Završni rad Metalne konstrukcije.doc

8/17/2019 Završni rad Metalne konstrukcije.doc

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GRAĐEVINSKI FAKULTETSVEUČILIŠTE J.J. STROSSMAYERA U OSIJEKU

ZAVRŠNI RADIZ METALNIH KONSTRUKCIJA

PRORAČUN CARINSKOG TERMINALA

U Osije!" #$.$%.&$$'.

J(si) U*+,

-,.i/es+0 &1#1

1



SADRŽAJ:

1. TEHNIČKI OPIS

2. DISPOZICIJA

3. KROVIŠTE

3.1. ANALIZA OPTEREĆENJA KROVIŠTA

4. PRORAČUN PODROŽNICE:

4.1. ANALIZA OPTEREĆENJA PODROŽNICE

4.2. KOMBINACIJE OPTEREĆENJA ZA PODROŽNICU 4.3. DIMENZIONIRANJE PODROŽNICE

5. PRORAČUN REDNO NOSAČA I KONZOLNO NOSAČA:

!.1. ANALIZA OPTEREĆENJA REDNO NOSAČA!.2. KOMBINACIJE OPTEREĆENJA ZA REDNI NOSAČ"

KONZOLNI NOSAČ I STUP !.3. DIMENZIONIRANJE REDNO NOSAČA!.4. DIMENZIONIRANJE REDE S OJAČANJIMA #$VUTAMA%&!.!. ANALIZA OPTEREĆENJA KONZOLNO NOSAČA

!.'. DIMENZIONIRANJE KONZOLNO NOSAČA

'. PRORAČUN STUPA

'.1. ANALIZA OKVIRA'.2. DIMENZIONIRANJE STUPA

(. PRORAČUN SPREA

(.1. ANALIZA OPTEREĆENJA SPREA(.2. DIMENZIONIRANJE SPREA

). PRORAČUN SPOJA STUP * TEMELJ SAMAC PREKO ANKERNE PLOČE

+. PRILOZI

2



#.Te2i3i ()is

Na lokaciji Slavonski Brod izvest će se carinski terminal sa svom pripadajućom opremom. Konstrukcija je poprečnog raspona 12,00 metara sa po2,00 metara konzolnog prepusta sa svake strane, dok je poduni rasponkonstrukcije tako!er 12,00 metara sa po 1 metar prepusta za stre"u.Konstrukciju čini okvirni sustav sa # okvira koji se sastoji od glavnog nosača

pro$ila %&' ##0 ojačani" (vutama) na svojim krajevima, konzolnog nosača pro$ila %&' 220 i stupovi pro$ila *'+ 20. - svr"u ukrućenja u podunomsmjeru izvodi se prečka %&' 20, dok se za ukrutu protiv djelovanja"orizontalni" sila koriste K spregovi. Sekundarni nosači se pro$ila %&' 200, anji"ova sta/ilnost na /očno izvijanje ostvarena je primjenom pridranaj u o/liku

spregova i zatega koje se sastoje od čelični" sajli ∅1.

+naliza opterećenja je u potpunosti izvedena prema ' 1 normi.imenzioniranje i proračun otpornosti poprečni" presjeka i elemenata suizvedeni prema ' # propisima.

3a numeričko modeliranje u svr"u proračuna rezni" sila na statičkom

sustavu kori4ten je programski paket 5adimpe6 7o8er 9.9.

Kori4teni materijal je čelik klase S 2#9 :;e #0< s granicom popu4tanja od2#9 N=mm2, vlačnom čvrstoćom od #0 N=mm2 i modulom elastičnosti od210.000,00 N=mm2. Svi presjeci kori4teni u konstruktivnom o/likovanjunastre4nice terminala su valjani % i * pro$ili.

&redvi!eno je projektiranje spoja stup temeljna stopa. Spoj je izvedenzavarivanjem stupa za ankernu ploču. +nkerna ploča učvr4ćena je u stopumodanikom pro$ila %&' 100 i konstruktivno usvojenim vijecima 2 6 > 20.Svi varovi su de/ljine # mm.

&. Dis)(4i5ij+

#



%. K,(6i78e

%.#. A+9i4+ ()8e,e:ej+ ,(6i78+

? S7+@NA A&7'5''NC'

&okrov DDDDDDDDDDDDDDDDDDDDDDDDDD0,10 KN=m2

%nstalacije DDDDDDDDDDDDDDDDDDDDDDDD.. 0,09 KN=m2

E F 0,19 KN=m2

? SN%C'E

Snijeg DDDDDDDDDDDDDDDDDDDDDDDDDD 1,29 KN=m2

S F 1,29 KN=m2

? GC'7+5

He F I re$ e:3e< cpe

v re$ F 22 m=s +@7 F 2 m=s

+@7 F 1 J 0,001 as

I re$ F 2 2 21,292,00 0,2 =

2 2v ref KN m

ρ × = × =

e:3e< F 1,9

pe ⇒ iz ta/lice.

GC'7+5 &5%7%SK+



&ovr4ina * ⇒ 0,2 1,9 :J0,< F 0,2 KN=m2

&ovr4ina ; ⇒ 0,2 1,9 :J1,< F 1,29 KN=m2

&ovr4ina E ⇒ 0,2 1,9 :J1,#< F 0,L0 KN=m2

&ovr4ina C⇒ 0,2 1,9 :J0,< F 0,2 KN=m2

GC'7+5 A%3+NC+

&ovr4ina * ⇒ 0,2 1,9 :?1,#< F ?0,L0 KN=m2

&ovr4ina ; ⇒ 0,2 1,9 :?2,0< F ?1,#L KN=m2

&ovr4ina E ⇒ 0,2 1,9 :?1,< F ?1,29 KN=m2

&ovr4ina C⇒ 0,2 1,9 :?1,9< F ?1,0 KN=m2

F

F

J JG GH H

9



;. P,(,+3! )(/,(*i5e

;.#. A+9i4+ ()8e,e:ej+ )(/,(*i5e

7'M%N+ &AK5AG+ J %NS7+@+%C' F 19 kg=m

I pokr F 0,#0 kN=m2

O F 9P

Q F 1,9 m

QR F Q = cos O F 1, m

I pokr F 0,19 × 1, F 0,21L KN=mRI pokr:< F 0,19 1, cos O F 0,21 KN=mR

I pokr:z< F 0,19 1, sin O F 0,01L KN=mR

7'M%N+ &A5AMN%'

E F 19, kg=mR :%&' 10<

I pod F 0,22 KN=mR

I pod:< F 0,22# KN=mR

I pod:z< F 0,01L KN=mR

7'M%N+ SN%C'E+

Sk F 129 kg=m2

Sk F 1,29 kN=m2

Is F 1,29 1, F 1,# KN=mR

Is:< F 1,2 KN=mR

Is:z< F 0,1 KN=mR



A&7'5''NC' A GC'75+

GC'7+5 &5%7%SK+T

&ovr4ina * ⇒ 1, 0,2 F 0,1 KN=mR

&ovr4ina ; ⇒ 1, 1,29 F 1,# KN=mR

GC'7+5 A%3+NC+T

&ovr4ina * ⇒ 1, :?0,L0< F ?1,#1 KN=mR

&ovr4ina ; ⇒ 1, :?1,#L< F ?2,02 KN=mR

.2. Kom/inacije opterećenja za podronicuT

γ E F 1,#9

γ U F 1,90

Ψ F 0,L

1< 1,#9 Ek J 1,90 Sk

2< 1,#9 Ek J 1,90 Ψ Sk J 1,90 Ψ × H p

#< 1,00 Ek J 1,90 Hs

V



5ezne sile iz kom/inacija opterećenja 1,#9 Ek J 1,90 Sk

Statički proračun

-

1

. 6

1

7

.

4 4

- 1

3 .

6

5

7

.

4 4

-

1

. 6

1

1.00 6.00 6.00 1.00

14.00

Opt. 3: 1.35xI+1.5xII

Utjecaji u gredi: max M3= 7.44 / min M3= -13.65 !m



3

. 2 2

- 7 . 6 4

1 1 . 6 5

- 1 1 . 6 5

7 . 6 4

- 3 . 2 2

1.00 6.00 6.00 1.00

14.00

Opt. 3: 1.35xI+1.5xII

Utjecaji u gredi: max "#= 11.65 / min "#= -11.65 !

5ezne sile iz kom/inacija opterećenja 1,#9 × Ek J 1,90 Ψ Sk J 1,90 Ψ H p

L



-

2

. 7 1

8 .

4 7

- 1 5 .

6 4

8 .

4 7

- 2

. 7 1

1.00 6.00 6.00 1.00

14.00

Opt. 4: 1.35xI+1.35xII+1.35xIII

Utjecaji u gredi: max M3= $.47 / min M3= -15.64 !m

5

.

4

1

-

9

. 7

8

1

3

. 4

8

- 1

3 .

4

8

9

.

7

8

-

5 .

