?????s? t?? F????sa? ??a??t?ta?

1
????????S ??? ??T?????S T?????OS??S 7? ??.
???-???. ??? - ??ad. ?t?? 2007 - 08
??????? 3 ?????s? t?? F????sa?
??a??t?ta? ?p?fa?e?a??? Teµe???se?? ?at? t??
??????d??a 7
21.11.2007
2
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
2. ????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
???sµ??
???se?? (actions F) F??t?a ?a? ???p??
ep?p???se?? (p.?. ?p?????s? st??????,
?e?µ???as?a?? µetaß???). Ge?te?????? d??se?? (G)
??d??? pe??pt?s? d??se?? p?? p???????ta? ap? t?
?daf?? (p.?. p?es? se t???? ???? ???s??
?a???) ?p?te??sµata t?? d??se?? (action effects
E) S???st?µe?e? d??se?? (p.?. s??????? f??t??
ped????, ???s? ?a??? t?????, ??p? a?at??p??
p?a????) ?a? e?tat??? µe???? (p.?. a??????
d??aµ?, t?µ???sa d??aµ?, ?aµpt??? ??p?) ?daf????
pa??µet??? (X) p.?. ????a t??ß??, s?????,
e?d??? ß????. ??t?st?se?? (Resistances R)
??t?st?se?? sta ap?te??sµata t?? d??se??. p.?.
f????sa ??a??t?ta ped????, a?t??? pass????,
a?t??? t????? se ???s??s?, ??p? st????e?? p?a????.
3
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
2. ????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
???sµ?? (s????e?a)
?a?a?t???st???? t?µ?? d??se?? (Fk) ?a? edaf????
pa?aµ?t??? (Xk) s??t???t???? e?t?µ?se?? t??
t?µ?? t??? (5 p??a??t?ta ?p??ßas??) ?a?a?t???st??
?? t?µ?? ?e?te?????? d??se?? (Gk), ap?te?esµ?t??
d??se?? (Ek) ?a? a?t?st?se?? (Rk) ?p????????ta?
µ?s? t?? ?a?a?t???st???? t?µ?? t?? µe?e??? p??
t?? ep??e????? T?µ?? s?ed?asµ?? d??se?? (Fd)
t?µ?? p?? p????pt??? ap? t?? ?a?a?t???st????
t?µ?? t?? d??se?? (Fk) µe efa?µ??? t??
a?t?st????? ep?µ????? s??te?est?? d??se?? (?F ?
1) ?a? t?? s??te?est?? s??d?asµ?? d??se?? (? ? 1)

