Spregnuti_nosac_meduspratne_konstrukcije.pdf

UNIVERZITET U NOVOM SADU Građevinski fakultet Subotica

Kandidat: Adam Mora

SPREGNUTI NOSAČ ME ĐUSPRATNE KONSTRUKCIJE - Semestralni rad iz predmeta SPREGNUTE KONSTRUKCIJE-

Subotica, april 2016.

SADRŽAJ ........................................................................... ............................................ ................... ‐ Zadatak grafičkog rada .................................................. Pretpostavljene dimenzije spregnute konstrukcije ..................................................... .....................................................1 1 ARMIRANO BETONSKA PLOČA Analiza opterećenje ................................................ ......................................................................... .................................................. ............................ ... 2 Statički proračun....................... un ................................................ .................................................. .................................................. ................................. ........ 2 ‐ 3 Dimenzionisanje AB ploče ............................................... ........................................................................ ............................................ ...................4 4 ‐ 7 SPREGNUTI NOSAČ Statička šema i geometrijske karakteristike preseka .................................................. ..................................................8 8 ‐ 11 Analiza opterećenja ................................................ ......................................................................... .................................................. ............................ ... 12 Statički uticaji – uticaji – statički proračun...................... un ............................................... .................................................. ................................. ........ 13 ‐ 14 Proračun napona ............................................... ........................................................................ .................................................. ................................. ........ 15 ‐ 24 ......................................................................... ............................................ ...................25 25 ‐ Tabelarni prikaz napona ................................................ Kontrola napona ................................................ ......................................................................... .................................................. ................................. ........ 26 Dijagrami napona..................... napona............................................... ................................................... .................................................. ................................. ........ 27 Kontrola ugiba......................... ugiba.................................................. .................................................... ................................................... ................................. .........28 28 Proračun sprezanje AB ploče i čeličnog nosača (čepovima)........................................ epovima) ........................................29 29 ‐ 32 Proračun sprezanje AB ploče i čeličnog nosača (moždanik + anker)........................... anker)........................... 33 ‐ 35

1. OSNOVNE DIMENZIJE KONSTRUKCIJE L≔ 19.4 m λ ≔ 7.0 m l duz ≔ 6 ⋅ λ = 42 m

‐ raspon

konstrukcije ‐ osovinski razmak rebra kons. ‐ dužina kons.

2. USVOJENE DIMENZIJE SPREGNUTE KONSTRUKCIJE 2.1 Visina nosača d max ≔

L

15

= 1293.333

d min ≔

mm

d ≔ 1100 mm

L

25

= 776

‐ usvojena

‐ preporuke

mm

visina spregnutog nosača

2.2 Visina AB ploče λ

35

= 20

cm

‐ preporučena

d p ≔ 20 cm

‐ usvojena

vrednost je d p ≥

λ

35

visina AB ploče

2.3 Dimenzije "I" nosača ‐ gornja flanša:

b2 ≔ 300 mm

‐

⎛

b2 ⎞

⎝

20 ⎠

t 2.min ≔ max 10 mm ,

b2.min = 200~250mm /Milenko Pržulj ‐ Spregnute konstrukcije (str.12)

= 15

‐ min

mm

t 2 ≔ 28 mm

debljina gornje flanše

‐ usvojena

debljina gornje flanše

t 1 ≔ 28 mm

‐ usvojena

debljina donje flanše

hw ≔ d − 2 ⋅ d p − t 1 − t 2 = 644 mm

‐ visina

‐ rebro:

⎛

hw

⎝

60

t w.min ≔ max 8 mm ,

,8

mm

+

L

⎞

mm

λ

⎠

= 10.771

mm

t w ≔ 20 mm

‐ min

rebra

debljina rebra

‐ usvojena

debljina rebra

‐ donja flanša:

b1.min ≔ max

⎛ d L , ― , 0.25 ⋅ hw + 100 ⎝ 10 120

⎞ = 261 ⎠

mm

mm

b1 ≔ 450 mm

donje flanše

‐ usvojena širina

⎛

b1 ⎞

⎝

20 ⎠

t 1.min ≔ max 10 mm ,

‐ min širina

= 22.5

‐ min

mm

Page 1 of 35

donje flanše

debljina donje flanše

AB PLOČA 1 Analiza opterećenja 1.1 Stalno opterećenje −2

‐ Slojevi

poda............................ ‐ AB ploča u polju...................... ‐ AB ploča nad osloncem...........

g pod ≔ 1.25 kN ⋅ m −3 −2 g AB.1 ≔ 0.20 m ⋅ 25 kN ⋅ m = 5 kN ⋅ m −3 −2 g AB.2 ≔ 0.40 m ⋅ 25 kN ⋅ m = 10 kN ⋅ m _________________________________

‐ opterećenje

g1 ≔ g pod + g AB.1 = 6.25 kN ⋅ m −2 g2 ≔ g pod + g AB.2 = 11.25 kN ⋅ m

u poljima............. ‐ opterećenje iznad oslonaca.....

−2

1.2 Korisno opterećenje ‐ Pokretno

opterećenje...............

p ≔ 3.5 kN ⋅ m

−2

2 Stački sistem i ucaji ‐ napomena: ‐ stalno

stački proračun je sprovedena pomoću programskog paketa Radimpex Tower

opterećenje je raspoređena po celoj dužini konstrukcije

‐ promenljivo

opterećenje izaziva merodavan moment savijanja u šahovskom rasporedu

Page 2 of 35

Ulazni podaci - Optere ć enje, Stati čk i prora č un Opt. 1: stalno opt (g) 0 0 . 7

p=11. 250

p=11. 250

p=6. 250

0

0 0 . 7

p=11. 250

p=6. 250

1

0 0 . 7

0 0 . 7

p=11. 250

p=6. 250

2

p=11. 250

p=6. 250

3

0 0 . 7

p=11. 250

p=6. 250

4

0 0 . 7

p=11. 250

p=6. 250

5

6

Opt. 2: pokretno opt (p) - polje 0

0 0 . 7

p=3. 0 500 . 7

0

1

0

0 0 . 7

p=3. 0 500 . 7

2

3

0

0 0 . 7

p=3. 0 500 . 7

4

5

6

Opt. 3: pokretno opt (p) - iznad oslonca 0 0 . 7

0

p=3. 500

0 0 . 7

1

2

0 5 . 2 3 0 0 . 7

0 0

5 8 . 3 2

0 0 . 7

1

0 0 . 7

2 4 . 0 1

6 6 . 3 2 -

2

0 7

3

4

0 6 . 6 2 -

6 6 . 3 2 -

0 0 . 7

6 1 . 3 1

0 0 . 7

p=3. 0 500 .

