2.2, Wymiarowanie zbrojenia slupa wewnetrznego na 1-ej kondygnacji:
fcd
13.3MPa
:=
Ecm
30GPa
:=
Beton C25/30(B25):
fyd
310MPa
:=
Es
200GPa
:=
ξ
eff.lim
0.55
:=
Stal zbrojeniowa A-II:
lcol
390cm
:=
Dlugosc slupa:
Wymiar poprzeczny slupa:
hs
30cm
:=
bs
30cm
:=
Dlugosc podciagu:
leff
620cm
:=
Wymiary podciagu:
bp
30cm
:=
hp
60cm
:=
Odsuniecie zbrojenia od krawedzi:
a1
4cm
:=
a2
4cm
:=
wyniki obliczen statycznych z programu RM-WIN:
Wezel 4:
N1.max
827
421
+
20
+
(
)kN
:=
M1.odp
1.2
0.8
+
0.0
+
(
)kN m
⋅
:=
N1.max 1268 kN
=
M1.odp 2 kN m
⋅
=
N1.odp
827
210
+
(
)kN
:=
M1.max
0
13
+
(
)kN m
⋅
:=
N1.odp 1037 kN
=
M1.max 13 kN m
⋅
=
Wezel 6:
N3.max
827
421
+
20
+
(
)kN
:=
M3.odp
1.2
1
+
0.0
+
(
)kN m
⋅
:=
N3.max 1.268 10
3
×
kN
=
M3.odp 2.2 kN m
⋅
=
N3.odp
827
210
+
(
)kN
:=
M3.max
0
25
+
(
)kN m
⋅
:=
N3.odp 1037 kN
=
M3.max 25 kN m
⋅
=
17
2.2.1. Wymiarowanie zbrojenia slupa w przekroju 1-1:
A) Na maksymalna sile osiowa i odpowiadajacy moment gnacy
N1.max 1268 kN
=
M1.odp 2 kN m
⋅
=
Obliczanie wspolczynnika wyboczeniowego z uwzglednieniem sztywnosci wezlow A i B:
••••
moment bezwl. slupa
moment bezwl podciagu
Jcol
bs hs
3
⋅
12
:=
bs hs
3
⋅
12
30 cm
⋅
30 cm
⋅
(
)
3
⋅
12
=
0.0007 m
4
=
Jp
bp hp
3
⋅
12
:=
bp hp
3
⋅
12
30 cm
⋅
60 cm
⋅
(
)
3
⋅
12
=
0.0054 m
4
=
kA
Jp
leff
lcol
2 Jcol
⋅
⋅
:=
Jp
leff
lcol
2 Jcol
⋅
⋅
0.0054 m
4
⋅
620 cm
⋅
390 cm
⋅
2 0.0007 m
4
⋅
⋅
⋅
=
2.43
=
wzor z [PN-03264] zal C, tab C2
kB
kA
:=
β
1
1
5 kA
⋅
1
+
+
1
5 kB
⋅
1
+
+
1
5 kA kB
+
(
)
⋅
+
:=
β
1.19
=
Wysokosc wyboczeniowa slupa:
l0
β
lcol
⋅
:=β
lcol
⋅
1.19 390 cm
⋅
⋅
=
4.64 m
=
Wspolczynnik smuklosci:
λ
l0
hs
:=
l0
hs
4.64 m
⋅
30 cm
⋅
=
15.47
=
λ
7
>
1
=
Mimosrody:
- mimosrod konstrukcyjny:
ee
M1.odp
N1.max
:=
M1.odp
N1.max
2 kN
⋅
m
⋅
1268 kN
⋅
=
1.6 mm
=
- mimosrod przypadkowy:
ea
max 10mm
lcol
600
,
hs
30
,
:=
max 10mm
lcol
600
,
hs
30
,
max 10 mm
⋅
390 cm
⋅
600
,
30 cm
⋅
30
,
=
10 mm
=
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:=
ee ea
+
0 mm
⋅
10 mm
⋅
+
=
10 mm
=
Ustroj o wezlach nieprzesownych!
