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<B()8TC U/W-FOCAL:DLT2NO/DA/TE?MB!HJS Z=Z1(D)-1;S D=D+1?MVNJJS Z=Z-1;S E=E+1;S X=X+1?MCCXJI (57-J1)12.2;T !!;S J1=J1+2;R ?MCMXTF C=J1,67;T !?M:=X^T "ING. - BUERO  B R A S S   ALFONSSTRASSE 9  8000 MUENCHEN 19   RUF 181081"!!?MDH0LI (FABS(X-R(1))-P)24.2;S 
=1?M[R0TF I=1,N-2;D 25?MD0[I (FABS(X-R(L))-P)24.3;S Y=1?M9,0^I (Y)24.4;G 24.1?M[(02S M(N)=-M(L)-2*R(L)-R(L-1);T M(N)?M\K2KI (FABS(X-R(A))-P)25.2;S Y=1?ME%2UI (FABS(X-R(A+1))-P)25.3;S Y=1?M\\2^R?ME>4TF I=2+J,4,2*N-3;S G((I-J)/2+1)=V(I)?M:M4^F I=5-J,4,2*N-3
S G((I+J+1)/2)=V(I)?M8ZBES LN=LN+1;O I D(LN),E?MF,BLI (KL)1.14;S H=1?M5"BMD 12;A 
L Z 
;F I=1,Z;D 20?M6TBOT !!"DL"!;F I=1,N;A DL(I)?M8JBVF I=1,N-2;S H=M(I)+M(I+1),MY(2*I)=-M(I)/2*H,MY(2*I+1)=-M(I+1)/2*H?MV+BXD 4?MHEB^S C=C1(E),A=A1(E),B=L-A-C?MHYB S X=C*(B+C/2)/L,Y=C*(A+C/2)/L;D 21?MH,B"S A=(A+C/2)/L,B=(B+C/2)/L,C=C/L?MINB$S X=L*L*C*A*(4*(1
A*A)-C*C)/4,Y=L*L*B*C*(4*(1-B*B)-C*C)/4;D 22?MI^B&I (I-3)1.4;I (P)1.45;G 1.5?MI)B(S XL=XL+Q(E)*X/2?MI/B+G 1.5?MI:B-S XR=XR-Q(E)*Y/2?MJBB2D 5;G 1.25?MJGB4D 4?M70B6I (Z)1.72?MJ	B9S A=(A+2*C/3)/L,B=(B+C/3)/L,C=C/L,H=1;D 23?MJ7B:I (I-3)1.6;I (P)1.65;G 1.7?MKB
D 1.4;G 1.7?MKFCAD 1.45?MKNCFD 5;G 1.54?MKSCHD 4?MK[CJI (Z)1.92?MV=CLD 1.3;S X=C*(B+2*C/3)/2*L,Y=C*(A+C/3)/2*L;D 21?MLECNI (I-3)1.8;I (P)1.85;G 1.9?MLNCPD 1.4;G 1.9?MLTCUD 1.45?ML\CZD 5;G 1.74?ML(C\S I=I+2;I (-P)1.24?ML6DJF I=,2*N-1;S M(I)=T(I)?MMIDOD 12;
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*N-4;S V(I)=H*U(I),H=-H?MWVD^Z J?M0LDI (3.5-N)2.48;S I=1?MO	D*I (V(2)-M(2))2.5?MO=D,D 3;T "AUSGLM. D. VOLLEINSPM. ERSETZT?MPLD.S M(2)=V(2);D 2.4;G 2.5?MPZD0D 26; F I=1,2,N-1;D 11?MW3D2S J=1;D 2.31,2.32,12;T "AUSGL. F. GERADE FELDER";D 24,12?MQUD4I (V(3)-M
