frame 17 gb design report
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MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Contract No.: T/MONORAIL/WJWC/2008 Project Title: MUMBAI MONORAIL
Document Title:
Design Calculations for Guideway Beams of Frame 17
(Definitive Design Review)
Revision History
A1 01-04-13 Initial Submission
MARK DATE DESCRIPTION SYSTEMS CIVIL
APPROVED BY (LTSE) Project Director Atul Jain Joint Project Director CheeChiak Yang
SCOMI ENGINEERING BERHAD LARSEN & TOUBRO LIMITED
Checked By (Civil) Zafrin Zakaria
Checked By (QA/QC Manager) Name
Checked By (QA/QC Manager)
Checked By (Project Manager) Name
Prepared By Vivek Pagnis Checked By
DATE: 10.04.2013 DATE
CONTRACTOR’S DOCUMENT No.:
DOCUMENT No.: MM001-D-DR-VSP-LTSE-311050
REVISION
A1
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
PRELIMINARY NOTE
This document is the exclusive property of LTSE. It is confidential and may not be used, reproduced or communicated either in whole or in part, in any form or manner without the prior written agreement of LTSE. This document shall not be distributed to third parties except under the terms of the contract. REVISION STATUS
A1 10-04-13 Initial Submission AMS VVP ZZ
Rev. Date Revision Note Designed by Checked by Approval by
MUMBAI MONORAIL
______________________________________________________________________________
Fig. 3.1 : 3D rendered model in MIDAS software
1.0 SUMMARY
This report contains the detailed superstructure guide-way beam design of Frame No. 17 with a curvedalignment in plan and 27+22+26m span configuration. The results are shown below:
(i) Guideway Beams : • Beam size : section consist of 800(width) x 2200(Depth) box section at mid-span & endblock • Concrete strength : 60 MPa
2.0 DESIGN CRITERIA
Refer to Definitive Design Review – Design Criteria for Guideway Structural Design(MM002-D-DR-VSP-LTSE-303001)References: - IRS Concrete Bridge Code 1997 - BS 5400 PART 4
3.0 COMPUTER MODEL
The finite element model of the structure is shown in Figure 3.1. The frame has 27+22+26m spanconfiguration. The linear static, dynamic and time-dependent analyses are carried out using the MIDAS software. Thestructure has been modeled by means of BEAM element with six degree of freedom per node. Elastic springsare included in the model to simulate the soil-structure interaction in both longitudinal and transverse direction.
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Fig. 3.2 : Sign convention of internal forces in the element's local coordinate system
Guideway 60 60 48 36000Piers 45 45 36 32500RC Portals 45 45 36 32500Pilecaps 35 35 28 29500Piles 35 35 28 29500
3.1 Section Properties
(A) Concrete The specified minimum 28-day compressive strengths of concrete used for the various structural members are as follows:
Structural Element
Concrete Grade Fcu (Mpa) Fc' (Mpa) Ec (Mpa)
B) Post-tensioning tendons: The following mechanical properties of prestressing tendon are adopted in the design.
Nominal diameter = 15.24 mm
Nominal tensile strength = 1860 MPa (GUTS)
Nominal strand area = 140 mm2
Specified characteristic breaking load = 260KN
Stress at anchorage (jacking) = 75% of GUTS
Class of relaxation = Normal
Modulus of elasticity, E = 195000 MPa
Friction coefficients, k = .17
Wobble coefficient, μ = .002 Draw-In at anchorage = 6 mm
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3.2 Construction Sequence
The following construction sequence has been assumed in the time-dependent construction stage analysis: 1. Stressing Span Tendon(Duration = 60 days) Time lapsed from concreting of first beam to launching of last beam. *Age of pre-cast beam at stressing = 3 days *Age of all pier elements at time of loading = 28 days
2. Casting Intermediate Stitching(Duration = 14 days) Time lapsed from concreting of to achieving sufficient strength before stressing continuity tendon. *Age of stitching concrete at stressing = 10 days
3. Stressing Middle Continuity Tendon(Duration =2 days) Time lapsed from threading strands to stressing last middle strand.