0 0 . 7

3

6 1 . 3 1

4

0

p=3. 0 500 . 7

5

0 5 . 2 3 0 0 . 7

2 4 . 0 1

6

Opt. 1: stalno opt (g)

0 0 . 7

5

5 8 . 3 2

6

Uticaji u gredi: max M3= 23.85 / min M3= -32.50 kNm Opt. 2: pokretno opt (p) - polje

0 0 . 7

0 0

7 0 . 9 -

1

4 5 . 0 2 0 0 . 7

0

9 3 . 2 1

0 0 . 7

2

0 0 . 7

3

0 0 . 7

4

0 0 . 7

5

6

Uticaji u gredi: max M3= 17.12 / min M3= -9.07 kNm Opt. 3: pokretno opt (p) - iznad oslonca

0 0 . 7

1

7 0 . 9 -

8 5 . 3 1

5 3 . 4 1

2 1 . 7 1

0

0 0 . 7

2 4 . 7 -

4 2 . 0 1

0 0 . 7

2

4 2 . 8 -

3

0 0 . 7

8 0 . 4 1

0 0 . 7

4

Uticaji u gredi: max M3= 17.10 / min M3= -20.54 kNm

2 1 . 9 -

0 0 . 7

5

6

0 1 . 7 1

Page 3 of 35 Tower - 3D Model Builder 7.0 - x64 Edition

For non-commercial use only

Radimpex - www.radimpex.rs

3 Dimenzionisanje AB ploče −2

f b ≔ 2.55 kN ⋅ cm −2 σ v ≔ 40 kN ⋅ cm

MB 40 => RA 400/500 => a0 ≔ 2.5 cm

3.1 Presek u polju 3.1.1 glavna armatura u polju Mg ≔ 23.85 kN ⋅ m M p ≔ 17.12 kN ⋅ m Mu ≔ 1.6 ⋅ Mg + 1.8 ⋅ M p = 68.976 kN ⋅ m ‐ pretpostavka:

h ≔ d p − a0 −

Aa` ≔ 1.54 cm

RΦ14

Φ

2

= 16.8

2

Φ ≔ 14

mm

cm

b ≔ 100 cm

‾‾‾ f b ⋅ b k ≔ h ⋅ ― = 3.23

k usv ≔ 3.203

Mu

Aa1 ≔ μ` ⋅ b ⋅ h ⋅ min μ`

f b

σ v

= 11.101

cm

=> εa / εb =10/1.9 ‰; μ` ≔ 10.365%

2

≔ 0.1%

min Aa1

≔ min μ` ⋅ b ⋅ d p = 2

emin ≔ min

⎛ Aa` ⎝ Aa1

⋅ 100

cm

⎞

cm

⎠

2

= 13.873

cm

e≔ 12.5 cm

Aa1.stv ≔

Aa` e

‐ usvojeni

⋅ 100

cm

= 12.32 cm

razmak između šipki

2

A

―a1 = 0.901

‐ iskorišćenost

armature

Aa1.stv

Usvojeno: RΦ14 /12.5 za glavnu armaturu u polju

Page 4 of 35

3.1.2 podeona armatura u polju ‐ pretpostavka:

min Aa1p

≔ max

e p.rač ≔

Aa` min Aa1p

Aa` ≔ 0.5 cm

RΦ8

2

0.2 ⋅ Aa1.stv , min μ pod ⋅ b ⋅ h = 2.464

⋅ 100

cm

Φ≔8

cm

Aa` e p

⋅ 100

≔ 0.085%

= 20.292 cm

‐ usvojeni

cm

min μ pod

2

e p ≔ 20 cm

Aa1p ≔

mm

= 2.5

e p.max ≔ min 4 ⋅ d p , 30 cm

cm


2

= 30

cm

Usvojeno: RΦ8 /20 za podeonu armaturu u polju

Page 5 of 35

3.2 Presek nad osloncem 3.2.1 glavna armatura nad osloncem Mg ≔ −32.50 kN ⋅ m M p ≔ −20.54 kN ⋅ m Mu ≔ 1.6 ⋅ Mg + 1.8 ⋅ M p = −88.972 kN ⋅ m ‐ pretpostavka:

h ≔ d p − a0 −

Φ

2

Aa` ≔ 2.01 cm

RΦ16

= 16.7

2

Φ ≔ 16

mm

cm

b ≔ 100 cm

k ≔ h ⋅

‾‾‾ f b ⋅ b Mu

Aa1 ≔ μ` ⋅ b ⋅ h ⋅ min μ`

= 2.827 f b

σ v

k usv ≔ 2.781

= 14.881

cm

=> εa / εb =10/2.4 ‰; μ` ≔ 13.978%

2

≔ 0.1%

min Aa1

≔ min μ` ⋅ b ⋅ d p = 2

emin ≔ min

⎛ Aa` ― ⋅ 100 ⎝ Aa1

cm

⎞

cm

⎠

2

= 13.507

cm

e≔ 12.5 cm

‐ usvojeni


Aa` 2 Aa1.stv ≔ ― ⋅ 100 cm = 16.08 cm e Aa1 Aa1.stv

= 0.925

‐ iskorišćenost

armature

Usvojeno: RΦ16 /12.5 za glavnu armaturu iznad osloncima

Page 6 of 35

3.2.2 podeona armatura nad osloncem ‐ pretpostavka:

min Aa1p

≔ max

e p.rač ≔

Aa` min Aa1p

Aa` ≔ 0.5 cm

RΦ8

2

0.2 ⋅ Aa1.stv , min μ pod ⋅ b ⋅ h = 3.216

⋅ 100

cm

Φ≔8

cm

Aa` e p

⋅ 100

≔ 0.085%

= 15.547 cm

‐ usvojeni

cm

min μ pod

2

e p ≔ 15 cm

Aa1p ≔

mm

= 3.333 cm

e p.max ≔ min 4 ⋅ d p , 30 cm


2

= 30

cm

Usvojeno: RΦ8 /12.5 za podeonu armaturu iznad osloncima

Page 7 of 35

SPREGNUTI NOSAČ 1 Stačka šema ‐ prosta greda, raspona "L":

L = 19.4 m

2 Geometrijske karakteriske preseka 2.1 Čelični deo preseka

As ≔ 338.8 cm

2

y s ≔ 79.17 cm Is ≔ 231204 cm

4

E s ≔ 21000 kN ⋅ cm γ s ≔ 78.5 kN ⋅ m

2

−

3

−

‐ transformacija:

E` ≔ E s = 21000 kN ⋅ cm

ns ≔

E s

=

2

−

1

E`

As` ≔ ns ⋅ As = 338.8 cm

2

Is` ≔ ns ⋅ Is = 231204 cm

4

Page 8 of 35

2.2 Betonski deo preseka E b ≔ 3400 k N ⋅ cm

MB 40 => γ b ≔ 25

⋅

kN m

−2

−3

‐ efekvna širina

‐ PBAB

`87 (tab.8)

