Geometrie
Lasten
a!"r!n#
ien G+1
Gleiten G+2
Gr!n#br!&h G+2 mit G#,in
Gr!n#br!&h G+2 mit G#,s!b
ma4. ie"emoment bs&h6t!n" rmier!n" bs&h6t!n" 8!r&hstan9i#erstan# ;et!n" (bs&h6t!n")
l [m] b [m] h [m] n,b [m] n,l [m] t [m] Nser(G) [kN] Nser(Q) [kN] Hser(G) [kN] Hser(Q) [kN] Mser(G) [kNm] Mser(Q) [kNm] gk [kN$m3] jk' [%] &k' [kN$m2] N,# [kN] M,# [kNm] e# [m] e"r [m] r [-] N,# [kN] /,# [kN] b' [m] /,# [kN] r [-] N,# [kN] /,# [kN] b' [m] s [kN$m2] N,# [kN] r [-] N,# [kN] /,# [kN] b' [m] s [kN$m2] N,# [kN] r [-] m# [kNm$m] s,er [mm2$m'] d (t=15) [mm] t&# [N$mm2] :,# [kN] r [-] <,=orbelast!n" [kN$m2] s [mm]
i"en"e9i&ht >!n#ament G,ser g# a!"r!n# jk' emess!n"s9erte j'# j'# &'# dk /ra"6hi"keit N< na&h /hera"i N& Ng s&
[kN] [kN$m3] [ra#] [%] [ra#] [kN$m2] [%] [?] [?] [?] [?]
Typ 1 2 2 0.3 0.15 0.15 0 125 75 20 10 0 55 20 35 0 252 -3 0.33 0.7 2.04 237 31 1.30 13-.0 4.45 23 237 31 1.30 1 10 3 1.54 32 322 2 1. 1 10 17 1.30 0 9 1 30 305 0.95 20 7
Typ 2 2 2 0.3 0.15 0.15 0 125 75 20 10 0 55 20 35 0 252 -3 0.33 0.7 2.04 237 31 1.30 13-.0 4.45 237 31 1.30 10 3 1.54 322 2 1. 10 17 1.30 0 9 1 305 0.95 20 7
Typ 3 2 2 0.3 0.15 0.15 0 125 75 20 10 0 55 20 35 0 252 -3 0.33 0.7 2.04 237 31 1.30 13-.0 4.45 237 31 1.30 10 3 1.54 322 2 1. 10 17 1.30 0 9 1 305 0.95 20 7
Typ 4 2 2 0.3 0.15 0.15 0 125 75 20 10 0 55 20 35 0 252 -3 0.33 0.7 2.04 237 31 1.30 13-.0 4.45 237 31 1.30 10 3 1.54 322 2 1. 10 17 1.30 0 9 1 305 0.95 20 7
30 20 0.1 30 3 0.2 0. 0.53 0 30 3 0.2 1-. 30.711 -.- 1.2
30 20 0.1 30.2 0.53 0 30.2 1-. 30.71-.- 1.2
30 20 0.1 30.2 0.53 0 30.2 1-. 30.71-.- 1.2
30 20 0.1 30.2 0.53 0 30.2 1-. 30.71-.- 1.2
8!r&hstanen ;et!n"
s< sg #& #< #g i& (G#,in) i< (G#,in) ig (G#,in) i& (G#,s!) i< (G#,s!) ig (G#,s!) r@ kr b' ser=i&e ??A b ??A a <,tot <,9ie#er <,ne!
[?] [?] [?] [?] [?] [?] [?] [?] [?] [?] [?] [m] [?] [m] [m] [m] [kN$m2] [kN$m2] [kN$m2]
1.50.0 1.00 1.00 1.00 0.70 0.71 0.2 0.70 0.71 0.2 1.07 0.71 1.5 1.5 2 20
1.50.0 1.00 1.00 1.00 0.70 0.71 0.2 0.70 0.71 0.2 1.07 0.71 1.5 1.5 2 20
1.50.0 1.00 1.00 1.00 0.70 0.71 0.2 0.70 0.71 0.2 1.07 0.71 1.5 1.5 2 20
1.50.0 1.00 1.00 1.00 0.70 0.71 0.2 0.70 0.71 0.2 1.07 0.71 1.5 1.5 2 20
Typ 5 2 2 0.3 0.15 0.15 0 125 75 20 10 0 55 20 35 0 252 -3 0.33 0.7 2.04 237 31 1.30 13-.0 4.45 237 31 1.30 10 3 1.54 322 2 1. 10 17 1.30 0 9 1 305 0.95 20 7 30 20 0.1 30.2 0.53 0 30.2 1-. 30.71-.- 1.2
Mser b
n,b Hser
l
n,l
Nser Mser
t h Hser l
8as ie"emoment 9irkt in einer Ha!tri&ht!n" #es >!n#amentes 8ie r#Bber#e&k!n" t #es >!n#amentes ist konser=ati= ein!seten, #a sonst #er Ci#erstan# beB"li&h Gr!n#br!&h Bbers&h6tt 9ir#.
