/-N AD-A016 778
FEASIBILITY STUDY ON DESIGN OF SELF-ERECTING AIRCRAFT SHELTER
Roy L. Johnson
New Mexico University
V_) C-
Prepared for:
Air Force Weapons Laboratories
October 1975
DISTRIBUTED BY:
National Technical Information Service U. S. DEPARTMENT OF COMMERCE
AD
A0
1Ö
77
8
315128 AFWL-TR-7 5-139 AFWL-TR-
75-139
A /1
1/
1/ 1/
FEASIBILITY STUDY ON DESIGN OF SELF-ERECTING
AIRCRAFT SHELTER
Roy L. Johnson
CERF, University of New Mexico
Albuquerque, New Mexico 87131
October 1975
Final Report
Approved for public release; distribution unlimited,
Reproduced by
NATIONAL TECHNICAL INFORMATION SERVICE
U S Department of Commerce
Springfield, VA 22151
AIR FORCE WEAPONS LABORATORY Air Force Systems Command
Kirtland Air Force Base, NM 87117
AFWL-TR-75-139
V
This final report was prepared by CERF, University of New Mexico, Albuquerque, New Mexico, under Contract F29601-74-C-0008, Job Order ILIR7425 with the Air Force Weapons Laboratory, Kirtland Air Force Base, Ní .» .'léxico. Lt Dennis Morrison (OL-AA, AFCEC/DEZ) was the Laboratory Project Officer-in-Charge. Captain Galen C. Bessert was the former project officer.
When US Covernment drawings, specifications, or other data are used for any purpose other than a definitely related Government procurement operation, the Government thereby incurs no responsibility nor an.v obligation whatsoever, and the fact that the Government may have formulated, furnished, or in any way sup¬ plied the said drawings, specifications, or other data, is not to be regarded by implication or otherwise, as in any manner licensing the holder o¡ any other- person or corporation, or conveying any eights or permission to manufacture, use, or sell any patented invention that may in any way be related thereto.
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DENNIS MORRISON Lt, USAF Project Officer
LOREN M. WOMACK Chief, Aerospace Facilities Division
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FEASIBILITY STUDY ON DESIGN OF SELF-ERECTING AIRCRAFT SHELTER ^
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Final Report
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Roy L. Johnson
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18 SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on reverse side if necessary and identify by block number)
Shelters Aircraft Shelters Structures Air Mobility Structural Analysis Computer Code Erection Bare Base
20 ABSTRACT (Continue on reverse side If necessary’ and identify by block number)
This research examined the feasibility of designing and constructing an air- transportable, self-erecting aircraft shelter. Behavior of the shelter during erection and diserection was studied by field testing a 1/4-scale, segmented arch model of semicircular geometry, and by analyzing the behavior of a cir¬ cular segmental prototype structure. Analyses of the structural behavior of the model and prototype were performed using the matrix-dispacement method. Large displacements of the structure were accommodated analytically by (OVER)
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ABSTRACT (Cont'd)
use of a procedure of incremental displacement followed by an updatinq of structure geometry. A computer program (BOOTSTRAP) was developed to perform these analyses. Analyses showed that stable configurations of the 1/4-scale semicircular arch were achieved only when a single internal hinge was allowed in the structure. A satisfactory diserection procedure for the full-scale prototype was not achieved.
I0L
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CONTENTS
Section
1
2
3
4
5
6
INTRODUCTION
MODEL TESTS
ANALYTICAL FORMULATION
MODEL STUDIES
PROTOTYPE STUDIES
CONCLUSIONS AND RECOMMENDATIONS
APPENDIX: PROGRAM BOOTSTRAP
PROGRAM STRUCTURE
INPUT INSTRUCTIONS
PROGRAM LISTING
Page
8
11
K
17
19 20
28
35
■
ILLUSTRATIONS
Figure Pm.
