1. Design Condition
Design code
Element
Node(I/J)
BS 5400-4:1990
1634
I
■ Section Properties
Section Type
Non-Composite
- Gross section
H
4450.000 (mm)
Ag
Iy
B
3650.000 (mm)
Czp
2398.780 (mm)
Czm
2051.220 (mm)
9.584E+06 (mm2)
1.323E+13 (mm4)
5.516E+09 (mm3)
6.450E+09 (mm3)
St
Sb
- Transformed section
H
4450.000 (mm)
Ag
Iy
B
3650.000 (mm)
Czp
2427.346 (mm)
Czm
2022.654 (mm)
1.033E+07 (mm2)
1.454E+13 (mm4)
5.990E+09 (mm3)
7.188E+09 (mm3)
St
Sb
■ Partial Safety Factors
- Partial Safety Factors for Ultimate Limit State
Characteristic
1.5
1.15
γmc for Concrete
γms for Reinforce/Prestress
- Partial Safety Factors for Serviceability Limit State
Type of Stress
γmc for concrete
Triangular Compressive
1.25
1.67
1.25
1.55
Uniform Compressive
Pre-tension
Post-tension
■ Material
- Concrete
fcu (MPa)
50.0
Ec (MPa)
31754.0
- Prestressing steel Information
No. Tendon name
Bond
type
dt
(mm)
Aps
(mm2)
fpu
(MPa)
Ep
(MPa)
1IDS_CVL_RPT_US_PSC_Bond
S_CR_004
: 미등록 2912.3
문자열
17400.0
1863.3
196500.6
2IDS_CVL_RPT_US_PSC_Bond
S_CR_007
: 미등록 1459.6
문자열
8700.0
1863.3
196500.6
3IDS_CVL_RPT_US_PSC_Bond
S_CR_006
: 미등록 1844.7
문자열
8700.0
1863.3
196500.6
4IDS_CVL_RPT_US_PSC_Bond
S_CR_008
: 미등록 1024.5
문자열
8700.0
1863.3
196500.6
5IDS_CVL_RPT_US_PSC_Bond
S_CR_001
: 미등록 4407.5
문자열
17400.0
1863.3
196500.6
6IDS_CVL_RPT_US_PSC_Bond
S_CR_003
: 미등록 3429.8
문자열
17400.0
1863.3
196500.6
7IDS_CVL_RPT_US_PSC_Bond
S_CR_002
: 미등록 3947.4
문자열
17400.0
1863.3
196500.6
8IDS_CVL_RPT_US_PSC_Bond
S_CR_005
: 미등록 2362.3
문자열
8700.0
1863.3
196500.6
* dt is Distance from extreme compression fiber to centroid of prestressing tendon.
- Longitudinal non prestressed steel reinforcement Information.
Es
(MPa)
fsy
(MPa)
200000.0
460.0
Bottom for flexure
Top for flexure
As
d
(mm)
d's
(mm)
(mm2)
3846.8
15531.2
Torsion
A's
AsL
(mm2)
(mm2)
1163.0
23444.1
27331.9
* ds or d's is Distance from extreme compression fiber to centroid of non prestressing reinforcement.
- Tranverse non prestressed steel reinforcement Information.
Es
(MPa)
fsy
(MPa)
200000.0
460.0
Shear
αv
(deg.)
Torsion
Asv
(mm2)
90.0
At
s
(mm)
2041.0
st
(mm)
(mm2)
150.0
1608.0
150.0
* α is angle between longitudinal and stirrup.
2. Flexure Design for a Section
■ Moment Direction :Positive
gLCB3
- Strength limit load combination :
- Strength limit load combination type : IDS_CVL_RPT_US_Lcom_Concurr_Type_Fx_max : 미등록 문자열
- Bending Moment due to ultimate loadsM
123913.97
=
(kN∙m)
1) Depth of neutral axis to compression face (x).