4. Stressing Top Continuity Tendon(Duration =1 day) Time lapsed from threading strands to stressing last top strand.
5. Casting End Stitching Concrete(Duration =7 days) Time lapsed from concreting to curing of concrete . *Age of stitching concrete at stressing = 3 days
6. 1 Month after Completion
Minimum time lapse required before SDL and LL can be applied.
7. 1 Year after Completion
8. 20 Years after Completion
To cater for total losses of pre-stressing force due to time-dependent effects.
The results of construction stage analysis are combined with the effect of loads on the completed structuredue to superimposed dead load, wind load, live load, seismic effectsand temperature effects.
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GUIDEWAY BEAMS
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Fig 4.1 End Section and Mid Box Section
Table 4.1 Summary of Post tensioned tendon details
T1 & T2T3 & T4
Table 4.2 Summary of reinforcement bars
GB 269,271
GB 270
GB 269,271
GB 270
4.0 Summary
This section documents the detailed design of the Prestressed Guideway Beams. Generally, the guidewaybeam consists of rectangular solid end blocks at both ends (2.2m height), and towards the mid span (2.2mheight) that is made of hollow box sections. There are three types of beams; Beam Type GB276 and GB278at ends and GB277 at intermediate span. Fig. 4.1 shows the dimensions and locations of post-tensionedtendons. Table 4.1 summarizes the details for post-tensioned tendons and Table 4.2 shows the summary ofmain bars and torsion/shear links. Further details are contained in the construction drawings.
Tendon Marking Type
No of strands per tendon
Jacking Force per tendon (KN)
Span Tendon 10 1953Continuity Tendon 12 2343
SectionBeam Type Top Bars Bottom Bars Side Bars
9T16 9T16 2T16 @ 200 c/c each face
2L-T16@100c/c outerrings+ 2L-T12@200c/cinner links
Torsion/ Shear Links
Mid Section
9T16 9T16 2T16 @ 200 c/c each face
2L-T16@100c/c outerrings+ 2L-T12@200c/cinner links
Solid Section
18T16 18T16 2T16 @ 200 c/c each face
4Legged T16 @100c/c 18T16 2T16 @ 200 c/c
each face
4Legged T16 @100c/c
4T25 + 4T25
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a) Transfer stage
b) Service stage
Allowable Stress
All Compressive Stress
Lesser of0.5 x 48 = 24 Mpa0.4 x 60 = 24 Mpa
Tensile stress 1.0 Mpa
The design calculations of the precast post-tensioned guideway beams comprise of thefollowing: (i) Pre-stressing design at SLS (ii) Check Bending Capacity of Beam at ULS (iii) Design for Shear force and Torsional Moment at ULS (iv) Design of Beam End Block.
The mechanical properties of prestressing tendon adopted in the design are as shown below. Nominal diameter = 15.24 mm (0.6”) Nominal tensile strength = 1860 MPa (GUTS) Nominal strand area = 140 mm2 Specified characteristic breaking load = 260 kN Stress at anchorage (jacking) = 75% of GUTS (1395 MPa) Class of relaxation = very low relaxation (relaxation at 1000h =2.50 % of GUTS) Modulus of elasticity, E = 195000 MPa Friction coefficients, k = 0.17 Wobble coefficient, μ = 0.002 rad/m Draw-In at anchorage = 6 mm
The stress limitations of prestressed concrete under serviceability loads are shown below.
Load Combination Type of stress
Load Combination Type of stress Allowable Stress
All Compressive Stress 0.4 x 60 = 24 MpaS1 Tensile stress 0.0 Mpa
S2a, S2b, S3a, S3b & S4 Tensile stress 0.36 x 60 = 2.79 Mpa
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4.1 SLS COMBINED AXIAL AND BENDING STRESSES CHECK
The prestressed guideway beams are designed to have a maximum tension of 1MPa at transfer, zero tensionat service (due to service load Combination 1) and 0.36(fcu)0.5 tension due to service load Combinations 2 to 4at top and bottom extreme fibres. The following tables summarize the maximum stresses of the beam (top andbottom fiber), followed by the envelope of combined stress diagrams along the beam. Maximum and minimumstresses and corresponding results along the beams are summarized. Negative indicates compressive stressand vice versa. All stresses are reported in N/mm2.
