?a????se?? ?p?fa?e?a??? Te

1
????????S ??? ??T?????S T?????OS??S 7? ??.
???-???. ??? - ??ad. ?t?? 2005 - 06
??????? 4 ?a????se?? ?p?fa?e?a???
Teµe???se?? ?????s? µe s??se?? e?ast???? µ??f??
08.01.2008
2
?a????se?? ?p?fa?e?a??? Teµe???se?? (ped????)
?? ?a????se?? (?ata????fe? ß???se??)
?fe????ta? st?? p??s?ete? t?se?? (?s) ?a?
?pe?p??se?? p???? (?u) p?? a?apt?ss??ta? st?
?daf?? ???? t?? f??t?s?? t?? ap? t? p?d???
q
??d??? d?ast?se?? B x L ?daf?? µe e?ast????
?d??t?te? ?, ?
B,L
?, ?
?? ?a????se?? d?a??????ta? se (1) ?µese?, (2)
e? ste?e?p???se??, (3) e?p?st???? (de?te?e???sa
ste?e?p???s?)
3
?a????se?? ?p?fa?e?a??? Teµe???se?? (ped????)
t?se?? (?sv)
?p?f??t?s? q
???s?ete? ?ata????fe? t?se?? (?sv) ???? f??t?s??
e?ast???? ?µ?????? (ed?f???) µe p?d??? p??t???
(?) p?? as?e? p?es? (q)
?a??de??µa Se ß???? z 3B, ?a? ap?stas? ap?
t?? ????a x 2B ????d?t? ?sv 0.1
q ?et?a?????? ?sv 0.02 q
????? ep?????? t?? f??t?s?? ????da
zmax ? 6B ?et?????? zmax ? 2B
????d?t? p?d???
?et?a?????? p?d???
4
?a????se?? ?p?fa?e?a??? Teµe???se?? (ped????)
?? ?a????se?? (?ata????fe? ß???se??) ?fe????ta?
st?? p??s?ete? t?se?? (?s) p?? a?apt?ss??ta? st?
?daf?? ???? t?? f??t?s?? t?? ap? t? p?d???
B
?p?f??t?s? q
?sx
?sz
1
1
2
2
?sz ?sv
???s? 21
?sx
????d?t? p?d???
???s?ete? ?ata????fe? t?se?? (?sv?sz) ????
f??t?s?? e?ast???? ?µ?????? (ed?f???) µe p?d???
p??t??? (?) p?? as?e? p?es? (q)
???s?ete? ?ata????fe? (?sz) ?a? ??????t?e? (?sx)
t?se?? ???? f??t?s?? e?ast???? ?µ?????? (ed?f???)
µe ????d?t? p?d??? p??t??? (?) p?? as?e? p?es? (p)
?at? t? DIN 4019, ?? ?a????se?? ep?fa?e?a???
?eµe???se?? ?p????????ta? ??a edaf??? ???? µ????
ß????? (z) ?p?? ? p??s?et? t?s? ?sv 0.20
svo. svo a????? (?e?stat???) e?e????
?ata????f? t?s? st? ß???? (z)
5
?a????se?? ?p?fa?e?a??? Teµe???se?? (ped????)
?p????? t?? pa???s?a? s?????? ep?fa?e?a???
st??s?? st? µe??s? t?? t?se?? e?t?? t??
?p??e?µe??? µa?a??? (s?µp?est??) st??s??, ?a?
s??ep?? st? µe??s? t?? µe?????? t?? ?a????se??
t?? ped????
B
??µ?? t?? ?ata????f?? t?s?? (?sv) d?a??eµ???? µe
t?? p?es? t?? ped???? (p) ??a d??f??a ß??? (z)
??t? ap? t? ???t?? ????d?t?? ped???? e????? (B).
? a??te?? edaf??? st??s? (p????? ?) ??e? µ?t??
e?ast???t?ta? ?1 ?a? ? ?at?te?? (µe????? p?????)
??e? µ?t?? ?2 lt ?1. ?? ?aµp??e? a?t?st?????? se
d??f??e? t?µ?? t?? ????? ?1 / ?2
p
p
S?µp??asµa ? a???s? t?? µ?t??? e?ast???t?ta?
t?? a??te??? st??s?? p???a?e? s?µa?t??? µe??s?
t?? p??se?? st?? ?at?te?? st??s? ? µe??s? t??
?a????se??
6
?p????? t?? pa???s?a? µ??? s?????? ep?fa?e?a???
st??s?? st?? ap?µe??s? t?? t?se?? st?? ?p??e?µe??
µa?a?? st??s?
?e??s? t?? ß???s?? t?? t????? ???? t?? ap?µe??s??
t?? t?se?? st?? ?µµ? ??t? ap? t?? µeta??????
p???e?
7
?ata??µ? t?se?? ?a? ?a????se?? st? ß?s? ped????
1. ??aµpta p?d??a
?ata??µ? t?se?? st? ß?s? ??aµpt?? ped???? p??
f??t??eta? µe ?µ???µ??f? p?es?. ?? ?a????se??
e??a? p??fa??? ?µ???µ??fe? (??aµpt? p?d???)
x
???ß?e?? t?? ?e???a? e?ast???t?ta? ??a t??
?ata??µ? t?? t?se?? st? ß?s? a??µpt?? ????d?t??
ped???? e????? (?) µe ?µ???µ??f? ep?f??t?s? q
P / B
?
?at? t?? e?ast???t?ta
S?µp??asµa ?? p??ß???e?? t?? ?e???a?
e?ast???t?ta? ????? pe?????sµ??? a???p?st?a sta
µ?-s??e?t??? (aµµ?d?) ed?f? (??????)
8
?ata??µ? t?se?? ?a? ?a????se?? st? ß?s?
?eµe???se??
2. ???aµpte? ?eµe???se?? (p.?. de?aµe???)
?ata??µ? ?a????se?? st? ß?s? e??aµpt?? ?eµe???s??
p?? f??t??eta? µe ?µ???µ??f? p?es? (q). ?? t?se??
e??a? p??fa??? ?µ???µ??fa ?ata?eµ?µ??e?.
???ß?e?? t?? ?e???a? e?ast???t?ta? ??a t??
?ata??µ? t?? ?a????se?? st? ß?s? e??aµpt??
?eµe???s?? (µe?a??te?e? ?a????se?? st? ???t??)
S?µp??asµa ?? p??ß???e?? t?? ?e???a?
e?ast???t?ta? ????? pe?????sµ??? a???p?st?a sta
µ?-s??e?t??? (aµµ?d?) ed?f? (??????)
9
?a????se?? ?p?fa?e?a??? Teµe???se?? (ped????)