T?µ?? s?ed?asµ?? edaf???? pa?aµ?t??? (Xd) t?µ??
p?? p????pt??? ap? t?? ?a?a?t???st???? t?µ??
edaf???? pa?aµ?t??? (Xk) µe efa?µ??? t??
a?t?st????? ep?µ????? s??te?est?? (?? ? 1)
4
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
2. ????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
???sµ?? (s????e?a)
T?µ?? s?ed?asµ?? ?e?te?????? d??se?? (Gd) t?µ??
p?? p????pt??? µe efa?µ??? t?? e?a??a?t????
s??se??
(t?p?? ? )
(t?p?? ?? )
T?µ?? s?ed?asµ?? ap?te?esµ?t?? d??se?? (?d)
t?µ?? p?? p????pt??? µe efa?µ??? t?? e?a??a?t????
s??se??
(t?p?? ? )
(t?p?? ?? )
?p?? ?? ep?µ????? s??te?est?? ap?te?esµ?t??
d??se?? (s?????? ?F)
T?µ?? s?ed?asµ?? a?t?st?se?? (Rd) t?µ?? p??
p????pt??? µe efa?µ??? t?? e?a??a?t???? s??se??
(t?p?? ? )
(t?p?? ?? )
5
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
2. ????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
2.1 ?pa?t??µe??? ??e???? (?e????? Ed ? Rd )
1. ??e???? f????sa? ??a??t?ta?
2. ??e???? ???s??s??
??µ?? s?ed?asµ?? (design values) t?? f??t???
(d??se??) e? t?? a??d?µ??
??µ?? s?ed?asµ?? t?? a?t???? t?? ed?f??? (f????sa
??a??t?ta) ?ata????f? ?a? ??????t?a s???st?sa
??µ? s?ed?asµ?? t?? ???s?? t?? ed?f??? st??
pa?e?? t?? ?eµe???? (?p?te ?p???e?)
6
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
2. ????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
2.2 ?p?????sµ?? d??se?? (µ???d?? 1)
?p??
t?p?? ?
t?p?? ??
?
? s??te?est?? s??d?asµ?? d??se?? (?1) Vk , Hk ,
ck , fk ?a?a?t???st??? t?µ?? t?? a?t?st?????
µe?e??? Gv , Gh ?ata????f? / ??????t?a
s???st?sa ?e?te?????? d??se?? (p?. ???s?
?a???) ?F ep?µ????? s??te?est?? d??se?? ??
ep?µ????? s??te?est?? a?t???? ??????
7
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
2. ????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
2.2 ?p?????sµ?? d??se?? (µ???d?? 2)
t?p?? ?
?p??
? s??te?est?? s??d?asµ?? d??se?? (?1) Vk , Hk ,
ck , fk ?a?a?t???st??? t?µ?? t?? a?t?st?????
µe?e??? Gv , Gh ?ata????f? / ??????t?a
s???st?sa ?e?te?????? d??se?? (p?. ???s?
?a???) ?? ep?µ????? s??te?est?? s???st?µe???
d??s?? (s?????? ?F)
8
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
2. ????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
2.3 ?p?????sµ?? a?t?st?se?? R , ?p?? i p, v
(t?p?? ? )
?
(t?p?? ?? )
? s??te?est?? s??d?asµ?? d??se?? (?1) ck , fk
?a?a?t???st??? t?µ?? t?? edaf???? pa?aµ?t???
a?t???? Fk ?a?a?t???st??? t?µ? d??s?? p??
?pe?s???eta? st?? ?p?????sµ? t?? a?t?stas?? ?F
ep?µ????? s??te?est?? d??se?? ?? ep?µ?????
s??te?est?? a?t???? ?????? ?R ep?µ?????
s??te?est?? a?t?st?se??
9
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
2. ????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
2.4 ?p?????sµ?? ??????t?a? a?t?stas?? Rh,d
2.4.1. ??e???? ?p? st?a???sµ??e? s?????e?
(t?p?? ? )
?
(t?p?? ?? )
2.4.2. ??e???? ?p? ast?????ste? s?????e?
(t?p?? ? )
(t?p?? ?I )
?
?? ep?µ????? s??te?est?? a?t???? ?????? ?R
ep?µ????? s??te?est?? a?t?st?se?? dk ?a?a?t.
t?µ? t?? ????a? t??ß?? st? ß?s? t?? ped????
(t??ß? ped????-ed?f???) dd t?µ? s?ed?asµ?? t??
????a? t??ß?? st? ß?s? t?? ped???? cu,k , cu,d
?a?a?t???st??? t?µ? / t?µ? s?ed?asµ?? t??
ast?????st?? d?atµ?t???? a?t????
a???
10
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
2. ????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
??µ?? t?? ep?µ????? s??te?est?? ?F , ?? , ?R
???p?? ?????s?? S??d?-asµ?? ??p?? ?p?????sµ?? ??µ?? t?? ep?µ????? s??te?est?? (ap? t??? p??a?e? p?? a????????? ?a? pe???aµß????? ta ?i, Mi, Ri)
1 S??d. 1 S??d. 2 ??p?? ?? (?1) (?1) (R1) (?2) (?2) (R1)
2 ??p?? ? (?1) (?1) (R2)
3 ??p?? ?I (?1) ? (?2) (?2) (R3)
G?a t?? ?p?????sµ? t?? d??se?? µp??e? ?a
efa?µ?s???? ?a? ?? t?p?? ? G?a d??se?? ap?
t?? a??d?µ? (d?µ?stat???? d??se??) G?a
?e?te?????? d??se?? (ap? t? ?daf??, p.?. ???se??
?a???)

• ?a?at???se??
• ? ep????? e??? e? t?? t???? ???p?? ?????s??
  ???eta? se ?????? ep?ped?
• St?? ???p? ?????s?? 1, efa?µ??eta? ?
  d?sµe??ste??? t?? S??d?asµ?? 1 2

11
????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
?p?µ????? s??te?est?? d??se?? (?F ?a? ??)
?p?µ????? s??te?est?? edaf???? ?????? (??)
12
????d?? t?? ep?µ????? s??te?est?? (partial
factors) ?at? t?? ??????d??a 7
?p?µ????? s??te?est?? a?t?st?se?? (?R) ??a
ep?fa?e?a??? ?eµe???se?? ??e???? ??a?t? f????sa?
??a??t?ta? ?a? ???s??s??
13
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
?a??de??µa efa?µ????

• ???sd????sµ?? t?? µ???st?? d??at?? f??t???
  ????d?t?? ped???? p?? ??e? ta e??? ?a?a?t???st???
  