1
2
3
4
5
6
7
Model of Self-Erecting Aircraft Shelter 3
Joint-Locking Device 4
Hinge-Rotation Limiting Device 5
Partially Erected Model Configurations 6
Computed Configurations of Model 13
Prototype Configurations 15
Distribution of Bending Moments in Low-Profile Prototype 16
ii
aaiMiaiaMiHIIHM diimuk
SECTION 1
INTRODUCTION
BACKGROUND
With funding from the AFWL, faculty members of the USAT Academy successfully
demonstrated the feasibility of constructing a model of a self-erecting air¬
craft shelter. Thus, a model consisting of sixteen 2-ft-long prefabricated
modules connected to one another by a hinge mechanism was developed, ion-
trolled buckling of the structure at the hinges is obtained by applying a
moment to opposite ends of the horizontal beam column by a cable attached to
the ends. Since the structure resists bending in one direction and not the
other, it is gradually erected into a semicircular arch. This relatively
rapid and simple construction technique could make practical immediate full-
scale prototype application in support of highly mobile tactical air forces.
Therefore, feasibility studies on developing a prototype and design of such a
structure were undertaken at the Civil Engineering Research Facility (CERF).
OBJECTIVE
The overall objective of this research effort was to design an air-transpo^tabk:
aircraft shelter which can be erected in the field with a minimum amount of
equipment other than that provided with the shelter. Therefore, che feasi¬
bility of such a structural system with respect to the self-erection technique
was examined.
SCOPE
Field tests and analytical studies of a 1/4-scale model of a semicircular arch
and analytical studies of a full-scale prototype were conducted. An existing
computer program was modified and used to model the large displacement behav¬
ior of the arch.
1
SECTION 2
MODEL TESTS
The 1/4-scale model in its fully erected position is shown in figure 1. De¬
tails of the joint-locking and hinging mechanisms are shown in figures 2 and 3.
When received at CERF, all joints of the model were free hinged with the excep¬
tion of the first two or three joints near the ends; these were equipped with
gravity-actuated latches to lock the joints in their fully closed positions
(fig. 2b). Each joint was equipped with a bolt mechanism (fig. 3) which lim¬
ited the relative rotations of adjacent members when the joint was opened.
Positive or negative relative rotations of the members may be obtained by
adjusting this bolt. (A positive relative rotation is measured counterclock¬
wise between longitudinal axes of adjacent members.) However, the bolts pro¬
vided with the model (as received from the USAF Academy) permitted only neg¬
ative relative rotations of the members (fig. 3a). Therefore, the bolt mech¬
anisms were modified at CERF to permit positive relative rotations as well
(fig. 3b).
Several tests were performed on the 1/4-scale model to observe overall behav¬
ior during erection and diserection. From these tests and from f ilms-of tests
at the USAF Academy, it was evident that when no positive rotation of adjacent
members is permitted (model as received), the maximum loading on the structure
occurs when the first panel is raised (fig. 4a). To minimize the bending mo¬
ment in the arch, the joints were modified to permit positive relative rotations
of the members so as to minimize the span over which the weight of the struc¬
ture is carried (fig. 4b).
Observation of the erection and diserection of the arch with the modified
joints revealed the following facts:
(1) Cable tensions during erection were more constant in the early
stages although somewhat higher than those when no positive rotations
were permitted. As expected, a number of panels remained flat on the
pad, thus reducing the load which the semierected arch carried.
2
Fig
ure
1.
Mod
el
of
Self-E
recting A
ircra
ft
Sh
elte
r
(a) Opened Joint
n.25c
(b) Locked Joint
Figure 2. Joint-Locking Device
aHHHltttfattlilaiHi
(a) Before Modification
(b) After Modification
10c
Figure 3. Hinge-Rotation Limiting Device
J matiili
Su
bse
qu
ent
Con
figu
rati
on
1
c o 4-> H3 o
XJ o :r CD cn c
CD s- o CD CÛ
cO
c o 4->
fO o
“O o
CD CT> c
s- CD
«4-
Fig
ure
4.
Part
iall
y
Ere
cted
Mod
el
Con
fig
ura
tio
ns
(2) The model assumed a symmetric mode during diserection; i.e., the
center joint opened and the structure symmetrically lowered. In the later
stages of diserection, the structure snapped-through into an asymmetric
mode and continued in this mode until diserection was completed. The snap-
through was violent and several joint pins failed. This snap-through was
also observed before joint modification; however, it was less violent be¬
cause of the restricted rotation of the joints.
To avoid snap-through, a modification was made to the cable arrangement to allow
the cable to be passed through a bracket at the second joint above the winch.
With this arrangement, the active cable tension was utilized to load the struc¬
ture asymmetrically, thus forcing it into an asymmetric mode for diserection.
Subsequent testing of the model with this arrangement showed that adequate con¬
trol of the configuration could be maintained during diserection and snap-
through of the arch could be avoided.