• ??t??µe?a
• ??t?µ?s? t?? µe?????? ?a? t?? ???????? e???????
  t?? ?a????se??
• ??t?µ?s? t?? µ???st?? ap?de?t?? ?a????se??
  (a?a????? t?? ?e?t???????? ?a? stat????
  apa?t?se?? t?? a??d?µ??)
• ?p?fas? ??a ta µ?t?a p?? p??pe? ?a ??f???? st??
  pe??pt?s? ?p?? ?? a?aµe??µe?e? ?a????se??
  ?pe?ßa????? t?? µ???ste? ap?de?t??
• ?a?ade??µata p??a??? µ?t???
• ??e????s? t?? ped????, ?eµe???s? µe ped???d?????
  / ???t?st??s?
• Teµe???s? µe pass?????
• ?e?t??s? t?? ed?f??? ?eµe???s?? (p.?. p??f??t?s?,
  d??aµ??? s?µp????s?, d???t??? s?µp????s?,
  ?a????p?ssa???, ??p)
• ?e??s? t?? f??t??? t?? a??d?µ??

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???a ap?de?t?? ?a????se?? ?atas?e???
1. S??????? (?µ???µ??f?) ?a????s? S??????, t?
???? t??eta? ap? t?? ?e?t???????? apa?t?se??
(p.?. s??d?se?? µe d??t?a, p??sßas? ap? t?
d??µ?) 2. ??af????? ?a????s? (?) µeta?? ??se?? se
ap?stas? (L) S?????? ep?ß???eta? ap? t??
stat???? apa?t?se?? t?? f???a (p.?. ??tas? ????
d?af?????? ?a????s?? ß????? ??f??a?, ???µ?? se
ep????sµata ?t?????)
L
?
S????e?? µ???ste? ap?de?t?? t?µ?? t?? ????? ? / L
(s?et??? st??f?)
??d?? ?atas?e??? ????ste? ap?de?t?? t?µ?? t?? ????? ? / L ????ste? ap?de?t?? t?µ?? t?? ????? ? / L
??d?? ?atas?e??? Se ?µµ? ? s????? ?????? Se µa?a?? ? s??e?t??? ??????
????d?µ?? ?a? f????se? t????p???e? ????? / ???? ? 3 ????? / ???? ? 5 1 / 3333 1/ 2000 1 / 2500 1 / 1500
??????fa ?t???a ap? t????p???a 1 / 1000 1 / 1000
??? ???? s?????? ?atas?e??? µe s?e?et? ap? s????deµa ? ????ßa ??a??? ???µat?se?? se ?a??? ?atas?e??? ??a??? ß?aß?? st?? f????ta st???e?a 1 / 500 1 / 300 1 / 150 1 / 500 1 / 300 1 / 150
11
?a????se?? ?p?fa?e?a??? Teµe???se?? (ped????)
??d? ?a????se?? ?a? a?t?a p?? t?? p???a????

1. ?µese? ?a????se?? ?a????se?? se ???? ? µe?????
   ???esµ??a ed?f?, ?a????se?? se ta????
   st?a?????µe?a ???esµ??a ed?f? (p.?. ?µµ???),
   ?µese? ?a????se?? ???? d?atµ?t???? (?s?-?????)
   pa?aµ??f?s?? se ???esµ??a a??????? ed?f? (ß???s?
   t?? ped???? ?a? f??s??µa ???? ap? t? p?d???).
2. ?a????se?? ???? ste?e?p???se?? ???????
   e?e??ss?µe?e? ?a????se?? ???? e?t???s?? t??
   ?pe?p??se?? p???? p?? a?apt?ss??ta? ?at? t??
   ta?e?a f??t?s? ???esµ???? edaf?? (??????
   a????????).

q
B,L
?, ?
12
?a????se?? ?p?fa?e?a??? Teµe???se?? (ped????)
??d? ?a????se?? ?a? a?t?a p?? t?? p???a????
3. ??p?st???? (de?te?e???se?) ?a????se??
??????? e?e??ss?µe?e? ?a????se?? ???? e?p?st????
s?µpe??f???? t?? edaf?? (?p? p?a?t???? sta?e???
e?e???? t?se??) µet? t? p??a? t?? ste?e?p???s??.
S?????? e??a? s?µa?t???? se ???a???? ed?f? ?a?
µa?a??? a??????? ?????? p?ast???t?ta?. Se aµµ?d?
ed?f? ?a? a??????? ?aµ???? p?ast???t?ta? s??????
aµe????ta?.
q
B,L
?, ?
13
?a????se?? ?p?fa?e?a??? Teµe???se?? (ped????)
??d? ?a????se?? ?a? a?t?a p?? t?? p???a????

• ???p? a?t?a ?a????se??
• ?a????s? ???? s?????s?? se
• ?a?a?? µ?-s??e?t??? ed?f? ?p? ta????
  epa?a?aµßa??µe?e? f??t?se?? (d???se??, se?sµ??,
  ??p).
• Ga??d? ? ?µ?-ß?a??d? ????? ep???s?? ????
  p??µµe???? s?µp????s??.
• ???????p?? ap? as?e?e?? ß?????? (p.?. ??????????,
  µa??a????? asßest???????, ??p) ???? ??a?s?? t??
  s?µe??? epaf?? t?? ??????.
• S?????s? ?e??s? t?? ????? ?p? p?a?t????
  sta?e??? ????? e?e???? t?se??.
• ?????s? (a???t??? ?a????s?) se d??????µe?a ed?f?,
  ???? a???s?? t?? ???as?a? ? ?a????s? ???? µe??s??
  t?? ???as?a?.
• ???????µe?a ed?f? ?d?f? µe ?s???? t?s? ??a
  d?????s? µe ap????f?s? ???as?a? (?????? ???????
  ?????? p?ast???t?ta?).
• ?a????s? ???? ?at???e?s?? t?? d?µ?? e?a?s??t??
  edaf?? (p.?. ???? ?atast??f?? t?? s???????t????
  desµ?? ?at? t?? ???a?s?).
• ?a??de??µa ?a?a???, as?e??? s???????µ??e?
  ?µµ?? (loess)