η
1.0
:=
Mimosrod ostateczny:
etot
η
e0
⋅
:= η
e0
⋅
1.0 10 mm
⋅
⋅
=
10.0 mm
=
Sumaryczne zbrojenie minimalne:
As.min
max 0.003 bs
⋅
hs
⋅
0.15
N1.max
fyd
⋅
,
:=
max 0.003 bs
⋅
hs
⋅
0.15
N1.max
fyd
⋅
,
6.14 cm
2
=
d
hs a1
−
:=
hs a1
−
30 cm
⋅
4 cm
⋅
−
=
26.0 cm
=
18
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=
etot
hs
2
+
a1
−
10 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
120.0 mm
=
ξ
eff
N1.max
bs d
⋅
fcd
⋅
:=
N1.max
bs d
⋅
fcd
⋅
1268 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
1.222
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
0
=
war. NIEspelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
Korekta zasiegu strefy sciskanej:
Parametry do rownania:
B
N1.max d a2
−
(
)
⋅
bs d
2
⋅
fcd
⋅
:=
B
1.034
=
A
2 N1.max
⋅
es1
⋅
bs d
2
⋅
fcd
⋅
:=
A
1.128
=
Rownanie:
W
ξ
eff
( )
ξ
eff
3
2
ξ
eff.lim
+
(
)
ξ
eff
2
⋅
−
1
ξ
eff.lim
+
a2
d
1
ξ
eff.lim
−
(
)
⋅
−
A
+
ξ
eff
⋅
+
A
ξ
eff.lim
⋅
−
B 1
ξ
eff.lim
−
(
)
⋅
−
:=
W
ξ
eff
( )
0
=
ξ
eff
1
:=
root W
ξ
eff
( )
ξ
eff
,
(
)
1.050
=
Zatem zasieg strefy sciskanej be. po korekcie:
ξ
eff
1.04
:=
ξ
eff
1
<
0
=
As1
N1.max
ξ
eff bs
⋅
d
⋅
fcd
⋅
−
(
)
1
ξ
eff.lim
−
(
)
⋅
2
ξ
eff
ξ
eff.lim
−
(
)
⋅
fyd
⋅
ξ
eff
1
<
if
N1.max bs d
⋅
fcd
⋅
−
2 fyd
⋅
ξ
eff
1
>
if
:=
As1 3.719cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
1
=
As.min 6.14 cm
2
=
Przyjeto minimalne zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16
)
As1.prov 0.5 As.min
⋅
>
1
=
As.min 6.14 cm
2
=
As2.prov
4.02cm
2
:=
2 prety
φ16
)
As2.prov 0.5 As.min
⋅
>
1
=
B) Na maksymalny moment i odpowiadajaca sile:
N1.odp 1.037 10
3
×
kN
=
M1.max 13 kN m
⋅
=
Mimosrody:
- mimosrod konstrukcyjny:
ee
M1.max
N1.odp
:=
M1.max
N1.odp
13 kN
⋅
m
⋅
1037 kN
⋅
=
12.5 mm
=
19
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:=
ee ea
+
12 mm
⋅
10 mm
⋅
+
=
22 mm
=
Mimosrod ostateczny:
η
1.0
:=
etot
η
e0
⋅
:= η
e0
⋅
1.0 22 mm
⋅
⋅
=
22.0 mm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=
etot
hs
2
+
a1
−
22 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
132.0 mm
=
ξ
eff
N1.odp
bs d
⋅
fcd
⋅
:=
N1.odp
bs d
⋅
fcd
⋅
