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Zbrojenie płyty
4. Rozkład obciążeń na symetryczne i antysymetryczne
ᇱ
=
+ 0,5 = 6,413 + 5,25 = 11,663/
ଶ
ᇱᇱ
= 0,5
= 5,25/
ଶ
= ′ + ′′ = 11,663 + 5,25 = 16,913/
ଶ
5.1 Momenty przęsłowe w polach narożnych (4):
ସ௫
=
ସ௫
ᇱ
±
ଵ௫
ᇱᇱ
௫
ଶ
ସ௫,௫
=
0,0166 ∙ 11,663 + 0,0231 ∙ 5,25 ∙ 7,8
ଶ
= 19,16
/
ସ௫,
=
0,0166 ∙ 11,663 − 0,0231 ∙ 5,25 ∙ 7,8
ଶ
= 4,40
/
ସ௬
=
ସ௬
ᇱ
±
ଵ௬
ᇱᇱ
௬
ଶ
ସ௬,௫
=
0,0387 ∙ 11,663 + 0,0547 ∙ 5,25 ∙ 6,3
ଶ
= 29,31
/
ସ௬,
=
0,0387 ∙ 11,663 − 0,0547 ∙ 5,25 ∙ 6,3
ଶ
= 6,52
/
5.2 Momenty przęsłowe w polach wewnętrznych (5):
ହ௫
=
ହ௫
ᇱ
±
ଵ௫
ᇱᇱ
௫
ଶ
ହ௫,௫
=
0,0156 ∙ 11,663 + 0,0231 ∙ 5,25 ∙ 7,8
ଶ
= 18,45
/
ହ௫,
=
0,0156 ∙ 11,663 − 0,0231 ∙ 5,25 ∙ 7,8
ଶ
= 3,69
/
ସ௬
=
ହ௬
ᇱ
±
ଵ௬
ᇱᇱ
௬
ଶ
ହ௬,௫
=
0,0315 ∙ 11,663 + 0,0547 ∙ 5,25 ∙ 6,3
ଶ
= 25,98
/
ହ௬,
=
0,0315 ∙ 11,663 − 0,0547 ∙ 5,25 ∙ 6,3
ଶ
= 3,18
/
5.3 Momenty przęsłowe w polach wewnętrznych (5’) w układzie globalnym:
ହᇱ௫
=
ହᇱ௬
ᇱ
±
ଵ௫
ᇱᇱ
௫
ଶ
ହᇱ௫,௫
=
0,0109 ∙ 11,663 + 0,0231 ∙ 5,25 ∙ 7,8
ଶ
= 15,11
/
ହᇱ௫,
=
0,0109 ∙ 11,663 − 0,0231 ∙ 5,25 ∙ 7,8
ଶ
= 0,36
/
ସ௬
=
ହᇱ௫
ᇱ
±
ଵ௬
ᇱᇱ
௬
ଶ
ହᇱ௬,௫
=
0,0291 ∙ 11,663 + 0,0547 ∙ 5,25 ∙ 6,3
ଶ
= 24,87
/
ହᇱ௬,
=
0,0291 ∙ 11,663 − 0,0547 ∙ 5,25 ∙ 6,3
ଶ
= 2,07
/
5.4 Momenty przęsłowe w polach środkowych (6):
௫
=
௫
ᇱ
±
ଵ௫
ᇱᇱ
௫
ଶ
௫,௫
=
0,0109 ∙ 11,663 + 0,0231 ∙ 5,25 ∙ 7,8
ଶ
= 15,11
/
௫,
=
0,0109 ∙ 11,663 − 0,0231 ∙ 5,25 ∙ 7,8
ଶ
= 0,36
/
ସ௬
=
௬
ᇱ
±
ଵ௬
ᇱᇱ
௬
ଶ
௬,௫
=
0,0252 ∙ 11,663 + 0,0547 ∙ 5,25 ∙ 6,3
ଶ
= 23,06
/
௬,
=
0,0252 ∙ 11,663 − 0,0547 ∙ 5,25 ∙ 6,3
ଶ
= 0,27
/
5.5 Momenty podporowe w osiach podpór:
= −
ℵ
ସ
16
+
ℵ
ହ
24
௫
ଶ
= −
0,302
16
+
0,462
24
16,913 ∙ 7,8
ଶ
= −39,23
/
= −
1 − ℵ
ସ
16
+
ℵ
ହᇱ
24
௬
ଶ
= −
1 − 0,302
16
+
0,821
24
16,913 ∙ 6,3
ଶ
= −52,24
/
= −
ℵ
ହᇱ
24
+
ℵ
ହ
′
24
௬
ଶ
= −
0,821
24
+
0,821
24
16,913 ∙ 6,3
ଶ
= −45,93
/
ௗ
= −
1 − ℵ
24
+
1 − ℵ
24
௬
ଶ
= −
1 − 0,302
24
+
1 − 0,302
24
16,913 ∙ 6,3
ଶ
= −39,05
/
= −
1 − ℵ
ହᇱ
16
+
ℵ
24
௫
ଶ
= −
1 − 0,821
16
+
0,302
24
16,913 ∙ 7,8
ଶ
= −24,46
/
= −
1 − ℵ
24
+
1 − ℵ
ହ
16
௬
ଶ
= −
1 − 0,302
24
+
1 − 0,462
16
16,913 ∙ 6,3
ଶ
= −42,09
/
6. Wymiarowanie zbrojenia
MPa
f
f
S
yk
yd
783
,
434
15
,
1
500
=
=
=
γ
5
,
0
10
200
783
,
434
0035
,
0
0035
,
0
8
,
0
8
,
0
3
1
1
lim
,
=
⋅