‐ spec.

težina armiranog betona

betonske flanše:

b0 ≔ 18.1 cm

‐ osovinsko

rastojanje čepova

Le3 ≔ 0.70 ⋅ L = 1358 cm

‐ EN

1994‐2/ Slika 5.1

λ − b0 bi ≔ ― 2

‐ EN

1994‐2/5.4.1.2

‐ EN

1994‐2/5.4.1.2

cm

⎞ , bi = 169.75 ⎝ 8 ⎠ be ff .1 ≔ b0 + 2 ⋅ bei = 357.6 cm bei ≔ min

⎛ Le3

= 340.95

cm

‐ efekvna širina

Page 9 of 35

betonske flanše /EN 1994‐2 (5.3)

‐ geometrijske

karakteris ke su određeni pomoću AutoCAD‐a:

---------------- REGIONS ---------------Area: 7982.9401 cm^2 Perimeter: 778.2940 cm Bounding box: X: -178.8000 -- 178.8000 cm Y: -28.0146 -- 11.9854 cm Centroid: X: 0.0000 Y: 11.9854 cm Moments of inertia: X: 536216.0743 cm^4 Y: 76343905.1533 cm^4

‐ efekvna

površina ‐ efekvni obim

‐ momen

inercije

_______________________________________________________ Ab ≔ 7982.94 cm

2

‐ površina

y b ≔ 11.9854 cm Ib ≔ 536216 cm

‐ težište

4

betonskog preseka

bet. preseka

‐ moment

inercije bet. preseka

‐ transformacija:

E` ≔ E s = 21000 kN ⋅ cm

nb ≔

E b E`

−2

‐ modul

= 0.162

‐ koef.

Ab` ≔ nb ⋅ Ab = 1292.476 cm Ib` ≔ nb ⋅ Ib = 86816 cm

4

2

elast. čelika

transformacije

‐

transformisana površina bet. preseka

‐

transformisani mom. inercije bet. preseka

Page 10 of 35

2.3 Spregnu presek y s = 79.17 cm y b = 11.985 cm

‐ težište čeličnog

dela ‐ težište betonskog dela

d c ≔ y s − y b = 67.185 cm

‐ rastojanje

2

As` = 338.8 cm 2 Ab` = 1292.476 cm A ≔ As` + Ab` = 1631.276 cm

transformisana površina čeličnog preseka ‐ transformisana površina betonskog preseka ‐

2

‐ površina

Ab` ⋅ d c Y s ≔ ―― = 53.231 cm A As` ⋅ d c Y b ≔ −― = −13.954 cm A Ib` = 86816 cm

spregnutog preseka

‐ težište čeličnog ‐ težište

dela spregnutog preseka

betonskog dela spregnutog preseka

4

Is` = 231204 cm I ≔ Ib` + Ab` ⋅ Y b

između težišta čeličnog i betonskog preseka

2

4

2

+ Is` + As` ⋅ Y s = 1529671.953

cm

4

Page 11 of 35

‐ mom.

inercije spregnutog preseka

3 Analiza optere ćenja 3.1 Faza I ‐ sopstvena

težina čeličnog nosača.............................

gI ≔ As ⋅ γ s = 2.66

kN

― m

3.2 Faza II ‐ sopstvena

težina svežeg betona...............................

gII ≔ Ab ⋅ γ b = 19.957

kN m

3.3 Faza III ‐ reakcija

privremenog oslonca...................................

Rc ≔

5 8

⋅ gII ⋅ L = 241.983

kN

3.4 Faza IV ‐ stalno

optere ćenje...................................................

Δg ≔ 1.25

kN m

2

⋅ λ = 8.75

3.5 Faza V ‐ pokretno

opterećenje...............................................

p` ≔ p ⋅ λ = 24.5

4 Stački ucaji ‐ stački

proračun je sproveden pomoću programskog paketa Radimpex Tower

Page 12 of 35

kN

― m

kN m

Ulazni podaci - Optere ć enje Faza 1: I Faza Opt. 1: sopstvena težina čeličnog nosača (gI)

p=2. 660

5 8 . 4

0

0

5 5 . 4 1

1

2

Faza 2: II Faza Opt. 2: težina svežeg betona (gII)

p=19. 957

5 8 . 4

0

0

5 5 . 4 1

1

2

Faza 3: III Faza Opt. 3: reakcija privremenog oslonca (Rc)

5 8 . 4

0

0

1

3 8 9 . 1 4 2 = P

5 5 . 4 1

2

Faza 4: IV Faza Opt. 4: težina poda (delta g)

p=8. 750

5 8 . 4

0

0

5 5 . 4 1

1

2

Faza 5: V Faza Opt. 5: korisno opterećenje (p`)

p=24. 500

5 8 . 4

0

0

5 5 . 4 1

1

2




Stati čk i prora č un Faza 1: I Faza Opt. 1: sopstvena težina čeličnog nosača (gI)

0 0

5 8 . 4

5 5 . 4 1

1

7 7 . 3 9

Faza 1: I Faza Opt. 1: sopstvena težina čeličnog nosača (gI)

5 8 . 4

0 2

0

4 1 . 5 2 1

0

5 8 . 4

5 5 . 4 1

1

9 7 6 6 . . 2 7 1 3 1 1

5 8 . 4

0 2

1

2

Uticaji u gredi: max T2= 25.80 / min T2= -25.80 kN Faza 2: II Faza Opt. 2: težina svežeg betona (gII)

8 . 2 3 2 -

0

5 5 . 4 1

0 9 . 2 1 -

0 8 . 5 2 -

Uticaji u gredi: max M3= 125.14 / min M3= -0.00 kNm Faza 2: II Faza Opt. 2: težina svežeg betona (gII) 0

0 8 . 5 2

0

9 6 . 2 3 1

0 0 . 4 2

9 7 . 2 7

5 5 . 4 1

1

9 7 . 2 7 -

Uticaji u gredi: max M3= 132.69 / min M3= -232.80 kNm Faza 3: III Faza Opt. 3: reakcija privremenog oslonca (Rc)

9 7 . 0 2 1

2

9 7 . 0 2 1 -

Uticaji u gredi: max T2= 120.79 / min T2= -120.79 kN Faza 3: III Faza Opt. 3: reakcija privremenog oslonca (Rc) 9 9 . 0 2 1

0 0

5 8 . 4

5 5 . 4 1

1 1 8 . 6 8 5

5 8 . 4

0 2

0

2 6 . 3 7 1 1

1

5 5 . 4 1

2

9 9 . 0 2 1 -

Uticaji u gredi: max M3= 1173.62 / min M3= -0.00 kNm Faza 4: IV Faza Opt. 4: težina poda (delta g)