1037 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
1.000
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
0
=
war. NIEspelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
Korekta zasiegu strefy sciskanej:
Parametry do rownania:
B
N1.odp d a2
−
(
)
⋅
bs d
2
⋅
fcd
⋅
:=
B
0.846
=
A
2 N1.odp
⋅
es1
⋅
bs d
2
⋅
fcd
⋅
:=
A
1.015
=
Rownanie:
W
ξ
eff
( )
ξ
eff
3
2
ξ
eff.lim
+
(
)
ξ
eff
2
⋅
−
1
ξ
eff.lim
+
a2
d
1
ξ
eff.lim
−
(
)
⋅
−
A
+
ξ
eff
⋅
+
A
ξ
eff.lim
⋅
−
B 1
ξ
eff.lim
−
(
)
⋅
−
:=
W
ξ
eff
( )
0
=
ξ
eff
1
:=
root W
ξ
eff
( )
ξ
eff
,
(
)
0.982
=
Zatem zasieg strefy sciskanej be. po korekcie:
ξ
eff
0.982
:=
ξ
eff
1
<
1
=
As1
N1.odp
ξ
eff bs
⋅
d
⋅
fcd
⋅
−
(
)
1
ξ
eff.lim
−
(
)
⋅
2
ξ
eff
ξ
eff.lim
−
(
)
⋅
fyd
⋅
ξ
eff
1
<
if
N1.odp bs d
⋅
fcd
⋅
−
2 fyd
⋅
ξ
eff
1
>
if
:=
As1 0.31 cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
0
=
As.min 6.14 cm
2
=
As1.prov
4.02cm
2
:=
(2 prety
φ16
)
As1.prov 0.5 As.min
⋅
>
1
=
As2.prov
4.02cm
2
:=
2 prety
φ16
)
As2.prov 0.5 As.min
⋅
>
1
=
20
Zatem w przekroju 1-
1111
przyjeto zbrojenia:
As.min 6.135cm
2
=
As1.prov
4.02cm
2
:=
(2 prety
φ16
)
As1.prov 0.5 As.min
⋅
>
1
=
As2.prov
4.02cm
2
:=
2 prety
φ16
)
As2.prov 0.5 As.min
⋅
>
1
=
2.2.2. Wymiarowanie zbrojenia slupa w przekroju
2222
-
2222
:
A) Na maksymalna sile osiowa i odpowiadajacy moment gnacy
N2.max
N1.max N3.max
+
2
:=
N2.max 1268 kN
=
Mimosrody:
ee
0.6 M1.odp
⋅
0.4 M3.odp
⋅
+
N1.max
:=
0.6 M1.odp
⋅
0.4 M3.odp
⋅
+
N1.max
0.6 2 kN
⋅
m
⋅
⋅
0.4 2.2 kN
⋅
m
⋅
⋅
+
1268 kN
⋅
=
1.6 mm
=
- mimosrod konstrukcyjny:
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:=
ee ea
+
0 mm
⋅
10 mm
⋅
+
=
10 mm
=
Wyznaczenie sily krytycznej:
wymiar miarodajny przekroju:
h0
2 bs
⋅
hs
⋅
2 bs
⋅
2 hs
⋅
+
:=
2 bs
⋅
hs
⋅
2 bs
⋅
2 hs
⋅
+
150 mm
=
==>>
φ
oo.t0
1.7
:=
wsp. uwzgledniajacy czesc obc.dlugotrwalego:
NSd.1
100% N2.max
⋅
:=
k1t
1
0.5
NSd.1
N2.max
⋅
φ
oo.t0
⋅
+
:=
k1t 1.85
=
Moment bezwladnosci zginanego przekroju betonowego:
Jcol 7 10
4
−
×
m
4
=
Moment bezwladnosci pola przekroju zbrojenia wzgledem srodka ciezkosci przekroju przy wstepnym zalozeniu
sumarycznego stopnia zbrojenia
ρ
0
1.1%
:=
Js
ρ