• ???t?? ?2.5m, ????? D1.5m, ep?f??t?s? q0
  (d?sµe??? pa?ad???)
• F??t?? ?ata????f? ? 0, µ?de???? e??e?t??t?ta
  (e0), ??????t?a ß?s? (a0).
• ?daf?? µe ?a?a?t???st???? ?d??t?te? ?k 20
  kN/m3, ck 10 kPa, fk25o
• ???? ?daf?? (?d??f???? ??????ta? se µe???? ß????)

14
?a??de??µa efa?µ????
1. ?p???s? µe t? µ???d? t?? s???????? s??te?est?
asfa?e?a? (µe FS3)
????d?? ?p?????sµ?? t?? pu ?at? t?? ??????d??a 7
/ DIN 4017
G?a e0 ? B B 2.5m G?a f25? ? ?c 20.72 ,
Nq 10.66 , N? 9.01 G?a a0 ? bc bq b? 1
G?a ????d?t? p?d??? (?/L0) ? sc sq s?
1 G?a ?0 ? ic iq i? 1
??a
pu 10 x 20.72 20 x 1.5 x 10.66 0.5 x 20 x
2.5 x 9.01 752.2 kPa
F????sa ??a??t?ta ped???? Pu pu B 752.2 x
2.5 1880.5 kN/m ? Pu 1880.5 kN/m ????st?
ep?t?ep?µe?? f??t?? ped???? (FS3) Vmax Pu /
FS 1880.5 / 3 ? Vmax 627 kN/m
15
?a??de??µa efa?µ???? (s????e?a)
2. ?p???s? µe t? µ???d? t?? ep?µ????? s??te?est??
(??????d??a? 7)
S??t???t??? a???e?ta? ? pa??t??? a?t?stas? st??
pa?e?? t?? ped???? Rp,d 0 Te??e?ta? ?t? t?
f??t?? t?? ped???? e??a? µ???µ? (permanent) ?a?
d?sµe??? (unfavourable)
2.1.1 ???p?? ?????s?? 1 / S??d?asµ?? 1
A1 ? ?F 1.35 (µ???µ? - d?sµe??? d??s? st?
p?d???) ?1 ? ?? 1.00 (??a t? f ?a? c) R1 ? ?R
1.00
?p?????sµ?? f????sa? ??a??t?ta? pu ap?
Fk 0 (? f????sa ??a??t?ta de? e?a?t?ta? ap? t??
d??se?? ??? ???? f??t?s?)
? 1 (µ???? µ???µe? d??se??)
S??ep??, ?p?????sµ?? t?? f????sa? ??a??t?ta? ??a
fdfk25?, cdck10 kPa
?p?te (?? a??t???) pu,d pu,k 752.2 kPa
??a Rv,d pu,d B 752.2 x 2.5 ? Rv,d
1880.5 kN/m
16
?a??de??µa efa?µ???? (s????e?a)
2. ?p???s? µe t? µ???d? t?? ep?µ????? s??te?est??
(??????d??a? 7)
2.1.2. ???p?? ?????s?? 1 / S??d?asµ?? 2
A2 ? ?F 1.0 (µ???µ? - d?sµe??? d??s? st?
p?d???) ?2 ? ?? 1.25 (??a t? f ?a? c) R1 ? ?R
1.00
?p?????sµ?? f????sa? ??a??t?ta? pu ap?
Fk 0 (? f????sa ??a??t?ta de? e?a?t?ta? ap?
d??se?? ??? ???? f??t?s?)
? 1 (µ???? µ???µe? d??se??)
S??ep??, ?p?????sµ?? t?? f????sa? ??a??t?ta? ??a
fd arctan (tanfk/?M) arctan (tan25?/1.25)
20.5o cd ck / ?M 10 / 1.25 8 kPa
G?a f20.5? ? ?c 15.30 , Nq 6 , N? 4.35
??a
pu,d 8 x 15.30 20 x 1.5 x 6.75 0.5 x 20 x
2.5 x 4.35 433.6 kPa
??a Rv,d pu,d B 433.6 x 2.5 1084 kN/m ?
Rv,d 1084 kN/m
17
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
?a??de??µa efa?µ???? (s????e?a)
2. ?p???s? µe t? µ???d? t?? ep?µ????? s??te?est??
(??????d??a? 7)
2.1.2. ???p?? ?????s?? 1 (s????e?a)
??µ? s?ed?asµ?? t?? ???a??? a?t???? (a?t?stas??)
t?? ped???? ( Rv,d ) Rv,d min (s??d?asµ?? 1
2) min (1880.5, 1084) ? Rv,d 1084 kN/m
?s?d??aµ? ?a?a?t???st??? t?µ? (Vk) t?? f??t???
t?? ped????, ?e????ta? ??a µ?s? ep?µ?????
