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Reinforced Concrete II. / Beton Armat II.
Faculty of Civil EngineeringDr.ing. Nagy‐György T.
Dr. NAGY‐GYÖRGY TamásProfessor
E‐mail: tamas.nagy‐[email protected]
Tel:+40 256 403 935
Web:http://www.ct.upt.ro/users/TamasNagyGyorgy/index.htm
Office:A219
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 2
Flat slab Thickness 26Concrete class C30/37Reinforcement ∅14/15
∅14/15Shear reinforcement 500Concrete cover 20
Interior column 40x40 cm
850
26
40
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 3
20 27 ?
20 14 41 ?
d ?
26
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 4
20 27 260 27 233
20 14 41 260 41 219
d 226
26
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 5
should be calculated as mean values taking into account a slab width equal to the column width plus 3d each side, see #6.4.4
· ∅4 ·
2 · 3?
, , · ?
3d a 3d
dad6As
As = As,tensile
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 6
should be calculated as mean values taking into account a slab width equal to the column width plus 3d each side, see #6.4.4
· ∅4 ·
2 · 3 · 144 ·
400 2 · 3 · 226150 1802
, , ·1802
400 2 · 3 · 226 · 226 0.0045
3d a 3d
dad6As
As = As,tensile
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 7
,· , 0,5 · ·
Column perimeter ?
Coefficient = f(MEd)
0,6 1 250 ?
?
, ?
, ? , ? ,
For structures where the lateral stability does not depend on frame action between the slabs and the columns, and where the adjacent spans do not differ in length by more than 25%,approximate values for β may be used
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 8
,· , 0,5 · ·
Column perimeter 1600
Coefficient = f(MEd)
0,6 1 250 0.53
20
, 2.70
, 5.28 , ,
For structures where the lateral stability does not depend on frame action between the slabs and the columns, and where the adjacent spans do not differ in length by more than 25%,approximate values for β may be used
design value of the maximum punching shear resistance along the control section considered
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 9
,· , , 100 /
Basic control perimeter 2 2 · 2 ?
, 0,18⁄ ?
1200
? 2
0,035 ⁄ · ⁄ ?
,
·?
, , 100 / ? , ? ,
2
basic control perimeter
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 10
,· , , 100 /
Basic control perimeter 2 2 · 2 4440
, 0,18⁄ 0.12
1200
1.94 2
0,035 ⁄ · ⁄ 0.52
,
·0.97
, , 100 / 0.57 , ,
transversal reinforcement is needed!
2
basic control perimeter
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 11
, ·?
Distance from the column edge to the control perimeter
2 2 4 2 · /2
?
2
? ?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 12
, ·7546
Distance from the column edge to the control perimeter
2 2 4 2 · /2
4.19
2 4.19
4.19 946
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 13
1.5 ? ?
2 4.19
The outermost perimeter of shear reinforcement ( ) should be placed at a distance not greater than 1.5d within
1.5
area with reinforcements
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 14
1.5 2.69 607
2 4.19
The outermost perimeter of shear reinforcement ( ) should be placed at a distance not greater than 1.5d within
2.69
1.5
area with reinforcements
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 15
uoutuopr 1,5d
0,75d
at least two perimeters
0,5d
0.75 ? ?
, 0.5 ?
, 0.3 ? , ?
Maximum distance between the face of a support and the nearest shear reinforcement
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 16
uoutuopr 1,5d
0,75d
at least two perimeters
0,5d
0.75 170 150
, 0.5 113
, 0.3 67.8 , 75
Maximum distance between the face of a support and the nearest shear reinforcement
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 17
1.5 ? inside
2 ? outside
sr
u1
2d
st 1,5d
st 2,0d
inside u1
outside u1
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 18
1.5 339 inside
2 452 outside
sr
u1
2d
st 1,5d
st 2,0d
inside u1
outside u1
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 19
The number of perimeters
1.5 2.69 607
1st perimeter distance = ? mm2nd perimeter distance= = ? mm3rd perimeter distance= = ? mm4th perimeter distance= = ? mm5th perimeter distance= = ? mm
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 20
The number of perimeters
1.5 2.69 607
1st perimeter distance = 75 mm2nd perimeter distance= (75+150) =225 mm3rd perimeter distance= (225+150) = 375 mm4th perimeter distance= (375+150) = 525 mm ?5th perimeter distance= (525+150) = 675 mm ???
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 21
The number of perimeters
1.5 2.69 607
1st perimeter distance = 75 mm2nd perimeter distance= (75+150) =225 mm3rd perimeter distance= (225+150) = 375 mm4th perimeter distance= (375+150) = 525 mm 48995th perimeter distance= (525+150) = 675 mm out of the outermost perimeter of
reinforcement
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 22
Required area of one bar in perimeter u1
, 0.08 ··1.5 ? → ? ?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 23
Required area of one bar in perimeter u1
, 0.08 ··1.5 29.7 → 8 50.3
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 24
Required area of one bar in perimeter u1
,, 0.75 ,
1.5 ,
, 250 0.25
, ? 500 ? ?
→ , ?
The necessary number of shear reinforcement per perimeter = ? ? ?
→ ? ? ?
→ / ? 1 < ? > , 2 ?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 25
Required area of one bar in perimeter u1
,, 0.75 ,
1.5 ,
, 250 0.25
, 307 500
→ , 788
The necessary number of shear reinforcement per perimeter = , / , = 15.7
→ 16 8 50.3
→ / 16 1 327 < , 2 452
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 26
7.5 15 15 15
< 45
cm
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 27
7.5 15 15 15
< 45
cm
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 28
7.5 15 15 15
< 45
cm
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 29(ASCE Library)
Dr. NAGY‐GYÖRGY TamásProfessor
E‐mail: tamas.nagy‐[email protected]: +40 256 403 935Web: http://www.ct.upt.ro/users/TamasNagyGyorgy/index.htm Office: A219
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