0 bs
⋅
hs
⋅
1
2
bs
⋅
a1
−
2
⋅
:= ρ
0 bs
⋅
hs
⋅
1
2
hs
⋅
a1
−
2
⋅
1.1 %
⋅
30 cm
⋅
⋅
30 cm
⋅
⋅
1
2
30 cm
⋅
⋅
4 cm
⋅
−
2
⋅
=
1198 cm
4
=
Sila krytyczna:
Ncrit
9
l0
2
Jcol Ecm
⋅
2 k1t
⋅
0.11
0.1
e0
hs
+
0.1
+
⋅
Es Js
⋅
+
⋅
:=
Ncrit
9
3.81 m
⋅
(
)
2
0.0007 m
4
⋅
30 GPa
⋅
⋅
2 1.85
⋅
0.11
0.1
10 mm
⋅
30 cm
⋅
+
0.1
+
⋅
200 GPa
⋅
1633 cm
4
⋅
⋅
+
⋅
=
Ncrit 3.2 MN
=
21
η
1
1
N1.max
Ncrit
−
:=
1
1
N1.max
Ncrit
−
1
1
1268 kN
⋅
3.2 MN
⋅
−
=
1.66
=
wsp zwiekszajacy sumaryczny mimosrod:
mimosrod ostateczny:
etot
η
e0
⋅
:= η
e0
⋅
1
1
N1.max
Ncrit
−
10 mm
⋅
⋅
=
17 mm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=
etot
hs
2
+
a1
−
17 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
127.0 mm
=
ξ
eff
N2.max
bs d
⋅
fcd
⋅
:=
N2.max
bs d
⋅
fcd
⋅
1268 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
1.222
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
0
=
war. NIEspelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
Korekta zasiegu strefy sciskanej:
Parametry do rownania:
B
N2.max d a2
−
(
)
⋅
bs d
2
⋅
fcd
⋅
:=
B
1.034
=
A
2 N2.max
⋅
es1
⋅
bs d
2
⋅
fcd
⋅
:=
A
1.194
=
Rownanie:
W
ξ
eff
( )
ξ
eff
3
2
ξ
eff.lim
+
(
)
ξ
eff
2
⋅
−
1
ξ
eff.lim
+
a2
d
1
ξ
eff.lim
−
(
)
⋅
−
A
+
ξ
eff
⋅
+
A
ξ
eff.lim
⋅
−
B 1
ξ
eff.lim
−
(
)
⋅
−
:=
W
ξ
eff
( )
0
=
ξ
eff
1
:=
root W
ξ
eff
( )
ξ
eff
,
(
)
0.995
=
Zatem zasieg strefy sciskanej be. po korekcie:
ξ
eff
0.995
:=
ξ
eff
1
<
1
=
As1
N2.max
ξ
eff bs
⋅
d
⋅
fcd
⋅
−
(
)
1
ξ
eff.lim
−
(
)
⋅
2
ξ
eff
ξ
eff.lim
−
(
)
⋅
fyd
⋅
ξ
eff
1
<
if
N2.max bs d
⋅
fcd
⋅
−
2 fyd
⋅
ξ
eff
1
>
if
:=
As1 3.85 cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
1
=
As.min 6.14 cm
2
=
Przyjeto zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16
)
As1.prov As1
>
1
=
As2.prov
4.02cm
2
:=
(2 prety
φ16
)
2 As1.prov
⋅
As.min
>
1
=
22
Kontrola minimalnego stopnia zbrojenia:
ρ
As1.prov As2.prov
+
d hs
⋅
:=
As1.prov As2.prov
+
d hs
⋅
4.02 cm
2
⋅
4.02 cm
2
⋅
+
26 cm
⋅
30 cm
⋅
⋅
=
1.03 %
=
ε
ρ
0
ρ
−
ρ
0
:=
ρ
0
ρ
−
ρ
0
1.1 %
⋅
1.03 %
⋅
−
1.1 %
⋅
=
6.36 %
=
ε
10%
<
1
=
zatem wstepne oszacowanie stopnia zbrojenia bylo wystarczajaco dobre aby zakonczyc iteracje!
