2. WYZNACZENIE ZBROJENIA W SLUPACH ZELBETOWYCH:
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
:=
2.1. Wymiarowanie zbrojenia slupa skrajnego na najnizszej kondygnacji:
wyniki obliczen statycznych z programu RM-WIN:
Wezel 1:
N1.max
435
209
+
10
+
(
)kN
:=
M1.odp
16
10
+
(
)kN m
⋅
:=
N1.max 654 kN
=
M1.odp 26 kN m
⋅
=
N1.odp
435
125
+
(
)kN
:=
M1.max
16
13
+
(
)kN m
⋅
:=
N1.odp 560 kN
=
M1.max 29 kN m
⋅
=
Wezel 3:
N3.max
435
209
+
10
+
(
)kN
:=
M3.odp
30
19
+
(
)kN m
⋅
:=
N3.max 654 kN
=
M3.odp 49 kN m
⋅
=
N3.odp
435
125
+
(
)kN
:=
M3.max
30
26
+
(
)kN m
⋅
:=
N3.odp 560 kN
=
M3.max 56 kN m
⋅
=
2.1.1. Wymiarowanie zbrojenia slupa w przekroju
α
α
α
α1-α
α
α
α1:
A) Na maksymalna sile osiowa i odpowiadajacy moment gnacy
N1.max 654 kN
=
M1.odp 26 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
=
6
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 "nieskonczonosc"
=
-slup utwierdzony w sztywnym fundamencie
β
1
1
5 kA
⋅
1
+
+
:= 1
1
5 kA
⋅
1
+
+
1
1
5 2.43
⋅
1
+
+
=
1.08
=
Wysokosc wyboczeniowa slupa:
l0
β l
col
⋅
:=β l
col
⋅
1.08 390 cm
⋅
⋅
=
4.21 m
=
Wspolczynnik smuklosci:
λ
l0
hs
:=
l0
hs
4.21 m
⋅
30 cm
⋅
=
14.03
=
λ
7
>
1
=
Mimosrody:
- mimosrod konstrukcyjny:
ee
M1.odp
N1.max
:=
M1.odp
N1.max
26 kN
⋅
m
⋅
654 kN
⋅
=
39.8 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
,
=
10.0 mm
=
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:= e
e
ea
+
40 mm
⋅
10 mm
⋅
+
=
50 mm
=
Ustroj o wezlach nieprzesownych!
η
1.0
:=
Mimosrod ostateczny:
etot
η e
0
⋅
:= η e
0
⋅
1.0 50 mm
⋅
⋅
=
50.0 mm
=
Sumaryczne zbrojenie minimalne:
As.min
max 0.003 bs
⋅
hs
⋅
0.15
N1.max
fyd
⋅
,
:= max 0.003 b
s
⋅
hs
⋅
0.15
N1.max
fyd
⋅
,
3.16 cm
2
=
d
hs a1
−
:= h
s
a1
−
30 cm
⋅
4 cm
⋅
−
=
26.0 cm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=e
tot
hs
2
+
a1
−
50 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
160.0 mm
=
ξ
eff
N1.max
bs d
⋅ f
cd
⋅
:=
N1.max
bs d
⋅ f
cd
⋅
654 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
0.630
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
0
=
war. nie spelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
Korekta zasiegu strefy sciskanej:
Parametry do rownania:
B
N1.max d a2
−
(
)
⋅
bs d
2
⋅
fcd
⋅
:=
B
0.533
=
A
2 N1.max
⋅
es1
⋅
bs d
2
⋅
fcd
⋅
:=
A
0.776
=
7
Rownanie:
W ξeff
( )
ξ
eff
3
2
ξ
eff.lim
+
(
)
ξ
eff
2
⋅
−
1
ξ
eff.lim
+
a2
d
1
ξ
eff.lim
−
(
)
⋅
−
A
+
ξ
eff
⋅
+
A ξeff.lim
⋅
−
B 1
ξ
eff.lim
−
(
)
⋅
−
:=
W ξeff
( )
0
=
ξ
eff
1
:=
root W ξeff
( )
ξ
eff
,
(
)
0.663
=