Case 1: Max Top Fiber Stress + corresponding resultsCase 2: Min Top Fiber Stress + corresponding resultsCase 3: Max Bottom Fiber Stress + corresponding resultsCase 4: Min Bottom Fiber Stress + corresponding results
Note:Bend (+z) = Bending stress due to moment about local y-axis in +z directionBend (-z) = Bending stress due to moment about local y-axis in -z direction
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AT TRANSFER STAGE
Envelope Stresses Diagrams for Track 1
Top Fiber
Span 1
Span 2
Span 3
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Bottom Fiber
Span 1
Span 2
Span 3
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Envelope Stresses Diagrams for Track 2Top Fiber
Span 1
Span2
Span 3
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Bottom FiberSpan 1
Span 2
Span 3
Conclusion
RemarkOKOKOKOK
Stresses Allowable (Mpa) Actual (Mpa)
Top FiberCompressive stress -24 -1.856
Tensile stress 1 1.03Bottom Fiber
Compressive stress -24 -4.892Tensile stress 1 0
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AT SERVICE STAGE
Stresses due to service load combinations 1 (zero tension design) for both track 1 & track 2
Envelope Stresses Diagrams for Track 1 as shown as follows:Top Fiber SPAN 1
SPAN2
SPAN 3
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Bottom Fiber
SPAN1
SPAN2
SPAN 3
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Envelope Stresses Diagrams for Track 2 as shown as follows:Top Fiber
SPAN 1
SPAN 2
SPAN 3
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Bottom Fiber SPAN 1
SPAN 2
SPAN 3
Conclusion
RemarkOKOKOKOK
Stresses Allowable (Mpa) Actual (Mpa)
Top FiberCompressive stress -24 -13.48
Tensile stress 0 0Compressive stress -24 -12.58
Tensile stress 0 0Bottom Fiber
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Stresses due to service load combinations 2 to 4 for both track 1 & track 2
Envelope Stresses Diagrams for Track 1 as shown as follows:Top FiberSPAN 1
SPAN2
SPAN 3
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Bottom Fiber
SPAN1
SPAN2
SPAN 3
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Envelope Stresses Diagrams for Track 2 as shown as follows:Top Fiber
SPAN 1
SPAN 2
SPAN 3
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Bottom Fiber SPAN 1
SPAN 2
SPAN 3
ConclusionRemarkOKOKOKOK
Stresses Allowable (Mpa) Actual (Mpa)
Top FiberCompressive stress -24 -13.92
Tensile stress-24 -13.77
Tensile stress 2.78 0
0.7982.78Bottom Fiber
Compressive stress
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4.2 ULTIMATE LIMIT STATE DESIGN OF HOLLOW SECTIONS
4.2.1 ULTIMATE LIMIT STATE DESIGN OF MID HOLLOW SECTION
SPAN 1
Table 4.2: Ultimate Load Combinations 1 - 5 (U1-U5) for span1
Elem Load Axial (kN)Moment-y
(kN·m)Moment-z
(kN·m)51 U4(max) 410.35 3363.71 215.0688 U3b(min) 447.42 2490.73 138.5795 U4(min) 211.43 4932.76 124.3584 U4(max) 230.7 7177.02 246.2485 U3b(min) 169.2 5914.15 493.8192 U3b(max) 97.31 6225.24 529.8
The ultimate limit state analysis is carried out by the AdSEC software for bending capacity check, whereas
combined shear and torsion design is done by using a spreadsheet. The figure below shows the arrangement
of bars in the box section at the mid span after the completion of the structure.
4.2.1.1 SUMMARY OF BEAM FORCES
The summary of the maximum element forces due to various ultimate load combinations is tabulated below. The 6 cases summarized below areCase 1 – Max & Min Axial Force + corresponding resultsCase 2 - Max & Min My + corresponding resultsCase 3 - Max & Min Mz + corresponding resultsNegative sign in axial force indicates compression and vice versa.