B) Na maksymalny moment i odpowiadajaca sile:
N2.odp
N1.odp N3.odp
+
2
:=
N2.odp 1037 kN
=
Mimosrody:
- mimosrod konstrukcyjny:
ee
0.6 M1.max
⋅
0.4 M3.max
⋅
+
N2.odp
:=
0.6 M1.max
⋅
0.3 M3.max
⋅
+
N2.odp
0.6 13 kN
⋅
m
⋅
⋅
0.3 25 kN
⋅
m
⋅
⋅
+
1037 kN
⋅
=
14.8 mm
=
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:=
ee ea
+
15 mm
⋅
10 mm
⋅
+
=
25 mm
=
Moment bezwladnosci zginanego przekroju betonowego:
Jcol 7 10
4
−
×
m
4
=
Moment bezwladnosci pola przekroju zbrojenia wzgledem srodka ciezkosci przekroju przy wstepnym zalozeniu
sumarycznego stopnia zbrojenia
ρ
0
1.5%
:=
Js
ρ
0 bs
⋅
hs
⋅
1
2
bs
⋅
a1
−
2
⋅
:= ρ
0 bs
⋅
hs
⋅
1
2
hs
⋅
a1
−
2
⋅
1.5 %
⋅
30 cm
⋅
⋅
30 cm
⋅
⋅
1
2
30 cm
⋅
⋅
4 cm
⋅
−
2
⋅
=
1633 cm
4
=
Sila krytyczna:
Ncrit
9
l0
2
Jcol Ecm
⋅
2 k1t
⋅
0.11
0.1
e0
hs
+
0.1
+
⋅
Es Js
⋅
+
⋅
:=
Ncrit
9
3.81 m
⋅
(
)
2
0.0007 m
4
⋅
30 GPa
⋅
⋅
2 1.85
⋅
0.11
0.1
24 mm
⋅
30 cm
⋅
+
0.1
+
⋅
200 GPa
⋅
1633 cm
4
⋅
⋅
+
⋅
=
Ncrit 3.03 MN
=
η
1
1
N1.max
Ncrit
−
:=
1
1
N1.max
Ncrit
−
1
1
1268 kN
⋅
3.03 MN
⋅
−
=
1.72
=
wsp zwiekszajacy sumaryczny mimosrod:
23
mimosrod ostateczny:
etot
η
e0
⋅
:= η
e0
⋅
1.72 25 mm
⋅
⋅
=
43 mm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=
etot
hs
2
+
a1
−
43 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
153.0 mm
=
ξ
eff
N2.odp
bs d
⋅
fcd
⋅
:=
N2.odp
bs d
⋅
fcd
⋅
1037 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
1.000
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
0
=
war. NIEspelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
Korekta zasiegu strefy sciskanej:
Parametry do rownania:
B
N2.odp d a2
−
(
)
⋅
bs d
2
⋅
fcd
⋅
:=
B
0.846
=
A
2 N2.odp
⋅
es1
⋅
bs d
2
⋅
fcd
⋅
:=
A
1.176
=
Rownanie:
W
ξ
eff
( )
ξ
eff
3
2
ξ
eff.lim
+
(
)
ξ
eff
2
⋅
−
1
ξ
eff.lim
+
a2
d
1
ξ
eff.lim
−
(
)
⋅
−
A
+
ξ
eff
⋅
+
A
ξ
eff.lim
⋅
−
B 1
ξ
eff.lim
−
(
)
⋅
−
:=
W
ξ
eff
( )
0
=
ξ
eff
1
:=
root W
ξ
eff
( )
ξ
eff
,
(
)
0.844
=
Zatem zasieg strefy sciskanej be. po korekcie:
ξ
eff
0.844
:=
ξ
eff
1
<
1
=
As1
N2.odp
ξ
eff bs
⋅
d
⋅
fcd
⋅
−
(
)
1
ξ
eff.lim
−
(
)
⋅
2
ξ
eff
ξ
eff.lim
−
(
)
⋅
fyd
⋅
ξ
eff
1
<
if
N2.odp bs d
⋅
fcd
⋅
−
2 fyd
⋅
ξ
eff
1
>
if
:=
As1 4.87 cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
1
=
As.min 6.14 cm
2
=
Przyjeto zbrojenia:
As1.prov
6.03cm
2
:=
(3 prety
φ16
)
As1.prov As1
>
1
=
As2.prov
6.03cm
2
:=
(3 prety
φ16
)
2As1.prov As.min
>
1
=
Kontrola minimalnego stopnia zbrojenia:
ρ
As1.prov As2.prov
+
d hs
⋅
:=
As1.prov As2.prov
+
d hs
⋅
6.03 cm
2
⋅
6.03 cm
2
⋅
+
26 cm
⋅
30 cm
⋅
⋅
=
1.55 %
=
24
ε
ρ
0
ρ
−
ρ
0
:=
ρ
0
ρ
−
ρ
0
1.5 %
⋅
1.55 %
⋅
−
1.5 %
⋅
=
3.33 %
=
ε
10%
<
1
=
zatem wstepne oszacowanie stopnia zbrojenia bylo wystarczajaco dobre aby zakonczyc iteracje!
