotation in Table 2. 
CONCI1JSIONS 
A technique for preloading a deployable box truss beam to improve 
truss predictability was studied to detennine if its application would 
result in unifonn loading of the truss joints without causing excessive 
defonnations in the truss. The technique presented allows only one face 
diagonal per bay of the truss beam to be preloaded. In this analysis four 
patterns of preloaded face diagonals were corcpared. 
7 
'!he results of the analysis indicate that all preload patterns 
considered give similar distributions of forces in the truss members. In 
the region of the truss beam away from any boundary constraints, the 
member forces are unifonn within two percent, and thus, the joints in this 
region are loaded unifo:rmly. In the regions near the bourrlary constraints 
(ends of the beam) the member forces become very non-unifonn and maximum 
member forces are greater than the corresp:>lxling member forces in the 
unifonn load region. Finally, the type of resulting defomation in the 
truss depends on the pattern of preloaded diagonals. 
REF'Em:NCES 
1. Greenberg, H. s.: Development of Deployable Structures for Large 
Space Platfonn Systems. NASA CR-170914, October 1983. 
2. Mikulas, Martin M., Jr., et. al.: Space station Truss structures 
and Construction Considerations. NASA'IM-86338, JanllillY 1985. 
Pmax(lbf)/Pmin(lbf) 
AWAY FROf1 END 
i~EMBER TYPE NEAR FIXED END CONSTRAINTS NEAR FREE END 
longerons ,1150/,0000 ,0754/,0741 ,1150/,0000 
face diagonals -,1245/-,0813 -,10C4/-,1057 -,1245/-,0813 
batten diagonals ,2237/,0813 ,2140/,2120 ,2237/,0813 
battens ,0000/,0000 ,0000/,0000 ,0000/,0000 
(Negative force is compression~ positive force is tension) 
Table 1,- Maximum and Minimum Member Forces in Three Beam Regions for All Preload 
Cases, 
(Xl 
PRELOAD CASE 
Average Free 
End Deflections* 1 2 3 4 
t.x (in x 10-5) 1.223 1.223 1.223 1.223 
t.y (in x 10-5) 3.065 3.055 3.055 3.065 
t.z (in x 10-5) -3.740 -3.765 -3.765 -18.500 
ex (degrees x 10-6) -4.218 
~----
-82.650 -82.650 
----
--
*These numbers represent the average of the deflections at each of 
the four Joints of the free end batten frame. 
Table 2.- Average Free End Deflections for Four Preload Cases. 
-4.059 
U) 
...---
z 
f 
cantil ever 
constraint 
region 
y face diagonals 
(a) reference truss configuration 
"infinite" 
beam 
region 
(b) 21-bay truss beam 
longerons 
Figure 1. - Finite Element Model Configuration 
10 
battens 
batten 
diagonal 
free end 
region 
x 
z ----
z --
z --
z~ 
---
CASE 1 
CASE 2 
----... X 
CASE 3 
----... X 
CASE 4 
----... X 
Figure 2. - Preload Diagonal Patterns 
11 
12 
XI8J ~ ~ ;~~&~;~~; ,', I' X ~'~::"'~:""~'::'.~ .. ':"~'::-""""'---I--. . . . ................. ~ ...... . 
z j (a) X-2 plane view 
y t 
~ ...... "'~'" ............... ~ .....~ ..... :~ ............lXJZ<f' ';' .. ~ . .; . . '" .' '.. '., . " '" • " • • • • • • • • • • • I • • ...-nv.. :: .. :: .. ": .. ": .............. : ............. : .... : .... : .... : .... : .... : .... ::-.. :: ____ ~- X 
(b) X-V plane view 
---1_- Z 
(c) V-Z plane view 
Figure 3. - Truss Deformation From Preload Case 1 
~­
J 
v f 
I 
(a) X-Z plane view 
~mS'J8_ 
(b) X-V plane view 
... Z 
(c) V-Z plane view 
Figure 4. - Truss Deformation From Preload Case 2 
13 
.. X 
.X 
I j (al X-I plane view 
y 1 
~~m_ 
(b) X-V plane view 
(c) V-Z plane view 
Figure 5. - Truss Deformation From Preload Case 3 
14 
~ ..... x 
--x 
15 
(a) X-Z plane view 
Yi 
. . . . . . . . . . . . .. .. . 
.. .. .... ....  . 
. .. . . - . . . ... . - .. ~~.....•.••••.•.•..••..........•••. 
-- X 
(b) x-v plane view 
• Z 
(c) V-Z plane view 
Figure 6. - Truss Deformation From Preload Case 4 
, I', ~ 
, ,,~ 
.. :r; .. 
I 2. Government Acceaion No. 3. Recipient's ~l<Ilog No. 1. R"~I No. 
t!ASA TM-87673 
~T~~ie "lid Subtitle 5. Report Olte 
Analysis of a Single-Fold Deployable Truss Beam 
Preloaded by Extension of Selected Face Diagonal Members 
April 1986 
6. Performmg Orglnization Code 
506-43-41-02 
--.-----------------------------------------------~~~~~~.~~ __ ~--_1 1 Authorls! 8. Performing Orglnliltion Report No. 
K. Chauncey Wu and Mark S. Lake 
~-_------.-----------------------I 10. Work Unit No. 
~ P~rfU"llIng OrYdnilallon Name dnd Address 
NASA Langley Research Center 
Hampton, VA 23665 11. Contract or Gr.nt No. 
13. Type of Report and Period Covered ~~-,-s-~·-r-I)-u-r-.n-g-A-~-n-Cy-N-an-oe-a-n-d--A-u-dr-e,-5---------------------1 Technical Memorandum 
National Aeronautics and Space Administration ~---------------14. Sponwring Agency Code Washington, DC 20546 
~·---_-_·------_----------------------------------.L..---------------------I 
I:>. SUPIJI~"'~nl~r V Notes 
- ---_ .. _ .. -----------------------------. 
A technique for preloading a deployable box truss beam by extension of one face 
diagonal per bay was studied to determine if it would result in uniform loading 
of truss joints without causing excessive truss deformations. Results indicate 
that it is possible to accomplish uniform loading in the beam region away from 
beam boundaries, whereas in the regions near boundaries the member loading 
becomes non-uniform with magnitudes greater than those in the uniform load 
region. Also, the type of deformation which results in the beam depends on the 
pattern of preloaded members. 
_.--. - ---------------r-::-::-:---::--:--:::-----:-----.-------, 
18. Distribution Statement I I ~ "'f Words ISU\I98Sted by Authorls)) 
Preload 
Deployable truss 
Member loads 
Truss deformations 
1 J S«uroty Clau.f. (of this report! 
Unclassified 
Unclassified - Unlimited 
20. Security C!auif. (of thIS page) 
Unclassified 
Subject Category 18 
21. No. of Pages 
16 
22. Price 
A02 
For sale by the National Technical InfO/matlOn SerVice, Springfield. Vuginla 22161 
End of Document 


Analysis of a single-fold deployable truss beam preloaded by extension of selected face diagonal members

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server