+
⋅
=
+
⋅
=
S
yd
CU
CU
eff
E
f
ε
ε
ζ
6.1 Otulenie prętów zbrojenia
=
+ ∆
ௗ௩
Założono klasę ekspozycji XC1, klasę konstrukcji S2 oraz stal zwykłą, pręty φ=10mm
= max
,
= 10
;
,ௗ௨
= 10
= 10
∆
ௗ௩
= 10
=
+ ∆
ௗ௩
= 10 + 10 = 20
6.2 Wysokość użyteczna przekroju
Zbrojenie na momenty przęsłowe
Zbrojenie na kierunku X znajduje się na spodzie
௫
= ℎ
−
− 0,5∅ = 16 − 2 − 0,5 = 13,5
௬
=
௫
− ∅ = 13,5 − 1 = 12,5
Zbrojenie na momenty podporowe
′
௫
=
௫
+
ż
6
= 13,5 +
25
6
= 17,667
′
௬
=
௬
+
ż
6
= 12,5 +
25
6
= 16,667
6.3 Minimalny przekrój zbrojenia podłużnego
Zbrojenie przęsłowe
2
min
,
1
036
,
2
755
,
1
036
,
2
5
,
13
100
0013
,
0
5
,
13
100
500
9
,
2
26
,
0
0013
,
0
26
,
0
cm
d
b
d
b
f
f
A
x
x
yk
ctm
x
S
=
=
⋅
⋅
⋅
⋅
⋅
=
⋅
⋅
⋅
⋅
⋅
=
2
min
,
1
885
,
1
625
,
1
885
,
1
5
,
12
100
0013
,
0
5
,
12
100
500
9
,
2
26
,
0
0013
,
0
26
,
0
cm
d
b
d
b
f
f
A
y
y
yk
ctm
y
S
=
=
⋅
⋅
⋅
⋅
⋅
=
⋅
⋅
⋅
⋅
⋅
=
Zbrojenie podporowe
2
min
,
1
664
,
2
297
,
2
664
,
2
667
,
17
100
0013
,
0
667
,
17
100
500
9
,
2
26
,
0
'
0013
,
0
'
26
,
0
cm
d
b
d
b
f
f
A
x
x
yk
ctm
x
S
=
=
⋅
⋅
⋅
⋅
⋅
=
⋅
⋅
⋅
⋅
⋅
=
2
min
,
1
513
,
2
167
,
2
513
,
2
667
,
16
100
0013
,
0
667
,
16
100
500
9
,
2
26
,
0
'
0013
,
0
'
26
,
0
cm
d
b
d
b
f
f
A
y
y
yk
ctm
y
S
=
=
⋅
⋅
⋅
⋅
⋅
=
⋅
⋅
⋅
⋅
⋅
=
6.4 Maksymalny rozstaw prętów
Zbrojenie główne
௫
= 3ℎ
= 48
=>
௫
= 40
Zbrojenie drugorzędne (rozdzielcze)
௫
= 3,5ℎ
= 56
=>
௫
= 45
6.5 Przykładowe obliczenie zbrojenia potrzebnego do zazbrojenie płyty 4 na kierunku x
045
,
0
135
,
0
1
33
,
23
10
16
,
19
2
3
2
max
=
⋅
⋅
⋅
=
⋅
⋅
=
−
d
b
f
M
cd
AB
eff
µ
50
,
0
2
1
1
lim
,
=
≤
⋅
−
−
=
eff
eff
eff
ξ
µ
ξ
50
,
0
046
,
0
045
,
0
2
1
1
lim
,
=
≤
=
⋅
−
−
=
eff
eff
ξ
ξ
Przekrój jest pojedynczo zbrojony
d
x
d
x
eff
eff
eff
eff
⋅
=
⇒
=
ξ
ξ
m
x
eff
0062
,
0
135
,
0
046
,
0
=
⋅
=
min
,
1
1
S
yd
eff
cd
S
A
f
d
b
f
A
≥
⋅
⋅
⋅
=
ξ
2
3
3
1
341
,
3
10
783
,
434
5
,
13
046
,
0
100
10
33
,
23
cm
A
S
=
⋅
⋅
⋅
⋅
⋅
=
−
−
2
2
10
785
,
0
4
1
cm
A
=
=
π
φ
cm
cm
A
A
b
s
S
23
46
,
23
341
,
3
785
,
0
100
1
8
≈
=
⋅
=
⋅
=
φ
2
10
1
413
,
3
23
100
785
,
0
cm
s
b
A
A
pro
S
=
⋅
=
⋅
=
φ
%
253
,
0
%
100
5
,
13
100
413
,
3
%
100
1
=
⋅
⋅
=
⋅
⋅
=
d
b
A
pro
S
L
ρ
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