14
?a????se?? ?p?fa?e?a??? Teµe???se?? (ped????)
?p?????sµ?? µe?????? ?a????se?? ep?fa?e?a???
?eµe???se??
S??????? ?a????s? ? ?i ?c ?s ?i
?µes? ?a????s? ?c ?a????s? e? ste?e?p???se?? ?s
e?p?st??? (de?te?e???sa) ?a????s?
?a?at???s? ?at? pe??pt?s?, ??p??e? ap? t??
a??t??? s???st?se? µp??e? ?a e??a? µ?d?? (p.?.
?µµ?? ?a? µe????? ???esµ??e? ??????? ?c ?s
0 ? ? ?i ) Se ???esµ??e? a???????, µe t??
ep?ß??? t?? f??t?s?? p???a?e?ta? (ta????) ? ?µes?
?a????s? t?? ed?f??? (?p? sta?e?? ????), st?
s????e?a ???? t?? ßa?µ?a?a? ap?t???s?? t??
?pe?p??se?? p???? e?e??ss??ta? ?? ?a????se?? e?
ste?e?p???se?? ?a?, µet? t?? ap?t???s? t??
?pe?p??se?? p????, s?µßa????? ?? e?p?st????
?a????se??.
15
?p?????sµ?? ?a????se?? ped???? (?) µe s??se??
e?ast???? µ??f??
q
?
B,L
?, ?

• ?? ?a????se?? ?fe????ta? st?? p??s?ete? t?se?? ?s
  ?a? st?? ?pe?p?es? p???? ?u p?? p???a?e?ta? ap?
  t?? ?s (se ???esµ??a ed?f? µ?????
  d?ape?at?t?ta?), ?a? e?a?t??ta? ap?
• ta ?a?a?t???st??? t?? ed?f??? (p.?. ?, ?),
• ta ?a?a?t???st??? t?? f??t?s?? (p.?. q) ?a?
• ta ?a?a?t???at??? t?? ped???? (p.?. B, L)

16
?p?????sµ?? ?a????se?? ped???? (?) µe s??se??
e?ast???? µ??f??
?q
?
B,L
?
?, ?
? ep?f??t?s? (?q) p?? p???a?e? ?a????se?? sta
ed?f? e??a? ? p??s?et? t?µ? t?? f??t?s??, p??a?
t?? a?????? ep?ßeß??µ???? (qo) st? st??µ?
?eµe???s??, d??ad? ?q q qo af?? ??
?a????se?? t?? ed?f??? ???? t?? (qo) ????? ?d?
s??te?es?e? (p??? t?? ep?ß??? t?? ?q)
?a??de??µa St?? pe??pt?s? ?eµe???s?? t??
ped???? se ß???? (D) ap? t? f?s??? ?daf??, ? µet?
ap? p??f??t?s? ????? (D) qo ? D
???s??? ??? ? ?eµe???s? (p?? ep?ß???e? p?es? q)
???e? st?? ep?f??e?a t?? ed?f???, ?a? st?
s????e?a ? pe????? ???? ap? t? p?d??? ep????e? se
???? (D), t?te ?q q ?a? ep?p????, ?a p??pe? ?a
??f???? ?p??? ?? ?a????se?? ???? t?? ep???s??
(p?es? ?D).
17
?p?????sµ?? ?a????se?? ped???? (?) µe s??se??
e?ast???? µ??f??
S??????? ?a????s? ? ?i ?c ?s ?i
?µes? ?a????s? ?c ?a????s? e? ste?e?p???se?? ?s
e?p?st??? (de?te?e???sa) ?a????s?
?e t?? pa?ad??? ??aµµ???? e?ast???? s?µpe??f????
??a t? ?daf??, µp????? ?a ?p?????s???? µe s??se??
e?ast???? µ??f?? ?? a??????e? ?a????se?? ped????

• ?µese? ?a????se?? (?i), se ???esµ??e? a???????
  (ast?????ste? s?????e?) µe e?ast???? pa?aµ?t????
  ? ?u ?a? ? 0.50 (ast?????ste? t?µ??).
• S???????? ?a????se?? (?) se ??a ta ed?f?
  (st?a???sµ??e? s?????e?) µe e?ast???? pa?aµ?t????
  ? ? ?a? ? ? (st?a???sµ??e? t?µ??).
• ?a?at???s? Se ?µµ??? ?a? ????? ? µe?????
  ???esµ??e? a??????? ?? s???????? ?a????se?? e??a?
  p?a?t???? ?se? µe t?? ?µese?

• ???s??? ? pa?ad??? ??aµµ???? e?ast????
  s?µpe??f????, s?????? de? e??a? ??a??p???t???
• se aµµ?d? ed?f? (epe?d? t? ? e?a?t?ta? ap? t?
  s?µp?es?)
• se a??????? ed?f? ???t? st?? ast???a (????
  µ?-??aµµ???t?ta?)

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?a????se?? ?p?fa?e?a??? Teµe???se?? (ped????)

• ?µese? ?a????se?? (?i )
• ?a????se?? se ???? ?a? µe????? ???esµ??a ed?f?
  (aµµ?d? ?a? a???????) ? ?i
• ?a????se?? se ta???? st?a?????µe?a ???esµ??a
  ed?f? (p.?. ?µµ???) ? ?i
• ?µese? ?a????se?? (?i lt ? ) se ???esµ??a a???????
  ed?f? ???? d?atµ?t???? (?s?-?????) pa?aµ??f?s??
  (ß???s? t?? ped???? ?a? f??s??µa ???? ap?
  a?t?).
• St?? pe??pt?s? ta?e?a? f??t?s?? ???esµ????
  a??????, a?apt?ss??ta? ?pe?p??se?? p???? (?u) ??
  ?p??e? µe t?? p???d? t?? ?????? e?t??????ta?,
  p???a???ta? ?a????se?? ???? ste?e?p???se?? (?a?
  st? s????e?a ??p??e? e?p?st???? ?a????se??)

?st?????st? f??t?s? s?µa??e? µ?de???? µetaß???
t?? ?????, ??? p??t?te µ?de???? pa?aµ??f?s?. St?
pa?ap?????? s??µa s?µßa????? d?atµ?t????
pa?aµ??f?se?? t?? ed?f??? (?p? sta?e?? ????) p??
d????? ?µese? ?a????se??
ta?e?a f??t?s? ?eµe????
19
?p?????sµ?? µe?????? ?a????se?? ep?fa?e?a???
?eµe???se??

• ?p?????sµ?? ?µes?? ?a????se?? (?i )
• ?e s??se?? e?ast???? µ??f?? ?????? se
  s??e?t??? (a???????) ed?f? ??a f??t?s? a??et?
  µ????te?? ap? t?? f????sa ??a??t?ta (Pu)
• ?e eµpe?????? s??se?? ?????? se µ?-s??e?t???
  (aµµ?d?) ed?f?