7
SECTION 3
ANALYTICAL FORMULATION
The structure was modeled analytically as a circular arch composed of straight-
line segments. Only one internal hinge was permitted at a time. Thrusts of
the arch were equilibrated by a cable tie capable of transmitting axial force
only Horizontal displacement of one of the supports was induced by lengthen¬
ing the cable tie and allowing the structure to displace under its own weight.
Displacements were applied in small increments to permit the use of a linear
stiffness matrix formulation. The geometry of the structure was updated at the
end of each displacement increment by adding algebraically the elastic displace¬
ments of the structure to the previous structure geometry. This permitted the
structure to undergo very large displacements without the use of a nonlinear
geometric formulation.
MATRIX FORMULATION
The s
were
tatic equations of equilibrium for a fixed configuration of the structure
{F} = [K]{u) (1)
where {F} and {ul are vectors of the generalized nodal forces and displacements,
respectively, and [K] is the assembled stiffness matrix of the structure formed
by appropriately summing the stiffness matrices for the individual elements of
the structure. An element is defined as that portion of the structure which
connects two nodes (joints). The formulation of [K] may be found in any stand¬
ard text on matrix structural analysis (ref. 1).
An equilibrium configuration is obtained from eq. (1).
{u} = [K]_1{F} (2)
1. Gere, J. M., and Weaver, W., Jr., Analysis of Framed Structures, Van Nostrand, New York, 1965.
iaiaMilllllHilfll
Here, the inversion of [K] is implied; but, in the actual computation a solu¬
tion was obtained by solving the set of simultaneous linear equations.
The vector {F} is a set of generalized nodal forces which consist of those de¬
rived from the gravity load, i.e., the weight of the structure, and those in¬
duced by initial support displacement. Accordingly, the vector {F} may be
written as the sum of the two parts; thus
í F} = IF] + {Fj g (3)
where the subscripts g and ui indicate gravity forces and forces due to initial
displacements, respectively. {F} is obtained by appropriately summing gener¬
alized nodal forces which are statically equivalent to the gravity loads for
each element of the structure.
Initial support displacements are transformed into equivalent generalized for¬ ces by
{nUi = [KjiuK (4)
where {u}^ is a set of initial displacements specified in small increments.
The stiffness matrix is reformulated at the end of each increment by algebra¬
ically adding the spatial coordinates of each node at the beginning of the in¬
crement to the corresponding nodal displacements occurring during that incre¬
ment. The updated geometry is then
Vi = xi f ui
Vl= ^i+ vi
2ifl = zi + wi (5)
where x, y, and z are spatial coordinates of a given node and u, v, and w are
nodal displacements in the corresponding directions. The subscript i indicates
the geometry at the beginning of the ith increment. The procedure is repeated
until the structure has been put through the full range of displacements desired,
9
The logic necessary to perform the computer analysis of the structure is pre¬
sented in the appendix.
10
SECTION
MODEL STUDIES
The behavior of the model during testing indicated that an analytical proce¬
dure capable of predicting equilibrium configurations and stresses in the arch
at various stages oc erection and diserection was necessary. Also, other than
semicircular configurations should be investigated in order to minimize struc¬
tural height while maintaining necessary work space. A computer solution
seemed most appropriate. Therefore, an existing University of New Mexico com¬
puter program for displacement analysis of elastic structures was extensively
modified for this purpose. (See appendix.)
The fully hinged 1/4-scale model was not successfully analyzed; however, modi¬
fications to permit analysis as well as to control configurations during dis¬
erection were investigated. With more than one joint opened in the arch, the
structure is a mechanism and only conditionally stable. The stiffness matrix
1's singular and a solution was not possible. Attempts to maintain small re¬
sidual bending and translational stiffnesses at the joints by using elements
with semirigid connections, such as those described by Gere and Weaver (ref.
I), also resulted in solutions which were unstable unless substantial residual
stiffness was maintained, but this resulted in structural models which were
too stiff when compared with the physical model.
In consultation with Captain Bessert and Lieutenant Morrison, AFWL/DEZ Task
Officers, it was decided to investigate the possible locking of certain joints
of the structure so as to maintain only one free hinge and permit unlocking of
subsequent joim; when the previously designated joint had fully opened and
regained bending stiffness. This locking and unlocking sequence could be de¬
termined in such a way that the structure could be forced to diserect in an
l. Gere, J. M., and Weaver, W., Jr. Nostrand, New York, 1965.