4

1

1.00 6.00 6.00 1.00

14.00

Opt. 4: 1.35xI+1.35xII+1.35xIII

Utjecaji u gredi: max "#= 13.4$ / min "#= -13.4$ !5ezne sile iz kom/inacija opterećenja 1,00 × Ek J 1,90 Hs

10



1 . 3 4

- 3 . 5 5

6 . 5 9

- 3 . 5 5

1 . 3 4

1.00 6.00 6.00 1.00

14.00

Opt. 3: I+1.5xII

Utjecaji u gredi: max M3= 6.5% / min M3= -3.55 !m

- 2 . 6 7

4 . 3 5

-

5 . 7 0

5 . 7

0

- 4 . 3 5

2 . 6 7

1.00 6.00 6.00 1.00

14.00

Opt. 3: I+1.5xII

Utjecaji u gredi: max "#= 5.7& / min "#= -5.7& !

5ezne sile iz kom/inacija opterećenja 1,#9 × Ek J 1,90 Sk :oko osi z z<

11



-

0 .

1 4

0 .

1 3

- 0 .

2 3

0 .

1 0

- 0 .

2 0

0 .

1 0

- 0 .

2 3

0 .

1 3

- 0 .

1 4

14.00

1.00 3.00 3.00 3.00 3.00 1.00

Opt. 3: 1.35xI+1.5xII

Utjecaji u gredi: max M3= &.13 / min M3= -&.#3 !m

0 . 2 8

-

0 . 3 9

0 . 4 5

- 0 . 4 3

0 . 4 1

-

0 . 4 1

0 . 4 3

- 0

. 4 5

0 . 3 9

- 0 . 2 8

14.00

1.00 3.00 3.00 3.00 3.00 1.00

Opt. 3: 1.35xI+1.5xII

Utjecaji u gredi: max "#= &.45 / min "#= -&.45 !

12



O/+<,+e ,e4e si9e0

M="s/ > #?"1; KN@V4"s/ > #%"; KN

M4"s/ > $"&% KN@V="s/ > $";% KN

;.%. Di@e4i(i,+je )(/,(*i5e

;.%.#. P(/+5i ( )(),e3(@ ),esje!

;e #0$ F 2#,9 kN=cm%&' 10

" F 10 mm / F 2 mm % F L,# cm

t8 F 9,0 mm %z F ,#1 cm

t$ F V, mm H F 10,V cmW+ F 20,0L cm Hz F 1, cmWd F 12V,2 mm %8 F #L0 cm 0 r F L mm %7 F #,0 cm

i F ,9 cm iz F 1, cm H pl, F 12#,L cmW

H pl,z

F 2,10 cmW;.%.&. K9+siBi+5ij+ )(),e3( ),esje+

1#



: ta/lica G%%%?2., >etalne konstrukcije 1<a< *r/at

;e #0 X Y F 1,0

12V,2 29,9,0

w

d t

= =

Uvjet za klasu 1:

X V2w

d

t ε ≤ ×

12V,2

V2 19,0

≤ ×

29, Z V2,00 X H,<+8 4+/(6(9j+6+ 9+s! I.

/< &ojasnica

21

2 2

bc mm= = =

Uvjet za klasu 1:

10 f

c

t ε ≤ ×

1,010 1

V, ⟨ ×

9,9 < 10 ⇒ P(j+si5+ 4+/(6(9j+6+ 9+s! I. :&roračun po teoriji plastičnosti<

P(),e3i ),esje0 KLASA I

;.%.%. O8)(,(s8 )(),e3( ),esje+ i49(*e( s+6ij+j!

a< savijanje oko osi ?

>,Sd ≤ >,5d

,

, , ,

0

12#,L 2#,92,L9 2,

1,1 pl y y

c Rd pl y Rd

M

W f M M KNcm KNm

γ

× ×= = = = =

>,Sd F 19, KNm Z 2, KNm

1



/< oko osi z?z

>z,Sd ≤ >z,5d

,

, , ,

0

2,10 2#,9

99V,9L 9,9V1,1 pl z y

c Rd pl z Rd

M

W f

M M KNcm KNmγ

× ×

= = = = =

>z,Sd F 0,2# KNm Z 9,9V KNm ? P(),e3i ),esje 4+/(6(9j+6+ + s+6ij+je

;.%.;. P(s@i3+ (8)(,(s8 )(),e3( ),esje+

a< - smjeru osi z?z

Lw

d

t ε < ×

12V,2

L 1,09,0

< ×

29, < L ije )(8,e<+ ),(6je,+ i4<(3+6+j+ 2,)8+ + )(s@i

2

,1,0 1,0 1 0,90 ,#2

V z w A h t cm= × × = × × =

, . ,

0#

y

pl z Rd V z

M

f V A

γ

= ××

F ,#22#,9

# 1,1

××

F102,L0 KN

Rd z pl d z V V ,,,

<

1#, KN Z 102,L0 KN

/< - smjeru osi ?

2

,2 : < 2 0,2 0,V :0,90 0,L< 0,90 1,L1

V y f w w A b t t r t cm= × × + + × = × × + + × =

, . ,

0

2#,9

1,L1 2#,2# # 1,1 y

pl y Rd V y

M

f

V A KN γ = × = × =× ×

Rd y pl d y V V ,,,

<

0,# KN Z 2#,2 KN

;.%.?. I8e,+5ij+ M= I M4 D6((s( s+6ij+je

19



!last"#$a "$terakc"jska f%rmula:

1,,,

,

,,,

, ≤

+

β α

Rd z V N

d z

Rd yV N

d y

M

M

M

M

O F 2 [ F 1

Os ==0

G,Sd ≤ 0.9 G,5d

0,# Z 0,9 2#,2 F 11,1 KN

?razina uzdune sileT

NSd F 0

NSd Z 0,29 N5d ⇒ is+ ,+4i+ !4/!*e si9e

? za nisku razinu uzdune sile i Gz,Sd Z A,9 \ G pl,z,5d vrijediT

, , ,

,

1 N V y Rd

y Rd

M

M = ,0 nema redukcije momenta savijanja

> N,G,,5d F 2, KNm

Os 440

Gz,Sd ≤ 0,9 Gz,5d

1#, Z 0.9 ×102,L0 F 91,9 KN


NSd Z A,29 N pl,5d ⇒ is+ ,+4i+ !4/!*e si9e

1,

,,, = Rd z

Rd z V N

M

M ,0

> N,G,z,5d F 9,9V KNm

2 1

19, 0,2#1

2, 9,9V

+ ≤ ÷ ÷

1



0,#9 J 0,0 F 0,#L Z 1 ⇒ i8e,+5ij+ MNV 4+/(6(9j+6+

;.%.1. O8)(,(s8 e9e@e8+ + s+6ij+je

( )

( )( )

2 222

1 2 22 2

t w z cr

w z z

k & ' ( ( ) ( k M * * + * +

k ( ) ( k &

π

π ×

× × × × × = × × × + × + + × ÷ × ××

@ F #00 cm

g F ?1

2 2

h= − F ? ,0 cm

1

2

2,V10,#2

K,V

K,V0,9

19,

ψ

ψ

= = −

= = −

−

2

11, 1,0 0,92 1, 1,0 0,#2 0,92 :0,102< 2,#9 2,V0* ψ ψ = − × + × = + × + × = ≤

1V



20* =

k F 1k 8 F 1 X 1 F 2,#9

2 F 0

( )20VV =

2 1

) ' KN cm

ν =

+

( )

( ) 222

2 2

1 #00 0VV #,0#,1 21000 ,#1 1 #L02,#90

1 ,#1 #,1 21000 ,#11 #00cr

M × × ×× × = × × × + ÷ × × ×

>cr F 9V9#,1 KNcm

? relativna vitkostT

, 1,0 12#,L 2#,90,V1

9V9#,1w pl y y

&,

cr

W f

M

β λ

× × × ×= = =

? mjerodavna linija izvijanja +

za 0,V1 &, λ = ⇒ χ@7 F 0,#0

β8 F 1

1

,

,

1 12#,L 2#,90,#0 22#1,# 22,#1

1,1w pl y y

b Rd &,

M

W f M KNcm KNm

β χ

γ

× × × ×= × = × = =

>,Sd ≤ > /,5d

19, KNm Z 22,#1 KNm X e9e@e8 4+/(6(9j+6+ + s+6ij+je

;.%.. I8e,+5ij+

1 1

. ,

. ,

1 &, y sd z z d

pl y y pl z y

&,

M M

k M k M

W f W f χ

γ γ

× ×+ ≤

× ××

1



1 1,0

0 1,0

&, d &,

z y

d &,

N k

A f

N k

µ

χ

×= − ≤

× ×

= ⇒ =

k @7 F 1,0

1 1,0

0 1,0

- d -

z y

d -

N k

A f

N k

µ

χ

×= − ≤

× ×

= ⇒ =

k 3 F 1,0

1,0 19 1,0 2#112#, L 2#, 9 2,10 2#, 9

0,#01,1 1,1

0,V9 1

× ×+ ≤× ××

<

X i8e,+5ij+ 4+/(6(9j+6+

1L



?. P,(,+3! ,e/( (s+3+ i (4(9( (s+3+

?.#.A+9i4+ ()8e,e:ej+ ,e/( (s+3+

• S7+@NA A&7'5''NC'T

? &okrov DDDDDDDDDDDDDDDDDDDDDDD 0,10 ,00 F 0,0 KN=mR? Sekundarni nosači DDDDDDDDDDDDDDDDDD.. 0,19 ,00 F 0,L0 KN=mR? Spregovi DDDDDDDDDDDDDDDDDDDDDD. 0,09 ,00 F 0,#0 KN=mR? %nstalacije DDDDDDDDDDDDDDDDDDDDD... 0,09 ,00 F 0,#0 KN=mR? G7 DDDDDDDDDDDDDDDDDDDDDDDD.. F 0,2 KN=mR