? ?p?????sµ?? t?? ?µes?? ?a????se?? µe s??se??
e?ast???? µ??f?? ßas??eta? st?? ?e???a
e?ast???t?ta?, µe ?at?????? e?t?µ?s? t??
e?ast???? sta?e??? t?? ed?f??? ?eµe???s?? (?,
?). ????d?? ??a t?? e?t?µ?s? t?? pa?aµ?t???
(?,?) d????ta? st? ep?µe?? ed?f??.
?p?????sµ?? (?µes??) ?a????se?? se µ?-s??e?t???
(aµµ?d?) ed?f? ?a? se ???? ? µe????? ???esµ??a
s??e?t??? (a???????) ed?f? Sta µ?-s??e?t???
ed?f?, t? µ?t?? e?ast???t?ta? µetaß???eta?
(a????e?) µe t?? a???s? t?? s?µp?es?? (p.?. t??
a???s? t?? ?e?stat???? t?se?? µe t? ß????, t??
s?µp?es? ??t? ap? t? p?d??? ???? t?? ep?f??t?s??,
??p). S??ep??, ?? s??se?? e?ast???t?ta? ?????
pe?????sµ??? efa?µ??? (epe?d? ?e????? ?sta?e??).
G?a t?? ???? a?t? ????? p??ta?e? ???e?
(eµpe??????) s??se?? ??a t?? e?t?µ?s? t?? ?µes??
?a????se?? se ?µµ???. ?ta? efa?µ????ta? ??
s??se?? e?ast???? µ??f?? se µ?-s??e?t??? ed?f?
(?µµ???) ?a? se ???? ? µe????? ???esµ??a
s??e?t??? ed?f? (a???????) ?, ? e??a? ??
e?ast???? sta?e??? p?? af????? st?a???sµ??e?
s?????e? (? ?? ?a? ? ?? ).
20
?p?????sµ?? ?µes?? ?a????se?? (?i )

• ?µese? ?a????se?? se s??e?t??? (a???????) ed?f?
• ??? ? f??t?s? ap??e? a??et? ap? t?? ?at?stas?
  ast???a? (Pu), ?? ?µese? ?a????se?? ped???? se
  s??e?t??? ed?f? e??a? pe??p?? ??aµµ????
  e?ast????.
• ??? ? f??t?s? p??s???e? t?? ?at?stas? ast???a?
  (Pu), ?? ?µese? ?a????se?? ?????ta? ??t??a µ?
  ??aµµ????.
• S??????, ?? ?µese? ?a????se?? se ???esµ??a
  s??e?t??? ed?f? ?p????????ta? µe ???s? s??se??
  e?ast???? µ??f??, µe e?ast???? sta?e??? (?,
  ?) p?? af????? ast?????ste? s?????e? (?s?-????
  pa?aµ??f?s?)
• ? ?u (ast?????st? t?µ? t?? µ?t???
  e?ast???t?ta?) ?a? ? ?u 0.5.

S?s??t?s? µeta?? t?? µ?t??? e?ast???t?ta? ? (?p?
st?a???sµ??e? s?????e?) ?a? t?? µ?t???
e?ast???t?ta? ?u ?p? ast?????ste? s?????e?
?aµp??e? f??t???-?a????s?? t?? ped????
G?a t?? s????? t?µ? ? 1/3 ? ?u 1.125 E
21
S????? ??T??O? ?????G?S??? ???SO? ??T???S?O? (?i )

• 1. ?µµ?d? ed?f?
• ? s??????? ?a????s? e??a? p?a?t???? ?µes? (?c
  ?s 0)
• ?pe?d? t? µ?t?? e?ast???t?ta? (E) de? e??a?
  sta?e?? (e?a?t?ta? ap? t? s?µp?es?), de?
  e?de????ta? ? e?t?µ?s? t?? ?a????s?? µe s??se??
  e?ast???? µ??f??. ???t?µ??ta? eµpe??????
  µ???d?? p?? ????? a?apt???e? e?d??? ??a aµµ?d?
  ed?f?.
• ??? efa?µ?s???? s??se?? e?ast???? µ??f?? , ?a
  p??pe? ?a d??e? p??s??? st?? ep????? ?at???????
  t?µ?? t?? e?ast???? pa?aµ?t??? ? ?a? ?
  (ßeßa??? st?a???sµ??e? t?µ?? ? ?, ?? ).
• 2. ???? ? µe????? ???esµ??a a??????? ed?f?
• ? s??????? ?a????s? e??a? p?a?t???? ?µes? (?c
  ?s 0)
• ??? ? f??t?s? ap??e? a??et? ap? t?? ?at?stas?
  ast???a?, ? ?a????s? e??a? ?at? p??s????s?
  ??aµµ??? ?a? µp??e? ?a e?t?µ??e? µe s??se??
  e?ast???? µ??f?? µe ???s? st?a???sµ???? t?µ?? (
  ? ?, ?? ).
• ???t? st?? ?at?stas? ast???a?, ? ?a????s? ???eta?
  µ?-??aµµ??? ?a? de? s???st?ta? ? e?t?µ?s? t?? µe
  s??se?? e?ast???? µ??f??. ?pa?te?ta? ???s?
  ?at??????? eµpe?????? µe??d?? ? µ?-??aµµ???
  a????s? µe pepe?asµ??a st???e?a.

22
S????? ??T??O? ?????G?S??? ???SO? ??T???S?O? (?i )

• 3. ???esµ??a a??????? ed?f?
• ? ?µes? ?a????s? (?i) ap?te?e? µ???? µ???? t??
  s???????? ?a????s??. ?e t?? p???d? t?? ??????
  p??st??eta? ?a????s? ste?e?p???se?? ?a? e?p?st???
  ?a????s?
• ??? ? f??t?s? ap??e? a??et? ap? t?? ?at?stas?
  ast???a?, ? ?µes? ?a????s? (?i) e??a? ?at?
  p??s????s? ??aµµ??? ?a? µp??e? ?a e?t?µ??e? µe
  s??se?? e?ast???? µ??f?? µe ???s? t??
  ast?????st?? t?µ?? t?? e?ast???? pa?aµ?t??? ( ?
  ?u , ? 0.5 ).
• ??? ? f??t?s? ap??e? a??et? ap? t?? ?at?stas?
  ast???a?, ?? s??se?? e?ast???? µ??f?? µp????? ?a
  ???s?µ?p??????? ?a? ??a t?? e?t?µ?s? t??
  s???????? ?a????s?? (?) µe ???s? t??
  st?a???sµ???? t?µ?? t?? e?ast???? pa?aµ?t??? (
  ? ? , ? ? ).
• ???t? st?? ?at?stas? ast???a?, ? ?µes? ?a????s?
  (a??? ?a? ? s??????? ?a????s?) e??a? µ? ??aµµ????
  ?a? de? s???st?ta? ? e?t?µ?s? t??? µe s??se??
  e?ast???? µ??f??. ?pa?te?ta? ???s? ?at???????
  eµpe?????? µe??d?? ? µ?-??aµµ??? a????s? µe
  pepe?asµ??a st???e?a)