Axial force in concrete (compressive zone)
x
a=γc
Ac
2459.668
2459.668
5048690.78
ac
Cc=α2f'cAc (kN)
1276.67
Cc(x-ac) (kN∙m)
88471.48
104661.31
Axial force in reinforcement steels
tensile zone
Ts=Asfsy (kN)
compressive zone
6131.33
No.
Cs=A'sf'sy (kN)
ΣAsfsy(ds-c) (kN∙m)
8505.16
ΣA'sf'sy(c-d's) (kN∙m)
7693.58
9975.65
Axial force in tendons(Bonded) by strain compatibility
εps
Tendon name
σpb (MPa)
Apsσpb (kN)
Apsσpb(dp-x) (kN∙m)
1
S_CR_004
0.005884
1156.14
20116.84
9104.72
2
S_CR_001
0.008286
1378.51
23986.05
46719.64
3
S_CR_003
0.006718
1302.10
22656.61
21980.09
4
S_CR_002
0.007422
1336.40
23253.37
34593.75
Σ
90012.87
112398.21
- Iterative calculation of Neutral Axis:
Compression force (kN)
Tensile force (kN)
Num
.
x (mm)
1
2225.000
73545.09
7229.73
6715.14
102296.47
0.74097
2
3337.500
136300.32
9278.32
2089.37
61491.28
2.28967
3
2781.250
108020.36
8357.26
4234.25
85592.01
1.29559
4
2503.125
91222.30
7716.04
5836.14
89520.01
1.03757
5
2364.063
82386.11
7474.85
6463.81
91160.95
0.92047
6
2433.594
86821.30
7679.73
6212.48
90317.04
0.97899
7
2468.359
89021.85
7698.14
6071.46
89912.91
1.00766
8
2450.977
87923.03
7689.00
6191.62
90113.54
0.99280
9
2459.668
88471.48
7693.58
6131.33
90012.87
1.00022
Cc
Cs
Ts
Tps
Tolerance
(C/T)
2) Flexural Resistance
▪ Ultimate Moment Resistance(Mu)
Mu =
235540.32
(kN∙m)
▪ Bending Moment Check
Mu ≥ M
Mu =
235540.32
M
≥
(kN∙m)
=
123913.97
(kN∙m)
IDS_CVL_RPT_US_OK
: 미등록 문자열
∴
■ Moment Direction :Negative
gLCB2
- Strength limit load combination :
- Strength limit load combination type : IDS_CVL_RPT_US_Lcom_Concurr_Type_Fx_min : 미등록 문자열
- Bending Moment due to ultimate loadsM
0.00
=
(kN∙m)
1) Depth of neutral axis to compression face (x).
Axial force in concrete (compressive zone)
x
a=γc
Ac
1537.738
1537.738
3383023.79
ac
Cc=α2f'cAc (kN)
673.95
Cc(x-ac) (kN∙m)
65438.80
56525.51
Axial force in reinforcement steels
tensile zone
Ts=Asfsy (kN)
compressive zone
10382.94
No.
Cs=A'sf'sy (kN)
ΣAsfsy(ds-c) (kN∙m)
16621.91
ΣA'sf'sy(c-d's) (kN∙m)
4339.31
5020.37
Axial force in tendons(Bonded) by strain compatibility
Tendon name
εps
σpb (MPa)
Apsσpb (kN)
Apsσpb(dp-x) (kN∙m)
1
S_CR_004
0.005240
1029.59
17914.89
0.03
2
S_CR_007
0.008107
1369.80
11917.27
17311.57
3
S_CR_006
0.007476
1339.04
11649.62
12436.55
4
S_CR_008
0.009017
1414.16
12303.19
23225.24
5
S_CR_005
0.006470
1271.31
11060.44
6083.26
Σ
64845.40
59056.66
- Iterative calculation of Neutral Axis:
Compression force (kN)
Tensile force (kN)
Num
.
