Univerzitet Crne Gore Građevinski fakultet u Podgorici Menađment u građevinarstvu BETONSKE KONSTRUKCIJE

VJEŽBA 5. Zadatak1. Izvršiti analizu opterećenja, izračunati statičke uticaje i dimenzionisati ploče POS101, POS102 i POS103. Nacrtati plan armature u osnovi i poprečnim presjecima. Povremeno opterećenje iznosi p=4kN/m2.

Kvalitet materijala: I Varijanta MB30, GA240/360. II Varijanta MB30, MA500/560.

Rješenje: POS101 1.1. Statička šema

1.2. Analiza opterećenja

1.2.1 Stalno -sopstvena težina 20.12 25 3.0 /kN m⋅ =

g=3.0 kN/m2

1.2.2 Povremeno p=4.0 kN/m2

Granično opterećenje 21.6 1.8 1.6 3 1.8 4 12 /q g p kN m= ⋅ + ⋅ = ⋅ + ⋅ =

1.3. Statički uticaji

/u x y

u x y

M k q l lQ k q l l l

= ⋅ ⋅ ⋅

= ⋅ ⋅ ⋅

0

0

0.031 12 3 5 5.58 /0.014 12 3 5 2.52 /

0.065 12 3 5 11.7 /

0.046 12 3 5 8.28 /

ux

uy

ux

uy

M kNm mM kNm m

M kNm mM kNm m

= ⋅ ⋅ ⋅ == ⋅ ⋅ ⋅ =

= ⋅ ⋅ ⋅ =

= ⋅ ⋅ ⋅ =

1

2

3

4

0.39 12 3 5 / 5 14.04 /0.256 12 3 5 / 5 9.22 /0.204 12 3 5 / 3 12.24 /0.15 12 3 5 / 3 9.0 /

u

u

u

u

Q kN mQ kN mQ kN mQ kN m

= ⋅ ⋅ ⋅ == ⋅ ⋅ ⋅ == ⋅ ⋅ ⋅ == ⋅ ⋅ ⋅ =

1.4. Dimenzionsanje

2

2

2

30 2.05 /

240 / 360 24 /

500 / 600 50 /

b

v

v

MB f kN cmGA kN cmMA kN cm

σσ

⇒ =

⇒ =

⇒ =

Debljina ploče se odredi na samom početku i ima istu vrijednost za sve pozicionirane ploče. Za ploču POS101 i POS 102:

0 0.8 500min 11.435(40 - ) 35p

ld cmkrovne ploce

⋅= = =

Za ploču POS 103: 2 200min 11.435pd cm⋅= =

Debljina ploče usvaja se na osnovu veće vrijednosti Usvojeno dp=12cm ly/lx=5.0/3.0=1.67

1.4.1 Dimenzionsanje iznad oslonca

0.812 2 9.62 2

6.41%9.6 4.01 lom po armaturi/ 10 /1.38‰11.7

1.0 2.05

p o

ba bu

b

h d a cm

hkMb f

φ

µε ε

= − − = − − =

⎧ ⎫=⎪ ⎪= = = ⇒ ⇒⎨ ⎬=⎪ ⎪⎩ ⎭

⋅⋅

Važi približni proračun armature. X pravac Y pravac

0

2.

2

2

2

2

11.7 /0.812 2 9.6

2 211.7 100 5.07 /9.6 24

: 8 /10(5.0 / )

0.2 5 1.0 /0.1/100 12 100 1.2 /

: 6 / 20(1.4 / )

5.07

ux

p o

upotr

v

ap

GAMA GA va a MA

v

M kNm m

h d a cm

MA cm mz

usvojeno cm m

cm mA

cm m

usvojeno cm m

A A

φ

σφ

φσσ

=

= − − = − − =

⋅= = =⋅ ⋅

⎧ ⎫⋅ =⎪ ⎪> ⎨ ⎬⋅ ⋅ =⎪ ⎪⎩ ⎭

= ⋅ = 2

2

24 2.43 /50

: 257(2.57 / )

cm m

usvojeno R cm m

⋅ =

0

2.