E F 2,92 KN=mR

• 7'M%N+ SN%C'E+

? Snijeg DDDDDDDDDDDDDDDDDDDDDDDD.1,29 ,00 F V,90 KN=mR

• A&7'5''NC' A GC'75+

GC'7+5 &5%7%SK+T

? &ovr4ina E DDDDDDDDDDDDDDDDDDDDD.0,L0 ,00 F 9,0 KN=mR? &ovr4ina * DDDDDDDDDDDDDDDDDDDDD.0,2 ,00 F 2,92 KN=mR? &ovr4ina C DDDDDDDDDDDDDDDDDDDDD...0,2 ,00 F 1, KN=mR

GC'7+5 A%3+NC+T

? &ovr4ina E DDDDDDDDDDDDDDDDDDDD.D?1,29 ,00 F ?V,90 KN=mR? &ovr4ina * DDDDDDDDDDDDDDDDDDDDD ?0,L0 ,00 F ?9,0 KN=mR? &ovr4ina C DDDDDDDDDDDDDDDDDDDDD. ?1,0 ,00 F ?,2 KN=mR

9.2. Kom/inacije opterećenja za gredni nosač, konzolni nosač i stupT

γ E F 1,#9

γ U F 1,90

Ψ F 0,L

1< 1,#9 × Ek J 1,90 Sk

2< 1,#9 × Ek J 1,90 Ψ Sk J 1,90 Ψ H p

#< 1,00 × Ek J 1,90 Hs

20



5ezne sile iz kom/inacija opterećenja 1,#9 Ek J 1,90 Ψ Sk J 1,90 Ψ ×H p

Statički proračun

120.32 -120.88

6 .

0 7

0 .

5 5

5 .

5 2

16.00

2.006.006.002.00

Opt. 4: 1.35xI+1.35xII+1.35xIII

Utjecaji u gredi: max M3= 1#6.1# / min M3= -16#.$5 !m

21.80 -21.90 6 . 0 7

0 . 5 5

5 . 5 2

16.00

2.006.006.002.00

Opt. 4: 1.35xI+1.35xII+1.35xIII

Utjecaji u gredi: max "#= %%.#$ / min "#= -%%.1$ !

21



-142.16 -142.25 6 .

0 7

0 .

5 5

5 .

5 2

16.00

2.006.006.002.00

Opt. 4: 1.35xI+1.35xII+1.35xIII

Utjecaji u gredi: max !1= -&.&& / min !1= -14#.#5 !

5ezne sile iz kom/inacija opterećenja 1,#9 Ek J 1,90 Sk

113.01 -113.01

6 .

0 7

0 .

5 5

5 .

5 2

16.00

2.006.006.002.00

Opt. 3: 1.35xI+1.5xII

Utjecaji u gredi: max M3= 115.&% / min M3= -14#.$% !m

22



20.47 -20.47 6 .

0 7

0 .

5 5

5 .

5 2

16.00

2.006.006.002.00

Opt. 3: 1.35xI+1.5xII

Utjecaji u gredi: max "#= $7.5& / min "#= -$7.5& !

-119.62 -119.62 6 .

0 7

0 .

5 5

5 .

5 2

16.00

2.006.006.002.00

Opt. 3: 1.35xI+1.5xII

Utjecaji u gredi: max !1= &.&& / min !1= -11%.6# !

2#



5ezne sile iz kom/inacija opterećenja 1,00 Ek J 1,90 Hs

-40.58 40.58

6 .

0 7

0 .

5 5

5 .

5 2

16.00

2.006.006.002.00

Opt. 3: I+1.5xII

Utjecaji u gredi: max M3= 57.54 / min M3= -45.53 !m

-7.35 7.35 6 .

0 7

0 .

5 5

5 .

5 2

16.00

2.006.006.002.00

Opt. 3: I+1.5xII

Utjecaji u gredi: max "#= 33.6$ / min "#= -33.6$ !

2



50.17 50.17 6 .

0 7

0 .

5 5

5 .

5 2

16.00

2.006.006.002.00

Opt. 3: I+1.5xII

Utjecaji u gredi: max !1= 5&.17 / min !1= -&.41 !

O/+<,+e ,e4e si9e 4+ ,e/i (s+3(@<i+5ij+ #"%? × G #"?$ S #"?$ × ) 0

M="s/ > #&1"#& KN@ V4"s/ > ''"& KN N"s/ > %$"## KN 89+

O/+<,+e ,e4e si9e 4+ (4(9i (s+3(@<i+5ij+ #"%? × G #"?$ S #"?$ × )0

M="s/ > ;#"' KN@ V4"s/ > ;$"1$ KN N"s/ > &"# KN 89+

O/+<,+e ,e4e si9e 4+ s8!)(@<i+5ij+ #"%? × G #"?$ S #"?$ × )0

M="s/ > #&$" KN@ V4"s/ > &#"'$ KN

N"s/ > #;&"&? KN 89+

29



?.%. Di@e4i(i,+je ,e/( (s+3+

?.%.#. P(/+5i ( )(),e3(@ ),esje!

;e #0

$ F 2#,9 kN=cm%&' ##0

" F ##0 mm / F 10 mm % F 11VV0 cm

t8 F V,9 mm %z F V,1 cm

t$ F 11,9 mm H F V1#,1 cmW+ F 2,1 cm Hz F L,92 cmWd F 2V1 mm %8 F 1LL100 cm 0 r F 1 mm %7 F 2,1V9cm

i F 1#,V1 cm iz F #,99 cm H pl, F 0,# cmW H pl,z F 19#,V cmW

?.%.&. K9+siBi+5ij+ )(),e3( ),esje+

: ta/lica G%%%?2., >etalne konstrukcije 1<a< *r/at izloen savijanju i tlaku

;e #0 X Y F 1,0

0

#0,110,L#

2#,92 0,V92

1,1

d

y

w

M

N a cm

f t

γ

= = =

× ×× ×

2



1 1 2V,1

0,L# 0,9#2 2V,1 2

d a

d α

= + = + = ÷ ÷

]0.9 X

Uvjet za klasu 1:

X#L

1# 1w

d

t

ε

α

×≤ × −

2V1 #L 1,0

V,9 1# 0,9# 1

×≤

× −

#,1# Z V,2# X H,<+8 4+/(6(9j+6+ 9+s! I.

/< &ojasnica izloena tlaku

10

02 2

bc mm= = =

Uvjet za klasu 1:

10 f

c

t ε ≤ ×

010 1

11,9⟨ ×

,L9 Z 10 ⇒ P(j+si5+ 9+s+ I. :&roračun po teoriji plastičnosti<.

P(),e3i ),esje0 KLASA I.

?.%.%. O8)(,(s8 )(),e3( ),esje+ ! 89+!

Nc,5d F N pl,5d F0

2,1 2#,9

1,1 y

M

A f

γ

× ×= F 1##V,9V KN

NSd ^ Nc,5d

NSd F #0,11 KN Z 1##V,9V KN )(),e3i ),esje 4+/(6(9j+6+ + 89+

?.%.;. O8)(,(s8 )(),e3( ),esje+ i49(*e( s+6ij+j!


>,Sd ≤ >,5d

,

, , ,

0

0,# 2#,9 1V12,VV1,1

pl y y

c Rd pl y Rd

M

W f M M KNcmγ

× ×= = = =

2V



>,Sd F 12,12 KNm Z 1V1,2 KNm

? P(),e3i ),esje 4+/(6(9j+6+ + s+6ij+je

?.%.?. P(s@i3+ (8)(,(s8 )(),e3( ),esje+

a< - smjeru osi z?z

Lw

d

t ε < ×

2V1

LV,9

< 1,0

#,1# < L ije )(8,e<+ ),(6je,+ i4<(3+6+j+ 2,)8+ + )(s@i

2

,1,0 1,0 ## 0,V9 29,V

V z w A h t cm= × × = × × =

, . ,

0#

y

pl z Rd V z

M

f V A

γ = ×

×F 29,V

2#,9

# 1,1× F #1,# KN

Rd z pl d z V V ,,,

<

LL,2 KN Z #1,# KN

?.%.1. I8e,+5ij+ MVN s+6ij+je")(),e3+ i !4/!*+ si9+

Os 440

Gz,Sd ≤ 0,9 Gz,5d

0 Z 0,9 #1,# F 19L,1 KN


NSd Z A,29 × N pl,5d

2,#0 KN Z 0,29 × 1##V,9V F ##,#L KN ⇒ is+ ,+4i+ !4/!*e si9e

1,

,,, = Rd z

Rd z V N

M

M ,0

2



>,Sd ≤ > N,G,z,5d

12,12 KNm Z 1V1,2 KNm ⇒ i8e,+5ij+ MNV 4+/(6(9j+6+

?.%.. D(+4 + ,+4ii e9e@e8+

#. U4/!*+ 89+3+ (8)(,(s8

? dokaz nosivosti prema χ postupkuT

N /,5d F χ Nc,5d

? os ? ? os z?z

-M%N' %3G%C+NC+li F 0# cm liz F 1 cm

';'K7%GN+ G%7KAS7

0#

#,L1#,V1

"y

y

y

l

"λ = = =

11,12

#,99"z

z

z

l

"λ = = =

SG''N+ G%7KAS7

2

1

1

Aβ λ

λ λ ⋅=

1

21000L#,L1

2#,9 y

)

f λ π π = × = × =

0,1= Aβ ?za ;e #0

1

2#,L 1,0 0,L#,L1 yλ = × =1,12

0,#VL#,L1 z λ = =

>C'5A+GN+ @%N%C+ %3G%C+NC+

##02, 0 1, 2

1011,9 100

f

h

bt mm mm

= = >

= <

linija izvijanja a linija izvijanja /

os os z z

2L



? odre!ivanje $aktora redukcije χ

0,L##

y χ = 0,L10 z χ =

@je,(/+6+ je @+ji 4 $"'#;$

, , ,0,L10 1##V,9V 1222,9#

z b Rd z c Rd N N KN χ = × = × =

, ,

#0,11 1222,9# sd z b Rd

N N

KN KN

≤

< X 4+/(6(9j+6+

?.%.. O8)(,(s8 e9e@e8+ + s+6ij+je

( )