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Specification
General Specification
Code of Practice BS5400
Country India
Bending Axes Biaxial
Section 1 Details
Definition
Name Mid-section
Type Concrete
Material C60
Perimeter
Section Area 1.407E+6mm2
Reinforcement Area 23710.mm2
Reinforcement 1.685%
Section Nodes
Node Y Z
[mm] [mm]
1 375.0 1100.
2 400.0 1075.
3 400.0 -1075.
4 375.0 -1100.
5 -375.0 -1100.
6 -400.0 -1075.
7 -400.0 1075.
8 -375.0 1100.
9 110.0 850.0
10 110.0 -750.0
11 -110.0 -750.0
12 -110.0 850.0
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Bars
Bar Y Z Diameter Material Type Pre-stress Pre-stress Appl. loads
Force Strain include/exclude
pre-stress
[mm] [mm] [mm] [kN]
1 -326.0 -1026. 16.00 Fe 500 Steel
2 -217.3 -1026. 16.00 Fe 500 Steel
3 -108.7 -1026. 16.00 Fe 500 Steel
4 0.0 -1026. 16.00 Fe 500 Steel
5 108.7 -1026. 16.00 Fe 500 Steel
6 217.3 -1026. 16.00 Fe 500 Steel
7 326.0 -1026. 16.00 Fe 500 Steel
8 -326.0 1026. 16.00 Fe 500 Steel
9 -217.3 1026. 16.00 Fe 500 Steel
10 -108.7 1026. 16.00 Fe 500 Steel
11 0.0 1026. 16.00 Fe 500 Steel
12 108.7 1026. 16.00 Fe 500 Steel
13 217.3 1026. 16.00 Fe 500 Steel
14 326.0 1026. 16.00 Fe 500 Steel
15 -326.0 -1010. 16.00 Fe 500 Steel
16 326.0 -1010. 16.00 Fe 500 Steel
17 -326.0 -804.0 16.00 Fe 500 Steel
18 326.0 -804.0 16.00 Fe 500 Steel
19 -326.0 872.0 16.00 Fe 500 Steel
20 326.0 872.0 16.00 Fe 500 Steel
21 -326.0 1010. 16.00 Fe 500 Steel
22 326.0 1010. 16.00 Fe 500 Steel
23 -225.0 0.0 42.22 Strands Steel -1860. exclude
24 -225.0 -925.0 42.22 Strands Steel -1530. exclude
25 -324.0 -899.0 20.00 Fe 500 Steel
26 -324.0 -699.0 20.00 Fe 500 Steel
27 -324.0 -499.0 20.00 Fe 500 Steel
28 -324.0 -299.0 20.00 Fe 500 Steel
29 -324.0 -99.00 20.00 Fe 500 Steel
30 -324.0 101.0 20.00 Fe 500 Steel
31 -324.0 301.0 20.00 Fe 500 Steel
32 -324.0 501.0 20.00 Fe 500 Steel
33 -324.0 701.0 20.00 Fe 500 Steel
34 326.0 -899.0 20.00 Fe 500 Steel
35 326.0 -699.0 20.00 Fe 500 Steel
36 326.0 -499.0 20.00 Fe 500 Steel
37 326.0 -299.0 20.00 Fe 500 Steel
38 326.0 -99.00 20.00 Fe 500 Steel
39 326.0 101.0 20.00 Fe 500 Steel
40 326.0 301.0 20.00 Fe 500 Steel
41 326.0 501.0 20.00 Fe 500 Steel
42 326.0 701.0 20.00 Fe 500 Steel
43 -148.0 -691.0 16.00 Fe 500 Steel
44 -148.0 -491.0 16.00 Fe 500 Steel
45 -148.0 -291.0 16.00 Fe 500 Steel
46 -148.0 -91.00 16.00 Fe 500 Steel
47 -148.0 109.0 16.00 Fe 500 Steel
48 -148.0 309.0 16.00 Fe 500 Steel
49 -148.0 509.0 16.00 Fe 500 Steel
50 -148.0 709.0 16.00 Fe 500 Steel
51 326.0 -788.0 16.00 Fe 500 Steel
52 148.0 -788.0 16.00 Fe 500 Steel
53 -326.0 -788.0 16.00 Fe 500 Steel
54 -148.0 -788.0 16.00 Fe 500 Steel
55 0.0 -788.0 16.00 Fe 500 Steel
56 326.0 888.0 16.00 Fe 500 Steel
57 148.0 888.0 16.00 Fe 500 Steel
58 -326.0 888.0 16.00 Fe 500 Steel
59 -148.0 888.0 16.00 Fe 500 Steel
60 0.0 888.0 16.00 Fe 500 Steel