Analyi'da of Frame.*i Van
II
asymmetric mode. Subsequent analytical studies of the 1/4-scale model indi¬
cated that such a procedure was feasible.
Figure 5 shows the computed configurations of the model at two different sta¬
ges of diserection. Joint 3 was initially designated as a hinge and all other
joints were locked. The first configuration shows the geometry of the displaced
structure with joint 3 fully opened and with continuity restored at that joint.
Subsequent hinges were designated at joints 5, 7, 9, and 11 and formed sequen¬
tially as the right end of the arch was further displaced. The second config¬
uration shows joint 11 partially opened with all other joints locked. No joint
was allowed to open until the previously designated hinged joint had fully
opened. If this procedure is followed, the arch immediately goes into an asym¬
metric, stable mode for diserection.
12
i, UMipRUfifiJI iw- m ,«11,
13
Fig
ure
5.
Com
pute
d C
onfi
gura
tions
of
Mod
el
SECTION 5
PROTOTYPE STUDIES
^ -..il ACill /nP7 nffirprs to âccommoddt0 t-hG lã totype structure were establead by AF ' Z ^ ft-long panels binged
r;f,r2.; “rr:; r: «rr, r tow-profile configuration when the arch is fully erected.
hinge ^;;“”^;irntsh\r!nr,0ysis slid that the crown of ing suosequent incremental disp ^erection, resulting r,n: n: zirr :11::::1, the _ resuitr r a nearfy'syletric displacement -i.nation.^Howeyer, the analysis showed
that this configuration goes unstab
The low-profile configuration 11111:11:1 ri-:11: - -— 11:1:1:1:1 elastic deformation of the
points of contraflexure are approximately locate a
Ich moments are negative and tend to substan. q1ons. Subsequent displacements of the right end of the arch no
tially change this until large displacements of the crown occur,
the structure becomes unstable.
14
Figu
re 6
. Pr
otot
ype
Con
figu
ratio
ns
Fig
ure
7.
Dis
trib
uti
on
of
Ben
ding
Mom
ents
in
Low
-Pro
file
Pro
toty
pe
SECTION 6
CONCLUSIONS AND RECOMMENDATIONS
The analytical studies of the 1/4-scale model showed that, for a semicircular
geometry, the single-hinge concept was successful in producing a stable con¬
figuration during diserection. This was supported by observations of the be¬
havior of the physical model during the tests. From this, it is also con¬
cluded that the analysis procedure incorporated into the computer program used
in the analytical studies is adequate to predict the large displacement be¬
havior of the structure.
The inability to identify joint-hinging sequences which result in a satisfac¬
tory diserection procedure for the prototype structure suggests that the self-
erecting technique is not feasible with the low-profile configuration for the
following reasons:
(1) There is a possibility of instabilities of the arch during diserection.
(2) The size of the cable necessary for erection and diserection of the
prototype appears to be excessive (possibly 1-inch iiameter) with sub¬
sequent requirements of large size and high cost as well as weight of the
cable winching apparatus.
Analytical studies of other configurations should be made in order to fully
assess the feasibility of constructing a self-erecting arch.
17/18
W. üwiwwipuwTwm» ...
APPENDIX
PROGRAM BOOTSTRAP
A Special Purpose Program for the Large Displacement
Analysis of Circular, Segmental, Tied Arches
19
..- MtfiilÉltibÉÉiUÉÉINÉMi
PROGRAM STRUCTURE
BASIC PROGRAM LOGIC
A solution is obtained by a two-step procedure as follows:
(1) A displacement increment is applied to one of the end
supports of the arch and an elastic analysis is per¬
formed using the displacement method to determine an
equilibrium configuration.
(2) The configuration of the structure is updated and a
new elastic solution is obtained using the new con¬
figuration. This step stress relieves the structure
of the forces induced by the incremental displacement.
The force in the cable tie is thus a result of the
elastic deformation of the structure due to gravity
load only, using the configuration computed in step 1
as a reference.
Possible events occurring during step 1 are as follows:
(1) The designated hinge joint may close. Action: Restore
continuity and resolve before proceeding to step 2.
(2) The designated hinge joint may partially open. Action:
Proceed to step 2.