Zatem zasieg strefy sciskanej be. po korekcie:
ξ
eff
0.6630
:=
ξ
eff
1
<
1
=
As1
N1.max ξeff bs
⋅
d
⋅ f
cd
⋅
−
(
)
1
ξ
eff.lim
−
(
)
⋅
2 ξeff ξeff.lim
−
(
)
⋅
fyd
⋅
ξ
eff
1
<
if
N1.max bs d
⋅ f
cd
⋅
−
2 fyd
⋅
ξ
eff
1
>
if
:=
As1
2.171
−
cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
0
=
As.min 3.16 cm
2
=
Przyjeto minimalne zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16 )
As1.prov 0.5 As.min
⋅
>
1
=
As.min 3.165 cm
2
=
As2.prov
4.02cm
2
:=
(2 prety
φ16 )
As2.prov 0.5 As.min
⋅
>
1
=
B) Na maksymalny moment i odpowiadajaca mu sile osiowa:
N1.odp 560 kN
=
M1.max 29 kN m
⋅
=
Mimosrody:
- mimosrod konstrukcyjny:
ee
M1.max
N1.odp
:=
M1.max
N1.odp
29 kN m
⋅
⋅
560 kN
⋅
=
52 mm
=
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:= e
e
ea
+
52 mm
⋅
10 mm
⋅
+
=
62 mm
=
Mimosrod ostateczny:
η
1.0
:=
etot
η e
0
⋅
:= η e
0
⋅
1.0 62 mm
⋅
⋅
=
62.0 mm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=e
tot
hs
2
+
a1
−
62 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
172.0 mm
=
ξ
eff
N1.odp
bs d
⋅ f
cd
⋅
:=
N1.odp
bs d
⋅ f
cd
⋅
560 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
0.540
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
1
=
war. spelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
8
2 a2
⋅
d
0.308
=
ξ
eff
2 a2
⋅
d
>
1
=
warunek wspolpracy betonu ze zbrojeniem sciskanym; spelniony
odleglosc sily sciskajacej od zbr A
s2
es2
etot 0.5 hs
⋅
−
a2
+
:=
es2
48
−
mm
=
As1
N1.odp es2
⋅
fyd d a2
−
(
)
⋅
ξ
eff
2
a2
d
⋅
<
if
N1.odp es1
⋅
ξ
eff
1
ξ
eff
2
−
⋅
hs
⋅
d
2
⋅
fcd
⋅
−
d
a2
−
(
)
fyd
⋅
ξ
eff
2
a2
d
⋅
>
if
:=
As1
1.467
−
cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
0
=
As.min 3.16 cm
2
=
Przyjeto minimalne zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16 )
As1.prov 0.5 As.min
⋅
>
1
=
As.min 3.165 cm
2
=
As2.prov
4.02cm
2
:=
(2 prety
φ16 )
As2.prov 0.5 As.min
⋅
>
1
=
Zatem w przekroju
α1
α1
α1
α1-α1
α1
α1
α1 przyjeto zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16 )
As1.prov 0.5 As.min
⋅
>
1
=
As.min 3.165 cm
2
=
As2.prov
4.02cm
2
:=
(2 prety
φ16 )
As2.prov 0.5 As.min
⋅
>
1
=
2.1.2. Wymiarowanie zbrojenia slupa w przekroju
α2
α2
α2
α2-α2
α2
α2
α2:
A) Na maksymalna sile osiowa i odpowiadajacy moment gnacy
N2.max
N1.max N3.max
+
2
:=
N2.max 654 kN
=
Mimosrody:
- mimosrod konstrukcyjny: e
e
0.6 M1.odp
⋅
0.4 M3.odp
⋅
+
N2.max
:=
0.6 M1.odp
⋅
0.4 M3.odp
⋅
+
N2.max
0.6 26 kN
⋅
m
⋅
⋅
0.4 49 kN
⋅
m
⋅
⋅
+
654 kN
⋅
=
54 mm
=
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:= e