( )( )

2 222

1 2 22 2

t w z cr

w z z

k & ' ( ( ) ( k M * * + * +

k ( ) ( k &

π

π ×

× × × × × = × × × + × + + × ÷ × ××

@ F 1 cm

g F ?##

2 2

h= − F ? 1,9 cm

k F 1k 8 F 1

#0



1

2

#

9,200,2VV

12,K9

9,200,LL

9,2

9,20,

LK,##LK,##

0,VK12,12

ψ

ψ

ψ

ψ

−= =

−

−= = −

= =

= =

2

11, 1,0 0,92 1, 1,0 0,V 0,92 :0,0< 2,1L2 2,V0* ψ ψ = − × + × = − × + × = ≤

20* =

( )

20VV =

2 1

) ' KN cm

ν

=

+

( )

( ) 222

2 2

1 1 0VV 2,1V9#,1 21000 V,1 1 1LL1002,1L2

1 V,1 #,1 21000 V,11 1cr M

× × ×× × = × × × + ÷ × × ×

>cr F 21L09,0 KNcm F 21L,09 KNm


, 1,0 0,# 2#,9 0,221L09,0

w pl y y &,

cr

W f M

β λ × × × ×= = =

#1




za 0,2 &, λ = ⇒ χ@7 F 0,LV

β8 F 1

1

,

,

1 0,# 2#,90,LV 1L9,2 1L,9

1,1w pl y y

b Rd &,

M

W f M KNcm KNm

β χ

γ

× × × ×= × = × = =

>,Sd ≤ > /,5d

12,12 KNm Z 1L,9 KNm X e9e@e8 4+/(6(9j+6+ + s+6ij+je

?.%.'. I8e,+5ij+ MN <e4 ),(<9e@+ <(3( i46ij+j+

1 1

,

,

min

1 y y d d

y pl y y

M M

k M N A f W f

χ γ γ

×+ ≤

× ××

? odre!ivanje β> :ta/l. G%%%?#1_ >et.konstr. 1 <T

( ), , ,

,

,

12,120,VV

12,K9

1, K 0, V 1, K 0, V : 0, VV< 2, #

1, #

12,12

2KK,LV

y

.

M M M . M

M

M .

.

M

M

M KNm

M KNm

ψ ψ

ψ

β β β β

ψ

β ψ

β

= + × −∆

= = −

= − = − × − =

=

=

∆ =

12,12: < 2,# :1,# 2,#< 1,L

2,LV y .

.

M M M M

M

M ψ ψ β β β β = + × − = + × − =

V

( ) ( ), ,

,

0,# V1#,12 0, 2 1,L 0,02 0.L

V1#,1 y

pl y el y y y M

el y

W W

W µ λ β

− −= × × − + = × × − + = <

#2



1 1,9

0,02 #0,111 1,9

0,L## 2,1 2#,9

0,LL 1,9

y d

y

y y

y

y

N k

A f

k

k

µ

χ

×= − ≤

× ×

×= − ≤

× ×= ≤

#0,11 0,LL 12121

2, 1 2#, 9 0, # 2#, 90,L10

1,1 1,1

0,V9 1

×+ ≤

× ××

<

X i8e,+5ij+ MN 4+/(6(9j+6+

?.%.#$. I8e,+5ij+ MN s+ ),(<9e@(@ <(3( i46ij+j+

1

11

,

,≤

⋅⋅

⋅+⋅

⋅

M

y y pl

&,

d y &,

M

y

z

d

f W M k

f A N

γ χ

γ χ

L,019,019,0,

≤−⋅⋅= &, M z &, β λ µ

? odre!ivanje β>,@7T

( ), , , ,

,

,

0,VK

1, K 0, V 1, K 0, V :0, VK< 1, 29

1, #

12,12

2KK,0

.

M &, M M . M

M

M .

.

M

M

M KNm

M KNm

ψ ψ

ψ

β β β β

ψ ψ

β ψ

β

= + × −∆

= =

= − = − × =

=

=

∆ =

, 12,12: < 1,29 :1,# 1,29< 1,2V2,LV.

. M &, M M M M

M ψ ψ β β β β = + × − = + × − =

V

##



,0,19 0,19 0,L

0,19 0,#V 1, 2V 0,19 0,0 0,L

z &, M &,

&,

µ λ β

µ

= × × − ≤

= × × − = − ≤

1 1,0

: 0,0< #0,111 1,000,L1 2,1 2#,9

&, d &,

z y

&,

N k

A f

k

µ

χ

×= − ≤

× ×

− ×= − =× ×

#0,11 1,00 12121

2,1 2#,9 0,# 2#,90,L10 0,2#

1,1 1,1

0,9 Z 1

×+ ≤

× ×× ×

X i8e,+5ij+ MN 4+/(6(9j+6+

#



?.;. Di@e4i(i,+je ,e/e s (j+3+ji@+ 6!8+@+

O/+<,+e ,e4e si9e 4+ 6!8!(@<i+5ij+ #"%? × G #"?$ S #"?$ ×) 0

M="s/ > #1&"? KN@ V4"s/ > ''"& KN N"s/ > %$"## KN 89+

?.;.#. O/,ei6+je s6(js8+6+ ),esje+0

2#01200 #0 1099

2 & mm= − − =

1

##0 ##1cos cos9 / 0 mm

α = = =

°

2 ##0 2 11,9 #0V f

* / t mm= − × = − × =

1099109L

cos cos9

&' mm

α = = =

°

1 1 #0Vtan tan 1,10

109L

*

'

β − − = × = × = ÷

9 1 21,10γ α β = + = °+ °= °

2

#0V 11, 9#1,#

cos cos 21,10 f

* t 0 mm

γ

+ += = =

°

##0tan tan 109L tan 9 tan1,10 #01,9 #02

2 2

/ M ' mmα β

= − × × = − × ° × °= ≈ ÷ ÷

11,9 11,Lcos cos1,10

* t N mmβ

= = =°

POVRŠINA0

+ F # 1,19 1,00 J 1,1L 1,00 J 0,V9 #0,V0 J 0,V9 #0,2 F 101,919 cm2

#9



TEIŠTE0

`

`

`

0

1,19 1,00 #,19 #0,V 0,V9 V,L 1,19 1,0 #1,L #0,2 0,V9 1,2L 1,1L 1,00 0,9L9

101,919

#1,L

,

" ,",

,

y cm

A z z

A

z cm

=

Σ ×= =

× × + × × + × × + × × + ×

=

STATIČKI MOMENT POVRŠINE0

#

,1,1L 1,00 #1,#9 0,V9 #0,20 19,V9 L92,21

y /1&2) cm= × × + × × =

#

, 1,19 1,00 #,19 0,V9 ##,00 1V,0V9 1090,L y '1R) cm= × × + × × =

PLASTIČNI MOMENT OTPORA POPREČNOG PRESJEKA0

#

, , ,L92,21 1090,L 200#,1V

pl y y /1&2) y '1R) W cm= + = + =

T

#



?.;.&.K9+siBi+5ij+ )(),e3( ),esje+ ! ),esje! #0

a3 !2AN(*) U K&A) 1

b3 4R5A, 1 2) K&AA 6 (&( V(7) 8!R),)9N 2) U V&AKU3

c3 4R5A, :

Napon u "rptu od uzdune sileT

2 2#0,110,2L = 2,L =

101,919 N KN cm N mmσ = = =

Napon za otpornost na savijanjeT

22#92,L 210,V# 211 =

1,1 y

M N

M1

f N mmσ σ

γ

= − = − = ≈ ÷ ÷

Napon na gornjoj točki ojačanjaT

#V



2211 2,L 20,1 20 = M N

N mmσ σ σ = − = − = ≈

-kupna visina presjeka 1T

1

1##0 #02 11,L #,L

h pre#ka hrbat d%$ja p%jas$"ca

h mm

= + += + + =

Napon u toj točkiT

29,V9211 2,L , =

#2,29a N mmσ = × + =

5avni dio "rpta u ojačanjuT

#02 1 2d M r mm= − = − =

Napon u toj točkiT

22211 2,L 1L,# =

#2,29b N mmσ = × + =

,0, 0#9 1

1KL,#ψ = = > −

Uvjet za klasu 6:

2

0, V 0, ##

2 2 1,0#V, 1,2

V,9 0,V 0,## 0,0#9

w

d

t

ε

ψ

×≤

+ ×

×= < =

+ ×

Uvjet za klasu :

#0,110, L# L, #

2 2#, 92 0,V91,1

)d

w y

M1

N a cm mm

t f γ

= = = =

× ×× ×

#

2#V, #, 00 1, 0 #, 00

V,9

w

d

t ε ≤ ×

= < × =

#



Uvjet za klasu 1:

##

2#V, ##, 00 1, 0 ##, 00V,9

w

d

t ε ≤ ×

= > × =

? ije 9+s+ #

H,<+8 je 9+se &

P(),e3i ),esje0 KLASA II.