(3) The designated hinge joint may open beyond the maximum
value specified. Action: Iterate to find the incre¬
mental displacement which just causes the joint to open
to its maximum specified value before proceeding to
step 2.
Possible events occurring during step 2 are as follows:
(1) The designated hinge joint may close. Action: Restore
continuity and resolve.
(2) The designated hinge joint may partially open. Action:
Accept the solution and print results.
20
(3) The designated hinge joint may open beyond the maximum
value specified. Action: Restore continuity and resolve.
The program consists of a main calling routine (BOOTSTRAP) and the following
subroutines :
Name Principal Function
(1) PLOTXY
(2) INPUT
(3) STIFF
(4) BEAM
(5) LOAD
(6) DID
(7) MERGE
(8) BOUND
(9) SOLVER
(10) FORCE
(11) MODIFY
(12) GEOM
(13) BM
(14) ROTATE
(15) ANGCHK
(16) SUPCHK
Plots deformed structure.
Reads input data.
Calls element stiffness routine.
Forms element stiffness matrix.
Computes element load vector.
Computes member forces due to gravity loads.
Assembles structure stiffness matrix and load vector.
Applies boundary constraints.
Solves structure stiffness equations.
Computes member forces.
Calls modified element stiffness routine.
Updates structure geometry.
Forms modified element stiffness matrix.
Performs coordinate transformations.
Checks relative member joint rotations.
Checks joints for negative coordinates.
MAIN CALLING ROUTINE
BOOTSTRAP is the main routine which calls INPUT, STIFF, MODIt-Y, BOUND, SOLVER,
FORCE, GEOM, and PLOTXY. The principal parameters which control branching are
NONLIN, IUPDTE, IMOD, ITER, LASTIT, and ICONV. NONLIN is an input parameter
with a value of 0 or 1 depending on whether a linear or nonlinear problem, re-
spectively, is to be solved. (See section 2.) IUPDTE, IMOD, LASTIT, and ICO;«
21
are defined in subroutine ANGCHK or SUPCHK and may have values of 0 or 1. ITER
is an integer set to 1 or 2. When ITER = 1, an incremental displacement is im¬
posed on the structure. ITER is set to 1 at three stages in the solution:
(1) When an incremental displacement is imposed initially;
(2) During iteration to find the incremental displacement
which just causes a joint to open fully; and
(3) At the completion of a solution cycle.
When ITER = 2, the structure geometry is updated and a new solution is obtained.
SUBROUTINES
PLOTXY
PLOTXY calls a standard IBM/360 system subroutine called PLOT which plots up¬
dated joint coordinates on the line printer. Any other plot routine may be used
in lieu of PLOT for operation on another system. The y-displacements of the
structure may be amplified by using the factor AMPLE. (See section 2.)
INPUT
INPUT reads and prints control parameters and basic structure data such as mate¬
rial data, nodal point coordinates, member data, boundary constraint data, mem¬
ber release data, joint release sequences, and structure loading codes. The
half-bandwidth of the structure stiffness matrix is computed and printed in
this subroutine.
STIFF
STIFF forms the structure stiffness matrix. Only structures without member re¬
leases are handled in this subroutine. Member stiffness matrices are generated
in BEAM and transformed to global coordinates in a call to ROTATE before being
assembled in MERGE.
22
BEAM
BEAM forms the element stiffness matrices for only those elements without mem¬
ber releases.
LOAD
LOAD reads and prints concentrated joint forces, computes member Gravity loads
in a call to DLD, reads and prints member fixed-end forces from distributed
loads, and computes and prints member forces due to initial joint displacements.
Member forces are transformed to global coordinates in a call to ROTATE before
being assembled in MERGE to form the structure load vector.
DLD
DLD computes the equilibrating end forces for each member for the g-load speci¬
fied. (See section 2.) Forces are computed for the following conditions of
end fixity: fixed-fixed, hinged-hinged, hinged left, and hinged right.
MERGE
MERGE forms the structure stiffness matrix and the load vector by merging the
element stiffness matrices and the load vectors. The structure stiffness ma¬
trix is stored in array A(NUMEQ,MBAND), where NUMEQ is the number of simultane¬
ous linear equations (NUMEQ = 2 * NUMNP) and MBAND is the half-bandwidth of
the stiffness matrix. The structure load vector is stored in array B(NUMEQ).