e
ea
+
54 mm
⋅
10 mm
⋅
+
=
64 mm
=
9
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
3.38 m
⋅
(
)
2
0.0007 m
4
⋅
30 GPa
⋅
⋅
2 1.85
⋅
0.11
0.1
ee ea
+
30 cm
⋅
+
0.1
+
⋅
200 GPa
⋅
1198 cm
4
⋅
⋅
+
⋅
=
Ncrit 2.52 MN
=
η
1
1
N1.max
Ncrit
−
:=
1
1
N1.max
Ncrit
−
1
1
654 kN
⋅
2.52 MN
⋅
−
=
1.35
=
wsp zwiekszajacy sumaryczny mimosrod:
mimosrod ostateczny:
etot
η e
0
⋅
:= η e
0
⋅
1.35 64 mm
⋅
⋅
=
86 mm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=e
tot
hs
2
+
a1
−
86 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
196.0 mm
=
ξ
eff
N2.max
bs d
⋅ f
cd
⋅
:=
N2.max
bs d
⋅ f
cd
⋅
654 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
0.630
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
0
=
war. nie spelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
Korekta zasiegu strefy sciskanej:
10
Parametry do rownania:
B
N1.max d a2
−
(
)
⋅
bs d
2
⋅
fcd
⋅
:=
B
0.533
=
A
2 N1.max
⋅
es1
⋅
bs d
2
⋅
fcd
⋅
:=
A
0.95
=
Rownanie:
W ξeff
( )
ξ
eff
3
2
ξ
eff.lim
+
(
)
ξ
eff
2
⋅
−
1
ξ
eff.lim
+
a2
d
1
ξ
eff.lim
−
(
)
⋅
−
A
+
ξ
eff
⋅
+
A ξeff.lim
⋅
−
B 1
ξ
eff.lim
−
(
)
⋅
−
:=
W ξeff
( )
0
=
ξ
eff
1
:=
root W ξeff
( )
ξ
eff
,
(
)
0.614
=
Zatem zasieg strefy sciskanej be. po korekcie:
ξ
eff
0.614
:=
ξ
eff
1
<
1
=
As1
N1.max ξeff bs
⋅
d
⋅ f
cd
⋅
−
(
)
1
ξ
eff.lim
−
(
)
⋅
2 ξeff ξeff.lim
−
(
)
⋅
fyd
⋅
ξ
eff
1
<
if
N1.max bs d
⋅ f
cd
⋅
−
2 fyd
⋅
ξ
eff
1
>
if
:=
As1 1.932 cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
1
=
As.min 3.16 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
=
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 560 kN
=
11
Mimosrody:
- mimosrod konstrukcyjny:
ee
0.6 M1.max
⋅
0.4 M3.max
⋅
+
N2.odp
:=
0.6 M1.max
⋅
0.4 M3.max
⋅
+
N2.odp
0.6 29 kN m
⋅
⋅
⋅
0.4 56 kN
⋅
m
⋅
⋅
+
N2.odp
=
71 mm
=
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:= e
e
ea
+
71 mm
⋅
10 mm
⋅
+
=
81 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
1.4%
:=
Js
ρ
0 bs
⋅
hs
⋅
1
2
bs
⋅
a1
−
2
⋅
:= ρ
0 bs
⋅
hs
⋅
1
2
hs
⋅
a1
−
2
⋅
1.4 %
⋅
30 cm
⋅
⋅
30 cm
⋅
⋅
1
2
30 cm
⋅
⋅
4 cm
⋅
−
2
⋅
=
1525 cm
4
=
Sila krytyczna:
Ncrit
9
l0
2
Jcol Ecm
⋅
2 k1t
⋅
0.11
0.1
e0
hs
+
0.1
+
⋅
Es Js
⋅
+
⋅
:=
Ncrit
9
3.38 m
⋅
(
)
2
0.0007 m
4
⋅
30 GPa
⋅
⋅
2 1.85
⋅
0.11
0.1
73 mm
⋅
30 cm
⋅
+
0.1
+
⋅
200 GPa
⋅
1633 cm
4
⋅
⋅
+
⋅
=
Ncrit 2.69 MN
=
η
1
1
N1.max
Ncrit
−
:=
1
1
N1.max
Ncrit
−
1
1
654 kN
⋅
2.69 MN
⋅
−
=
1.32
=
wsp zwiekszajacy sumaryczny mimosrod:
mimosrod ostateczny:
etot
η e
0
⋅
:= η e
0
⋅
1.32 81 mm
⋅
⋅
=