?.;.%. O8)(,(s8 )(),e3( ),esje+ ! 89+!

Nc,5d F N pl,5d F0

101,919 2#,91,1

y

M

A f γ

× ×= F 21,V# KN

NSd ^ Nc,5d

NSd F #0,11 KN Z 21,V# KN )(),e3i ),esje 4+/(6(9j+6+ + 89+

?.;.;. O8)(,(s8 )(),e3( ),esje+ i49(*e( s+6ij+j!


>,Sd ≤ >,5d

,

, , ,

0

200#,1V 2#,92VL,LL

1,1 pl y y

c Rd pl y Rd

M

W f M M KNcm

γ

× ×= = = =

>,Sd F 12,9 KNm Z 2V,L KNm

? P(),e3i ),esje 4+/(6(9j+6+ + s+6ij+je

?.;.?. P(s@i3+ (8)(,(s8 )(),e3( ),esje+

2

,1,0 1,0 ,#L 0,V9 90,22

V z w A h t cm= × × = × × =

, . ,

0#

y

pl z Rd V z

M

f V A

γ = ×

×F 90,22

2#.9

# 1.1× F 21,1 KN

Rd z pl d z V V ,,,

<

LL,2 KN Z 21,1 KN

#L



?.;.1. I8e,+5ij+ MVN s+6ij+je")(),e3+ i !4/!*+ si9+

Os 440

Gz,Sd ≤ 0,9 Gz,5d

LL,2 Z 0,9 21,1 F #10,9V KN


NSd Z A,29 N pl,5d

#0,11 KN Z 0,29 21,V# F 92,1 KN ⇒ is+ ,+4i+ !4/!*e si9e

1

,

,,, = Rd z

Rd z V N

M

M .0

>,Sd ≤ > N,G,z,5d

12,9 KNm Z 2V,L KNm ⇒ i8e,+5ij+ MNV 4+/(6(9j+6+

0



K(4(9i (s+3

?.?. A+9i4+ ()8e,e:ej+ (4(9( (s+3+

• S7+@NA A&7'5''NC'T

? &okrov DDDDDDDDDDDDDDDDDDDDDDD 0,10 ,00 F 0,0 KN=mR? Sekundarni nosači DDDDDDDDDDDDDDDDDD.. 0,19 ,00 F 0,L0 KN=mR? Spregovi DDDDDDDDDDDDDDDDDDDDDD. 0,09 ,00 F 0,#0 KN=mR? %nstalacije DDDDDDDDDDDDDDDDDDDDD... 0,09 ,00 F 0,#0 KN=mR? G7 DDDDDDDDDDDDDDDDDDDDDDDD.. F 0,2 KN=mR

E F 2,# KN=mR

• 7'M%N+ SN%C'E+

? Snijeg DDDDDDDDDDDDDDDDDDDDDDDD.1,29 ,00 F V,90 KN=mR

• A&7'5''NC' A GC'75+

GC'7+5 &5%7%SK+T

? &ovr4ina E DDDDDDDDDDDDDDDDDDDDD.0,L0 ,00 F 9,0 KN=mR? &ovr4ina * DDDDDDDDDDDDDDDDDDDDD.0,2 ,00 F 2,92 KN=mR

GC'7+5 A%3+NC+T

? &ovr4ina E DDDDDDDDDDDDDDDDDDDD... ?1,29 ,00 F ?V,90 KN=mR? &ovr4ina * DDDDDDDDDDDDDDDDDDDD... ?0,L0 ,00 F ?9,0 KN=mR

1



?.1. Di@e4i(i,+je (4(9( (s+3+

?.1.#. P(/+5i ( )(),e3(@ ),esje!

;e #0$ F 2#,9 kN=cm

%&' 220

" F 220 mm / F 110 mm % F 2VV2 cm

t8 F 9,L mm %z F 20,L cm

t$ F L,2 mm H F 292 cmW

+ F ##,#V cm Hz F #V,29 cmWd F 1VV, mm %8 F 22V0 cm 0 r F 12 mm %7 F L,0Vcm

i F L,11 cm iz F 2, cm H pl, F 29, cmW H pl,z F 9,11 cmW

?.1.&. K9+siBi+5ij+ )(),e3( ),esje+

: ta/lica G%%%?2.,>etalne konstrukcije 1<a< *r/at izloen savijanju i tlaku

;e #0 X Y F 1,0

0

2,1V0,0K

2#,92 0,9L2

1,1

d

y

w

M

N a cm

f t

γ

= = =

× ×× ×

1 1 1V,V

0,0 0,902 1V,V 2

d

ad α

= + = + = ÷ ÷ ]0,9 X

2



Uvjet za klasu 1:

X#L

1# 1w

d

t

ε

α

×≤

× −

1VV, #L 1,0

9,L 1# 0,90 1

×≤ × −

#0,10 Z V1,#9 X H,<+8 4+/(6(9j+6+ 9+s! I.

d< &ojasnica izloena tlaku

110

992 2

bc mm= = =

Uvjet za klasu 1:

10 f

c

t ε ≤ ×

9910 1

L,2⟨ ×

9,LV Z 10 ⇒ P(j+si5+ 9+s+ I. :&roračun po teoriji plastičnosti<.


?.1.%. O8)(,(s8 )(),e3( ),esje+ ! 89+!

Nc,5d F N pl,5d F0

##,#V 2#,9

1,1 y

M

A f

γ

× ×= F V12,L0 KN

NSd ^ Nc,5d

NSd F 2,1V KN Z V12,L0 KN )(),e3i ),esje 4+/(6(9j+6+ + 89+

?.1.;. O8)(,(s8 )(),e3( ),esje+ i49(*e( s+6ij+j!


>,Sd ≤ >,5d

,

, , ,

0

29, 2#,90LV,1

1,1 pl y y

c Rd pl y Rd

M

W f M M KNcm

γ

× ×= = = =

>,Sd F 1,LV KNm Z 0,LV KNm ? P(),e3i ),esje 4+/(6(9j+6+ + s+6ij+je

#



?.1.?. P(s@i3+ (8)(,(s8 )(),e3( ),esje+

a< - smjeru osi z?z

Lw

d

t ε < ×

1VV,

L9,L

< 1,0

#0,10 < L ije )(8,e<+ ),(6je,+ i4<(3+6+j+ 2,)8+ + )(s@i

2

,1,0 1,0 22 0,9L 1#,90

V z w A h t cm= × × = × × =

, . ,

0#

y

pl z Rd V z

M

f V A

γ

= ××

F 1#,902#,9

# 1,1× F 1,LV KN

Rd z pl d z V V ,,,

<

0,0 KN Z 1,LV KN

?.1.1. I8e,+5ij+ MVN s+6ij+je")(),e3+ i !4/!*+ si9+

Os 440

Gz,Sd ≤ 0,9 Gz,5d

0,0 Z 0,9 ×1,LV F #, KN


NSd Z A,29 × N pl,5d

2,1V KN Z 0,29 V12,L0 F 1V,22 KN ⇒ is+ ,+4i+ !4/!*e si9e

1,

,,, = Rd z

Rd z V N

M

M .0

>,Sd ≤ > N,G,z,5d

1,LV KNm Z 0,LV KNm ⇒ i8e,+5ij+ MNV 4+/(6(9j+6+



?.1.. D(+4 + ,+4ii e9e@e8+

#. U4/!*+ 89+3+ (8)(,(s8


N /,5d F χ Nc,5d

? os ? ? os z?z

-M%N' %3G%C+NC+

li F 2 l F 02 cm liz F 10 cm

';'K7%GN+ G%7KAS7

02

,12L,11

"y

y

y

l

"λ = = =

10V2,9

2,"z

z

z

l

"λ = = =

SG''N+ G%7KAS7

2

1

1

Aβ λ

λ λ ⋅=

121000 L#,L12#,9

y

) f

λ π π = × = × =

0,1= Aβ ?za ;e #0

1

2,12

1,0 0,LL#,L1 y

λ = × =V2,9

0,VV2L#,L1 z λ = =

>C'5A+GN+ @%N%C+ %3G%C+NC+

2202, 00 1, 2

110L,2 100

f

h

bt mm mm

= = >

= <

linija izvijanja a linija izvijanja /

os os z z


0,L##

y χ = 0,V2

z χ =

9



@je,(/+6+ je @+ji 4 $";&

, , ,0,V2 V12,L0 92L,9


, ,

2,1V 92L,9 sd z b Rd N N

KN KN

≤

< X 4+/(6(9j+6+

?.1.. O8)(,(s8 e9e@e8+ + s+6ij+je

( )