S?s??t?s? µeta?? t?? µ?t??? e?ast???t?ta? ? (?p?
st?a???sµ??e? s?????e?) ?a? t?? µ?t???
e?ast???t?ta? ?u ?p? ast?????ste? s?????e?
G?a t?? s????? t?µ? ? 1/3 ? ?u 1.13 E
23
??t?µ?s? t?? e?ast???? sta?e??? t?? ed?f??? (?,
?)
??t?? e?ast???t?ta? a?????? ?p? ast?????ste?
s?????e? (?u)
??µ?? t?? ????? Eu / cu ?u µ?s? t?µ? t??
µ?t??? e?ast???t?ta? ?p? ast?????ste? s?????e? cu
ast?????st? d?atµ?t??? a?t??? ( ½ t?? a?t????
se a?eµp?d?st? ?????)
24
??µ?? t?? ????? Eu / cu se ?a??????
ste?e?p???µ??e? a???????, ??a d??f??e? t?µ?? t??
d?atµ?t???? t?s?? (th) - ?p?te??sµata ap? d???µ??
ap??? d??tµ?s??
25
??µ?? t?? ????? Eu / cu se ?pe?-ste?e?p???µ??e?
a??????? (OCR ????? ?pe?-ste?e?p???s??), ??a
d??f??e? t?µ?? t?? d?atµ?t???? t?s?? (th) -
?p?te??sµata ap? d???µ?? ap??? d??tµ?s??
26
??µ?? t?? ast?????st?? d?atµ?t???? a?t???? (cu)
se ?pe?-ste?e?p???µ??e? a??????? (OCR ?????
?pe?-ste?e?p???s??). ?p?te??sµata ap? d???µ??
ap??? d??tµ?s??
27
S?s??t?s? t?? µ?t??? e?ast???t?ta? (?) µe t??
a?t?stas? a??µ?? (Rp qc) t?? d???µ?? ??e?d?s??
????? (CPT) (?at? Sanglerat) G?a ?µµ??? ?
E (st?a???sµ???) G?a a??????? ? Eu
(ast?????st?)
28
S?s??t?s? t?? µ?t??? e?ast???t?ta? ?µµ?? µe t??
a?t?stas? a??µ?? (qc) t?? d???µ?? ??e?d?s?? ?????
(CPT) - (?at? Baldi) E50 ??a d?atµ. t?s? 50
t?? a?t???? , E25 ??a d?atµ. t?s? 25 t??
a?t????
?50
?25
1 bar 0.1 MPa
29
??p???? t?µ?? t?? st?a???sµ???? µ?t???
e?ast???t?ta? (? ?) ??a d??f??a e?d? edaf??
30
??p???? t?µ?? t?? st?a???sµ???? µ?t???
e?ast???t?ta? (?) ??a d??f??a ed?f?
31
??p???? t?µ?? t?? µ?t??? e?ast???t?ta? (? se MPa)
µ?-s??e?t???? edaf?? µe ß?s? ta ap?te??sµata t??
ep?t?p?? ????µ?? ???t?p?? ??e?sd?s?? (SPT)
?at? Tassios Anagnostopoulos (1974)
(E se MPa)
??d?? ed?f??? C
????d?? ?µµ?? ?ept?????? ?µµ?? ?es?????? ?µµ?? ???d??????? ?µµ?? ?a????d?? ?µµ?? ?µµ?de?? ?????e? 3 3.5 4.5 7 10 12
? a
?lt15 ?gt15 a 0 a 40
?at? Papadopoulos Anagnostopoulos (1987)
(E se MPa)
??d?? ed?f??? C1 C2
?µµ?d?? ???? ????d?? ?µµ?? ?ept?????? ?µµ?? 3.2 2.6 7.5 0.49 0.69 0.80
32
?p?????sµ?? µe?????? ?a????se?? ep?fa?e?a???
?eµe???se??
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
1. ????d?? Steinbrenner ?a????s? (?) t??
????a? e??aµpt?? ??????????? ped???? (d??.
?µ???µ??f?? p?es?? ?q), p??t??? ? ?a? µ????? L
(? B) se ß???? D ap? t?? ep?f??e?a. ?? s?µp?est?
st??µa ??e? p???? ? ?a? e?ast???? sta?e??? (?,
?).
???s??? ?q q qo (qo a????? p?es?)
?D s??te?est?? ß?????. G?a ep?fa?e?a??
?eµe???s? (D0) ?D 1 F1 , F2 s??te?est??
s??µat??. ??a?t??ta? ap? t?? t?µ?? t?? L/B ?a?
H/B (ß??pe ep?µe?a)
?fa?µ??? t?? µe??d?? Steinbrenner 1. S???????
?a????s? (?µes? ste?e?p???s?) ?p? st?a???sµ??e?
s?????e?, µe ???s? t?? e?ast???? pa?aµ?t??? ?
? ?a? ? ? (st?a???sµ??e? t?µ??) 2. ?µes?
?a????s? ?p? ast?????ste? s?????e?, µe e?ast????
pa?aµ?t???? E Eu ?a? ? 0.50
33
?p?????sµ?? µe?????? ?a????se?? ep?fa?e?a???
?eµe???se??
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
1. ????d?? Steinbrenner
? ?a????s? t?? ????a? t?? ped????
?? s??te?est?? ep?????? F1 ?a? F2 ?p????????ta?
ap? t?? s??se??
?p??
34
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
1. ????d?? Steinbrenner
???a??p???µ??e? t?µ?? t?? s??te?est?? F1 ?a? F2
? ?a????s? t?? ????a? t?? ped????
35
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
1. ????d?? Steinbrenner - S?s??t?s? t?? ?i ?a? ?
se ???esµ??e? a???????
? ?a????s? t?? ????a? t?? ped????
1. ?fa?µ??? t?? µe??d?? Steinbrenner st?? ?µes?
?a????s? (?i) t?? ????a? ped????
E Eu ?a? ? 0.50
2. ?fa?µ??? t?? µe??d?? Steinbrenner st? s???????
?a????s? (?) t?? ????a? ped????
S?s??t?s? t?? ?i ?a? ?
G?a ? 1/3
( epe?d? 0 lt F2/F1 lt 1 )
S??ep?? ?at? Steinbrenner, ? ?µes? ?a????s?
?s??ta? µe t? 50-75 t?? s????????. ??????
s?µp??asµa ??a f??t?se?? a??et? µa???? ap? t??
ast???a (a????? ? gtgt ?i )
36
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
1. ????d?? Steinbrenner ??a ? 0.30 (s??????
t?µ? ??a st?a???sµ??e? s?????e?)
???a??p???µ??e? t?µ?? t?? s??te?est? f
?q q - qo
? ?a????s? t?? ????a? t?? ped????
?p??
?fa?µ??? t?? µe??d?? Steinbrenner ?p?
st?a???sµ??e? s?????e?, ??a ? ? ?a? ?
?0.30
37
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
1. ????d?? Steinbrenner
S??te?est?? ß????? ?eµe???s?? ?D
(p??s??? ?D 1 ??a D0)
38
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
1. ????d?? Steinbrenner
?pa?????a tess???? ?????????? ??a t?? ?p?????sµ?
t?? ?a????s?? se ?p???d?p?te s?µe?? t??
ep?f??e?a? t?? ed?f??? ???? ap? ?????????? p?d???