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61 148.0 -691.0 16.00 Fe 500 Steel
62 148.0 -491.0 16.00 Fe 500 Steel
63 148.0 -291.0 16.00 Fe 500 Steel
64 148.0 -91.00 16.00 Fe 500 Steel
65 148.0 109.0 16.00 Fe 500 Steel
66 148.0 309.0 16.00 Fe 500 Steel
67 148.0 509.0 16.00 Fe 500 Steel
68 148.0 709.0 16.00 Fe 500 Steel
69 225.0 0.0 42.22 Strands Steel -1860. exclude
70 225.0 -925.0 42.22 Strands Steel -1530. exclude
71 225.0 250.0 42.22 Strands Steel -1860. exclude
72 -225.0 250.0 42.22 Strands Steel -1860. exclude
Elastic Properties
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y 0.0mm
z -12.51mm
Area 1.407E+6mm2
Second Moments of Area Iyy 632.2E+9mm4
Izz 92.26E+9mm4
Iyz 33.06E-6mm4
Principal Second Moments of Area Iuu 632.2E+9mm4
Izz 92.26E+9mm4
Angle 0.0°
Shear Area Factor ky 0.0
kz 0.0
Torsion Constant 0.0mm4
Section Modulus Zy 568.2E+6mm3
Zz 230.6E+6mm3
Plastic Modulus Zpy 825.1E+6mm3
Zpz 332.2E+6mm3
Radius of Gyration Ry 670.4mm
Rz 256.1mm
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y 0.01648mm
z -6.685mm
EA 55.91E+6kN
EI EIyy 23.64E+6kNm2
EIzz 5.135E+6kNm2
EIyz -85.09kNm2
Principal EI EIuu 23.64E+6kNm2
EIzz 5.135E+6kNm2
Angle -263.5E-6°
Maximum compressive force Nu -17270.kN
Strain at Nmax 0.0[-]
Moment at ref. pt. for Nmax Myy 0.1622kNm
Mzz 407.4E-6kNm
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Note: Nmax is the maximum compressive force which can be carried by the section.
This is calculated by applying a constant strain across the entire section, using
ultimate material properties.
Section Material Properties
Type Concrete
Name C60
Weight Normal Weight
Density 2.300t/m3 Cube Strength fcu 60000.kPa
Tensile Strength fct 3718.kPa
Elastic Modulus (short E 37.00E+6kPa
term)
Poisson's Ratio 0.2000
Coeff. Thermal Expansion 12.00E-6/°C
Partial Safety Factor mc,ULS 1.500
mc,SLS 1.000
Maximum Strain 0.003500[-]
ULS Compression Curve Recto-parabolic
ULS Tension Curve No-tension
SLS Compression Curve Linear
SLS Tension Curve No-tension
Aggregate Size 20.00mm
Reinforcement Properties
Name Fe 500
fy 500000.kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Name Strands
fy 1.857E+6kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Loading
Reference Point
All loading acts through the Reference Point.
All strain planes are defined relative to the Reference Point.
Definition Geometric
Centroid
Reference Point Coordinates y 0.0mm
z -12.51mm
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Applied loads
Load Case N Myy Mzz
[kN] [kNm] [kNm]
Load Case 1 410.3 3364. 215.1
Load Case 2 447.4 2491. 138.6
Load Case 3 211.4 4933. 124.3
Load Case 4 230.7 7177. 246.2
Load Case 5 169.2 5914. 493.8
Load Case 6 97.31 6225. 529.8
Section 1 Details
1.69% reinforcement in section 1 (Mid-section). Check this against code requirements.
