;/()F1C U/W-FOCAL:SOB2NO/DA/TE?MB!HJS Z=Z1(D)-1;S D=D+1?MW8JJS 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 !?MC7X^T "ING. - BUERO  B R A S S   ALFONSSTRASSE 9  8000 MUENCHEN 19   RUF 181081"!!?M\OX(S J1=6;T "*"!!"BETR.:    
   POS.:";T :60,"SEITE"!!!!?MD&0LI (FABS(X-R(1))-P)24.2;S Y=1?M\40TF I=1,N-2;D 25?MEA0[I (FABS(X-R(L))-P)24.3;S Y=1?M]J0^I (Y)24.4;G 24.1?M]+02S M(N)=-M(L)-2*R(L)-R(L-1);T M(N)?M^N2KI (FABS(X-R(A))-P)25.2;S Y=1?MFC2UI (FABS(X-R(A+1))-P)25.3;S Y=1?M^
2^R?MF\4TF I=2+J,4,2*N-3;S G((I-J)/2+1)=V(I)?M8W4^F I=5-J,4,2*N-3;S G((I+J+1)/2)=V(I)?MGKBCT "*"!!"BERT.:        POS.:";T :60,"SEITE"!!!!?MGYBES LN=LN+1;O I D(LN),E?M;BHZ;A 
LN LM N 
?MG.BLI (KL)1.14;S H=1?M7%BMD 12;A 
L Z 
;F I=1,Z;D 20?M9BOT !!"DL"!;F I=1,N;A DL(I)?M:6BVF 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?MXEBXD 4?MIGB^S C=C1(E),A=A1(E),B=L-A-C?MI[B S X=C*(B+C/2)/L,Y=C*(A+C/2)/L;D 21?MI.B"S A=(A+C/2)/L,B=(B+C/2)/L,C=C/L?MJPB$S X=L*L*C*A*(4*(1-
*A)-C*C)/4,Y=L*L*B*C*(4*(1-B*B)-C*C)/4;D 22?MJ B&I (I-3)1.4;I (P)1.45;G 1.5?MJ+B(S XL=XL+Q(E)*X/2?MJ1B+G 1.5?MJ<B-S XR=XR-Q(E)*Y/2?MKDB2D 5;G 1.25?MKIB4D 4?M:\B6I (Z)1.72?MK)B9S A=(A+2*C/3)/L,B=(B+C/3)/L,C=C/L,H=1;D 23?MK9B:I (I-3)1.6;I (P)1.65;G 1.7?MLBB
D 1.4;G 1.7?MLHCAD 1.45?MLPCFD 5;G 1.54?MLUCHD 4?ML]CJI (Z)1.92?MXWCLD 1.3;S X=C*(B+2*C/3)/2*L,Y=C*(A+C/3)/2*L;D 21?MMGCNI (I-3)1.8;I (P)1.85;G 1.9?MMPCPD 1.4;G 1.9?MMVCUD 1.45?MM^CZD 5;G 1.74?MM*C\S I=I+2;I (-P)1.24?MM8DJF I=,2*N-1;S M(I)=T(I)?MNKDOD 12;
 "AUSGL. F. G-AUFL.";D 24?MN%DQD 3;T "G-AUFL.";D 3;T V+V(1)+(M(2)-M(1))/O(1)?MOKDSF I=2,N-1;T V(2*I-2)+V(2*I-1)-(M(I)-M(I-1))/O(I-1)-(M(I)-M(I+1))/O(I)?MO"DVT V(2*N-2)+V(2*N-1)+(M(N-1)-M(N))/O(N-1)?MO0DWS V(2)=-XL,V(2*N-3)=XR?MPLDXI (N-3.5)2.3;S H=1;F I=3
2*N-4;S V(I)=H*U(I),H=-H?MX0D^Z J?MP%D"T "  I    X0L    XMF    MF     X0R?M2ODI (3.5-N)2.48;S I=1?MP=D*I (V(2)-M(2))2.5?MQSD,D 3;T "AUSGLM. D. VOLLEINSPM. ERSETZT?MQ"D.S M(2)=V(2);D 2.4;G 2.5?MQ0D0D 26; F I=1,2,N-1;D 11?MYMD2S J=1;D 2.31,2.32,12;T "AUSGL.