107 mm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=e
tot
hs
2
+
a1
−
107 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
217.0 mm
=
ξ
eff
N2.odp
bs d
⋅ f
cd
⋅
:=
N2.odp
bs d
⋅ f
cd
⋅
560 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
0.540
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
1
=
war. nie spelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
12
Korekta zasiegu strefy sciskanej:
Parametry do rownania:
B
N1.max d a2
−
(
)
⋅
bs d
2
⋅
fcd
⋅
:=
B
0.533
=
A
2 N1.max
⋅
es1
⋅
bs d
2
⋅
fcd
⋅
:=
A
1.052
=
Rownanie:
W ξeff
( )
ξ
eff
3
2
ξ
eff.lim
+
(
)
ξ
eff
2
⋅
−
1
ξ
eff.lim
+
a2
d
1
ξ
eff.lim
−
(
)
⋅
−
A
+
ξ
eff
⋅
+
A ξeff.lim
⋅
−
B 1
ξ
eff.lim
−
(
)
⋅
−
:=
W ξeff
( )
0
=
ξ
eff
1
:=
root W ξeff
( )
ξ
eff
,
(
)
0.602
=
Zatem zasieg strefy sciskanej be. po korekcie:
ξ
eff
0.602
:=
ξ
eff
1
<
1
=
As1
N1.max ξeff bs
⋅
d
⋅ f
cd
⋅
−
(
)
1
ξ
eff.lim
−
(
)
⋅
2 ξeff ξeff.lim
−
(
)
⋅
fyd
⋅
ξ
eff
1
<
if
N1.max bs d
⋅ f
cd
⋅
−
2 fyd
⋅
ξ
eff
1
>
if
:=
As1 4.115 cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
1
=
As.min 3.16 cm
2
=
Przyjeto zbrojenia:
As1.prov
6.03cm
2
:=
(3 prety
φ16 )
As1.prov As1
>
1
=
As2.prov
6.03cm
2
:=
(3 prety
φ16 )
2 As1.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 %
=
ε
ρ
0
ρ
−
ρ
0
:=
ρ
0
ρ
−
ρ
0
1.4 %
⋅
1.5 %
⋅
−
1.4 %
⋅
=
7.14 %
=
ε
10%
<
1
=
zatem wstepne oszacowanie stopnia zbrojenia bylo wystarczajaco dobre aby zakonczyc iteracje!
Zatem w przekroju
α2
α2
α2
α2-α2
α2
α2
α2 przyjeto zbrojenia:
As1.prov 0.5 As.min
⋅
>
1
=
As.min 3.165 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
=
13
2.1.3. Wymiarowanie zbrojenia slupa w przekroju
α3
α3
α3
α3-α3
α3
α3
α3:
A) Na maksymalna sile osiowa i odpowiadajacy moment gnacy
N3.max 654 kN
=
M3.odp 49 kN m
⋅
=
Mimosrody:
- mimosrod konstrukcyjny:
ee
M3.odp
N3.max
:=
M3.odp
N3.max
49 kN
⋅
m
⋅
654 kN
⋅
=
75 mm
=
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:= e
e
ea
+
75 mm
⋅
10 mm
⋅
+
=
85 mm
=
Mimosrod ostateczny:
η
1.0
:=
etot
η e
0
⋅
:= η e
0
⋅
1.0 85 mm
⋅
⋅
=
85.0 mm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=e
tot
hs
2
+
a1
−
85 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
195.0 mm
=
ξ
eff
N1.max
bs d
⋅ f
cd
⋅
:=
N3.max
bs d
⋅ f
cd
⋅
654 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
0.630
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
0
=
war. nie spelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
Korekta zasiegu strefy sciskanej:
Parametry do rownania:
B
N1.max d a2
−
(