Uticaji u gredi: max T2= 120.99 / min T2= -120.99 kN Faza 4: IV Faza Opt. 4: težina poda (delta g) 8 8 . 4 8

0 0

5 8 . 4

5 5 . 4 1

1

5 4 . 8 0 3

5 8 . 4

0 2

0

4 6 . 1 1 4

2

4 4 . 2 4 -

8 8 . 4 8 -

Uticaji u gredi: max M3= 411.64 / min M3= -0.00 kNm Faza 5: V Faza Opt. 5: korisno opterećenje (p`)

1

5 5 . 4 1

Uticaji u gredi: max T2= 84.88 / min T2= -84.88 kN Faza 5: V Faza 5 6 Opt. 5: korisno opterećenje (p`) . 7 3 2

0 0

5 8 . 4

5 5 . 4 1

1

5 6 . 3 6 8

0 6 . 2 5 1 1

5 8 . 4

0 2

Uticaji u gredi: max M3= 1152.60 / min M3= -0.00 kNm

0

5 6 . 7 3 2 -

1

5 5 . 4 1

2

2 8 . 8 1 1 -

Uticaji u gredi: max T2= 237.65 / min T2= -237.65 kN




5 Proračun napona 5.1 Faza I ‐ postavljanje čeličnog nosača gI nb = 0.162 ns = 1 d = 110 cm y s = 79.17 cm

‐ visina

spregnutog nosača ‐ težište čeličnog dela od gornje ivice betonskog preseka

y 1 ≔ d − y s = 30.83 cm y 2 ≔ 2 d p − y s = −39.17 cm Is = 231204 cm

4

5.1.1 napon na mestu L/2 (t=0): M ≔ 125.14 kN ⋅ m

σ s2 ≔ ns ⋅

σ s1 ≔ ns ⋅

M Is M Is

kN

⋅ y 2 = −2.12 ―2 cm

kN

⋅ y 1 = 1.669 ―2 cm


σ s2 ≔ ns ⋅

σ s1 ≔ ns ⋅

M Is M Is

⋅ y 2 = −1.589

kN cm

2

kN

⋅ y 1 = 1.25 ―2 cm

Page 15 of 35

5.2 Faza II ‐ podupiranje i betoniranje AB ploče gII nb = 0.162 ns = 1 y 1 = 30.83 cm y 2 = −39.17 cm Is = 231204 cm

4

5.2.1 napon na mestu L/2 (t=0): M ≔ −232.80 kN ⋅ m

σ s2 ≔ ns ⋅

σ s1 ≔ ns ⋅

M Is M Is

kN

⋅ y 2 = 3.944 ―2 cm

⋅ y 1 = −3.104

kN cm

2


σ s2 ≔ ns ⋅

σ s1 ≔ ns ⋅

M Is M Is

kN

⋅ y 2 = −1.994 ―2 cm

⋅ y 1 = 1.569

kN cm

2

Page 16 of 35

5.3 Faza III ‐ uklanjanje privemenog osloca (Rc) d = 110 cm d p = 20 cm Y b = −13.954 cm

ns = 1 nb = 0.162

y 3 ≔ Y b − y b = −25.939 cm y 2 ≔ 2 d p + y 3 = 14.061 cm y 1 ≔ d + y 3 = 84.061 cm I= 1529671.953 cm

kontrola ≔ y 3 − y 2

4


σ b3 ≔ nb ⋅ σ b2 ≔ nb ⋅

σ s2 ≔ ns ⋅

σ s1 ≔ ns ⋅

M I M I

M I M I

kN

⋅ y 3 = −0.322 ―2 cm kN

⋅ y 2 = 0.175 ―2 cm

kN

⋅ y 2 = 1.079 ―2 cm

kN

⋅ y 1 = 6.449 ―2 cm


σ b3 ≔ nb ⋅

σ b2 ≔ nb ⋅

σ s2 ≔ ns ⋅

σ s1 ≔ ns ⋅

M I M I

M I M I

kN

⋅ y 3 = −0.161

cm

2

kN

⋅ y 2 = 0.087 ―2 cm

kN

⋅ y 2 = 0.539 ―2 cm

kN

⋅ y 1 = 3.225 ―2 cm

Page 17 of 35

= 40

cm

(debljina betonske ploče)

5.4 Faza IV ‐ dopunsko stalno optere ćenje Δg y 1 = 84.061 cm y 2 = 14.061 cm y 3 = −25.939 cm I= 1529671.953 cm

ns = 1 nb = 0.162

4


σ b3 ≔ nb ⋅

σ b2 ≔ nb ⋅

σ s2 ≔ ns ⋅

σ s1 ≔ ns ⋅

M I M I

M I M I

kN

⋅ y 3 = −0.113 ―2 cm

kN

⋅ y 2 = 0.061

cm

2

kN

⋅ y 2 = 0.378 ―2 cm

kN

⋅ y 1 = 2.262 ―2 cm


σ b3 ≔ nb ⋅

σ b2 ≔ nb ⋅

σ s2 ≔ ns ⋅

σ s1 ≔ ns ⋅

M I M I

M I M I

kN

⋅ y 3 = −0.085

cm

2

kN

⋅ y 2 = 0.046 ―2 cm

kN

⋅ y 2 = 0.284 ―2 cm

⋅ y 1 = 1.695

kN cm

2

Page 18 of 35

5.5 Faza V ‐ pokretno opterećenje (p) y 1 = 840.61 mm y 2 = 140.61 mm y 3 = −259.39 mm I= 1529671.953 cm

ns = 1 nb = 0.162

4


σ b3 ≔ nb ⋅

σ b2 ≔ nb ⋅

σ s2 ≔ ns ⋅

σ s1 ≔ ns ⋅

M I M I

M I M I

kN

⋅ y 3 = −0.316 ―2 cm

kN

⋅ y 2 = 0.172

cm

2

kN

⋅ y 2 = 1.059 ―2 cm

kN

⋅ y 1 = 6.334 ―2 cm


σ b3 ≔ nb ⋅

σ b2 ≔ nb ⋅

σ s2 ≔ ns ⋅

σ s1 ≔ ns ⋅

M I M I

M I M I

kN

⋅ y 3 = −0.237

cm

2

kN

⋅ y 2 = 0.129 ―2 cm

kN

⋅ y 2 = 0.794 ―2 cm

⋅ y 1 = 4.746

kN cm

2

Page 19 of 35

5.6 Ucaji od skupljanja betona ‐ geometrijske

karakteris ke usled skupljanja u vreme t=n

Ab = 7982.94 cm

2

‐ površina

O ≔ 2 ⋅ be ff .1 = 715.2 cm

2 Ab

d m ≔

= 22.324

O

‐ približni

efekvnog betonskog preseka obim izložene površine

‐ približna

cm

srednja debljina preseka

‐ srednja

debljina preseka ~20cm ‐ opterećenje nakon 90 dana, uklanjanje privremenih oslonaca ‐ relavna vlažnost sredine 90% φn ≔ 1.3