ULS Cases Analysed
Name Loading Pre-stress
Factor
Strength Analysis - Loads
Case N Myy Mzz M
[kN] [kNm] [kNm] [kNm] [°]
1 410.3 3364. 215.1 3371. -3.658
2 447.4 2491. 138.6 2495. -3.184
3 211.4 4933. 124.3 4934. -1.444
4 230.7 7177. 246.2 7181. -1.965
5 169.2 5914. 493.8 5935. -4.773
6 97.31 6225. 529.8 6248. -4.864
Strength Analysis - Summary
Governing conditions are defined as:
A - reinforcing steel tension strain limit
B - concrete compression strain limit
Effective centroid is reported relative to the reference point.
Case Eff. Eff. N M Mu M/Mu Governing Neutral Neutral
Centroid Centroid Condition Axis Axis
(y) (z) Angle Depth
[kN] [kNm] [kNm] [°] [mm]
Maxima 4 -0.8899 7282. 230.7 7181. 16250. 0.4419 B: Node 1
Minima 2 -0.4688 3749. 447.4 2495. 15960. 0.1563 B: Node 1
From above it is observed that the Max. M/Mu ratio = 0.442 which is less than unity. Hence section is safe.
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4.2.2 ULTIMATE LIMIT STATE DESIGN OF MID HOLLOW SECTIONSPAN 2The ultimate limit state analysis is carried out by the AdSEC software for bending capacity check, whereas
combined shear and torsion design is done by using a spreadsheet. The figure below shows the
arrangement of bars in the box section at the mid span after the completion of the structure.4.2.2.1 SUMMARY OF BEAM FORCESThe summary of the maximum element forces due to various ultimate load combinations is tabulated below. The 6 cases summarized below areC 1 M & Mi A i l F + di lt
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Table 4.3: Ultimate Load Combinations 1 - 5 (U1-U5) for span2
Elem Load Axial (kN)Moment-y
(kN·m)Moment-z
(kN·m)26 U4(min) 322.47 5222.48 726.0527 U4(max) 484 61 713 76 355 32
Case 1 – Max & Min Axial Force + corresponding resultsCase 2 - Max & Min My + corresponding resultsCase 3 - Max & Min Mz + corresponding resultsNegative sign in axial force indicates compression and vice versa.
27 U4(max) 484.61 713.76 355.3226 U4(min) 215.35 6264.1 693.3129 U4(max) 270.58 1948.86 29.7834 U3b(min) 270.65 3857.16 840.2834 U3b(max) 142.96 1550.93 997.87
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002‐D‐DR‐EPW‐LTSE‐311050 Rev. A1
Page 28 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Specification
General Specification
Code of Practice BS5400
Country India
Bending Axes Biaxial
Section 1 Details
Definition
Name Mid-section
Type Concrete
Material C60
Perimeter
Section Area 1.407E+6mm2
Reinforcement Area 23710.mm2
Reinforcement 1.685%
Section Nodes
Node Y Z
[mm] [mm]
1 375.0 1100.
2 400.0 1075.
3 400.0 -1075.
4 375.0 -1100.
5 -375.0 -1100.
6 -400.0 -1075.
7 -400.0 1075.
8 -375.0 1100.