( )( )

2 222

1 2 22 2

t w z cr

w z z

k & ' ( ( ) ( k M * * + * +

k ( ) ( k &

π

π ×

× × × × × = × × × + × + + × ÷

× ××

@ F 10 cm

g F ?22

2 2

h= − F ? 11,0 cm

k F 1k 8 F 1 X 1 F 1,29

2 F 1,92

( )20VV =

2 1 ) ' KN cm

ν =

+

( )

( )( )

2222

2 2

1 10 0VV L,0V#,1 21000 20,L 1 22V01,29 1,92 11,0 1,92 11,0

1 20,L #,1 21000 20,L1 10cr

M × × ×× × = × × − × + × + + × ÷ × × ×

>cr F V2#9,1 KNcm F V2,#9 KNm


, 1,0 29, 2#,90,L

V2#9,1w pl y y

&,

cr

W f

M

β λ

× × × ×= = =


za 0,L &, λ = ⇒ χ@7 F 0,L#

β8 F 1



1

,

,

1 29, 2#,90,L# 22V,V 2,2V

1,1w pl y y

b Rd &,

M

W f M KNcm KNm

β χ

γ

× × × ×= × = × = =

>,Sd ≤ > /,5d

1,LV KNm Z 2,2V KNm X e9e@e8 4+/(6(9j+6+ + s+6ij+je

?.1.'. I8e,+5ij+ MN <e4 ),(<9e@+ <(3( i46ij+j+

1 1

,

,

min

1 y y d d

y pl y y

M M

k M N A f W f

χ γ γ

×+ ≤

× ××


( ), , ,

,

,

0

1, K 0, V 1, K 0, V :0< 1, K0

1, #

1,LV

1,LV

y

.

M M M . M

M

M .

.

M

M

M kNm

M kNm

ψ ψ

ψ

β β β β

ψ

β ψ

β

= + × −∆

=

= − = − × =

=

=

∆ =

1,LV: < 1,0 :1,# 1,0< 1,#0

1,LV y .

.

M M M M

M

M ψ ψ β β β β = + × − = + × − =

V

( ) ( ), ,

,

29, 292,02 0,L 2 1,#0 0,92 0,L

292,0 y

pl y el y y y M

el y

W W

W µ λ β

− −= × × − + = × × − + = − <

1 1,9

: 0,92< 2,1V1 1,90,L## ##,#V 2#,9

1, 00 1, 9

y d

y

y y

y

y

N k

A f

k

k

µ

χ

×= − ≤

× ×

− ×= − ≤× ×= ≤

2,1V 1,00 1LV1

##, #V 2#, 9 29, 2#, 90,V2

1,1 1,1

0,L 1

×+ ≤

× ××

<

Xi8e,+5ij+ MN 4+/(6(9j+6+

V



?.1.#$. I8e,+5ij+ MN s+ ),(<9e@(@ <(3( i46ij+j+

1

11

,

,≤

⋅⋅

⋅+

⋅⋅

M

y y pl

&,

d y &,

M

y

z

d

f W

M k

f A

N

γ χ

γ χ

L,019,019,0,

≤−⋅⋅= &, M z &, β λ µ


( ), , , ,

,

,

01, K 0, V 1, K 0, V :0< 1, K0

1, #

1,LV

1,LV

.

M &, M M . M

M

M .

.

M

M

M kNm

M kNm

ψ ψ

ψ

β β β β

ψ β ψ

β

= + × −∆

=

= − = − × =

=

=

∆ =

,

1,LV: < 1,0 :1,# 1,0< 1,#0

1,LV.

.

M &, M M M

M

M ψ ψ β β β β = + × − = + × − =

V

,0.19 0,19 0,L

0,19 0, VV2 1,#0 0,19 0, 0009 0,L

z &, M &,

&,

µ λ β

µ

= × × − ≤

= × × − = ≤

1 1,0

0,0009 2,1V1 0,LL 1,0

0,V2 ##,#V 2#,9

&, d &,

z y

&,

N k

A f

k

µ

χ

×= − ≤

× ×

×= − = <

× ×

2,1V 0,LL 1LV1

##,#V 2#,9 29, 2#,90,V2 0,L#

1,1 1,1

0,L Z 1

×+ ≤

× ×× ×

X i8e,+5ij+ MN 4+/(6(9j+6+



1. P,(,+3! s8!)+

1.#. A+9i4+ (6i,+

#. U86,i6+je )(@i3(s8i )(),e3( (6i,+

0,L 2 12,210, 020 0,1

992 2#,9d

d

V h 4 δ

× × ×= = <

∑ ⇒ Okvir je nepomičan.

&. U86,i6+je )(@i3(s8i )(/!*( (6i,+

2,01 12,21 :2 12,21= 2<0, 0V 0,1

992 1#,d

d

V h 4 δ

× × + ×= = <

∑ ⇒ Okvir je nepomičan.

%. U86,i6+je /!*ie i46ij+j+ 9i =

? stupT *'+ 20 ⇒ %c F VV# cm

? prečkaT %&' ##0 ⇒ %/ F 11 VV0 cm

1

11 12*

Kc K K K

η =+ + 2

21 22*

Kc K K K

η =+ +

#VV#1,0

992*

*

*

( K cm

&= = =

#11

11VV0

12001,0 1,0 L,0b

b

b

( K K cm

&= ×= = × =

10,9L

1,01,0 L,0

η ==+

20: < z+l%bη =

= 0,9"y

& & =

0,9 0,9 992 L,20"y & & cm= × = × =

L



;. U86,i6+je /!*ie i46ij+j+ 9i 4

? stupT *'+ 20 ⇒ %c F 2VL cm

? prečkaT %&' 20 :pretpostavljeno< ⇒ %/ F 2#, cm

1

11 12*

Kc K K K

η =+ + 2

21 22*

Kc K K K

η =+ +

#2VL9,01

992*

*

*

( K cm

&= = =

#11

2#,

00

1,0 1,0 0,Vbb

b

( K K cm

&= ×= = × =

1 0,L19,01

9, 01 0, Vη ==

+ 2

0: < z+l%bη =

= 0,L"z

& & =

0,L 0,L 992 92L,L2"z & & cm= × = × =

90



&omaci u 6 smjeru poprečnog okvira iz kom/inacije 1,#9 Ek J 1,#9 Sk × 1,#9 H p

-9.48 9.48

2.00 6.00 6.00 2.00

16.00

5 .

5 2

0 .

5 5

6 .

0 7

Opt. 4: 1.35xI+1.35xII+1.35xIII

Utjecaji u gredi: max 'p= %.4$ / min 'p= -%.4$ m / 1&&&

&omaci u z smjeru poprečnog okvira iz kom/inacije 1,#9 Ek J 1,#9 Sk × 1,#9 H p

-0.33 -0.33

2.00 6.00 6.00 2.00

16.00

5 . 5 2

0 . 5 5

6 . 0 7

Opt. 4: 1.35xI+1.35xII+1.35xIII

Utjecaji u gredi: max (p= 3.&5 / min (p= -5#.%4 m / 1&&&

91



5ezne sile od reakcije spregaStatički proračun

- 1 9 . 8 6

1 7 . 7 9

-

1 7 . 8 2

1 9 . 9 3

19.9335.6119.86

6.00 6.00

12.00

5 . 5 2

Opt. 1: )eacija *d prega

Utjecaji u gredi: max M3= 35.61 / min M3= -1%.$6 !m

-

6 .

2 9

3.616.453.60

6.00 6.00

12.00

5 .

5 2


Utjecaji u gredi: max "#= 6.45 / min "#= -6.#% !

92



- 1 0 . 0 5

6.29-0.02-6.27

6.00 6.00

12.00

5 . 5 2


Utjecaji u gredi: max !1= 6.#% / min !1= -1&.&5 !

R1 = 23.65

R 3

=

1 4 2 .

2 1

R1 = 23.65

R 3

=

1 4 2 .

2 1

6 . 0 7

0 . 5 5

5 . 5 2

16.00

2.006.006.002.00

Opt. 4: 1.35xI+1.35xII+1.35xIII

)eacije ,e-ajea

9#



&omaci u 6 smjeru podunog okvira iz kom/inacije 1,#9 Ek J 1,#9 Sk 1,#9 ×H p

- 2 0 . 4 8

-20.48-20.41-20.38

6.00 6.00

12.00

5 . 5 2

Opt. 1: Optereenje na tup*e + reacija *d prega

Utjecaji u gredi: max 'p= -&.&& / min 'p= -#&.4$ m / 1&&&

&omaci u z smjeru poprečnog okvira iz kom/inacije 1,#9 Ek J 1,#9 Sk × 1,#9 H p

- 0 . 1 8

1 . 5 2

- 1 . 2 8

0 . 6 4

-

1 . 9 2

-0.15-0.33-0.18

6.00 6.00

12.00

5 . 5 2

Opt. 1: Optereenje na tup*e + reacija *d prega

Utjecaji u gredi: max (p= 1.5# / min (p= -1.%# m / 1&&&

9



1.&. Di@e4i(i,+je s8!)+

1.&.#. P(/+5i ( )(),e3(@ ),esje!