BOUND
BOUND imposes boundary constraints on the structure stiffness matrix and on the
structure load vector.
SOLVER
SOLVER uses Cholesky's Method (ref. 2) for symmetrical matrices (Square Root
2. Ketter, Robert L., and Prawel, Sherwood P., Jr., n'în:'' c-
Engineering Computation, McGraw-Hill Book Co., New fork, 1969.
23
Method or Banachiewicz Method) to solve the system of simultaneous linear
equations. The stiffness matrix is reduced in a forward sweep only when mod¬
ifications to the structure occur, i.e., when the geometry is updated or addi¬
tional hinges are formed. The partially reduced stiffness matrix is used to
obtain solutions for each new load vector during iteration to find the incre¬
mental displacement which just causes the designated joint to open fully.
FORCE
FORCE computes member forces in global coordinates and transforms them to mem¬
ber coordinates in a call to ROTATE. Member forces are printed in the member
coordinate system. Element stiffness matrices are regenerated for use in FORCE
rather than written on and read from an external input/output unit.
MODIFY
MODIFY forms the structure stiffness matrix including members with releases.
Member stiffness matrices are generated in BM or in BEAM depending on whether
or not the member contains a release and transformed to global coordinates in
ROTATE before being assembled in MERGE.
GEOM
GEOM updates structure geometry by summing nodal spatial coordinates and cor¬
responding nodal displacements. Relative rotations of adjacent members at each
joint are computed using the updated geometry. A check on maximum and minimum
values of joint angles and minimum values of joint coordinates are made in
ANGCHK and SUPCHK which are called from this subroutine.
BM
BM generates stiffness matrices for members containing releases. Three types
of stiffness matrices are generated depending on the type of member release
specified: hinged-hinged, hinged left, and hinged right.
24
ROTATE
ROTATE transforms member stiffness matrices and load vectors into global coor¬
dinates. Member force vectors are transformed from global coordinates to mem¬
ber coordinates.
ANGCHK
ANGCHK checks relative member rotations to detect joint openings and closings.
The check is made on the angle <i> (defined in section 2) for the interior joint
which has been designated as a hinge. Only three hinges, including supports,
are permitted in the structure. A hinge is modeled by specifying releases in
members joined at the designated hinge joint. A boundary constraint at the
joint which prohibits rotation of the joint about the z-axis is necessary to
reduce the singularity in the stiffness matrix resulting from zero bending
stiffness at the joint. The current and previous member releases are stored
in two arrays, IREL(NUMEM,2) and JREL(NUMEM,2); the first column contains the
previous releases and the second column contains the current releases. The
values in IREL and JREL are 1 or 0 depending on whether the member is or is
not released, respectively. These values change as joints open and close.
The principal parameters assigned in this subroutine and used to control branch¬
ing are ICLOSE, JCLÜSE, IUPDTE, IMOD, LASTIT, and ICONV. These parameters are
assigned values of 0 or 1 as indicated in the following table:
Set Flag ER
ICLOSE JCLOSE LASTIT IUPDTE IMOD ICONV
10 1 1 0 10
10 0 1 10 1
1 0 0 1 0 0 0
Event
Designated hinge joint closes on first iteration (JITER = 1) 4» < min
Designated hinge joint opens partially. 4
min <4 max
Designated hinge joint opens fully (JITER = 1 ). ¢) > ci>max. (Iterate to find new incremen tal displacement.)
25
table (Cont'd)
Event
Solution has converged. í =
tmax ■ Next joint in sequence is opened.
Designated hinge joint closes,
'min
Designated hinge joint opens partially. 4>min < 0 < ^max-
Designated hinge joint opens fullv. i > $ I U I ' J * T tmax
ITER ICL
1 0
Set Hag
¡CLOSE JCLOSE LASTIT IUPDTE ¡MOD ¡CpNV_
0 1 111
2 0
0 0 1
0 1 o
LASTIT = 1
1 sig- JITER is a counter incremented at the end of each solution cycle,
signals that one or more additional iterations are necessary. ICOT,
nais convergence of the iteration process when finding the incremental dis¬
placement which just causes the designated hinge joint to open fully, the
Regula Falsi Method (ref. 3) is used to find this displacement increment.
IUPDTE = 1 signals that the structure geometry is to be updated for the next
solution cycle. IMOD = 1 signals opening or closing of a joint not previously
opened or closed. When IUPDTE or IMOD is 1, the structure stiffness matrix is
reformulated for the next solution cycle.