2

2

2

2

8.28 /0.812 2 9.6

2 28.28 100 3.6 /9.6 24

: 8 /10(5.0 / )

0.2 5 1.0 /0.1/100 12 100 1.2 /

: 6 / 20(1.4 / )23.6

ux

p o

upotr

v

ap

GAMA GA va a MA

v

M kNm m

h d a cm

MA cm mz

usvojeno cm m

cm mA

cm m

usvojeno cm m

A A

φ

σφ

φσσ

=

= − − = − − =

⋅= = =⋅ ⋅

⎧ ⎫⋅ =⎪ ⎪> ⎨ ⎬⋅ ⋅ =⎪ ⎪⎩ ⎭

= ⋅ = ⋅ 2

2

4 1.728 /50

: 196(1.96 / )

cm m

usvojeno R cm m

=

1.4.2 Dimenzionsanje u polju X pravac Ypravac

2.

2

2

2

5.58 /0.812 2 9.6

2 25.58 100 2.42 /9.6 24

: 8 / 20(2.5 / )242.42 1.16 /50

: 131(1.31 / )

ux

p o

upotr

v

GAMA GA va a MA

v

M kNm m

h d a cm

MA cm mz

usvojeno cm m

A A cm m

usvojeno Q cm m

φ

σφσσ

=

= − − = − − =

⋅= = =⋅ ⋅

= ⋅ = ⋅ =

2.

2min

2

2

2

2.52 /

0.812 2 0.8 8.82 22.52 100 1.2 /8.8 24

0.15 /100 12 100 1.8 /

: 6 /15(1.86 / )241.8 0.86 /50

: 131(1.31 / )

uy

p o

upotr

v

a

GAMA GA va a MA

v

M kNm m

h d a cm

MA cm mz

A cm musvojeno cm m

A A cm m

usvojeno Q cm m

φ

σ

φσσ

=

= − − = − − − =

⋅= = =⋅ ⋅

= ⋅ ⋅ =

= ⋅ = ⋅ =

POS102 1.1 Statička šema

1.2 Analiza opterećenja

1.2.1 Stalno -sopstvena težina 20.12 25 3.0 /kN m⋅ =

g=3.0 kN/m2

1.2.2 Povremeno p=4.0 kN/m2

Granično opterećenje 21.6 1.8 1.6 3 1.8 4 12 /q g p kN m= ⋅ + ⋅ = ⋅ + ⋅ =

1.3 Statički uticaji

/u x y

u x y

M k q l lQ k q l l l

= ⋅ ⋅ ⋅

= ⋅ ⋅ ⋅

0

0

0.026 12 5 5 7.8 /0.021 12 5 5 6.3 /

0.06 12 5 5 18 /

0.055 12 5 5 16.5 /

ux

uy

ux

uy

M kNm mM kNm m

M kNm mM kNm m

= ⋅ ⋅ ⋅ == ⋅ ⋅ ⋅ =

= ⋅ ⋅ ⋅ =

= ⋅ ⋅ ⋅ =

1

2

3

0.274 12 5 5 / 5 16.44 /0.19 12 5 5 / 5 11.4 /0.262 12 5 5 / 5 15.72 /

u

u

u

Q kN mQ kN mQ kN m

= ⋅ ⋅ ⋅ == ⋅ ⋅ ⋅ == ⋅ ⋅ ⋅ =

1.4 Dimenzionsanje

2

2

2

30 2.05 /

240 / 360 24 /

500 / 600 50 /

b

v

v

MB f kN cmGA kN cmMA kN cm

σσ

⇒ =

⇒ =

⇒ =

1.4.1 Dimenzionsanje iznad oslonca

Usvojeno dp=12cm ly/lx=5.0/5.0.0=1.0

1.012 2 9.52 2

10.36%9.5 3.21 lom po armaturi/ 10 /1.9‰18

1.0 2.05

p o

ba bu

b

h d a cm

hkMb f

φ

µε ε

= − − = − − =

⎧ ⎫=⎪ ⎪= = = ⇒ ⇒⎨ ⎬=⎪ ⎪⎩ ⎭

⋅⋅

Važi približni proračun armature. X pravac Y pravac

0

2.