?(1)(2)(3)(4)
?(1)-(2)-(3)(4)
39
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
1. ?p??p???µ??? µ???d?? Steinbrenner ??a e??aµpta
?a? ??aµpta ?eµ???a d?af???? s??µ?t?? se
?µ????e??? ?daf?? µe????? ß?????
?p? t?? p??????µe?? s??s? t?? Steinbrenner,
p????pte? ? pa?ap?e???? ap??p???µ??? s??s? ??a
t?? ?a????s? se d??f??a s?µe?a ped????
??µ?? t?? s??te?est? ?s
t? ?D ?p??????eta? ?p?? p??????µ????
?a?at???s? ?fa?µ??? t?? µe??d??
Steinbrenner St?a???sµ??e? s?????e? ? ? ?a?
? ? ?st?????ste? s?????e? E Eu ?a? ? 0.50
40
?a?at???s? 1 ?p? t?? p??????µe?? p??a?a
p????pte? ? a??????? p??se???st??? s??s? µeta??
t?? ?a????s?? (?c) t?? ???t??? e??aµpt??
?eµe???s?? ?a? t?? e??a?a? ?a????s?? (?a) ?µ??a?
??aµpt?? ?eµe???s?? µe t?? ?d?a f??t?s?
?a ?a????s? ??aµpt?? ped???? ?c ?a????s?
???t??? e??aµpt?? ped???? (Steinbrenner) (2/3 ?
3/4) t?µ? a?a????? t?? s??µat?? t?? ?eµe????
?a?at???s? 2 ? ap??p???µ??? s??s? Steinbrenner
???s?µe?e? ?a? st?? e?t?µ?s? t?? µ?t???
e?ast???t?ta? t?? ed?f??? ap? µet??se?? t??
s?µp?es?? ?at? t?? ep?t?p?? d???µ? f??t?s??
p???a?. ?at? t? d???µ? a?t?, f??t??eta? µ??
??aµpt? ??????? ? ?????????? p???a (d?ast?se?? ?)
p?? t?p??ete?ta? st?? ep?f??e?a t?? ed?f??? (D0
? ID1) ?a? µet??ta? ? ?a????s? (?) p??
a?t?st???e? st?? efa?µ??? p?es?? (?q). ?? µ?t??
e?ast???t?ta? ?p??????eta? ap? t? s??s?
?p?? Is 0.99 (??a ??aµpt? tet?a??????
p?d???-p???a) ?a? Is 0.79 (??a ??aµpt? ???????
p?d???-p???a) ?a? G?a ?µµ??? ? 1/3 . ?
?p???????µe?? t?µ? t?? ? e??a? ? ? G?a
???esµ??e? a??????? ? ?u 0.5 . ?
?p???????µe?? t?µ? t?? ? e??a? E Eu
41
?fa?µ??? t?? µe??d?? Steinbrenner se p???st??t?
?daf??
St??s? 1 p???? ?1, ?d??t?te? ?1, ?1 St??s? 2
p???? ?2, ?d??t?te? ?2, ?2 .... St??s? n p????
?n, ?d??t?te? ?n, ?n
?a????s? (?) ??t? ap? t? ????a t?? ped????
?p?? ?i , j ?a????s? t?? ????a? ped???? ep?
edaf???? st??µat?? p????? zi (?1?2 .. Hi )
µe ?d??t?te? ?j , ?j
?a??de??µa d?st??t?? s??µat?sµ??
?p?? ?2,2 ?a????s? ep? edaf???? st??µat??
p????? (?1?2 ) µe ?d??t?te? ?2 , ?2 ?1,2
?a????s? ep? edaf???? st??µat?? p????? (?1) µe
?d??t?te? ?2 , ?2 ?1,1 ?a????s? ep? edaf????
st??µat?? p????? (?1 ) µe ?d??t?te? ?1 , ?1
42
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
1a. ????d?? Milovic (1970) ??a e??aµpta ???????
?eµ???a ?a????s? (?) se a?t????? ap?stas? (r)
ap? t? ???t?? e??aµpt?? ???????? ped???? (d??.
?µ???µ??f?? p?es?? ?q), a?t??a? R st??
ep?f??e?a t?? ed?f???. ?? s?µp?est? st??µa ??e?
p???? ? ?a? e?ast???? sta?e??? (?, ?).
?a?at???se?? 1. ? ?a????s? (?a) ??aµpt??
???????? ?eµe????, µp??e? ?a ?p?????s?e? ap? t?
s??s?
?p?? (?c) e??a? ? ?a????s? t?? ???t??? t??
?s?d??aµ??? e??aµpt?? ?eµe????. 2. Se p???st??t?
?daf??, µp??e? ?a ???s?µ?p????e? µ???d??
epa?????a? ?p?? ??a ?????????? p?d??a
(Steinbrenner)
43
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
2. ????d?? Kany (DIN 4019) ??a t?? ?a????s? (?)
??aµpt?? ??????????? ped???? (BxL) se ?daf?? µe
???? Poisson ? ? 0
? ?a????s? e??? ??aµpt?? ??????????? ped????
d?ast?se?? ?xL, ?e??e?ta? ?s? µe t?? ?a????s? t??
?a?a?t???st???? s?µe??? C e??? ?s?d??aµ??
e??aµp?? ped????, ?p?te
?q q qo q ? D
??T?GO???? ??????
Es µ?t?? µ???d??stat?? s?µp?es??
L gt B
?, ? t?µ?? t?? st?a???sµ???? e?ast????
pa?aµ?t??? ?, ?
?
44
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
S?s??t?s? t?? µe??d?? Steinbrenner ?a? Kany ??a
?????????? p?d??a
?f?s?? ? µ???d?? Kany ?p??????e? t?? ?a????s?
e??? ??aµpt?? ped???? µ?s? t?? ?a????s?? t??
?a?a?t???st???? s?µe??? C t?? a?t?st?????
e??aµpt?? ped????, ?? d?? µ???d?? µp????? ?a
s?????????
(4)
(2)
1.1 ????d?? Kany (??a p?d??a st?? ep?f??e?a t??
ed?f???)
(1)
(3)
?fa?µ??? ??a L/?2 ?a? ?/?3 ? f 0.85 ?