SUPCHK
SUPCHK checks the updated y-coordinates of each interior joint for negative
values. This may occur during an initial displacement increment, whereupon an
iteration procedure is used to find the incremental displacement which just
causes the y-coordinate of the most critical joint to have a value of zero.
The most critical joint is taken to be the joint having the least value of
the y-coordinate algebraically less than zero. The Regula Falsi Method is
used in this iteration.
3 Carnahan, Brice, Luther, H. A., and Wilkes, J^mes 0., /.y < ■ - Methods , John Wiley & Sons, Inc., New York, 1969.
26
.11111,11111111(,111. 1111.1,..1 ».i. i¡iii : y- .l'iumii .1 11
Both ANGCHK and SUPCHK are executed at each solution cycle. The smaller of
the two incremental displacements computed in ANGCHK and SUPCHK is taken as
the next incremental displacement during iteration.
27
input instructions
STRUCTURE TYPE IDENTIFICATION (15)
Columns Variable Name
1-5 MTYPE
6-10 NONE IN
11-15 ITMAX
16-20 MAX IT
21-30 PHMAX
31-40 PHMIN
41-50 DX
51-60 AMPLE
Structure type identifier
1 = plane truss. 2 = plane frame. 3 = space truss. 4 = space frame.
Nonlinear solution control parameter
Any positive integer causes the program to branch to the nonlinear solution.
Maximum number of iteration cycles in a given displacement step
Maximum number of displacement steps
Limit of relative counterclockwise ro¬ tation in degrees of two adjacent mem-
Limit of relative clockwise rotation in degrees of two adjacent members
PHMIN
Negative Relative Rotation
Size of displacement increment in inches
Amplification factor to be applied to vertical displacements if required for plotting
23
TITLE (20A4)
Columns Variable Name
I- 80 TITLE
CONTROL PARAMETERS (615)
Columns Variable Name
I- 5 NUMNP
6-10 NBEAM
II- 15 N ST RUT
16-20 NUMAT
21-25 NRNP
26-30 NMREL
MATERIAL DATA (3E10.4)
Repeat NUMAT times (one card for each
Columns Variable Name
1-10 E(IM)
II- 20 PR(IM)
21-30 RHO(IM)
Entry
Any alphanumeric identifier
Entry
Total number of nodes including supports
Total number of beam-type members
Total number of two-force members
Number of different materials
Number of constrained (supported) nodes
Number of member releases
different material ).
Entry
Young's modulus of elasticity
Poisson's ratio
Material density (wt/unit vol.)
29
NODAL POINT COORDINATES (15, 3E10.4)
Repeat NUMNP times (one card for each nodal point including supports).
Columns Variable Name Ln.trX
1 -5 NN
6-15 X(NN)
16-25 Y(NN)
26-35 Z(NN)
MEMBER DESCRIPTIONS (415, 5E10.4, 15)
Repeat NUMEM times (one card for each
Columns Variable Name
1-5 ID
6-10 ND( ID ,1 )
11-15 NO ( ID ,2 )
16-20 MD(ID)
21-30 XA(ID)
31-40 ZI(ID)
41-50 YI(ID)
51-60 XJ( ID )
61-70 ALFA(ID)
Number of nodal point (must bo less than NUMNP)
x-coordinate
y-coordinate
z-coordinate
member). NUMEM = NBEAM + NSTRUT.
Entry
Member identification number (must be less than NBEAM + NS1RUT)
Nodal point number - node i
Nodal point number - node j
Material identification number
Cross sectional area (L‘)
Second moment of area about the local z-axis of the cross section (L" )
Second moment of area about the local y-axis of the cross section (L‘* )
Second moment of area about the local x-axis of the cross section (L4)
Angle of rotation in degrees of the principal y-axis of the cross section with respect to a vertical plane
30
71-80 MLC(IÛ)
Rotation
BOUNDARY CONDITIONS (13, II, 611, 6E10.4)
Repeat NRNP times (one card for each restrained node).
Columns
1-3
4
Variable Name
N
NTYPE(N)
5-10 IR(N,J)
11-20 UI(N,1)
Entry
Number of restrained node
Boundary condition type
0 or blank node is constrained against motion - no initial displacement spe¬ cified .
1 is initial displacement specified.