9 110.0 850.0
10 110.0 -750.0
11 -110.0 -750.0
12 -110.0 850.0
Page 29 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Bars
Bar Y Z Diameter Material Type Pre-stress Pre-stress Appl. loads
Force Strain include/exclude
pre-stress
[mm] [mm] [mm] [kN]
1 -326.0 -1026. 16.00 Fe 500 Steel
2 -217.3 -1026. 16.00 Fe 500 Steel
3 -108.7 -1026. 16.00 Fe 500 Steel
4 0.0 -1026. 16.00 Fe 500 Steel
5 108.7 -1026. 16.00 Fe 500 Steel
6 217.3 -1026. 16.00 Fe 500 Steel
7 326.0 -1026. 16.00 Fe 500 Steel
8 -326.0 1026. 16.00 Fe 500 Steel
9 -217.3 1026. 16.00 Fe 500 Steel
10 -108.7 1026. 16.00 Fe 500 Steel
11 0.0 1026. 16.00 Fe 500 Steel
12 108.7 1026. 16.00 Fe 500 Steel
13 217.3 1026. 16.00 Fe 500 Steel
14 326.0 1026. 16.00 Fe 500 Steel
15 -326.0 -1010. 16.00 Fe 500 Steel
16 326.0 -1010. 16.00 Fe 500 Steel
17 -326.0 -804.0 16.00 Fe 500 Steel
18 326.0 -804.0 16.00 Fe 500 Steel
19 -326.0 872.0 16.00 Fe 500 Steel
20 326.0 872.0 16.00 Fe 500 Steel
21 -326.0 1010. 16.00 Fe 500 Steel
22 326.0 1010. 16.00 Fe 500 Steel
23 -225.0 -200.0 42.22 Strands Steel -1860. exclude
24 -225.0 -925.0 42.22 Strands Steel -1530. exclude
25 -324.0 -899.0 20.00 Fe 500 Steel
26 -324.0 -699.0 20.00 Fe 500 Steel
27 -324.0 -499.0 20.00 Fe 500 Steel
28 -324.0 -299.0 20.00 Fe 500 Steel
29 -324.0 -99.00 20.00 Fe 500 Steel
30 -324.0 101.0 20.00 Fe 500 Steel
31 -324.0 301.0 20.00 Fe 500 Steel
32 -324.0 501.0 20.00 Fe 500 Steel
33 -324.0 701.0 20.00 Fe 500 Steel
34 326.0 -899.0 20.00 Fe 500 Steel
35 326.0 -699.0 20.00 Fe 500 Steel
36 326.0 -499.0 20.00 Fe 500 Steel
37 326.0 -299.0 20.00 Fe 500 Steel
38 326.0 -99.00 20.00 Fe 500 Steel
39 326.0 101.0 20.00 Fe 500 Steel
40 326.0 301.0 20.00 Fe 500 Steel
41 326.0 501.0 20.00 Fe 500 Steel
42 326.0 701.0 20.00 Fe 500 Steel
43 -148.0 -691.0 16.00 Fe 500 Steel
44 -148.0 -491.0 16.00 Fe 500 Steel
45 -148.0 -291.0 16.00 Fe 500 Steel
46 -148.0 -91.00 16.00 Fe 500 Steel
47 -148.0 109.0 16.00 Fe 500 Steel
48 -148.0 309.0 16.00 Fe 500 Steel
49 -148.0 509.0 16.00 Fe 500 Steel
50 -148.0 709.0 16.00 Fe 500 Steel
51 326.0 -788.0 16.00 Fe 500 Steel
52 148.0 -788.0 16.00 Fe 500 Steel
53 -326.0 -788.0 16.00 Fe 500 Steel
54 -148.0 -788.0 16.00 Fe 500 Steel
55 0.0 -788.0 16.00 Fe 500 Steel
56 326.0 888.0 16.00 Fe 500 Steel
57 148.0 888.0 16.00 Fe 500 Steel
58 -326.0 888.0 16.00 Fe 500 Steel
59 -148.0 888.0 16.00 Fe 500 Steel
60 0.0 888.0 16.00 Fe 500 Steel
Page 30 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
61 148.0 -691.0 16.00 Fe 500 Steel
62 148.0 -491.0 16.00 Fe 500 Steel
63 148.0 -291.0 16.00 Fe 500 Steel
64 148.0 -91.00 16.00 Fe 500 Steel
65 148.0 109.0 16.00 Fe 500 Steel
66 148.0 309.0 16.00 Fe 500 Steel
67 148.0 509.0 16.00 Fe 500 Steel
68 148.0 709.0 16.00 Fe 500 Steel
69 225.0 -200.0 42.22 Strands Steel -1860. exclude
70 225.0 -925.0 42.22 Strands Steel -1530. exclude
71 225.0 250.0 42.22 Strands Steel -1860. exclude
72 -225.0 250.0 42.22 Strands Steel -1860. exclude
Elastic Properties
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y 0.0mm
z -12.51mm
Area 1.407E+6mm2
Second Moments of Area Iyy 632.2E+9mm4
Izz 92.26E+9mm4
Iyz 33.06E-6mm4
Principal Second Moments of Area Iuu 632.2E+9mm4
Izz 92.26E+9mm4
Angle 0.0°
Shear Area Factor ky 0.0
kz 0.0
Torsion Constant 0.0mm4
Section Modulus Zy 568.2E+6mm3
Zz 230.6E+6mm3
Plastic Modulus Zpy 825.1E+6mm3
Zpz 332.2E+6mm3
Radius of Gyration Ry 670.4mm
Rz 256.1mm
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y 0.01648mm
z -8.317mm
EA 55.91E+6kN
EI EIyy 23.64E+6kNm2
EIzz 5.152E+6kNm2
EIyz -83.55kNm2
Principal EI EIuu 23.64E+6kNm2
EIzz 5.152E+6kNm2
Angle -259.0E-6°
Maximum compressive force Nu -16360.kN
Strain at Nmax 0.0[-]
Moment at ref. pt. for Nmax Myy -0.03001kNm
Mzz -784.9E-6kNm
Page 31 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Note: Nmax is the maximum compressive force which can be carried by the section.