;e #0$ F 2#,9 kN=cm

*'+ 20

" F 2#0 mm / F 20 mm % F VV# cm

t8 F V,9 mm %z F 2VL cm

t$ F 12,0 mm H F V9,1 cmW+ F V, cm Hz F 2#0,V cmWd F 1 mm %8 F #2900 cm 0 r F 21 mm %7 F 1,99 cm

i F 10,09 cm iz F ,00 cm H pl, F V, cmW H pl,z F #91,V cmW

1.&.&. K9+siBi+5ij+ )(),e3( ),esje+: ta/lica G%%%?2.,>etalne konstrukcije 1<a< *r/at izloen savijanju i tlaku

;e #0 X Y F 1,0

0

12,29,

2#,92 0,V92

1,1

d

y

w

M

N a cm

f t

γ

= = =

× ×× ×

1 1 1,, 0,VV

2 1, 2

d a

d α

= + = + = ÷ ÷

]0,9 X

99



Uvjet za klasu 1:

X#L

1# 1w

d

t

ε

α

×≤

× −

1 #L 1,0V,9 1# 0,VV 1

×≤× −

21, Z #,L9 X H,<+8 4+/(6(9j+6+ 9+s! I.


20

1202 2

bc mm= = =

Uvjet za klasu 1:

10 f

c

t ε ≤ ×

12010 1

12,0⟨ ×

10,0 F 10 ⇒ P(j+si5+ 9+s+ I. :&roračun po teoriji plastičnosti<.


1.&.%. O8)(,(s8 )(),e3( ),esje+ ! 89+!

Nc,5d F N pl,5d F0

V, 2#,9

1,1 y

M

A f

γ

× ×= F 11,9 KN

NSd ^ Nc,5d

NSd F 12,29 KN Z 11,9 KN )(),e3i ),esje 4+/(6(9j+6+ + 89+

1.&.;. O8)(,(s8 )(),e3( ),esje+ i49(*e( s+6ij+j!


>,Sd ≤ >,5d

,

, , ,

0

V, 2#,919L0V,#

1,1 pl y y

c Rd pl y Rd

M

W f M M KNcm

γ

× ×= = = =

>,Sd F 120, KNm Z 19L,0V KNm ? P(),e3i ),esje 4+/(6(9j+6+ + s+6ij+je

9



1.&.?. P(s@i3+ (8)(,(s8 )(),e3( ),esje+

a< - smjeru osi z?z

Lw

d

t ε < ×

1

LV,9

< 1,0

21, < L ije )(8,e<+ ),(6je,+ i4<(3+6+j+ 2,)8+ + )(s@i

2

,1,0 1,0 2# 0,V9 1V,L

V z w A h t cm= × × = × × =

, . ,

0#

y

pl z Rd V z

M

f V A

γ

= ××

F 1V,L2#,9

# 1,1× F 221, KN

Rd z pl d z V V ,,,

<

21,L0 KN Z 221, KN

1.&.1. I8e,+5ij+ MVN s+6ij+je" )(),e3+ i !4/!*+ si9+

Os 440

Gz,Sd ≤ 0,9 Gz,5d

21,L0 Z 0,9 ×221, F 110,L KN


NSd Z A,29 N pl,5d

12,29 KN Z 0,29 11,9 F 10,#L KN ⇒ is+ ,+4i+ !4/!*e si9e

1,

,,, = Rd z

Rd z V N

M

M .0

>,Sd ≤ > N,G,z,5d

120, KNm Z 19L,0V KNm ⇒ i8e,+5ij+ MNV 4+/(6(9j+6+

1.&.. D(+4 + ,+4ii e9e@e8+

9V



#. U4/!*+ 89+3+ (8)(,(s8


N /,5d F χ Nc,5d

? os ? ? os z?z

-M%N' %3G%C+NC+

li F L,20 cm liz F 92L,L2 cm

';'K7%GN+ G%7KAS7

L,20 ,10,09"y

y

y

l

"λ = = =92L,L2

,#2,00"z z

z

l

"λ = = =

SG''N+ G%7KAS7

2

1

1

Aβ λ

λ λ ⋅=

1

21000L#,L1

2#,9 y

)

f λ π π = × = × =

0,1= Aβ ?za ;e #0

1

2,

1,0 0,LVL#,L1 yλ = × =

,#20,L0

L#,L1 z λ = =

>C'5A+GN+ @%N%C+ %3G%C+NC+

2#00,L 1, 2

20

12,0 100 f

h

b

t mm mm

= = <

= <

linija izvijanja / linija izvijanja c

os os z z


0,12

y χ = 0,9V99 z

χ =

@je,(/+6+ je @+ji 4 $"???

9



, , ,0,9V99 11,9 L,V2


, ,

12,29 L,V2

sd z b Rd N N

KN KN

≤

< X 4+/(6(9j+6+

1.&.. O8)(,(s8 e9e@e8+ + s+6ij+je

( )

( )( )

2 222

1 2 22 2

t w z cr

w z z

k & ' ( ( ) ( k M * * + * +

k ( ) ( k &

π

π ×

× × × × × = × × × + × + + × ÷ × ××

@ F 992 cm

g F ?2#

2 2

h= − F ? 11,9 cm

k F 1k 8 F 1 X 1 F 1,VL

2 F 0

( )20VV =

2 1

) ' KN cm

ν =

+

( )

( ) 222

2 2

1 992 0VV 1,99#,1 21000 2VL 1 #29001,VL

1 2VL #,1 21000 2VL1 992cr M

× × ×× × = × × × + ÷ × × ×

>cr F 0L1,9V KNcm F 0L,1 KNm


, 1,0 V, 2#,9 0,20L1,9V

w pl y y &,

cr

W f M

β λ × × × ×= = =


za 0,2 &, λ = ⇒ χ@7 F 0,L21

β8 F 1

1

,, 1 V, 2#,90,L21 1922,2 19,221,1

w pl y yb Rd &,

M

W f M kNcm KNmβ χ γ

× × × ×= × = × = =

9L



>,Sd ≤ > /,5d

120, KNm Z 19,22 KNm X e9e@e8 4+/(6(9j+6+ + s+6ij+je

1.&.'. I8e,+5ij+ MN <e4 ),(<9e@+ <(3( i46ij+j+

1 1

,

,

min

1 y y d d

y pl y y

M M

k M N A f W f

χ γ γ

×+ ≤

× ××


( ), , ,

,

,

0

1, K 0, V 1,K 0, V 0 1, K0

1,

120,KK

120,KK

y

.

M M M . M

M

M .

.

M

M

M KNm

M KNm

ψ ψ

ψ

β β β β

ψ

β ψ

β

= + × −∆

=

= − = − × =

=

=

∆ =

120,: < 1,0 :1, 1,0< 1,0

120, y .

.

M M M M

M

M ψ ψ

β β β β = + × − = + × − =V

( ) ( ), ,

,

V, V9,102 0,LV 2 1,0 0,L 0,L

V9,10 y

pl y el y y y M

el y

W W

W µ λ β

− −= × × − + = × × − + = − <

1 1,9

: 0,L< 12,11 1,9

0,12 V, 2#,9

1, 09 1, 9

y d

y

y y

y

y

N k

A f

k

k

µ

χ

×= − ≤

× ×

− ×= − ≤

× ×

= ≤

12,1 1,09 120#21

V, 2#, 9 V, 2#, 90,9V99

1,1 1,1

0,L 1

×+ ≤

× ××

<

Xi8e,+5ij+ MN 4+/(6(9j+6+

1.&.#$. I8e,+5ij+ MN s+ ),(<9e@(@ <(3( i46ij+j+

0



1

11

,

,≤

⋅⋅

⋅+

⋅⋅

M

y y pl

&,

d y &,

M

y

z

d

f W

M k

f A

N

γ χ

γ χ

L,019,019,0,

≤−⋅⋅= &, M z &, β λ µ


( ), , , ,

,

,

0

1, K 0, V 1,K 0, V 0 1, K0

1,

120,KK

120,KK

.

M &, M M . M

M

M .

.

M

M

M KNm

M KNm

ψ ψ

ψ

β β β β

ψ

β ψ

β

= + × −∆

=

= − = − × =

=

=

∆ =

,

120,: < 1,0 :1, 1,0< 1,0

120,.

.

