dr. nagy gyÖrgy tamás 2 (rc and... · reinforced concrete ii. / beton armat ii....
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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
RC beam6004001100
Load 400Load eccentricity 50
50
Concrete class 30/37, . 2.00
Reinforcement → ∅20→ ∅10
Reinforcement strength 500
Exposure class XC3
50
50
400
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 3
? ?
?
Δ
, ; , ; 10, ?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 4
20 1.33
434.8
Δ
, ; , ; 10, 25
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 5
20 1.33
434.8
Δ
, ; , ; 10, 25
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 6
20 1.33
434.8
Δ
, ; , ; 10, 25
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 7
LONGITUDINAL REINFORCEMENT TRANSVERSAL REINF. (stirrup)
, ; , ; 10
20 ; 25 ; 10 10 ; 25 ; 10
, 25mm , 25mm
Δ 10 (A.N.) Δ 10 (A.N.)
, ,
, , 25 , , 45
, 22 , 35 , 45 , 35
, OK!!!
, ,
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 8
20 1.33
434.8
, 45
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 9
50
50
400
?
?
?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 10
50
50
400
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 11
, 2
? , 2 ?
? ?
?
Centeraxis
Centeraxis
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 12
, 2
55, 2 110
2400002000
120
Centeraxis
Centeraxis
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 13
, 2
55, 2 110
2400002000
120
? ???
Centeraxis
Centeraxis
2 2
uk
2
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 14
, 2
55, 2 110
2400002000
120
2804801520134400
Centeraxis
Centeraxis
2 2
uk
2
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 15
? 0.8 1 0.4 ?
Where 3.5
3.5 1000 / ?
?
1 1 2 ?
, ?
, ? 20 ?
? 400
?
?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 16
0.177 0.8 1 0.4 0.372
Where 3.5
3.5 1000 / 0.617
545
1 1 2 0.196
, 1965
, 7 20 2199
360 400
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 17
, max , 100 /?
Where
,0,18
?
1200
? 2
? 0.02
0,035 / · / ?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 18
, max , 100 /max
130.985.0 130.9
Where
, 0,18⁄ 0.12
1200
2 1.61
0.010 0.02
0,035 / · / 0.390
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 19
, 130.9 < 400
?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 20
, 130.9 < 400
shear reinforcement is required
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 21
, 130.9 < 400
shear reinforcement is required
Computation of
, · · · ?
Where1 for non‐prestressed structures
0,6 1 250 ?
45°
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 22
, · · · 1035.9
Where1 for non‐prestressed structures
0,6 1 250 0.528
45°
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 23
, 1035.9 > 400
?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 24
, 1035.9 > 400
cross section could be reinforced for shear
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 25
TORSIONAL CRACKING MOMENTS
, 2 ?
with
Torsional cracking moments
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 26
TORSIONAL CRACKING MOMENTS
, 2 43.0
with
Torsional cracking moments
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 27
TORSIONAL CRACKING MOMENTS
, 2 43.0 < 60
?
Torsional cracking moments
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 28
TORSIONAL CRACKING MOMENTS
, 2 43.0 < 60
reinforcement for torsion is required
Torsional cracking moments
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 29
FOR APPROXIMATELY RECTANGULAR SOLID SECTIONS
YES NOCalculation for combined shear and torsion is required , ,
1 no reinforcement calculation required
Torsional cracking moments
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 30
FOR APPROXIMATELY RECTANGULAR SOLID SECTIONS
6043.0
400130.9 ?
YES NOCalculation for combined shear and torsion is required , ,
1 no reinforcement calculation required
Torsional cracking moments
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 31
FOR APPROXIMATELY RECTANGULAR SOLID SECTIONS
6043.0
400130.9 4.45 1
YES NOCalculation for combined shear and torsion is required , ,
1 no reinforcement calculation required
Torsional cracking moments
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 32
CAPACITY OF COMPRESSED STRUTS
, 2 ?
1 for non‐prestressed structures
0,6 1 250 ?
45°
Maximum resistance of concrete struts
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 33
CAPACITY OF COMPRESSED STRUTS
, 2 170.3
1 for non‐prestressed structures
0,6 1 250 0.528
45°
Maximum resistance of concrete struts
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 34
CAPACITY OF COMPRESSED STRUTS
, 2 170.3 > 60
?
Maximum resistance of concrete struts
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 35
CAPACITY OF COMPRESSED STRUTS
, 2 170.3 > 60
cross section could be reinforced for torsion
Maximum resistance of concrete struts
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 36
THE MAXIMUM RESISTANCE OF A MEMBER SUBJECTED TO TORSION AND SHEAR IS LIMITED BY THE CAPACITY OF THE CONCRETE STRUTS
YES next step = reinforcementcalculation
NOreconsider of the cross section , ,
1
Notes about ,‐ in solid cross sections the full width of the web may be used‐ for non‐solid sections replace by
Maximum resistance of concrete struts
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 37
THE MAXIMUM RESISTANCE OF A MEMBER SUBJECTED TO TORSION AND SHEAR IS LIMITED BY THE CAPACITY OF THE CONCRETE STRUTS
YES next step = reinforcementcalculation
NOreconsider of the cross section , ,
1
Maximum resistance of concrete struts
60170.3
4001035.9 ?
?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 38
THE MAXIMUM RESISTANCE OF A MEMBER SUBJECTED TO TORSION AND SHEAR IS LIMITED BY THE CAPACITY OF THE CONCRETE STRUTS
YES next step = reinforcementcalculation
NOreconsider of the cross section , ,
1
Maximum resistance of concrete struts
60170.3
4001035.9 0.738 1
cross section could be reinforced for combined shear and torsion
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 39
The condition of rational use of stirrups ,
With 45°and α 90°
· · ?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 40
The condition of rational use of stirrups ,
With 45°and α 90°
· · 1.876
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 41
Transversal torsional reinforcement
The condition of rational use of stirrups ,
With 45°
2 ?
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 42
Transversal torsional reinforcement
The condition of rational use of stirrups ,
With 45°
2 0.513
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 43
Longitudinal torsional reinforcement
Required area of the longitudinal bars is obtained from ,
With 45°
2 ?
Proposals ? 6or ? 8or ? 10or ? 12or ? 14
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 44
Longitudinal torsional reinforcement
Required area of the longitudinal bars is obtained from ,
With 45°
2 780
Proposals 16 8 804or 10 10 785or 7 12 792or 6 14 924or 4 16 804
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 45
Structural elements are subjected to
should take account of superposition of the effects of all the effects
‐
‐ / / /
. . .
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 46
Structural elements are subjected to
1.876 0.513 2.389
For n 2 2 · ? ?
?
? 80
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 47
Structural elements are subjected to
1.876 0.513 2.389
For n 2 2 · 157
65.8
60 80
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 48
Structural elements are subjected to
1.876 0.513 2.389
For n 4 4 · ?
?
? 80min 0.75 , 8⁄ , 400
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 49
Structural elements are subjected to
1.876 0.513 2.389
For n 4 4 · 314
131.5
80min 0.75 , 8⁄ , 400
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 50
50
50
400
hook
7 20
6 14
2 10/13
33
5353 53 5315
Faculty of Civil Engineering
Reinforced Concrete II. / Beton Armat II.
Dr.ing. Nagy‐György T. 51
50
50
400
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