)
⋅
bs d
2
⋅
fcd
⋅
:=
B
0.533
=
A
2 N1.max
⋅
es1
⋅
bs d
2
⋅
fcd
⋅
:=
A
0.946
=
Rownanie:
W ξeff
( )
ξ
eff
3
2
ξ
eff.lim
+
(
)
ξ
eff
2
⋅
−
1
ξ
eff.lim
+
a2
d
1
ξ
eff.lim
−
(
)
⋅
−
A
+
ξ
eff
⋅
+
A ξeff.lim
⋅
−
B 1
ξ
eff.lim
−
(
)
⋅
−
:=
W ξeff
( )
0
=
ξ
eff
1
:=
root W ξeff
( )
ξ
eff
,
(
)
0.614
=
Zatem zasieg strefy sciskanej be. po korekcie:
ξ
eff
0.614
:=
ξ
eff
1
<
1
=
As1
N1.max ξeff bs
⋅
d
⋅ f
cd
⋅
−
(
)
1
ξ
eff.lim
−
(
)
⋅
2 ξeff ξeff.lim
−
(
)
⋅
fyd
⋅
ξ
eff
1
<
if
N1.max bs d
⋅ f
cd
⋅
−
2 fyd
⋅
ξ
eff
1
>
if
:=
As1 1.932 cm
2
=
14
As2
As1
:=
As1 As2
+
As.min
>
1
=
As.min 3.16 cm
2
=
Przyjeto zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16 )
As1.prov As1
>
1
=
As2.prov
4.02cm
2
:=
(2 prety
φ16 )
As1.prov As.min
>
1
=
B) Na maksymalny moment i odpowiadajaca sile:
N3.odp 560 kN
=
M3.max 56 kN m
⋅
=
Mimosrody:
- mimosrod konstrukcyjny:
ee
M3.max
N3.odp
:=
M3.max
N3.odp
56 kN
⋅
m
⋅
560 kN
⋅
=
100 mm
=
Calkowity mimosrod poczatkowy:
e0
ee ea
+
:= e
e
ea
+
100 mm
⋅
10 mm
⋅
+
=
110 mm
=
Mimosrod ostateczny:
η
1.0
:=
etot
η e
0
⋅
:= η e
0
⋅
1.0 110 mm
⋅
⋅
=
110.0 mm
=
odleglosc sily sciskajacej od zbr A
s1
es1
etot
hs
2
+
a1
−
:=e
tot
hs
2
+
a1
−
110 mm
⋅
30 cm
⋅
2
+
4 cm
⋅
−
=
220.0 mm
=
ξ
eff
N3.odp
bs d
⋅ f
cd
⋅
:=
N3.odp
bs d
⋅ f
cd
⋅
560 kN
⋅
30 cm
⋅
26 cm
⋅
⋅
13.3 MPa
⋅
⋅
=
0.540
=
ξ
eff.lim
0.55
=
ξ
eff
ξ
eff.lim
<
(
)
1
=
war. spelniony:
|TAK= DUZY MIMOSROD
|NIE= MALY MIMOSROD
2 a2
⋅
d
0.308
=
ξ
eff
2 a2
⋅
d
>
1
=
warunek wspolpracy betonu ze zbrojeniem sciskanym; spelniony
odleglosc sily sciskajacej od zbr A
s2
es2
etot 0.5 hs
⋅
−
a2
+
:=
es2 6.9 10
15
−
×
mm
=
As1
N1.odp es2
⋅
fyd d a2
−
(
)
⋅
ξ
eff
2
a2
d
⋅
<
if
N1.odp es1
⋅
ξ
eff
1
ξ
eff
2
−
⋅
hs
⋅
d
2
⋅
fcd
⋅
−
d
a2
−
(
)
fyd
⋅
ξ
eff
2
a2
d
⋅
>
if
:=
As1 2.474 cm
2
=
As2
As1
:=
As1 As2
+
As.min
>
1
=
As.min 3.16 cm
2
=
15
Przyjeto minimalne zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16 )
As1.prov 0.5 As.min
⋅
>
1
=
As.min 3.165 cm
2
=
As2.prov
4.02cm
2
:=
(2 prety
φ16 )
As2.prov 0.5 As.min
⋅
>
1
=
Zatem w przekroju
α3
α3
α3
α3-α3
α3
α3
α3 przyjeto zbrojenia:
As1.prov
4.02cm
2
:=
(2 prety
φ16 )
As1.prov 0.5 As.min
⋅
>
1
=
As.min 3.165 cm
2
=
As2.prov
4.02cm
2
:=
(2 prety
φ16 )
As2.prov 0.5 As.min
⋅
>
1
=
2.1.4. Podsumowanie slupa skrajnego:
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 3.16 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
φ8 rostawione w odleglosci:
•
s
20cm
:=
16
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