Zatem w przekroju
2222
-
2222
przyjeto zbrojenia:
As1.prov 0.5 As.min
⋅
>
1
=
As.min 6.135cm
2
=
As1.prov
6.03cm
2
:=
(3 prety
φ16
)
As2.prov
6.03cm
2
:=
(3 prety
φ16
)
As2.prov 0.5 As.min
⋅
>
1
=
2.2.3. Wymiarowanie zbrojenia slupa w przekroju
3333
-
3333
:
A) Na maksymalna sile osiowa i odpowiadajacy moment gnacy
N3.max 1268 kN
=
M3.odp 2.2 kN m
⋅
=
Mimosrody:
- mimosrod konstrukcyjny:
ee
M3.odp
N3.max
:=
M3.odp
N3.max
2.2 kN
⋅
m
⋅
1268 kN
⋅
=
1.7 mm
=
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:=
ee ea
+
0 mm
⋅
10 mm
⋅
+
=
10 mm
=
Mimosrod ostateczny:
η
1.0
:=
etot
η
e0
⋅
:= η
e0
⋅
1.0 10 mm
⋅
⋅
=
10.0 mm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=
etot
hs
2
+
a1
−
10 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
120.0 mm
=
ξ
eff
N3.max
bs d
⋅
fcd
⋅
:=
N3.max
bs d
⋅
fcd
⋅
1268 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
1.222
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
0
=
war. NIEspelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
Korekta zasiegu strefy sciskanej:
Parametry do rownania:
B
N3.max d a2
−
(
)
⋅
bs d
2
⋅
fcd
⋅
:=
B
1.034
=
A
2 N3.max
⋅
es1
⋅
bs d
2
⋅
fcd
⋅
:=
A
1.128
=
Rownanie:
W
ξ
eff
( )
ξ
eff
3
2
ξ
eff.lim
+
(
)
ξ
eff
2
⋅
−
1
ξ
eff.lim
+
a2
d
1
ξ
eff.lim
−
(
)
⋅
−
A
+
ξ
eff
⋅
+
A
ξ
eff.lim
⋅
−
B 1
ξ
eff.lim
−
(
)
⋅
−
:=
W
ξ
eff
( )
0
=
ξ
eff
1
:=
25
root W
ξ
eff
( )
ξ
eff
,
(
)
1.050
=
Zatem zasieg strefy sciskanej be. po korekcie:
ξ
eff
1.05
:=
ξ
eff
1
<
0
=
As1
N3.max
ξ
eff bs
⋅
d
⋅
fcd
⋅
−
(
)
1
ξ
eff.lim
−
(
)
⋅
2
ξ
eff
ξ
eff.lim
−
(
)
⋅
fyd
⋅
ξ
eff
1
<
if
N3.max bs d
⋅
fcd
⋅
−
2 fyd
⋅
ξ
eff
1
>
if
:=
As1 3.72 cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
1
=
As.min 6.14 cm
2
=
Przyjeto zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16
)
As1.prov As1
>
1
=
2 As1.prov
⋅
As.min
>
1
=
As2.prov
4.02cm
2
:=
(2 prety
φ16
)
B) Na maksymalny moment i odpowiadajaca sile:
N3.odp 1.037 10
3
×
kN
=
M3.max 25 kN m
⋅
=
Mimosrody:
- mimosrod konstrukcyjny:
ee
M3.max
N3.odp
:=
M3.max
N3.odp
25 kN
⋅
m
⋅
1037 kN
⋅
=
24.1 mm
=
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:=