F. GERADE FELDER";D 24,12?MR+D4I (V(3)-M(2))2.63;D 2.44;S M(2)=V(3);D 2.4;G 2.63?MY D<D 26;F I=2,2,N-1;D 11?M2(EAD 24;F I=1,N-1;S X=(M(I)-M(I+1))/O(I),V(2*I-1)=W(2*I-1)-X,V(2*I)=W(2*I)+X?MS1EFD 12;T "AUSGL. F. STUETZE?MTIEJT %2,1;Z J;D 8;S M=U;D 24;I (DL(
)-.01)2.8?MY7ELD 3;T "    X0L   MRED    XOR";D 3?MT*ERS J=-1;F K=2,N-1;D 9?MZ1ETD 2.7;T %2,N;S X=N/2,Y=FITR(X),Z=1;I (X-Y-.01)2.86;Z Z?M2:EXF I=3-Z,4,2*N-2;D 7?MBTFJT !;S J1=J1+1?MU,P
F I=1-J,4,2*N-1;D 7?M"$P F I=2+J,4,2*N-1;D 7?MVFRKF I=2*K,4,2*N-1;D 7?M";RLF I=2+J,4,2*K-2;D 7?MV$RNI (J)9.2;I (K-2.5)9.2;S M=U?MWDRTD 24;S J=-J;I (-M(K))9.3;D 2.76;S I=K-1,L=O(I)-DL(I+1)-.05?M74RYZ S;D 2.4;S I=K,L=DL(I)-.05;D 2.4;G 9.4?M8DR(S W(2*K-3)=G,
(2*K-2)=W(2*K-2)-(M(K)-M(K-1))/O(K-1)?M[XNJS M(I)=U(I)?M
K"TR?MH7BYS P=2*N-3-I,L=O(I/2);I (Z)1.52?ML7CMS A=(A+C/3)/L,B=(B+2*C/3)/L,C=C/L,H=-1;D 23?MYD
D 2.1;F I=1-J,4,2*N-1;D 7?M13D F I=2+J,4,2*N-1;D 7?MROD3D 2.34;I (3.5-N)2.6;S I=2;D 2.4?MR9D?D 12;T "AUSGL.F. VOLLAST";F I=,2*N-1;D 7?MZ[END 13;S I=1,L=DL(1)-.05,S=M(1)+W*DL(1);I (.045-DL(1))2.79;S S=M(1)?MZ!EOD 2.4?MT]EPS G=W(1)-(M(1)-M(2))/O(1)?MUHEVD 2
1;F I=Z,4,2*N-2;D 7?M0&E\S I=N-1,L=O(I)-DL(N)-.05;D 2.76;Z S;D 2.4?MU
PND 2.1?M[9VTD 2.4;I (M(I)-G(I))11.3;I (M(I+1)-G(I+1))11.3;R ?MB0V^D 2.44;S M(I)=G(I),M(I+1)=G(I+1);D 2.4?M!>ZTT "  K.NST?MDU0JS P=.003,L=2*N-2,Y=-1,X=R(1),R(1)=-.5*(R(2)+M+M(1))?MD00YS X=R(L),R(L)=-.5*(R(L-1)+M(L)+M(L+1))?MEL0(D 3;F I=1,N-1;S M(I)=M(2*I-
)+2*R(2*I-1)+R(2*I);T %5.02,M(I)?M^2IS A=2*I,H=R(A-1)+M(A)+M(A+1)+R(A+2)?ME 2JS X=R(A),R(A)=MY(A)*H?ME12TS X=R(A+1),R(A+1)=MY(A+1)*H?MFG4JS G(1)=M(1),G(N)=M(N)?M3R\LD 3;T "LF";F K=1,Z;D 3;A A1(E),C1(E),G(E),Q(E);S E=E+1?M
(JD 3;A A,B,X,Y;S C=A+B/2;I (H)20.2;S C=L-C?M5"(TS T(K)=T(K)+H*X*B*C,U(K)=U(K)+H*Y*B*C?M P*JS V(I-1)=V(I-1)+G(E)*X,V(I)=V(I)+G(E)*Y?M 	*TS W(I-1)=W(I-1)+Q(E)*X,W(I)=W(I)+Q(E)*Y?M!F,JS T(I-1)=T(I-1)-G(E)*(2*Y-X)/3,T(I)=T(I)+G(E)*(2*X-Y)/3?M!%,TS U(I-1)=U(I
1)-Q(E)*(2*Y-X)/3,U(I)=U(I)+Q(E)*(2*X-Y)/3?M:.JS X=L*L*C*(270*(A-A^3)-C*C*(45*A-2*H*C))/540?M^-\JD 12;T "STW + KZ";D 3;A O(I+1);Z Z;F K=1,3;A Z1(I*3+K);S Z=Z+Z1(I*3+K)?MU9RJD 2.7;T %2,K;D 2.1;F I=2*K-1,4,2*N-1;D 7?MVSRMF I=3+J,4,2*K-2;D 7?M"6CS Z=Z1(D+1)+
1(D+2);I (-Z)27.4;I (1-Z1(D))27.4?M36EI (C1(E)-O(I))27.4;S Z=Q(E)?M$K6HS 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$,6JT P?M.06LT X,M;D 17?M$<6TD 13,27.12?M%B6^D 13;R?M%G6(D 29?M%(7FI (O(I)-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&U7KS 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&27OI (B-XR)27.8;D 13?M&67PR?M	V8AS D=3*(I-1)+1,E=1;Z P;I (I-1.5)28.03;F C=1,D-1;S E=E+Z1(