‐ koeficijent

E b = 3400 kN ⋅ cm E bφ ≔

−2

E b

‐ modul

= 2028.64

1 + 0.52 ⋅ φn

tečenja nearmiranog betona /PBAB`87 (tab.59/1)

⋅

kN cm

−2

elasčnos betona /PBAB`87

‐ imaginarni

računski modul elasčnos prema Fritz‐u / Milenko Pržulj S.Kons. (tab.4.1)

‐ srednja

debljina preseka ~20cm ‐ relavna vlažnost sredine 90% 1 εsk ≔ −0.12 ⋅ ― 1000

‐ konačan

vr. skupljanja nearmir. betona /PBAB`87 (tab.57/1)

______________________________________________ E` = 21000 kN ⋅ cm

−2

‐ merodavan

ψsk ≔ 0.55 nsk ≔

E` E b

modul elasčnos

‐ mulplikator koef. tečenja

⋅

1 + ψsk ⋅ φn = 10.593

‐ koef.

/EN 1994‐2 (5.4.2.2)/ Fritz=0.52

trans. pri skupljanju betona /EN 1994‐2 (5.4.2.2)

______________________________________________ Ask ≔ As +

Ab nsk

= 1092.43

cm

2

‐ idealna

y s = 79.17 cm y b = 11.985 cm

površina spregnutog preseka pri skupljanju



d c ≔ y s − y b = 67.185 cm

‐ rastojanje


−1

⋅ Ab ⋅ d c Y s.sk ≔ ――― Ask nsk

As ⋅ d c Y b.sk ≔ −― Ask Isk ≔

Ib nsk

+

Ab nsk

= 46.348

= −20.836 2


cm

‐ težište

cm

2

⋅ Y b.sk + Is + As ⋅ Y s.sk = 1336813.459 cm



4

Page 20 of 35

‐ mom.

inerc. pri skupljanju

‐ rastojanje

karakteris čnih tačaka

y 3.sk ≔ Y b.sk − y b = −32.822 cm y 2.sk ≔ 2 d p + y 3.sk = 7.178 cm y 1.sk ≔ d + y 3.sk = 77.178 cm ‐ presečne

kontrola ≔ y 3.sk − y 2.sk

sile usled skupljanja

Nsk ≔ E bφ ⋅ Ab ⋅ εsk = −1943.341 kN Msk ≔ Nsk ⋅ Y b.sk = 404.919 kN ⋅ m

‐ napon

u betonu (t=n):

kN

εsk ⋅ E bφ = −0.243 ― cm

σ 3.sk.b ≔

Nsk nsk ⋅ Ask

+

2

Msk nsk ⋅ Isk

⋅ y 3.sk − εsk ⋅ E bφ = −0.018

kN cm

2

Nsk Msk kN σ 2.sk.b ≔ ―― + ― ⋅ y 2.sk − εsk ⋅ E bφ = 0.096 ―2 nsk ⋅ Ask nsk ⋅ Isk cm

‐ naponi u čeliku (t=n):

σ 2.sk.č ≔

Nsk Ask

+

Msk Isk

⋅ y 2.sk = −1.561

Nsk Msk σ 1.sk.č ≔ ― + ― ⋅ y 1.sk = 0.559 Ask Isk

kN cm

2

kN

―2 cm

Page 21 of 35

= 40

cm


5.7 Ucaji usled tečenje betona 5.7.1 karakteris ke preseka usled tečenje u vreme t=n

E` = 21000 kN ⋅ cm

−2

‐ merodavan

φn = 1.3 ψL ≔ 1.10 nte ≔

E` E b

‐ mulplikator

⋅

1 + ψL ⋅ φn = 15.009

Ate ≔ As +

Ab nte

= 870.683

cm

‐ koef.

2


As ⋅ d c Y b.te ≔ −― Ate

nte

‐ rastojanje


−1

⋅ Ab ⋅ d c Y s.te ≔ ――― Ate

Ib

površina spregnutog preseka pri tečenju


d c ≔ y s − y b = 67.185 cm

Ite ≔

koef. tečenja /EN 1994‐2 (5.4.2.2)/ Fritz=1,10

trans. pri skupljanju betona /EN 1994‐2 (5.4.2.2)

‐ idealna

y s = 79.17 cm y b = 11.985 cm

nte

modul elasčnos

+

Ab nte

= 41.042

= −26.143 2


cm

‐ težište

cm

2

⋅ Y b.te + Is + As ⋅ Y s.te = 1201128.772



cm

4

Page 22 of 35

‐ mom.

inerc. pri tečenju

y 3.te ≔ Y b.te − y b = −38.128 cm y 2.te ≔ 2 d p + y 3.te = 1.872 cm y 1.te ≔ d + y 3.te = 71.872 cm

kontrola ≔ y 3.te − y 2.te

5.7.2 napon u preseku L/2 (t=n): MIII ≔ 1173.62 kN ⋅ m MIV ≔ 411.64 kN ⋅ m MIII.IV ≔ MIII + MIV = 1585.26 kN ⋅ m ‐ napon

u betonu:

σ 3.te ≔

MIII.IV nte ⋅ Ite

cm

MIII.IV σ 2.te ≔ ― ⋅ y 2.te = 0.016 nte ⋅ Ite ‐ napon

kN

⋅ y 3.te = −0.335

2

kN

―2 cm

u čeliku:

MIII.IV σ 2.te ≔ ― ⋅ y 2.te = 0.247 Ite

―2


―2

kN

cm

kN

cm

5.7.3 napon u preseku L/4 (t=n): MIII ≔ 586.81 kN ⋅ m MIV ≔ 308.45 kN ⋅ m MIII.IV ≔ MIII + MIV = 895.26 kN ⋅ m ‐ napon

u betonu:

MIII.IV σ 3.te ≔ ― ⋅ y 3.te = −0.189 nte ⋅ Ite

σ 2.te ≔

‐ napon

MIII.IV nte ⋅ Ite

⋅ y 2.te = 0.009

kN

―2 cm

kN cm

2

u čeliku:


kN

―2


cm

kN

―2 cm

Page 23 of 35

= 40

cm


5.8 Ucaji od temperaturne promene ΔT ≔ 15

‐ temperaturna

−5

αt ≔ 1.2 ⋅ 10

‐ koef.