1.50.0 1.00 1.00 1.00 0.70 0.71 0.2 0.70 0.71 0.2 1.07 0.71 1.5 1.5 2 20
P1 ;@stem
[m] 0.0 0.5 1.0 1.5 2.0 3.0 .0 5.0 .0 7.0 -.0 .0 10.0 12.5 15.0 20.0 25.0 35.0 50.0 100.0
Cie#er? Ne!? belast!n" belast!n" Me' () [GN$m2] 150 200 250 275 300 325 350 375 00 150 150 150 150 150 ,000 ,000 ,000 ,000 ,000 ,000
Cie#er? Ne!? belast!n" belast!n" 20 49 [kN$m2] ???A Me () D2 (a,b,) #s' #s [GN$m2] [E] [mm] [mm] 0 1,000 0 -0.1 0. 0 0.0 0.3 0 557 0.0 0.3 0 70 0.0 0.2 15 32 0.0 0.5 15 2- 0.0 1.1 15 23 0.0 0. 15 11 0.0 0.7 15 150.0 0. 15 131 0.0 0.5 0 111 0.0 0.2 0 0.0 0.1 0 5 0.0 0.2 0 7 0.0 0.1 0 20.0 0.2 0 10.0 0.1 200 10 0.0 0.1 200 5 0.0 0.0 200 1 0.0 0.0 0.3 6.3
P2 ;@stem
[m] 0.0 0.5 1.0 1.5 2.0 3.0 .0 5.0 .0 7.0 -.0 .0 10.0 12.5 15.0 20.0 25.0 35.0 50.0 100.0
Cie#er? Ne!? belast!n" belast!n" Me' () [GN$m2] 150 200 250 275 300 325 350 375 00 150 150 150 150 150 ,000 ,000 ,000 ,000 ,000 ,000
Cie#er? belast!n" 20 [kN$m2] ???A Me () D2 (a,b,) #s' [GN$m2] [E] [mm] 0 1,000 0 -0.1 0 0.0 0 557 0.0 0 70 0.0 15 32 0.0 15 2- 0.0 15 23 0.0 15 11 0.0 15 150.0 15 131 0.0 0 111 0.0 0 0.0 0 5 0.0 0 7 0.0 0 20.0 0 10.0 200 10 0.0 200 5 0.0 200 1 0.0 0.3
P3 Ne!? belast!n" 49 #s [mm] 0. 0.3 0.3 0.2 0.5 1.1 0. 0.7 0. 0.5 0.2 0.1 0.2 0.1 0.2 0.1 0.1 0.0 0.0 6.3
;@stem
[m] 0.0 0.5 1.0 1.5 2.0 3.0 .0 5.0 .0 7.0 -.0 .0 10.0 12.5 15.0 20.0 25.0 35.0 50.0 100.0
Cie#er? Ne!? belast!n" belast!n" Me' () [GN$m2] 150 200 250 275 300 325 350 375 00 150 150 150 150 150 ,000 ,000 ,000 ,000 ,000 ,000
Cie#er? Ne!? belast!n" belast!n" 20 49 [kN$m2] ???A Me () D2 (a,b,) #s' #s [GN$m2] [E] [mm] [mm] 0 1,000 0 -0.1 0. 0 0.0 0.3 0 557 0.0 0.3 0 70 0.0 0.2 15 32 0.0 0.5 15 2- 0.0 1.1 15 23 0.0 0. 15 11 0.0 0.7 15 150.0 0. 15 131 0.0 0.5 0 111 0.0 0.2 0 0.0 0.1 0 5 0.0 0.2 0 7 0.0 0.1 0 20.0 0.2 0 10.0 0.1 200 10 0.0 0.1 200 5 0.0 0.0 200 1 0.0 0.0 0.3 6.3
P4 ;@stem
[m] 0.0 0.5 1.0 1.5 2.0 3.0 .0 5.0 .0 7.0 -.0 .0 10.0 12.5 15.0 20.0 25.0 35.0 50.0 100.0
Cie#er? Ne!? belast!n" belast!n" Ge' () [GN$m2] 150 200 250 275 300 325 350 375 00 150 150 150 150 150 ,000 ,000 ,000 ,000 ,000 ,000
[kN$m2] ???A Me' () Me () [GN$m2] [E] 0 1,000 0 -0 0 557 0 70 15 32 15 2- 15 23 15 11 15 1515 131 0 111 0 0 5 0 7 0 20 1200 10 200 5 200 1
0 Cie#er? Ne!? belast!n" belast!n" 20 49 #s' #s [mm] [mm] 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.3
