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
⋅ =