−6

εsk = −120 ⋅ 10

temperaturne dilatacije /EN 1994‐2 (5.4.2.5)

‐ konačan

−6

εtemp ≔ αt ⋅ ΔT = 180 ⋅ 10

razlika između čelika i betona

vr. skupljanja nearmir. betona /PBAB`87 (tab.9)

‐ dilatacija pri

temperaturne promene

| εtemp | ― = 1.5 | εsk | ‐ napon

u betonu:

σ 3.temp ≔

| εtemp | kN ― ⋅ σ 3.sk.b = −0.028 ―2 | εsk | cm

σ 2.temp ≔

| εtemp | kN ― ⋅ σ 2.sk.b = 0.144 ―2 | εsk | cm

‐ napon

u čeliku:

σ 2.temp ≔

σ 1.temp ≔

| εtemp | kN ― ⋅ σ 2.sk.č = −2.342 ―2 | εsk | cm | εtemp | |

εsk

|

⋅ σ 1.sk.č = 0.838

kN cm

2

6 Tabelarni prikaz rezultata ‐ rezulta

su prikazani na sledećoj strani

Page 24 of 35

E + O J t Δ σ O K N E + N S Ć V V N E + O U R g N P E σ ) S O T = q n O D P σ = O t

7 9 6 . 0 -

8 2 4 . 0

3 7 7 . 0 -

E + O J t Δ σ O K N E + N S Ć V V N E + O U R g σ N P E = S O T q O D P σ O

2 7 4 . 0 -

8 7 3 . 0

2 5 5 . 6 -

9 1 3 . 4 1

0 1 6 . 8

E s J k σ O N + N E φ V Ć σ O E + I I N R + S E I O T g P = O σ

7 0 2 . 0 -

5 0 1 . 0

4 0 0 . 5 -

5 3 7 . 8

8 4 4 . 4 1

E + O J t Δ σ O K N E + S N Ć V V N E + g O U R σ N P E = O T S q O D P σ O

1 1 5 . 0 -

6 0 4 . 0

8 0 3 . 4 -

3 2 3 . 3 1

E J V O N I + N E I I V Ć I E I O + I N R + E S T I O P = g O σ

6 4 2 . 0 -

3 3 1 . 0

0 6 7 . 2 -

9 3 7 . 7

8 2 0 . 0 -

4 4 1 . 0

2 4 3 . 2 -

8 3 8 . 0

) e V I j ; n I I e I ( f č e = t φ

9 8 1 . 0 -

9 0 0 . 0

0 4 1 . 0

7 5 3 . 5

e j n ) a j s l k σ p ( u k s

8 1 0 . 0 -

6 9 0 . 0

1 6 5 . 1 -

9 5 5 . 0

7 3 2 . 0 -

9 2 1 . 0

4 9 7 . 0

6 4 7 . 4

a z ) a g f Δ ( V I

5 8 0 . 0 -

6 4 0 . 0

4 8 2 . 0

5 9 6 . 1

a z ) a c f R I ( I I

1 6 1 . 0 -

7 8 0 . 0

9 3 5 . 0

5 2 2 . 3

4 9 9 . 1 -

9 6 5 . 1

9 8 5 . 1 -

0 5 2 . 1

2 8 7 . 5 1

(

x a m

σ

E s J k σ O N + N E φ V Ć σ O E + I I N R + S E I O T g P = O σ

E + O J t Δ σ O K N E + S N Ć V V N E + g O U R σ N P E = O T q ) S 0 O D P σ = O t

x a m

σ

3 5 3 . 0 -

9 7 7 . 0 -

2 1 1 . 0

2 5 5 . 0

0 1 5 . 0

8 9 9 . 1

(

x a m

σ

A N O P A N Z A K I R P I N R A L E B A T

E J V O N I + N E I I V Ć I E I O + I N R + E S T I O P = g O σ

) n = t ( i

σ

) 0 = t ( i

σ

σ

6 3 2 . 0

1 8 2 . 3

6 7 2 . 7

8 2 0 . 0 -

4 4 1 . 0

2 4 3 . 2 -

8 3 8 . 0

) e V I j ; n I I e I ( f č e = t φ

5 3 3 . 0 -

6 1 0 . 0

7 4 2 . 0

6 8 4 . 9

e j n ) a j s l k σ p ( u k s

8 1 0 . 0 -

6 9 0 . 0

1 6 5 . 1 -

9 5 5 . 0

6 1 3 . 0 -

2 7 1 . 0

9 5 0 . 1

4 3 3 . 6

a z ) a g f Δ ( V I

3 1 1 . 0 -

1 6 0 . 0

8 7 3 . 0

2 6 2 . 2

a z ) a c f R I ( I I

2 2 3 . 0 -

5 7 1 . 0

9 7 0 . 1

9 4 4 . 6

) n = t ( σ

) 0 = t ( σ

a z a f I 3

2

4 4 9 . 3

4 0 1 . 3 -

0 2 1 . 2 -

9 6 6 . 1

2 1 b b s s σ σ σ σ

σ

a z ) a p f ( V

i

a z a f I I

2 / L

. t p ) m Δ σ e ( t

i

σ

a z ) a p f ( V

) 0 = t (

x a m

5 3 4 . 0 -

. t p ) m Δ σ e ( t

) n = t (

a z a f I I a z a f I

4 / L

Page 25 of 35

3

2

2 1 b b s s σ σ σ σ

7 Kontrola napona 7.1 Kontrola napona u čeliku: ‐ Osnovni

čelik S 235

materijal:

16 < t ≤ 40

mm

σ v ≔ 23.5 kN ⋅ cm ‐ drugi

−2

slučaj opterećenja II.S.O.:

ν II ≔

4 3

= 1.333

σ s.dop ≔ σ v ⋅ ν II

−1

= 17.625

σ s.max.II ≔ 15.782 kN ⋅ cm ‐ prvi

⋅

kN cm

−2

σ s.max.II

−2

σ s.dop

= 0.895

‐ iskorišćenost preseka

slučaj opterećenja I.S.O.: ν I ≔ 1.5 σ s.dop ≔ σ v ⋅ ν I

−1

= 15.667

σ s.max.I ≔ 14.448

⋅

k N cm

⋅

kN cm

−2

−2

σ

s.max.I = 0.922 ―

‐ iskorišćenost

preseka

σ s.dop

7.2 Kontrola napona u betonu: ‐ MB

40; debljina ploče = 20 / 40 cm>16cm σ b.dop ≔ 1.3 kN ⋅ cm

−2

σ b.max ≔ −0.779 kN ⋅ cm

‐ Milenko

−2

| σ b.max | | σ b.dop |

Page 26 of 35

= 0.599

Pržulj S.Kons. (tab.9)

‐ iskorišćenost preseka

II

I

III

IV

V

sigma g (t=0)

sigma q (t=0)

kN

[cm2]