1.2 ????d?? Steinbrenner ??a ? 0.30 (?s?d??aµ?
s??s? µ?s? t?? Es ??a p?d??a st?? ep?f??e?a t??
ed?f???)
?a? ??a ?0.30
?p?????sµ?? t?? ?a????s?? t?? s?µe??? C e???
e??aµpt?? ped???? µe L/?2 ?a? ?/?3, ?? ?????sµa
t?? ?a????se?? t?? ????a? t?? tess???? tµ?µ?t??
t?? ped????
45
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
S?s??t?s? t?? µe??d?? Steinbrenner ?a? Kany ??a
?????????? p?d??a
?µ?µa 1 L 0.87 L 1.74 B , B 0.87 B ?
L/B 2 , H/B 3.45 ? F1
0.44, F2 0.075 ? 1.225 F1 0.70 F2 0.592
?µ?µa 2 L 0.87 ? , B 0.13 L 0.26 B ?
L/B 3.35 , H/B 11.5 ? F1 0.68, F2
0.05 ? 1.225 F1 0.70 F2 0.868
?µ?µa 3 L 0.87 L 1.74 B , B 0.13 B
? L/B 13.4 , H/B 23 ? F1 0.76, F2
0.12 ? 1.225 F1 0.70 F2 1.015
?µ?µa 4 L 0.13 L 0.26 B , B 0.13 B ?
L/B 2 , H/B 23 ? F1 0.67, F2 0.03
? 1.225 F1 0.70 F2 0.842
S??ep??
? (q/Es) (0.87 B) x 0.592 (0.26 B) x 0.868
(0.13 B) x 1.015 (0.13 B) x 0.842 ?
??a, s?????s? ??a ? 0.30 Steinbrenner
Kany
??? ?a?? s?s??t?s?
46
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
S?s??t?s? t?? µe??d?? Steinbrenner ?a? Kany ??a
?????????? p?d??a
1.3 ????d?? Steinbrenner ??a ? 0 (?s?d??aµ?
s??s? µ?s? t?? Es ??a p?d??a st?? ep?f??e?a t??
ed?f???)
?a? ??a ? 0
?p?????sµ?? t?? ?a????s?? t?? s?µe??? C e???
e??aµpt?? ped???? µe L2B ?a? ?/?3, ?? ?????sµa
t?? ?a????se?? t?? ????a? t?? tess???? tµ?µ?t??
t?? ped????
?µ?µa 1 L 0.87 L 1.74 B , B 0.87 B ?
L/B 2 , H/B 3.45 ? F1
0.44, F2 0.075 ? F1 F2 0.515
?µ?µa 2 L 0.87 ? , B 0.13 L 0.26 B ?
L/B 3.35 , H/B 11.5 ? F1 0.68, F2
0.05 ? F1 F2 0.73
?µ?µa 3 L 0.87 L 1.74 B , B 0.13 B
? L/B 13.4 , H/B 23 ? F1 0.76, F2
0.12 ? F1 F2 0.88
?µ?µa 4 L 0.13 L 0.26 B , B 0.13 B ?
L/B 2 , H/B 23 ? F1 0.67, F2 0.03
? F1 F2 0.70
47
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
S?s??t?s? t?? µe??d?? Steinbrenner ?a? Kany ??a
?????????? p?d??a
1.3 ????d?? Steinbrenner ??a ? 0 (?s?d??aµ?
s??s? µ?s? t?? Es ??a p?d??a st?? ep?f??e?a t??
ed?f???)
S??ep??
? (q/Es) (0.87 B) x 0.515 (0.26 B) x 0.73
(0.13 B) x 0.88 (0.13 B) x 0.70 ?
??a, s?????s? ??a ? 0 Steinbrenner
Kany
S??ep??, ? µ???d?? Kany d??e? ?a?? p??s????s? t??
?a????s?? ??a f??t???? ?atast?se?? t?? ed?f???
?p?? ? pa?ad??? ? 0 e??a? e?????. ?ed?µ???? ?t?
? 0, ??s?ast??? s?µa??e? µ?de???? p?e?????
pa?aµ??f?s? t?? ed?f???, ? pe??pt?s? a?t? µp??e?
?a ?e????e? ?t? d??e? t?? ?a????s? ????
ste?e?p???se?? t?? ed?f??? ??t? ap? t? p?d???
?p? s?????e? s?µp?es?µ?t???, d??ad? t??
?a????s? (?c1). ? ?a????s? a?t? s??????eta? st?
?ef??a?? pe?? ?a????se?? ep?fa?e?a??? ?eµe???se??
se a??????? ed?f?.
48
?p?????sµ?? ?µes?? ?a????se?? µe s??se??
e?ast???? µ??f??
2. ????d?? Leonhardt (DIN 4019) ??a t?? ?a????s?
(?) ??aµpt?? ???????? ped???? d?aµ?t??? ? 2 R,
se ?daf?? µe ???? Poisson ? ? 0
? ?a????s? e??? ??aµpt?? ???????? ped????
d?aµ?t??? ? 2R, ?e??e?ta? ?s? µe t?? ?a????s?
t?? ?a?a?t???st???? s?µe??? C e??? ?s?d??aµ??
e??aµp?? ped????, ?p?te
0.845R
?q q qo q ? D
??aµpt? p?d???
Es µ?t?? µ???d??stat?? s?µp?es??
rc 0.845 R
?
49
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
3. ????d?? Janbu, Bjerrum Kjaernsli (1959),
?p?? t??p?p??????e ap? t??? Christian Carrier
(1978), ??a t?? ?µes? ?a????s? ??aµpt??
??????????? ?eµe???? d?ast?se?? L x B se
???esµ??a a??????? ed?f? (ast?????st? f??t?s?)
?p?? ?i ?µes? ?a????s? ??aµpt?? ped???? µ?
s??te?est?? ß????? (D) ?eµe???s?? µ1
s??te?est?? p????? (?) s?µp?est?? st??s??
?u µ?t?? e?ast???t?ta? ?p? ast?????ste? s?????e?
B p??t?? ped???? L µ???? ped???? ( L ? B )
?q q qo q ? D
??µ?? t?? µ? ?at? Christian Carrier (1978)
50
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
3. ????d?? Janbu, Bjerrum Kjaernsli ??a t??