ee ea
+
24 mm
⋅
10 mm
⋅
+
=
34 mm
=
Mimosrod ostateczny:
η
1.0
:=
etot
η
e0
⋅
:= η
e0
⋅
1.0 34 mm
⋅
⋅
=
34.0 mm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=
etot
hs
2
+
a1
−
34 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
144.0 mm
=
ξ
eff
N3.odp
bs d
⋅
fcd
⋅
:=
N3.odp
bs d
⋅
fcd
⋅
1037 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
1.000
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
0
=
war. NIEspelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
Korekta zasiegu strefy sciskanej:
Parametry do rownania:
B
N3.odp d a2
−
(
)
⋅
bs d
2
⋅
fcd
⋅
:=
B
0.846
=
A
2 N3.odp
⋅
es1
⋅
bs d
2
⋅
fcd
⋅
:=
A
1.107
=
26
Rownanie:
W
ξ
eff
( )
ξ
eff
3
2
ξ
eff.lim
+
(
)
ξ
eff
2
⋅
−
1
ξ
eff.lim
+
a2
d
1
ξ
eff.lim
−
(
)
⋅
−
A
+
ξ
eff
⋅
+
A
ξ
eff.lim
⋅
−
B 1
ξ
eff.lim
−
(
)
⋅
−
:=
W
ξ
eff
( )
0
=
ξ
eff
1
:=
root W
ξ
eff
( )
ξ
eff
,
(
)
0.893
=
Zatem zasieg strefy sciskanej be. po korekcie:
ξ
eff
0.893
:=
ξ
eff
1
<
1
=
As1
N3.odp
ξ
eff bs
⋅
d
⋅
fcd
⋅
−
(
)
1
ξ
eff.lim
−
(
)
⋅
2
ξ
eff
ξ
eff.lim
−
(
)
⋅
fyd
⋅
ξ
eff
1
<
if
N3.odp bs d
⋅
fcd
⋅
−
2 fyd
⋅
ξ
eff
1
>
if
:=
As1 2.34 cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
0
=
As.min 6.14 cm
2
=
Przyjeto zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16
)
As1.prov As1
>
1
=
2 As1.prov
⋅
As.min
>
1
=
As2.prov
4.02cm
2
:=
(2 prety
φ16
)
Zatem w przekroju
3333
-
3333
przyjeto zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16
)
As.min 6.14 cm
2
=
As2.prov
4.02cm
2
:=
(2 prety
φ16
)
2.2.4. Podsumowanie slupa wewnetrznego na 1-ej kondygnacji:
Przyjete wymiary slupa:
•
bs 30 cm
=
hs 30 cm
=
W celu ujednolicenia zbrojenia na calej jego dlugosci, przyjmujemy zbrojenia:
•
As1.prov 0.5 As.min
⋅
>
1
=
As.min 6.14 cm
2
=
As1.prov
6.03cm
2
:=
(3 prety
φ16
)
As2.prov
6.03cm
2
:=
(3 prety
φ16
)
As2.prov 0.5 As.min
⋅
>
1
=
Na calej dlugosci slupa przyjeto 6 pretow
φ16
.
•
Maksymalny rostaw strzemion:
•
smax
16mm 15
⋅
:=
smax 24 cm
=
Zastosowano strzemiona dwuciete, srednicy
φ
8 rostawione w odleglosci:
•
s
20cm
:=
27
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