3

-

+

-

+

-

+

-

+

-

+

L/2

2

t=0 -

+

-

+

1

skupljanje

tecenje (III+IV)

sigma g (t=n)

temperatura

sigma q (t=n)

3

-

+

-

+

-

+

-

+

-

+

L/2 t=n

2

1

II

I

III

IV

V

sigma g (t=0)

sigma q (t=0)

3

-

+

-

+

-

+

-

+

-

kN

[cm2]

+

L/4 2

t=0

-

+

-

+

1

skupljanje

tecenje (III+IV)

sigma g (t=n)

temperatura

sigma q (t=n)

3

-

+

-

+

-

+

-

+

-

+

L/4 t=n

2

Page 27 of 35 1

8 Kontrola ugiba δ≔

1 EI

⋅

MM` d z

4

Is = 231204 cm 4 I= 1529671.953 cm −1

gI = 2.66 kN ⋅ m −1 gII = 19.957 kN ⋅ m −1

Δg = 8.75 kN ⋅ m −1 p` = 24.5 kN ⋅ m

8.1 Pomeranje usled faze I:

⎛ ⎛ g⋅ 1 1 δI ≔ ⋅ ⎜2 ⋅ ⋅ 9.7 ⋅ 4.85 ⋅ ⎜125.14 + I ⎝ E` ⋅ Is ⎝ 3

2

0.5 L 8

⎞⎞ ⎟⎟ ⋅ kN ⋅ m ⎠⎠ 1

⋅

kN m

3

= 10.104

mm

8.2 Pomeranje usled faze III: 1 δIII ≔ ― E` ⋅ I

⋅

⎛ 1 ⎞ 2 ⋅ ⋅ 9.7 ⋅ 4.85 ⋅ 1173.62 ⎝ 3 ⎠

⋅

kN m

3

= 11.459

mm

8.3 Pomeranje usled faze IV: 2 ⎛ ⎛ ⎞⎞ g L Δ 1 ⋅ 0.5 1 ⎟⎟ δIV ≔ ― ⋅ ⎜2 ⋅ ⋅ 9.7 ⋅ 4.85 ⋅ ⎜411.64 + ――― ⋅ ― ⎝ E` ⋅ I ⎝ 3 kN ⋅ m ⎠⎠ 8

1

⋅

3

= 5.024

⋅

3

= 14.067

kN m

mm

8.4 Pomeranje usled faze V:

⎛ ⎛ p` ⋅ 1 ⎜ 1 δV ≔ ⋅ 2 ⋅ ⋅ 9.7 ⋅ 4.85 ⋅ ⎜1152.60 + ⎝ E` ⋅ I ⎝ 3

2

0.5 L 8

⎞⎞ ⎟⎟ ⋅ kN ⋅ m ⎠⎠ 1

kN m

mm

8.5 Pomeranje usled skupljanja betona: Msk = 404.919 kN ⋅ m

1 δsk ≔ ― E` ⋅ I

L

⋅ ⋅ 4.85 ⋅ Msk ⋅ m = 5.93

mm

2

8.6 Ukupni ugib: ‐ stalno

optere ćenje:

Σδ ≔ δI + δIII + δIV + δsk = 3.252

‐ stalno+korisno optere ćenje:

Σδ ≔ δI + δIII + δIV + δV + δsk = 4.658

cm

L f dop ≔ ― 300

= 6.467

Page 28 of 35

cm

cm

9 Proračun sprezanja AB ploče i čeličnog nosača ‐ ČEPOVIMA

2

As` = 338.8 cm Y s = 532.31 mm Sb ≔ Ab` ⋅ Y b = 18034.669 cm 3 Ss ≔ As` ⋅ Y s = 18034.669 cm I= 1529671.953 cm ‐ "T"

3

‐ kontrola

4

iznad oslonaca:

T I.o ≔ −25.80 kN T II.o ≔ −72.79 kN T III.o ≔ −120.99 kN T IV.o ≔ −84.88 kN T V.o ≔ −237.65 kN T o ≔ ‐ "T"

1 2

⋅

T I.o + T II.o

+ T III.o + T IV.o + T V.o = −492.815

kN

na polovini raspona:

T 0.5L ≔ T III.o = −120.99 kN

‐ Smičući

τ o ≔

naponi usled opterećenja

| T o ⋅ Sb | |

τ 0.5L ≔

I

|

= 5.81

kN

‐ iznad

oslonaca

cm

| T 0.5L ⋅ Sb | kN ―― = 1.426 ― | I | cm

‐ na

polovini raspona

________________________________________________

Page 29 of 35

‐ smičući

naponi usled skupljanja i temperaturne promene

be ff .1 = 357.6 cm b ΔT ≔

L

10

= 194

cm

b ΔT.usv ≔ min be ff .1 , b ΔT

= 194

‐ usvojena

dužina gde se uzima u obzir dejstva temperature i skupljanja kod proračuna smicanja

cm

nb = 0.162 −1 nb = 6.176 nsk = 10.593 ‐ položajni

Sb.sk ≔

‐ koef.

transformacije betonskog preseka ‐ primenjeni oblik koef. transformacija betonskog preseka ‐ koef. transformacija čeličnog dela preseka

moment inercije nakon skupljanja

| Ab | ― ⋅ Y b.sk = 15702.824 | nsk |

cm

Ss.sk ≔ As ⋅ Y s.sk = 15702.824 cm

3

3

‐ kontrola

Sb.sk ⎛ Ib ⎞ T sk ≔ εsk ⋅ E b ⋅ nsk ⋅ ― ⋅ Is + ― = 1025.336 kN Y b ⋅ Isk ⎝ nsk ⎠

T ΔT ≔ −αt ⋅ ΔT ⋅ E b ⋅ nb

−1

⎛ S I ⎞ ⋅ ―b ⋅ ⎜Is + ―b−1 ⎟ = 1015.711 Y b ⋅ I ⎝ nb ⎠

kN

‐ smi čuća

sila usled skupljanja

‐ smi čuća

sila usled temp. promene

_____________________________________________________________________

2 ⋅ T sk + T ΔT τ ΔT ≔ ――― b ΔT.usv

kN

= 21.042 ―

‐ napon

smicanja usled skupljanja i temp. promene na kraju nosača

cm

Page 30 of 35

‐ Proračun

napona smicanja u merodavnim presecima i određivanje dužine osiguranje:

τ a ≔ 0.13 kN ⋅ cm

−2

‐ dozvoljeni

b2 = 30 cm

‐ širina

τ dop ≔ τ a ⋅ b2 = 3.9

τ ≔ τ o + τ ΔT = 26.852 τ o − τ dop λ ≔ ―― τ o − τ 0.5L λusv ≔ 500 ‐ Dimenzije

⋅

kN cm

−1

⋅

kN cm

L

betonskog preseka na mestu kontakta sa čelikom

‐ dozvoljeni

−1

⋅ = 422.679

‐ ukupno

cm

2

cm

smičući napon u betonu MB40

smičući napon u betonu

smicanje iznad oslonaca

‐ potrebna

dužina osiguranje moždanicima

‐ usvojena

dužina osiguranje

i nosivost usvojenog čepa:

d ≔ 22 mm

‐ prečnik čepa

hč ep.min ≔ 4 ⋅ d = 88 mm

‐ min

hč ep ≔ 240 mm

‐ usvojena

Hdop.1 ≔ 87 kN

‐ nosivost čepa

h p.min ≔ hč ep + 4 cm = 28 cm ‐ Horizontalne

τ x2 ≔

visina čepa /M.P.S.Kons (str. 84, tab.6.2)

h p ≔ 2 ⋅ d p = 40 cm

‐ visina

smičuće sile:

τ o + τ dop

2

τ + τ x2 τ x1 ≔ ― 2 τ = 26.852

<

visina čepa

= 4.855

kN cm kN

= 15.854 ― cm

kN cm

λusv X 1 ≔ ― = 125 cm 4

τ + τ x1 H1 ≔ ― ⋅ X 1 = 2669.094 kN 2

λusv X 2 ≔ ― = 125 cm 4

τ x1 + τ x2 H2 ≔ ―― ⋅ X 2 = 1294.291 kN 2

X 3 ≔

λusv

2

= 250

cm

H3 ≔

τ x2 + τ dop

2

⋅ X 3 = 1094.39

Page 31 of 35

kN

ploče sa vutom

m≔3

‐ broj čepova

Hdop.1V ≔ m ⋅ Hdop.1 = 261 kN

‐ nosivost jedne

‐ potreban

n1 ≔

H1 Hdop.1V

H3 Hdop.1V

‐ podužni

= 10.226

= 4.193

<

n1.usv ≔ 11

<

n2.usv ≔ 5

<

n3.usv ≔ 5

razmak čepova

X 1 e1.1 ≔ ― = 11.364 cm n1.usv X 2

e1.2 ≔ ― = 25 cm n2.usv X 3 e1.3 ≔ ― = 50 cm n3.usv ‐ poprečni

veze

broj redova

H2 n2 ≔ ―― = 4.959 Hdop.1V n3 ≔

u jednoj vezi (u jednom redu)

‐ kriterijumi

>

e1.1.usv ≔ 10 cm

rasporeda čepova

e1min ≔ min 5 ⋅ d , 10 cm

= 10

cm

h p ≔ 2 ⋅ d p − hč ep = 16 cm

>

e1.2.usv ≔ 25 cm e1max ≔ max 4 ⋅ h p , 60 cm

>

= 64

cm

= 6.5

cm

e1.3.usv ≔ 50 cm

razmak čepova

‐ kriterijumi

e2 ≔ 9.0 cm

rasporeda čepova

e2min ≔ min 6.5 cm , 4 ⋅ d

e2.max ≔ b2 − 2 ⋅ 0.5 ⋅ d + 5 cm = 17.8 cm

Page 32 of 35

10 Proračun sprezanja AB ploče i čeličnog nosača ‐ MOŽDANIK + ANKER 10.1 dimenzije usvojenog moždanika ‐ UPN 200 b1 ≔ 200 mm h1 ≔ 125 mm c1 ≔ 75 mm s1 ≔ 8.5 mm

‐ dim.

paralelna sa flanšom ‐ dim. upravno na flanšu ‐ dim. paralelna sa rebrom ‐ debljina

10.2 dopuštena sila priska na beton ispred moždanika d o ≔ 2 d p = 40 cm

‐ debljina

bo ≔ b2 = 30 cm

‐ širina

F 1 ≔ b1 ⋅ h1 = 250 cm

‐ dop.

−2

betona na kontaktu sa čeličnom flanšom

2

F 2 ≔ max bo ⋅ d o , 2 d p

σ o ≔ 1 kN ⋅ cm

betonske ploče kod vute

2

,3

F 1 = 1200 cm

‐ dopušten

2

napon priska u betonu

lokalni prisak na beton usled troosnog naponskog stanja:

σ 1 ≔ σ o ⋅

‾‾ F 2

3

F 1

kN

= 1.687 ―2 cm

Nd ≔ σ 1 ⋅ F 1 = 421.716 kN

‐ dopuštena

sila priska u betonu

10.3 Dopuštena sila zatezanja u ankeru GA 240/360; II.S.O. σ v ≔ 24 kN ⋅ cm

σ a ≔

σ v ν

= 18

−2

⋅

kN cm

ν ≔

4 3

= 1.3

Φ ≔ 16

−2

μ ≔ 0.7

‐ za

Φ

2

⋅ π

Aa.1 ≔ ― 4

mm

= 2.011

cm

zatvorena sidra ‐ omče

2

Sa ≔ 2 ⋅ μ ⋅ Aa.1 ⋅ σ a = 50.668 kN

α ≔ 45

prvoj i krajnjoj trećini nosača petlje od glatke armature nagnute su prema horizonzali pod uglom 45 ° _______________________________________________________ °

‐ na

Ddop ≔ Nd + Sa ⋅ cos α = 457.544 kN

Page 33 of 35

10.4 Raspored moždanika ‐ horizontalne

smičuće sile

H1 = 2669.094 kN H2 = 1294.291 kN H3 = 1094.39 kN ‐ potreban

n1 ≔

broj moždanika

H1 Ddop

H2 n2 ≔ ― Ddop n3 ≔

H3 Ddop

‐ podužni

= 5.834

<

n1.usv ≔ 6

= 2.829

<

n2.usv ≔ 3

= 2.392

<

n3.usv ≔ 3

razmak moždanika

X 1 = 125 cm

X 1 e1.1 ≔ ― = 20.833 cm n1.usv

>

e1.1.usv ≔ 20 cm

X 2 = 125 cm

X 2 e1.2 ≔ ― = 41.667 cm n2.usv

>

e1.2.usv ≔ 40 cm

X 3 = 250 cm

e1.3 ≔

>

e1.3.usv ≔ 80 cm

X 3 n3.usv

= 83.333

cm

emax ≔ 2 ⋅ 2 ⋅ d p

= 80

cm

_________________________________________________________________ H1 Nmax ≔ ――― e1.1 n1.usv ⋅ ― e1.1.usv

= 427.055

kN

N prit.max ≔ Nmax − Sa ⋅ cos α = 391.228 kN

‐ max

sila koja se pripisuje najopterećenijem moždaniku

‐ max

sila priska na jedan moždanik (učešća sidra se zanemaruje, jer je ona zategnuta)

Page 34 of 35

Spregnuti_nosac_meduspratne_konstrukcije.pdf

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