2))2.63;D 2.44;S M(2)=V(3);D 2.4;G 2.63?MXFD<D 26;F I=2,2,N-1;D 11?M0%EAD 24;F I=1,N-1;S X=(M(I)-M(I+1))/O(I),V(2*I-1)=W(2*I-1)-X,V(2*I)=W(2*I)+X?MR[EFD 12;T "AUSGL. F. STUETZE?M9LEJT %2,1;Z J;D 8;S M=U;D 24;I (DL(1)-.01)2.8?MSERS J=-1;F K=2,N-1;D 9?MYWET
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F I=1-J,4,2*N-1;D 7?M !P F I=2+J,4,2*N-1;D 7?MT\RKF I=2*K,4,2*N-1;D 7?M 8RLF I=2+J,4,2*K-2;D 7?MT:RNI (J)9.2;I (K-2.5)9.2;S M=U?MUZRTD 24;S J=-J;I (-M(K))9.3;D 2.76;S I=K-1,L=O(I)-DL(I+1)-.05?M51RYZ S;D 2.4;S I=K,L=DL(I)-.05;D 2.4;G 9.4?M6AR(S W(2*K-3)=G,
(2*K-2)=W(2*K-2)-(M(K)-M(K-1))/O(K-1)?MY>NJS M(I)=U(I)?M]H"TR?MF!BKT !!"AB"!;F I=1,N;A AB(I)?MG5BYS P=2*N-3-I,L=O(I/2);I (Z)1.52?MK5CMS A=(A+C/3)/L,B=(B+2*C/3)/L,C=C/L,H=-1;D 23?MW&D
D 2.1;F I=1-J,4,2*N-1;D 7?M/0D F I=2+J,4,2*N-1;D 7?MP9D3D 2.34;I (3.5-N)2.6;S I=2;D 2.4?MQD?D 12;T "AUSGL.F. VOLLAST";F I=,2*N-1;D 7?MYAEND 13;S I=1,L=DL(1)-.05,S=M(1)+W*DL(1);I (.045-DL(1))2.79;S S=M(1)?MYGEOD 2.4?MR3EPS G=W(1)-(M(1)-M(2))/O(1)?MS^EVD 2.
;F I=Z,4,2*N-2;D 7?M.E\S I=N-1,L=O(I)-DL(N)-.05;D 2.76;Z S;D 2.4?MS5PND 2.1?MZ
VTD 2.4;I (M(I)-G(I))11.3;I (M(I+1)-G(I+1))11.3;R ?MB0V^D 2.44;S M(I)=G(I),M(I+1)=G(I+1);D 2.4?MC70JS P=.003,L=2*N-2,Y=-1,X=R(1),R(1)=-.5*(R(2)+M+M(1))?MDR0YS X=R(L),R(L)=-.5*(R(L-1)+M(L)+M(L+1))?M[=2IS A=2*I,H=R(A-1)+M(A)+M(A+1)+R(A+2)?MEB2JS X=R(A),R(A)
MY(A)*H?MES2TS X=R(A+1),R(A+1)=MY(A+1)*H?ME)4JS G(1)=M(1),G(N)=M(N)?M1O\LD 3;T "LF";F K=1,Z;D 3;A A1(E),C1(E),G(E),Q(E);S E=E+1?M] (JD 3;A A,B,X,Y;S C=A+B/2;I (H)20.2;S C=L-C?M3
(TS T(K)=T(K)+H*X*B*C,U(K)=U(K)+H*Y*B*C?M^M*JS V(I-1)=V(I-1)+G(E)*X,V(I)=V(I)+G(E)*Y?M^$*TS W(I-1)=W(I-1)+Q(E)*X,W(I)=W(I)+Q(E)*Y?M
C,JS T(I-1)=T(I-1)-G(E)*(2*Y-X)/3,T(I)=T(I)+G(E)*(2*X-Y)/3?M
",TS U(I-1)=U(I-1)-Q(E)*(2*Y-X)/3,U(I)=U(I)+Q(E)*(2*X-Y)/3?M7T.JS X=L*L*C*(270*(A-A^3)-C*C*(45*A-2*H*C))/540?M\*\JD 12;T "STW + KZ";D 3;A O(I+1);Z Z;F K=1,3;A Z1(I*3+K);S Z=Z+Z1(I*3+K)?MTORJD 2.7;T %2,K;D 2.1;F I=2*K-1,4,2*N-1;D 7?MT)RMF I=3+J,4,2*K-2;D 7
M!