?µes? ?a????s? ??aµpt?? ??????????? ?eµe????
d?ast?se?? L x B se ???esµ??a a??????? ed?f?
(ast?????st? f??t?s?)
µ1 s??te?est?? p????? (?) s?µp?est?? st??s??
?q q qo q ? D
?
??µ?? t?? µ1 ?at? Christian Carrier (1978)
51
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
????d?? Butler (1975) ?a????s? ??t? ap? t?
????a e??aµpt?? ??????????? ped???? d?ast?se?? L
x B (LgtB) se ???esµ??a a??????? ed?f?
(ast?????st? f??t?s?) µe ??aµµ??? a??a??µe??
ast?????st? µ?t?? e?ast???t?ta?
?uo ast?????st? µ?t?? e?ast???t?ta? st? st??µ?
?d?as?? t?? ped????
G?aµµ??? a???s? t?? ast?????st?? µ?t???
e?ast???t?ta? µe t? ß???? (z) ?at? t? s??s?
z
?a????s? t?? ????a? t?? ped????
?q q qo q ? D
?? t?µ?? t?? s??te?est? ep?????? fa????ta? sta
ep?µe?a s??µata (??a d??f??e? t?µ?? t?? L / B)
52
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
????d?? Butler (1975) ?a????s? ??t? ap? t?
????a e??aµpt?? ??????????? ped???? d?ast?se?? L
x B (LgtB) se ???esµ??a a??????? ed?f?
(ast?????st? f??t?s?) µe ??aµµ??? a??a??µe??
ast?????st? µ?t?? e?ast???t?ta?
53
?p?????sµ?? ?a????se?? µe s??se?? e?ast????
µ??f??
????d?? Butler (1975) ?a????s? ??t? ap? t?
????a e??aµpt?? ??????????? ped???? d?ast?se?? L
x B (LgtB) se ???esµ??a a??????? ed?f?
(ast?????st? f??t?s?) µe ??aµµ??? a??a??µe??
ast?????st? µ?t?? e?ast???t?ta?
?a?at???s? ?e epa?????a ?????????? (?p?? µe t?
µ???d? Steinbrenner) µp??e? ?a ?p?????s?e? ?
?a????s? ?p????d?p?te s?µe??? e??aµpt??
??????????? ped????
54
?p?????sµ?? ?a????se?? ped???? µe s??se??
e?ast???? µ??f??
S????? µe??d?? ?p?????sµ??
1. ????d?? Steinbrenner ?a? Milovic
?µes? ? s??????? ?a????s? se t???? s?µe??
e??aµpt?? ??????????? / ???????? ped????
?µes? (?i) ?fa?µ??? se ???esµ??e? a??????? µe ?
?u ?a? ? 0.50. S??????? (?) ?fa?µ??? se
?µµ??? (?p? p???p???se??) ?a? a??????? µe ?,
?. ?????ta? ?a? d?????t???? s??te?est?? ??a t??
?a????s? ??aµpt?? ped????
2. ????d?? Kany ?a? Leonhardt
?a????s? ??aµpt?? ??????????? / ???????? ped????
?p? s?????e? ? 0 . ?p??e? ?a ?e????e? ?t?
d??e? t?? ?a????s? t?? ed?f??? ??t? ap? t? p?d???
?p? s?????e? s?µp?es?µ?t???. ?s µ?t??
µ???d??stat?? s?µp?es??.
3. ????d?? Janbu ?a? Butler
?µes? ?a????s? (?p? ast?????ste? s?????e?)
??aµpt?? / e??aµpt?? ??????????? ped???? se
???esµ??a a??????? ed?f? (?u ast?????st? µ?t??
e?ast???t?ta?)
55
???S??? ?p????? t?? e????? t?? f??t???µe???
ep?f??e?a? st? µ??e??? t?? ?a????s?? st??
pe??pt?s? a??µ????e???? ed?f???
?et?ap?as?asµ?? t?? e????? p???a?e? pe??ss?te??
ap? tet?ap?as?asµ? t?? ?a????s??
?pa?????a t?? d?? f??t??? p???a?e? pe??ss?te??
ap? d?p?as?asµ? t?? ?a????s??
56
?a?aµ??f?s?µ?t?ta ??aµpt?? ped???? se e?ast???
?daf?? (?at? API)
??? ??a ??aµpt? ?????????? p?d??? d?ast?se??
?at??e?? (B, Lgt?) f??t?s?e? µe e?tat??? µe????
V, Hx , Hy , Mx , My t? ???t?? t?? ?a
µeta?????e? ?at? ux , uy ?a? uz ?a? t? p?d??? ?a
st?afe? ?at? ?x , ?y .
?e pa?ad??? ?d?as?? t?? ped???? ep? e?ast????
ed?f???, ?? a?t?st???e? d?s?aµ??e? (d??ad? ??
sta?e??? t?? ?s?d??aµ?? e?at????? e??a?
?ata????f? e?at???? (?at? Steinbrenner)
G?a tet?a?????? p?d??? e????? ? st?? ep?f??e?a
(?D1)
??????t?? e?at???? (?at? x ?a? ?at? y)
57
?a?aµ??f?s?µ?t?ta ??aµpt?? ped???? se e?ast???
?daf?? (?at? API)
??? ??a ??aµpt? ?????????? p?d??? d?ast?se??
?at??e?? (B, Lgt?) f??t?s?e? µe e?tat??? µe????
V, Hx , Hy , Mx , My t? ???t?? t?? ?a
µeta?????e? ?at? ux , uy ?a? uz ?a? t? p?d??? ?a
st?afe? ?at? ?x , ?y .
?e pa?ad??? ?d?as?? t?? ped???? ep? e?ast????
ed?f???, ?? a?t?st???e? d?s?aµ??e? (d??ad? ??
sta?e??? t?? ?s?d??aµ?? e?at????? e??a?
St??f??? e?at???? (st??f? pe?? t?? ????a x)
?a? ??a ????d?t? p?d??? p??t??? ?
St??f??? e?at???? (st??f? pe?? t?? ????a y)