x (mm)
1
2225.000
98084.18
5595.95
7878.48
31196.11
2.65339
2
1112.500
47342.69
3710.99
11136.92
73680.08
0.60193
3
1668.750
71031.08
4548.75
10131.61
45609.26
1.35591
4
1390.625
59178.37
4129.87
10634.26
67408.18
0.81120
5
1529.688
65096.20
4339.31
10382.94
64996.96
0.92114
6
1599.219
68055.71
4548.75
10131.61
46283.53
1.28697
7
1564.453
66575.66
4339.31
10382.94
46643.13
1.24355
8
1547.070
65835.93
4339.31
10382.94
46829.00
1.22658
9
1538.379
65466.07
4339.31
10382.94
46923.51
1.21811
10
1534.033
65281.14
4339.31
10382.94
64914.95
0.92460
11
1536.206
65373.60
4339.31
10382.94
64874.12
0.92633
12
1537.292
65419.84
4339.31
10382.94
64853.75
0.92720
13
1537.836
65442.95
4339.31
10382.94
46929.45
1.21758
14
1537.564
65431.39
4339.31
10382.94
64848.66
0.92741
15
1537.700
65437.17
4339.31
10382.94
64846.12
0.92752
16
1537.768
65440.06
4339.31
10382.94
46930.19
1.21751
17
1537.734
65438.62
4339.31
10382.94
64845.48
0.92755
18
1537.751
65439.34
4339.31
10382.94
46930.38
1.21749
19
1537.742
65438.98
4339.31
10382.94
46930.47
1.21749
20
1537.738
65438.80
4339.31
10382.94
64845.40
0.92755
Cc
Cs
Ts
Tps
Tolerance
(C/T)
* Based on the placement of rebars and tendons, program failed to find the exact neutral axis
2) Flexural Resistance
▪ Ultimate Moment Resistance(Mu)
Mu =
137224.45
(kN∙m)
▪ Bending Moment Check
Mu ≥ M
Mu =
137224.45
(kN∙m)
≥
M
=
-35268.09 (kN)
3. Shear Design for a Section
- Strength limit load combination :
gLCB1
- Strength limit load combination type : -Axial force due to ultimate loads
P
=
- Shear force due to ultimate loads
V
=
-13424.54 (kN)
- Bending moment due to ultimate loads M
=
119672.00 (kN∙m)
0.00
(kN∙m)
IDS_CVL_RPT_US_OK
: 미등록 문자열
∴
1) Crack Check for Flexure
- Cracking moment (Mcr)
(see BS 5400 - 6.3.4.3)
Mcr =
where,
fpt =
I =
y =
=
184976.69
(kN∙m)
23.12 (MPa) : Stress due to prestress only at the tensile fibre
1.4539E+13 (mm4) : Second moment of area
2022.65 (mm) : Tensile fibre distance
Since,
Mcr > M : Section is uncracked in flexure
2) Shear resistance of Concrete
▪ Maximum Principal Tensile Stress of Section (ft).
ft
=
=
(see BS 5400 - 6.3.4.2)
1.70
(MPa)
▪ Ultimate Shear Resistance of Concrete (Vco = Vc).
Vco =
where,
γfL =
Vp =
fcp =
b =
h =
=
11.91 Mpa
1450.00 (mm)
4450.00 (mm)
V ≤ Vc
31779.11
(kN)
: Partial factor for prestressing force
1.15
-9570.98 (kN)
Vc = Vco =
(see BS 5400 - 6.3.4.2 Eq 28)
31779.11
: Vertical component of prestressing force
: Total direct stress at the location of the section
: Breadth of the member at the location of the section
: Overall depth of the member
(kN)
∴ No need to check shear reinforcement
3) Shear reinforcement
Since shear force due to ultimate loads is lower than ultimate shear resistance of concrete
Shear reinforcement check will be skipped
4)Shear resistance
▪ Maximum Shear force (Vmax)
Vmax =
(see BS 5400 - 6.3.4.5 Table 28)
(N/mm2) *
5.30
b
*
d
28478.38
=
(kN)
where,
b : Breadth of the member at the location of the section
1450.00 (mm)
=
d : Distance from the compression face to the centroid of the area of steel in the tension zone
3705.71 (mm)
=
▪ Shear Check
Vu ≥
V
Vmax =
5)
28478.38
(kN)
V
≥
=
-13424.54
(kN)
IDS_CVL_RPT_US_OK
: 미등록 문자열
∴
Joint Shear
- There are no segmental construction considered for joint, skip this check
4. Torsional Design for a Section
- Strength llimit load combination :
gLCB2
- Strength llimit load combination type :IDS_CVL_RPT_US_Lcom_Concurr_Type_Fx_max : 미등록 문자열
- Torque due to ultimate loads
T
=
- Shear force due to ultimate loads
V
=
9598.19 (kN∙m)
-13073.82 (kN)
1) Torsional resistance
▪ Minimum Ultimate Torsional Shear Stress(vtmin).