6CS Z=Z1(D+1)+Z1(D+2);I (-Z)27.4;I (1-Z1(D))27.4?M!06EI (C1(E)-O(I))27.4;S Z=Q(E)?M"H6HS M=B+A*A/2*Z,X=A/Z,C=A*A+2*Z*B;I (C)27.2?M"$6IS R=FSQT(C)/Z,P=X-R,R=R+X;I (-P)27.1;D 13;G 27.12?M")6JT P?M,-6LT X,M;D 17?M"96TD 13,27.12?M"?6^D 13;R?MD6(D 29?M%7FI (O(
)-P-.05)27.79;I (-B*Y)27.73;S Y=-Y;T P+.04;I (-R)27.8?M;7II (XR*R)27.77;S R=1;I (Y*YY)27.75;D 13?M$R7KS M=B-XR;T P-.01,M;D 17;I (-B)27.77;D 13?M$7MS P=P+.05,D=D-3,E=E-X;G 27.4?M$/7OI (B-XR)27.8;D 13?M$37PR?M%S8AS D=3*(I-1)+1,E=1;Z P;I (I-1.5)28.03;F C=1,D
1;S E=E+Z1(C)?M%-8CS Z=Z1(D+1)+Z1(D+2);I (-Z)28.2;I (1-Z1(D))28.2?M&A8EI (C1(E)-A1(E)-O(I))28.2;S Z=Q(E)?M&
8GS C=A*A+2*Z*B;I (S)28.15;S S=M(I+1)+W(2*I)*DL(I+1),H=1?M	8II (C)28.1;S C=A/Z+H*FSQT(C)/Z;I (O(I)-C)28.1;I (C)28.1;T C;R?M	F8JD 13;R?M,:8OS M=B+A*DL(I);I (M-S)28.18;S M=S?M	^8TD 29?M-J83I (S)28.6;I (-B*Y)28.53?M	685I (L-P)28.55?M(G86S P=P+.05,D=D-3,E=E-X
G 28.2?M(R87I (-R)28.56;D 13?M(
88I (-S)28.57;S S=B;R?M(,89I (S+B)28.58;S B=-S?M(78:T B;S CL(I)=B;R?M)8<I (P-L)28.63?M)L8=I (S-B)28.62;S S=B?M)Z8>T S;S CL(I)=S,L=L+O(I)?M)18?I (B*Y)28.64;I (P+.11-O(I))28.54;D 13;R?M)99T P+.04;R?M*B:^I (-P)29.46?M* :(S P=.01,R=-1;Z XL;I (-B-.02)29.45;S Y
-1,YY=Y;G 29.46?M*+:-S Y=1,YY=Y,R=-.5?M*3:.Z X,H;D 4?M+U:/I (Z)29.49;I (P-A1(E))29.48;I (A1(E)+C1(E)-P)29.48;S H=H+Q(E)?M+^:0D 5;G 29.47?M-]:1D 4?M++::D 5;G 29.5?M+0:;D 4?M.M:<I (Z)29.69;I (P-A1(E))29.68;I (A1(E)+C1(E)-P)29.68?M,T;DD 5;G 29.6?M1%;ES H=.05
H,XR=(A-XL-.5*H)*.05,XL=XL+H,B=B+XR?M"16OI (O(I)-R)27.3;T R;R?M	Y8RT M;S CL(I)=M,H=-1;G 28.09?M	-84S R=R+.6,Y=-Y;I (R)28.53;T P+.04?M-9:2I (Z)29.59;I (P-A1(E))29.58;I (A1(E)+C1(E)-P)29.58?M+:3S H=H+Q(E)*(.01483+P-A1(E))/C1(E)?M,L:=S H=H+Q(E)*(1-(.01483+P-
1(E))/C1(E))?M/DE^I (DL(N)-.01)2.98;S M=M(N)+W(2*N-1)*DL(N);I (M-S)2.96;S M=S?M/PE S CL(N)=M;T M;D 13?MS+E"S W(2*N-2)=W(2*N-2)-(M(N)-M(N-1))/O(N-1),W(2*N-3)=G;G 30.1?M84D!D 12;T "AUSGL. F. UNGERADE FELDER";S NX=27;D 24,12?MO\D(S B=M(I),A=W(2*I-1)-(M(I)-M(
