CALCS PROC058
PIPE GIMBAL LOADS

NOTATION

AngD Uangle, node C, displaced & undisplaced geometry
AX AY AZaccelerations, a/c avionics bay, global
Ax Ay Azaccelerations, a/c avionics bay, local
Ddiameter, pipe, external
DeltaTdisplacement, thermal
Dssdisplacement, structural strain
Effefficiency, v-band clamp in torsion
EtaTstrain, thermal
fbstress, bending, applied
FCfactor, stress concentration, moment acting on pipe bend
fhstress, hoop, applied
fsstress, shear, applied
Fystress, yield (.2% proof)
Ksfactor, stress, shear, design acceptance
lamdafactor, esdu75014
Mmoment
M1 M2moments, at pipe group ends
MA MB MCmoments, at gimbals A B C
mbemass, point b, effective
Mbomoment, gimbal, breakout
Mclmoment, v-band clamp, allowable
mgmass, gimbal
mpmass, line, pipe
mucoefficient of friction
NA NB NCnode Ids, gimbals
NmID, material
pbppressure, bursting, proof
pfrpressure, failure, reselection
phiangle, bend
pipeID, pipe=1 from N1 to A, pipe=2 A-B, pipe=3 B-C, pipe=4 C-2
PxB PyBforce, thermal, parallel to x & y axes, at node B
Rradius, pipe bend
rradius, pipe, mean
rhodensity, ?
tthickness, pipe
Tnuttorque, nut, v-band clamp

APPLICATION

Aircraft pipe systems composed of 'hard' pipe sections, pipe supports and 'gimbal' pipe connections which accomodate limited rotation

OUTPUT

bending moments at specified points on pipe sections, pipe bending stresses, gimbal rotations, thermal and structural strain displacements

SEE ALSO

PROC057

THEORY

space vector analysis

GUIDANCE

* The analysis must be preceded by obtaining the local coordinate system of the pipe using PROC057.
* Expansion of a pipe section is directed along line between the two fixing gimbals (one at each end).
* Thermal expansion is proportional to the distance between between end gimbals.
* The plane of two adjoining pipe sections is defined as containing the two remote end gimbals and the common connecting gimbal.
Gimbal axes should lie in the plane of any two adjoining pipes.
* Two coaxial gimbals, connected by a pipe section can accomodate relative displacement in any transverse direction.
* Two gimbals, differently orientated but with in-plane axes, can accomodate relative displacement only normal to the line joining the gimbals and in the plane containing the axes.
* Two gimbals, differently orientated with non-coplanar axes can (probably) accomodate no relative transverse displacement.

INPUT FORMAT

LET MA=:MB=:MC=:PROC058
LET pipe=:Ni=:PROC058A
LET Nm=:R=:N1=:N2=:N3=:M=:FC=:fh=:PROC058B
LET N1=:N2=:N3=:VX=:VY=:VZ=:EtaT=:PROC058C

EXAMPLE

Call Statement

LET MA=-2500:MB=2500:MC=-2500:PROC058
LET pipe=4:Ni=1:PROC058A
LET Nm=1:R=50:r=12.5:t=1.6:N1=1:N2=3:N3=7:fh=.85*1.1*12.1/.8:M=3896:FC=3.7:PROC058B
LET N1=NB:N2=NC:N3=NA:VX=-.002*(X(1)-X(17)):VY=0:VZ=0:EtaT=24*110/1E6:PROC058C