M &, M M M

M

M ψ ψ β β β β = + × − = + × − =

V

,0,19 0,19 0,L

0,19 0,L0 1, 0 0,19 0, 0 0,L

z &, M &,

&,

µ λ β

µ

= × × − ≤

= × × − = ≤

1 1,0

0,0 12,11 0,LL 1,0

0,9V99 V, 2#,9

&, d &,

z y

&,

N k

A f

k

µ

χ

×= − ≤

× ×

×= − = <

× ⟨

12,1 0,LL 120#21

V, 2#,9 V, 2#,90,9V99 0,L21

1,1 1,1

0,L1 Z 1

×+ ≤

× ×× ×

X i8e,+5ij+ MN 4+/(6(9j+6+

1



. P,(,+3! s),e+

.#. A+9i4+ ()8e,e:ej+ s),e+

#. U8je5+j 8,ej+ )( )9(2i ,(6+

;tr F I re$ e:3e< $r +$r

+$r F :,00 = cos9° 1 2< J :2,00=cos9° 1×2< F 22,L0 m2

;tr F 0,2 1,9 0,0 22,L0 F ,2# KN

I8 F ;tr = :n @s< F ,2# = :1×1,0< F 0,#L KN=mR

I8d F 1,90 0,#L F 0,9 KN=mR

&. U8je5+j (/ <(3( i46ij+j+ 9+6( (s+3+

Ned F >ed = " F 12,12 = 0,## F #2,1 KN

Σ Ned F #×#2,1 F 11,9 KN

Σ I F ς = #, Σ Ned = @ F :1,00 = #,< :11.9 = 1,0< F 1,12 KN=mR

!!)+ si9+0

I8d JΣ

I F 0,9 J 1,12 F 1,V0 KN=mR

,e+5ije (/ ,(6( s),e+0

5a F 5/ F I @ = 2 F 1,V0 1,0 = 2 F 1#, KN

Ra Rb

2



S%@' KAC' C'@-C- N+ S&5'ET

& 1 F I l F 1,V0 0,L0 F 1,9# KN

& 2 F I l F 1,V0 1,# F 2,VV KN

&# F I l F 1,V0 1, F 2, KN

-N-7+5NC' S%@' - S&5'E-T

1.80 1.46 1.46 1.46 1.46 1.46 1.46 1.46 1.46 1.80

6 .

0 0

Opt. 1:

Utjecaji u gredi: max !1= 3.$4 / min !1= -%.17 !

#



.&. Di@e4i(i,+je s),e+

.&.#. P(/+5i ( )(),e3(@ ),esje!

;e #0$ F 2#,9 kN=cm

Kvadratni cijevni pro$il #06 #06 1,

"a F #0,00 mmd F #0,00 mm

/ F #0,00 mm t$ F 1,0 mm t8 F 1,0 mm

+ F 1,V9 cm2

% F 2,#1 cm

H F 1,9 cm#

i F 1,19 cm

.&.&. K9+siBi+5ij+ )(),e3( ),esje+

a< *r/at

;e #0 X Y F 1,00

Uvjet za klasu 1:

X#0, 00 # 1, 0

19,V91,0

w

d mm

t

− ×= =

##

w

d

t ε ≤ ×

19,V9 Z ##,00 X H,<+8 4+/(6(9j+6+ 9+s! I.

"

/

z

zt$

t8




Uvjet za klasu 1:

## f

bt

ε ≤ ×

#0, 00 # 1, 0

## 1,001,0

− ×⟨ ×

19,V9 < ##,00 ⇒ P(j+si5+ 4+/(6(9j+6+ 9+s! I.

P(),e3i ),esje0 KLASA I

.&.%. O8)(,(s8 )(),e3( ),esje+ ! 89+!

Nc,5d F N pl,5d F0

1,V9 2#,9

1,1 y

M

A f

γ

× ×= F #V,# KN

N'd ^ Nc,5d

N'd F #,11 KN Z #V,# KN )(),e3i ),esje 4+/(6(9j+6+ + 89+

.&.;. D(+4 + ,+4ii e9e@e8+

#. U4/!*+ 89+3+ (8)(,(s8


N /,5d F χ \ Nc,5d

? os ? ? os z?z

-M%N' %3G%C+NC+

li F ### cm liz F ### cm

';'K7%GN+ G%7KAS7

###

2L,91,19

"y

y

y

l

"λ = = =

###2L,9

1,19"z

z

z

l

"λ = = =

SG''N+ G%7KAS7

9



1

2

1

A

λ λ β

λ = ×

1

21000L#,

2#,9 y

)

f λ π π = × = × =

0,1= Aβ ?za klasu %.

1

22L,9

1,0 #,09L#, yλ = × =

2L,9#,09

L#, z λ = =

>C'5A+GN+ @%N%C+ %3G%C+NC+

#01, 00 1, 2

#01, 100

f

h

bt mm mm

= = <

= <

9iij+ i46ij+j+ < 29+/((<9i(6+i ),(Bi9


0,0LL

y χ =

, ,0,0LL #V,# #,V1

b Rd y c Rd N N KN χ = × = × =

,

#,11 #,V1 )d b Rd

N N

KN KN

≤

< X 4+/(6(9j+6+



. P,(,+3! s)(j+ s8!) 8e@e9j s+@+5 ),e( +e,e )9(3e

+nkerna ploča

ApterećenjeT

N F 12,21 KNG F 2#,9 KN

BetonT 1=20

ma6 $jd F 1, $ck F 1, 1,0 F 2,# KN=cm2

c F 1,V9 dp F 1,V9 2,00 F #,90 cm

&ro$il stupaT *'+ 20

" F 2#0 mm / F 20 mm

t8 F V,9 mmt$ F 12,00 mm+ F V, cm2

c ctg

/e$$

c

/

c

l e $ $

#

%

&

V



2

1 # : 2 < : 2 < :2,0 2 #,90< :1,20 2 #,90< 29,20* * A A b c tf c cm= = + × × + × = + × × + × =

2

22: 2 <: 2 < :0,V9 2 #,90< :2#,00 2 1,20 2 #,90< 109,0

w f * c A t c h t cm− ×= + × − × = + × × − × − × =

: 2 2 < 12, 21 0, V9 :2#, 00 2 1, 20 2 #, 902 1,

V,

w f N t h t c N KN

A

× − × − × × × − × − ×= = =

1 12, 21 1,1 # 1,V

2 2,00

N N N N KN

− −= = = =

Naprezanje /etonaT

2 2

1

1

1 1,V0,2 = ma6 2,# =

29,20* jd

*

N KN cm f KN cm

Aσ = = = < =

2 2

1

2

2 1, 0,1 = ma6 2,# =109,0* jd

*

N KN cm f KN cm A

σ = = = < =

e/ljina ankerne pločeT

dp F 20 mm

2 20,2 #,901,L =

2 2*

)d

c M KN cm

σ × ×= = =

2 22,00 2#,901,2

1,10 yk

Rd

M1

dp f M KNcm

γ

× ×= = =

× ×

)/ R/ M M <

1,L KNcm Z 1,2 KNcm

&rjenos "orizontalne sileT

/

e $ $

σc

t 8 J

2 a

r

c

c

/

1 1

2

N.S/.A

σc

V

" m

HEA&;$

N.S/.A

2



&rjenos "orizontalne sile vr4i se preko anker modanika zavarenim sa donje strane anker ploče.

&ro$il modanikaT %&' 100

+ F 10,#2 cm2H.pl F #L,1 cm#

" F 100 mm / F 99 mmt$ F 9,V mmt8 F ,1 mmr F V mm"m F cm ? visina modanika

'$ektivna povr4ina djelovanja opterećenjaT

2#,9

1,100,9V 1,#2# # 2,90

2,292,29

y

M1 f

*k

f

c t cm f γ = × = × =× ×

2 2 0,1 2 0,V0 2 1,#0 ,eff w

b t r c cm= + × + × = + × + × =

2, ,00 #9,9eff

; b hm cm= × = × =

&ritisak na /etonT

2 22#,9 #,000,V = 1,## =#9,9 2,29 2,29

*k * jd

f V KN cm f KN cm ;

σ = = = ≤ = = =

Naprezanje u pojasu modanika :presjek 1 1<T

2 20,V 1,#20,9 =

2 2*

d

c M KNcm cm

σ × ×= = =

2 2#

1,00 1,00 0,9V0,0 =

f

pl

t W cm cm

× ×= = =

0,0 2#,91,V

1,10 pl yd

Rd

M1

W f M KNcm

γ

× ×= = =

d Rd M M <

0,9 KNcm Z 1,V KNcm

L



Naprezanje u pojasu modanika :presjek 2 2<T

.

,00: < 2#,9 : < 1 #,0 .2 #,0 2 #,0 y d

hm M V KNcm pretp%stavka cmm%rta za "zrav$ava$je= × = × = −

+ +

.

.

#L,0 2#,921,10

y pl yd

y Rd

M1

W f M KNcmγ

× ×= = =

. . y d y Rd M M <

1, KNm Z ,2 KNm

Kontrola zavaraT

&retpostavkaT var na "rptu preuzima silu G. Gar na pojasima preuzima moment >.Sd.

Nosivost vara na "rptu

a F # mm ? de/ljina vara

lv F " 2 :t$ J r< F 10,00 2 :0,9V J 0,V0< F V, cm ? duina vara

Nosivost varaT

.

#,002 0,#0 V, 2 11,#

# # 0,0w Rk

w

fu ; a & KN

β

= × × × = × × × =× ×

Sila u pojasu modanikaT

. 11V,0

: < 10,00 0,9V y d

d

f

M N KN

h t = = =

− −

Nosivost vara na pojasu

a F # mm ? de/ljina vara

lv F 2 / ? t8 ? 2 r F 2 9,90 0,1 2 0,V0 F L,1L cm ? duina vara

Nosivost varaT

.

#,000,#0 L,1L V1,0

# # 0,0w Rk

w

fu ; a & KN

β = × × = × × =

× ×

V0



-vjetT

Gar na "rptu

G Z ;8.5k

2#,9 KN Z 11,2L KNm

Gar na pojasu

N.Sd Z ;8.5k

1V,9 KN Z V1,# KNm

'. P,i9(4i

#. R+/i(i3i +5,8 9+6( (6i,+ s+ s)e5iBi+5ij(@ M #0#$

V1



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