+1))/O(I);D NX?MRKECS V=W,V(2*N-1)=W(2*N-1),NX=28?MY&EZS M(2*N-1)=U(2*N-1);D 24;I (DL(N)-.01)2.94?MVW"JI (FABS(M)-FABS(MF(I)))17.2;S MF(I)=M?M19<JD 12;T "MAXIMALE QUERKRAEFTE";Z K?M5A<TD 12;T "  I      QL       QR      AMAX?M2-<(S K=K+1;I (O(K)-.7*O(K+1))
0.9;I (O(K+1)-.7*O(K))30.9?M3H<2I (K+2.5-N)30.4;D 12;T "QUERKRAEFTE AUS VOLLAST?M3V<<F I=,2*N-1;S W(I)=V(I)?M:6=FD 30.2,30.3?M36(^S V(K)=V(K)+X*B,W(K)=W(K)+Y*B;I (H)20.7?M4P((S R=FITR(10*AB(1)+HA/10)/20;I (-AB(1))20.5;Z R?M4!(2S P=Y*(A+B+R-L);I (-P)20.6;R
M6:(<S WL=WL-P;R?M49)PS P=Y*(S-A);I (-P)20.9;R?M]6)ZS WR=WR-P?M2O<^F I=,N-1;D 3;T %2,I+1,%7.02,W(2*I),W(2*I+1),W(2*I)+W(2*I+1)?MF<BNS LL=L,E=1;F I=,N-2;D 14?MU1R^T "  MS POS";S CL(K)=M(K)?MZDR)S G=W(2*K-1)-(M(K)-M(K+1))/O(K)?M8&BPI (KR)1.18;S K=2*N-1,H=-1
D 1.13;S LR=L?MGLBTF I=1,N-1;S M(I)=1/O(I)?M4*)FS S=FITR(10*AB(N)+HA/10)/20;I (-AB(N))20.8;Z S?MZ5.TS Y=L*L*C*(270*(B-B^3)-C*C*(45*B+2*H*C))/540;D 22?MJOB8D 1.3;S X=C*(B+C/3)/2*L,Y=C*(A+2*C/3)/2*L;D 21?MG0BWS D=1,E=1,I=2?MFSBCD 12.4?M;ZBHZ;A 
PR LN LM N 
?M6+BRI (2.5-N)1.2;L R DLT4?MOOD"T "  I      X0L      XMF      MF       X0R?MX]ELD 3;T "      X0L     MRED      XOR";D 3?M
;ZTT "    K.NST?MD.0(D 3;F I=1,N-1;S M(I)=M(2*I-1)+2*R(2*I-1)+R(2*I);T %7.02,M(I)?M!E6AS D=3*(I-1)+1,E=1;Z P;D 3;T %2,I,%7.02;I (I-1.5)27.03;F C=1,D-1;S E=E+Z1(C)?M=ZL R DLT3?M9X(S J1=5;T "*"!!!"BETR.:"%4,PR,"  POS.:":60"SEITE"!!!!?MV[BJS J1=14;A 
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,!;S HA=H,SE=BS/10,BR=CALB*10?I=1,N-2;D 25?MEA0[I (FABS(X-R(L))-P)24.3;S Y=1?M
V0^I (Y)24.4;G 24.1?M
702S M(N)=-M(L)-2*R(L)-R(L-1);T M(N)?M Z2KI (FABS(X-R(A))-P)25.2;S Y=1?MFC2UI (FABS(X-R(A+1))-P)25.3;S

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