s??te?est? d??se?? a??d?µ?? ?F1.40
Vk ? Rv,d / ?F min 1880.5 / 1.40 , 1084 /
1.0 ? Vk 1084 kN/m
18
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
?a??de??µa efa?µ???? (s????e?a)
?p???s? µe t? µ???d? t?? ep?µ????? s??te?est??
(??????d??a? 7)
2.2. ???p?? ?????s?? 2
A1 ? ?F 1.35 (µ???µ? - d?sµe??? d??s? st?
p?d???) ?1 ? ?? 1.00 (??a t? f ?a? c)
R2 ? ?R 1.40
?p?????sµ?? f????sa? ??a??t?ta? pu ap?
Fk 0 (? f????sa ??a??t?ta de? e?a?t?ta? ap?
d??se?? ??? ???? f??t?s?)
? 1 (µ???? µ???µe? d??se??)
S??ep??, ?p?????sµ?? t?? f????sa? ??a??t?ta? ??a
fdfk25?, cdck10 kPa
?p?te (?? a??t???) pu,d 752.2 / ?R 752.2 /
1.40 537.3 kPa
??a Rv,d pu,d B 537.3 x 2.5 1343.2 kN/m
? Rv,d 1343 kN/m
?s?d??aµ? ?a?a?t???st??? t?µ? (Vk) t?? f??t???
t?? ped????, ?e????ta? ??a µ?s? ep?µ?????
s??te?est? d??se?? a??d?µ?? ?F1.40
Vk ? Rv,d / ?F 1343 / 1.40 ? Vk 960 kN/m
19
?a??de??µa efa?µ???? (s????e?a)
?p???s? µe t? µ???d? t?? ep?µ????? s??te?est??
(??????d??a? 7)
2.3. ???p?? ?????s?? 3
A1 ? ?F 1.35 (µ???µ? d?sµe??? d?µ?stat???
d??s? st? p?d???) ?2 ? ?? 1.25 (??a t? f ?a? c)
, R3 ? ?R 1.00
?p?????sµ?? f????sa? ??a??t?ta? pu ap?
Fk 0 (? f????sa ??a??t?ta de? e?a?t?ta? ap?
d??se?? ??? ???? f??t?s?)
? 1 (µ???? µ???µe? d??se??)
S??ep??, ?p?????sµ?? t?? f????sa? ??a??t?ta? ??a
fd arctan (tanfk/?M) arctan (tan25?/1.25)
20.5o cd ck / ?M 10 / 1.25 8 kPa
G?a f20.5? ? ?c 15.30 , Nq 6 , N? 4.35
??a
pu,d 8 x 15.30 20 x 1.5 x 6.75 0.5 x 20 x
2.5 x 4.35 433.6 kPa
??a Rv,d pu,d B 433.6 x 2.5 1084 kN/m ?
Rv,d 1084 kN/m
?s?d??aµ? ?a?a?t???st??? t?µ? (Vk) t?? f??t???
t?? ped????, ?e????ta? ??a µ?s? ep?µ?????
s??te?est? d??se?? a??d?µ?? ?F1.40
Vk ? Rv,d / ?F 1084 / 1.40 ? Vk 774 kN/m
20
??e???? ep???e?a? ep?fa?e?a??? ?eµe???se?? ??a?t?
?p??ßas?? t?? F????sa? ??a??t?ta?
?a??de??µa efa?µ???? (s????e?a)
S?????s? t?? t???? ???p?? ?????s?? t?? ??????d??a
7 (EC-7) ?a? t?? µe??d?? t?? s???????? s??te?est?
asfa?e?a?
???p?? ?????s?? ??µ? s?ed?asµ?? t?? ???a??? a?t?stas?? (Rv,d) ?a?a?t???st??? t?µ? (Vk) t?? f??t??? t?? ped???? Vk ? Rv,d / 1.40
???p?? ?????s?? 1 1084 kN/m 1084 kN/m
???p?? ?????s?? 2 1343 kN/m 960 kN/m
???p?? ?????s?? 3 1084 kN/m 774 kN/m
????d?? s???????? s??t. asfa?e?a? (FS3) - 1881 / 3 627 kN/m
?e????ta? ??a µ?s? ep?µ????? s??te?est?
d??se?? a??d?µ?? ?F1.40 ?e????ta? t?
ep?t?ep?µe?? f??t?? ?? ?a?a?t???st??? t?µ? t??
f??t???
S?µp??asµa ? ???p?? ?????s?? 1 d??e? t??
o????te?? s??t???t??? t?µ? ???? ??
???p?? t?? EC-7 d????? µe?a??te?a f??t?a ap? t??
µ???d? FS. ???s??? ?????????? ??? ???G??S
???????O? ??T???S?O?