2

2

2

2

18 /1.012 2 9.5

2 218 100 7.9 /9.5 24

: 10 /10(7.85 / )

0.2 7.85 1.6 /0.1/100 12 100 1.2 /

: 6 /15(1.86 / )

7.9

ux

p o

upotr

v

ap

GAMA GA va a MA

v

M kNm m

h d a cm

MA cm mz

usvojeno cm m

cm mA

cm m

usvojeno cm m

A A

φ

σφ

φσσ

=

= − − = − − =

⋅= = =⋅ ⋅

⎧ ⎫⋅ =⎪ ⎪> ⎨ ⎬⋅ ⋅ =⎪ ⎪⎩ ⎭

= ⋅ = 2

2

24 3.792 /50

: 378(3.78 / )

cm m

usvojeno R cm m

⋅ =

0

2.

2

2

2

2

16.5 /1.012 2 9.5

2 216.5 100 7.23 /9.5 24

: 10 /10(7.85 / )

0.2 7.85 1.6 /0.1/100 12 100 1.2 /

: 6 /15(1.86 / )

ux

p o

upotr

v

ap

GAMA GA va a M

v

M kNm m

h d a cm

MA cm mz

usvojeno cm m

cm mA

cm m

usvojeno cm m

A A

φ

σφ

φσσ

=

= − − = − − =

⋅= = =⋅ ⋅

⎧ ⎫⋅ =⎪ ⎪> ⎨ ⎬⋅ ⋅ =⎪ ⎪⎩ ⎭

= ⋅ 2

2

247.23 3.47 /50

: 378(3.78 / )

A cm m

usvojeno R cm m

= ⋅ =

1.4.2 Dimenzionsanje u polju X pravac Y pravac

2.

2

2

2

7.8 /0.812 2 9.6

2 27.8 100 3.38 /9.6 24

: 8 /15(3.33 / )243.38 1.62 /50

: 188(1.88 / )

ux

p o

upotr

v

GAMA GA va a MA

v

M kNm m

h d a cm

MA cm mz

usvojeno cm m

A A cm m

usvojeno Q cm m

φ

σφσσ

=

= − − = − − =

⋅= = =⋅ ⋅

= ⋅ = ⋅ =

2

.

2

2

2

6.3 /

0.812 2 0.8 8.82 26.3 100 2.98 /8.8 24

: 8 /15(3.33 / )242.98 1.43 /50

: 188(1.88 / )

uy

p o

upotr

v

GAMA GA va a MA

v

M kNm m

h d a cm

MA cm mz

usvojeno cm m

A A cm m

usvojeno Q cm m

φ

σφσσ

=

= − − = − − − =

⋅= = =⋅ ⋅

= ⋅ = ⋅ =

POS103 1.1 Statička šema

Usvojeno dp=12cm

1.2 Analiza opterećenja 1.2.1 Stalno -sopstvena težina 20.12 25 3.0 /kN m⋅ =

g=3.0 kN/m2

1.2.2 Povremeno p=4.0 kN/m2

Granično opterećenje 21.6 1.8 1.6 3 1.8 4 12 /q g p kN m= ⋅ + ⋅ = ⋅ + ⋅ =

1.3 Statički uticaji

2 22.012 24 / '2 212 2.0 24 / '

u

u

lM q kNm m

Q q l kN m

= ⋅ = ⋅ =

= ⋅ = ⋅ =

1.4 Dimenzionsanje

2

2

30 2.05 /

240 /360 24 /b

v

MB f kN cmGA kN cmσ

⇒ =

⇒ =

2min 0.15 /100 12 100 1.8 /aA cm m= ⋅ ⋅ = 1.4.1 Dimenzionsanje iznad oslonca

X pravac

2.

2

2

2

2

24 /1.012 2 9.5

2 224 100 10.5 /9.5 24

: 12 /10(11.3 / )

0.2 11.3 2.26 /0.1/100 12 100 1.2 /

: 8 / 20(2.5 / )

10.

ux

p o

upotr

v

ap

GAMA GA va a MA

v

M kNm m

h d a cm

MA cm mz

usvojeno cm m

cm mA

cm m

usvojeno cm m

A A

φ

σφ

φσσ

=

= − − = − − =

⋅= = =⋅ ⋅

⎧ ⎫⋅ =⎪ ⎪> ⎨ ⎬⋅ ⋅ =⎪ ⎪⎩ ⎭

= ⋅ = 2

2

245 5.04 /50

: 503(5.03 / )

cm m

usvojeno R cm m

⋅ =