0. 0.3 0.3 0.2 0.5 1.1 0. 0.7 0. 0.5 0.2 0.1 0.2 0.1 0.2 0.1 0.1 0.0 0.0 6.3
;@stem
[m] 0.0 0.5 1.0 1.5 2.0 3.0 .0 5.0 .0 7.0 -.0 .0 10.0 12.5 15.0 20.0 25.0 35.0 50.0 100.0
Cie#er? Ne!? belast!n" belast!n" Me' () [GN$m2] 150 200 250 275 300 325 350 375 00 150 150 150 150 150 ,000 ,000 ,000 ,000 ,000 ,000
Cie#er? Ne!? belast!n" belast!n" 20 49 [kN$m2] ???A Me () D2 (a,b,) #s' #s [GN$m2] [E] [mm] [mm] 0 1,000 0 -0.1 0. 0 0.0 0.3 0 557 0.0 0.3 0 70 0.0 0.2 15 32 0.0 0.5 15 2- 0.0 1.1 15 23 0.0 0. 15 11 0.0 0.7 15 150.0 0. 15 131 0.0 0.5 0 111 0.0 0.2 0 0.0 0.1 0 5 0.0 0.2 0 7 0.0 0.1 0 20.0 0.2 0 10.0 0.1 200 10 0.0 0.1 200 5 0.0 0.0 200 1 0.0 0.0 0.3 6.3
a$bF $bF 0.0 0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 4.0 5.0 7.0 10.0 20.0
1.0 1,000 - 557 70 32 2- 23 11 15 131 111 5 7 21 10 5 1
1.5 1,000 2757 1 52 12 33 27 235 1 1 15 125 0 7 0 27 1 7 2
2.0 1,000 37 7-3 571 37 3021 22 1 1 110-2 51 3 1 2
3.0 1,000 3 -13 705 22 500 13 327 257 22 17 175 133 10 7 2 1
5.0 1,000 -2 730 0 553 3 33 221 231 20 15 12-5 321
10 1,000 5 -2 7375 5-5 513 50 3 350 311 277 2 15 15111 - 5 33 11
20 1,000 5 -2 73 77 50 523 5 1 37 3330 27 225 1- 13 103 7 3 1
100 1,000 5 -2 73 77 50 52 7 1 373 31 2-23202 155 125 - 1 2-
1,000,000 1,000 1,000 5 -2 73 77 50 52 7 1 373 31 2-23202 155 125 - 1
Geometrie
Lasten
a!"r!n#
ien G+1
Gleiten G+2
Gr!n#br!&h G+2 mit G#,in
Gr!n#br!&h G+2 mit G#,s!b
ma4. ie"emoment bs&h6t!n" rmier!n" bs&h6t!n" 8!r&hstan9i#erstan# ;et!n" (bs&h6t!n")
l b h n,l n,b t Nser(G) Nser(Q) Hser(G) Hser(Q) Mser(G) Mser(Q) gk jk' &k' N,# M,# e# e"r r N,# /,# b' /,# r N,# /,# b' s N,# r N,# /,# b' s N,# r m# s,er d (t=15) t&# :,# r <,=orbelast!n" s
i"en"e9i&ht >!n#ament G,ser g# a!"r!n# jk' emess!n"s9erte j'# j'# &'# dk /ra"6hi"keit N< na&h /hera"i N& Ng s&
[m] >!n#amentl6n"e F bmess!n", #ie #as Moment a!ni [m] >!n#amentbreite [m] >!n#ament#i&ke [m] ;tBtenabmess!n" in i&ht!n" l [m] ;tBtenabmess!n" in i&ht!n" b [m] ;t6n#i"e r#Bber#e&k!n" #es >!n#amentes ??A 9ir# b [kN] Nomralkrat inol"e st6n#i"er Lasten a! ;er=i&e?Ni=ea [kN] Normalkrat inol"e =er6n#erli&hen Lasten a! ;er=i&e? [kN] Horiontalkrat inol"e st6n#i"er Lasten a! ;er=i&e?Ni= [kN] Horiontalkrat inol"e =er6n#erli&hen Lasten a! ;er=i& [kNm] Moment inol"e st6n#i"er Lasten a! ;er=i&e?Ni=ea! [kNm] Moment inol"e =er6n#erli&hen Lasten a! ;er=i&e?Ni=e [kN$m3] &harakteristis&her Cert #es