Output

PROC058 PIPE GIMBAL LOADS, Rev 291199
LET MA=-2500:MB=2500:MC=-2500:PROC058
PROC058 PIPE GIMBAL LOADS, Rev 291199
LET a=y(NB)-y(NA):b=-(x(NB)-x(NA)):c=MA-MB:d=-(y(NB)-y(NC)):e=(x(NB)-x(NC)):f=MB-MC
PxB= (c-b*f/e)/(a-b*d/e)= -49.71
PyB= (c-a*PxB)/b= 0
LET PxA=PxB:PyA=PyB:PxC=PxB:PyC=PyB
END058
LET pipe=4:Ni=1:PROC058A
PROC058A, MOMENT AT POINT X Y Z,
M= -MC-PxC*(y(NC)-y(Ni))+PyC*(x(NC)-x(Ni))= 1.417E4
END058A
LET Nm=1:R=50:r=12.5:t=1.6:N1=1:N2=3:N3=7:fh=.85*1.1*12.1/.8:M=3896:FC=3.7:PROC058B
PROC058B, PIPE BEND STRESSES, REF.ESDU 75014,
FC READ FROM FIG3,
LET N1=N1:N2=N2:PROC057B:l1=l:m1=m:n1=n
PROC057B,DIRECTION COSINES,VECTOR SUBTRACTION,
LET l=X(N1)-X(N2):m=Y(N1)-Y(N2):n=Z(N1)-Z(N2)
L= SQR(l^2+m^2+n^2)= 232
LET l=l/L:m=m/L:n=n/L
END057B
LET N1=N3:N2=N2:PROC057B:l2=l:m2=m:n2=n
PROC057B,DIRECTION COSINES,VECTOR SUBTRACTION,
LET l=X(N1)-X(N2):m=Y(N1)-Y(N2):n=Z(N1)-Z(N2)
L= SQR(l^2+m^2+n^2)= 384.1
LET l=l/L:m=m/L:n=n/L
END057B
phi= DEG(ACS(l1*l2+m1*m2+n1*n2))= 140.2
phi= 180-phi= 39.82
lamda= t*R/r^2= 0.512
fb= FC*ABS(M)/(PI*r^2*t)= 18.35
UF= (fb+fh)/Fy(Nm)= 9.2859.285
END058B
LET N1=NB:N2=NC:N3=NA:VX=-.002*(X(1)-X(17)):VY=0:VZ=0:EtaT=24*110/1E6:PROC058C
PROC058C,GIMBAL B ROTATION,
GIMBAL B ANGLE,UNDEFORMED GEOM,
LET La=FNl(N2,N3):Lb=FNl(N1,N3):Lc=FNl(N1,N2):PROC057D
PROC057D, COSINE RULE,
ANG= DEG(ACS((La^2-Lb^2-Lc^2)/(2*Lb*Lc)))= 38.15
END057D
AngU= ANG= 38.15
GIMBAL B ROTATION,DEFORMED GEOM,
.002 STRUCTURAL STRAIN DISPLACEMENT OF GIMBAL C RELATIVE TO A,
PROC057C, VECTOR TRANSFORMATION,FROM V to v,
vx= VX*a11+VY*a12+VZ*a13= -1.066
vy= VX*a21+VY*a22+VZ*a23= 2.085
vz= VX*a31+VY*a32+VZ*a33= 0
END057C
LET Dssx=vx:Dssy=vy:Dssz=vz
THERMAL + STRUCTURAL STRAIN DISPLACEMENTS,
LET NAd=Nn+2:NCd=Nn+4
x(NAd)= x(NA)+EtaT*(x(NA)-x(17))= 0.8773
y(NAd)= y(NA)+EtaT*(y(NA)-y(17))= 55.91
z(NAd)= z(NA)+EtaT*(z(NA)-z(17))= 0.2957
x(NCd)= x(NC)+EtaT*(x(NC)-x(1))+Dssx= 598.2
y(NCd)= y(NC)+EtaT*(y(NC)-y(1))+Dssy= 59.95
z(NCd)= z(NC)+EtaT*(z(NC)-z(1))+Dssz= 0
LET N1=NB:N2=NCd:N3=NAd
LET La=FNl(N2,N3):Lb=Lb*(1+EtaT):Lc=Lc*(1+EtaT):PROC057D
PROC057D, COSINE RULE,
ANG= DEG(ACS((La^2-Lb^2-Lc^2)/(2*Lb*Lc)))= 40.37
END057D
AngD= ANG= 40.37
ANG= ABS(AngD-AngU)= 2.218
END058