vtmin =
(see BS 5400 - 5.3.4.4 Table 10)
0.42 (MPa)
▪ Torsional Shear Stress(vt).
vt
T
=
=
2 hwA0
(see BS 5400 - 5.3.4.4 Eq 9)
0.23
(MPa)
where,
T : Torque due to ultimate loads
9598.19 (kN∙m)
=
A0 : Area enclosed by the median wall line
= 9583750.00 (mm2)
hw : Thickness of the thinnest wall
2225.00 (mm)
=
2) Check Torsion
▪ Check Torsion Reinforcement
vt ≤ vtmin
∴ Torsion reinforcement can be ignored
▪ Ultimate Shear Stress (vtu)
vtu =
(see BS 5400 - 5.3.4.4 Table 10)
4.75 (MPa)
▪ Check Torsional Shear Stress
`
vtu > ( v + vt )
( v + vt )
=
where,
v : Shear stresses from shear force
-2.43 (MPa)
=
-2.21 (MPa)
IDS_CVL_RPT_US_OK
: 미등록 문자열
∴
∴ Shear stresses resulting from torsion satisfy criteria
5. Concrete stress check at transfer and during constuction
Class 1 Limit Check
(see BS 5400 - 6.3.2)
▪ Check If Stresses are Within Class 1 Limits
1) Girder
■ Compression
- Critical Stage NameCS5
:
│σc,limit │= min (
0.5 fci
,
0.4 fcu
)
=
20.00
(MPa)
f'ci : Concrete strength at transfer
72.52 (MPa)
=
σc,conc : Compressive stress on the prestressed concrete
15.99 (MPa)
=
σc,limit : Flexural compressive stress limit
│σc,conc ││σ
: 미등록 문자열
≤ c,limit │ IDS_CVL_RPT_US_OK
∴
■ Tension
- Critical Stage NameCS5
:
│σt,conc │≤ │σt,limit │
σt,limit =
0.00
(MPa)
σt,conc : Tensile stress on the prestressed concrete
1.10 (MPa)
=
σt,limit : Flexural tensile stress limit
* Concrete is under compression. Thus, tension check is OK.
6. Concrete stress check for service load combination
Class 1 Limit Check
(see BS 5400 - 6.3.2)
▪ Check If Stresses are Within Class 1 Limits
1) Girder
■ Compression
- Service limit load combination gLCB4
:
- Service limit load combination -type :
│σc,conc │≤
0.4 fcu
= │σc,limit │ =
20.00
σc,conc : Compressive stress on the prestressed concrete
15.99 (MPa)
=
σc,limit : Flexural compressive stress limit
│σc,conc ││σ
: 미등록 문자열
≤ c,limit │ IDS_CVL_RPT_US_OK
∴
(MPa)
■ Tension
- Service limit load combination gLCB4
:
- Service limit load combination -type :
│σt,conc │≤ │σt,limit │
σt,limit =
0.00
(MPa)
σt,conc : Tensile stress on the prestressed concrete
1.10 (MPa)
=
σt,limit : Flexural tensile stress limit
* Concrete is under compression. Thus, tension check is OK.
7. Joint stress check for service load combination
- There are no segmental construction considered for joint, skip this check