a!m"e9i&htes #es o#en [%] &harakteristis&her Cert #es Cinkels #er inneren eib!n [kN$m2] &harakteristis&her Cert #er #rainierten oh6sion [kN] ;!mme #er Normalkr6te a! 8esi"n Ni=ea! (Nser(G)0 [kNm] ;!mme #er Momente a! 8esi"n Ni=ea! (Mser(G)0. [m] 4entriit6t beo"en a! #en >!n#amentmittel!nkt in [m] !l6ssi"e ma4imale 4entriit6t (e"r F 1$3b) [-] eser=e beB"li&h ien (r F e"r$e#) [kN] ;!mme #er Normalkr6te a! 8esi"n Ni=ea! (Nser(G)0 [kN] ;!mme #er Horiontalkr6te a! 8esi"n Ni=ea! (Ftreibe [m] 9irksame >!n#amentbreite bere&hnet mit #en Lasten a [kN] Ci#erstan# "e"en Gleiten [-] eser=e beB"li&h Gleiten (r F /,# $ /,#) [kN] ;!mme #er Normalkr6te a! 8esi"n Ni=ea! (Nser(G)0 [kN] ;!mme #er Horiontalkr6te a! 8esi"n Ni=ea! (Nser(G [m] 9irksame >!n#amentbreite bere&hnet mit #en Lasten a [kN$m2] !l6ssi"e o#enress!n" a! 8esi"n Ni=ea! bere&hnet [kN] Ci#erstan# "e"en Gr!n#br!&h [-] eser=e beB"li&h Gr!n#br!&h (r F N,# $ N,#) [kN] ;!mme #er Normalkr6te a! 8esi"n Ni=ea! (Nser(G)1 [kN] ;!mme #er Horiontalkr6te a! 8esi"n Ni=ea! (Nser(G [m] 9irksame >!n#amentbreite bere&hnet mit #en Lasten a [kN$m2] !l6ssi"e o#enress!n" a! 8esi"n Ni=ea! bere&hnet [kN] Ci#erstan# "e"en Gr!n#br!&h [-] eser=e beB"li&h Gr!n#br!&h (r F N,# $ N,#) [kNm$m] ma4imales i"emoment im >!n#ament bere&hnet mit # [mm2$m'] bs&h6t!n" #er eror#erli&hen rmier!n" mit (Hebel [mm] eror#erli&her rmier!n"s#!r&hmesser bei einem bsta [N$mm2] emess!n"s9ert #er ;&h!bsann!n"s"rene [kN] 8!r&hstan9i#erstan# [-] eser=e beB"li&h 8!r&hstan9i#erstan# [kN$m2] :orbelast!n" #es a!"r!n#es a! #em Ni=ea! #er >!n [mm] ;et!n" #es kennei&hnen#en I!nktes #es >!n#amen [kN] i"en"e9i&ht #es >!n#amentes [kN$m3] emess!n"s9ert #er a!mlast #es o#ens mit gg F 1.0 [ra#] Jharakteristis&her Cert #es Cinkels #er inneren eib! [%] emess!n"s9ert #es Cinkels #er inneren eib!n" mit [ra#] emess!n"s9ert #es Cinkels #er inneren eib!n" im [kN$m2] emess!n"s9ert #er #rainierten oh6sion mit g& F 1.5 [%] Jharakteristis&her Cert #es ;ohlreib!n"s9inkels [?] /ra"6hi"keitsaktor Br #ie /ra"6hi"keitsormel na&h / [?] /ra"6hi"keitsaktor Br #ie /ra"6hi"keitsormel na&h / [?] /ra"6hi"keitsaktor Br #ie /ra"6hi"keitsormel na&h / [?] >ormaktor Br #ie /ra"6hi"keitsormel na&h /era"hi
8!r&hstanen ;et!n"
s< sg #& #< #g i& (G#,in) i< (G#,in) ig (G#,in) i& (G#,s!) i< (G#,s!) ig (G#,s!) r@ kr b' ser=i&e ??A b ??A a <,tot <,9ie#er <,ne!