)?M	08CS Z=Z1(D+1)+Z1(D+2);I (-Z)28.2;I (1-Z1(D))28.2?M(D8EI (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)C8II (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)I8JD 13;R?M.=8OS M=B+A*DL(I);I (M-
)28.18;S M=S?M)!8TD 29?M/M83I (S)28.6;I (-B*Y)28.53?M)985I (L-P)28.55?M*J86S P=P+.05,D=D-3,E=E-X;G 28.2?M*U87I (-R)28.56;D 13?M*"88I (-S)28.57;S S=B;R?M*/89I (S+B)28.58;S B=-S?M*:8:T B;S CL(I)=B;R?M+C8<I (P-L)28.63?M+O8=I (S-B)28.62;S S=B?M+]8>T S;S CL(I)
S,L=L+O(I)?M+48?I (B*Y)28.64;I (P+.11-O(I))28.54;D 13;R?M+<9T P+.04;R?M,E:^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,6:.Z X,H;D 4?M-X:/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-3:;D 4?M0P:<I (Z)29.69;I (P-A1(E))29.68;I (A1(E)+C1(E)-P)29.68?M.W;DD 5;G 29.6?M3(;ES H=.05*H,XR=(A-XL-.5*H)*.05,XL=XL+H,B=B+XR?M$46OI (O(I)-R)27.3;T R;R?M)\8RT M;S CL(I)=M,H=-1;G 28.09?M)084S R=R+.6,Y=-Y;I (R)28.53;T 
+.04?M/<:2I (Z)29.59;I (P-A1(E))29.58;I (A1(E)+C1(E)-P)29.58?M-&:3S H=H+Q(E)*(.01483+P-A1(E))/C1(E)?M.O:=S H=H+Q(E)*(1-(.01483+P-A1(E))/C1(E))?M1GE^I (DL(N)-.01)2.98;S M=M(N)+W(2*N-1)*DL(N);I (M-S)2.96;S M=S?M1SE S CL(N)=M;T M;D 13?MUUE"S W(2*N-2)=W(2*N-2
-(M(N)-M(N-1))/O(N-1),W(2*N-3)=G;G 30.1?MPQD!D 12;T "AUSGL. F. UNGERADE FELDER";S NX=27;D 24,12?MP2D(S B=M(I),A=W(2*I-1)-(M(I)-M(I+1))/O(I);D NX?MS!ECS V=W,V(2*N-1)=W(2*N-1),NX=28?M[EZS M(2*N-1)=U(2*N-1);D 24;I (DL(N)-.01)2.94?MXA"JI (FABS(M)-FABS(MF(I)))
7.2;S MF(I)=M?M3<<JD 12;T "MAXIMALE QUERKRAEFTE";Z K?M7D<TD 12;T "  I      QL       QR      AMAX?M40<(S K=K+1;I (O(K)-.7*O(K+1))30.9;I (O(K+1)-.7*O(K))30.9?M5K<2I (K+2.5-N)30.4;D 12;T "QUERKRAEFTE AUS VOLLAST?M5Y<<F I=,2*N-1;S W(I)=V(I)?M;Z=FD 30.2,30.3?M
9(^S V(K)=V(K)+X*B,W(K)=W(K)+Y*B;I (H)20.7?M6S((S R=FITR(10*AB(1)+HA/10)/20;I (-AB(1))20.5;Z R?M6$(2S P=Y*(A+B+R-L);I (-P)20.6;R?M9&(<S WL=WL-P;R?M6<)PS P=Y*(S-A);I (-P)20.9;R?M
9)ZS WR=WR-P?M4R<^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)?MG>BNS LL=L,E=1;F I=,N-2;D 14?MW[R^T "  MS POS";S CL(K)=M(K)?M[^R)S G=W(2*K-1)-(M(K)-M(K+1))/O(K)?MH6AS D=3*(I-1)+1,E=1;Z P;D 3;T %2,I,%5.02;I (I-1.5)27.03;F C=1,D-1;S E=E+Z1(C)
M;LBPI (KR)1.18;S K=2*N-1,H=-1;D 1.13;S LR=L?MHNBTF I=1,N-1;S M(I)=1/O(I)?M6-)FS S=FITR(10*AB(N)+HA/10)/20;I (-AB(N))20.8;Z S?M\W.TS Y=L*L*C*(270*(B-B^3)-C*C*(45*B+2*H*C))/540;D 22?MKQB8D 1.3;S X=C*(B+C/3)/2*L,Y=C*(A+2*C/3)/2*L;D 21?MH2BWS D=1,E=1,I=2?MGB
S J1=9;A 
KL KR 
?M9WBRI (2.5-N)1.2;L R SOB3?M;)=ZD 12.2,12.3;I (-LM)1.03?M=
T "*"?M"?L S SOB2?M?M?MH2BWS D=1,E=1,I=2?

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