Type of constraint identifier
This is a six-digit integer, each digit of which is either 0 or 1 depending on whether mccion in the corresponding di¬ rection is constrained or unconstrained.
Examples
For a completely fixed node, IR(N,J) = 111111. This specifies that transla¬ tions and rotations are restrained in al 1 possible directions.
For a node restrained from translation in the global y-direction with all other motions free, IR(N,J) = 01000Ü.
For a node restrained from rotation in the globdl x-direction with all other motions free, IR(N,J) = 000100.
Specified initial translation in global x-direction (L)
31
- -TT"*-! ^
21-30
31-40
41-50
51-60
61-70
UI(N ,2 )
UI(N ,3 )
UI(N,4 )
UI ( N , 5 )
UI(N ,6)
Specified initial translation in global y-direction (L)
Specified initial translation in global z-direction (L)
Specified initial rotation about global x-axis (RAD)
Specified initial rotation about global y-axis (RAD)
Specified initial rotation about global z-axis (RAD)
If initial displacements are specified, a 1 must appear in the columns corresponding to the direction of the specified displace¬ ments .
MEMBER RELEASES (13, 211)
These data are required for members with initially specified releases only.
Repeat NMREL times (one card for each released member).
Columns
1-3
4
Variable Name
IM
MREL(IM,1 )
MREL(IM,2)
Entry
Member number
Release code for node i of member as specified in member data
Release code for node j of member
The release code is specified by a two- digit integer; either 1 or 0 is used depending on whether the i or j nodes of the member are released or not re¬ leased, respectively.
LOADING PARAMETERS (3I5,3F10.4)
Columns
1-5
Variable Name
NLND
Entry
Number of nodes with concentrated loads
32
mm
6-10 NLMEM
11-15 LGRAV
16-25 AX
26-35 AY
36-45 AZ
CONCENTRATED NODAL LOADS (I5.6F10.4)
One card per loaded node for each loading
omitted if NLND is zero.
Columns
1-5 NL
6-15 P(l)
16-25 P(2)
26-35 P(3 )
36-45 P(4)
46-55 P(5)
56-65 P(6)
MEMBER LOADS
Number of members having distributed loads along their length between nodes in addition to the member dead load
Member gravity load parameter
If 1, member dead load generalized forces are computed for a g-force as specified below.
Specified constant acceleration in the global x-direction (Not currently used)
Specified constant g-acceleration in the global y-direction
Specified constant acceleration in the global z-direction (Not currently used)
condition is required. Cards are
Entry
Node number
Component of concentrated force in globa x-direction
Force in global y-direction
Force in global z-direction
Component of concentrated couple about global x-axis
Couple about global y-axis
Couple about global z-axis
Variable Name
Two cards per loaded member (NLMEM members) are required for each loading con¬
dition involving members with intermediate loads Cards are omitted if NLMEM
is zero.
33
..
"W“1'f™ «ngpppoipqppqpr
FIRST CARD (2I5,6F10.4)
Coluinns Variable Name
1 -5 MM
6-10 I
11-20 P(l)
21-30 P(2)
31-40 P(3)
41-50 P(4)
51-60 P ( 5 )
61-70 P(6 )
SECOND CARD (5X, 15, 6F10.4)
Columns
1-5
6-10
11-20
21-30
31-40
41-50
51-60
61-70
Variable Name
J
P(7 )
P (8 )
P(9)
P(10)
P(H)
P(12)
Entry
Member number
Node number
Fixed-end axial force at node i
Fixed-end y-shear at node i
Fixed-end z-shear at node i
Fixed-end x-moment (torque) at node i
Fixed-end y-moment at node i
Fixed-end z-moment at node i
Entry
B1 ank
Node number
Fixed-end axial force at node j
Fixed-end y-shear at node j
Fixed-end z-shear at node j
Fixed-end x-moment (torque) at node j
Fixed-end y-moment at node j
Fixed-end z-moment at node j
3
Directions of Positive Fixed-End Forces
PROGRAM LISTING
BOOTSTRAP
PLOTXY
INPUT
STIFF
BEAM
LOAD
OLD
MERGE
BOUND
SOLVER
FORCE
MODIFY
GEOM
BM
ROTATE
ANGCHK
SUPCHK
Page
36
41
41
44
4b
46
49
bO
51
52
54
55
56
58
59
62
64
35
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