[?] [?] [?] [?] [?] [?] [?] [?] [?] [?] [?] [m] [?] [m] [m] [m] [kN$m2] [kN$m2] [kN$m2]
>ormaktor Br #ie /ra"6hi"keitsormel na&h /era"hi >ormaktor Br #ie /ra"6hi"keitsormel na&h /era"hi /ieenaktor Br #ie /ra"6hi"keitsormel na&h /era"hi /ieenaktor Br #ie /ra"6hi"keitsormel na&h /era"hi /ieenaktor Br #ie /ra"6hi"keitsormel na&h /era"hi Lastnei"!n"saktor Br #ie /ra"6hi"keitsormel na&h /e Lastnei"!n"saktor Br #ie /ra"6hi"keitsormel na&h /e Lastnei"!n"saktor Br #ie /ra"6hi"keitsormel na&h /e Lastnei"!n"saktor Br #ie /ra"6hi"keitsormel na&h /e Lastnei"!n"saktor Br #ie /ra"6hi"keitsormel na&h /e Lastnei"!n"saktor Br #ie /ra"6hi"keitsormel na&h /e ei9ert !r ere&hn!n" #es 8!r&hstan9i#erstan#es ei9ert !r ere&hn!n" #es 8!r&hstan9i#erstan#es 9irksame >!n#amentbreite ermittelt mit #en ;er=i&e La >!n#amentbreite als in"abe9ert Br #ie ;et!n"sbere >!n#amentl6n"e als in"abe9ert Br #ie ;et!n"sbere ;ohlress!n" =eo"en a! b !n# a Cie#erbelast!n"santeil #er ;ohlress!n" Ne!belast!n"santeil #er ;ohlress!n"
mt
i #er rmittl!n" #es Gr!n#br!&h9i#erstan#es berB&ksi&hti"t
i=ea! a! e?Ni=ea!
a! s "
.Nser(Q)1.5) Mser(Q)1.5) i&ht!n" b (e# F M,# $ N,#)
.-Nser(Q)1.5) n#e r6te) (Nser(G)0.-Nser(Q)1.5) 8esi"n Ni=ea! !n# #en Br #ie rmittl!n" #er Normalkr6te =er9en#eten Lastaktoren
.-Nser(Q)1.5) )0.-Nser(Q)1.5) 8esi"n Ni=ea! !n# #en Br #ie rmittl!n" #er Normalkr6te =er9en#eten Lastaktoren mit #er /ra"6hi"keitsormel na&h /era"hi (="l. Lan"$H!#er)
.35Nser(Q)1.5) )1.35Nser(Q)1.5) 8esi"n Ni=ea! !n# #en Br #ie rmittl!n" #er Normalkr6te =er9en#eten Lastaktoren mit #er /ra"6hi"keitsormel na&h /era"hi (="l. Lan"$H!#er)
en Certen a!s +eilen 33 ? 35 rm #er inneren r6te) F 0.- h !n# ;tahl 500 # #er rmier!n"seisen =on 15 &m
amentsohle es bere&hnet mit #er mit9irken#en >!n#amentbreite !n# #er si&h #ara!s er"eben#en "lei&hm6ssi"en ;ohlsan
" im o"enmass gj F 1.2 o"enmass
rha"i rha"i rha"i
ra"hi ra"hi ra"hi ra"hi ra"hi ra"hi
ten hn!n" (es 9ir# #er kleinere Cert =on b' !n# a =er9en#et) hn!n" (es 9ir# #er "rKssere Cert =on b' !n# a =er9en#et)
n!n"