This is calculated by applying a constant strain across the entire section, using
ultimate material properties.
Section Material Properties
Type Concrete
Name C60
Weight Normal Weight
Density 2.300t/m3 Cube Strength fcu 60000.kPa
Tensile Strength fct 3718.kPa
Elastic Modulus (short E 37.00E+6kPa
term)
Poisson's Ratio 0.2000
Coeff. Thermal Expansion 12.00E-6/°C
Partial Safety Factor mc,ULS 1.500
mc,SLS 1.000
Maximum Strain 0.003500[-]
ULS Compression Curve Recto-parabolic
ULS Tension Curve No-tension
SLS Compression Curve Linear
SLS Tension Curve No-tension
Aggregate Size 20.00mm
Reinforcement Properties
Name Fe 500
fy 500000.kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Name Strands
fy 1.857E+6kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Loading
Reference Point
All loading acts through the Reference Point.
All strain planes are defined relative to the Reference Point.
Definition Geometric
Centroid
Reference Point Coordinates y 0.0mm
z -12.51mm
Page 32 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Applied loads
Load Case N Myy Mzz
[kN] [kNm] [kNm]
Load Case 1 322.5 5222. 726.0
Load Case 2 484.6 713.8 355.3
Load Case 3 215.3 6264. 693.3
Load Case 4 270.6 1949. 29.78
Load Case 5 270.6 3857. 840.3
Load Case 6 143.0 1551. 997.9
Section 1 Details
1.69% reinforcement in section 1 (Mid-section). Check this against code requirements.
ULS Cases Analysed
Name Loading Pre-stress
Factor
Strength Analysis - Loads
Case N Myy Mzz M
[kN] [kNm] [kNm] [kNm] [°]
1 322.5 5222. 726.0 5273. -7.915
2 484.6 713.8 355.3 797.3 -26.46
3 215.3 6264. 693.3 6302. -6.316
4 270.6 1949. 29.78 1949. -0.8755
5 270.6 3857. 840.3 3948. -12.29
6 143.0 1551. 997.9 1844. -32.76
Strength Analysis - Summary
Governing conditions are defined as:
A - reinforcing steel tension strain limit
B - concrete compression strain limit
Effective centroid is reported relative to the reference point.
Case Eff. Eff. N M Mu M/Mu Governing Neutral Neutral
Centroid Centroid Condition Axis Axis
(y) (z) Angle Depth
[kN] [kNm] [kNm] [°] [mm]
Maxima 3 -0.9519 11230. 215.3 6302. 15670. 0.4023 B: Node 2
Minima 2 -0.4344 4982. 484.6 797.3 10120. 0.07880 B: Node 2 From above it is observed that the Max. M/Mu ratio = 0.402 which is less than unity. Hence section is safe.
Page 33 of 71
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______________________________________________________________________________
4.2.3 ULTIMATE LIMIT STATE DESIGN OF MID HOLLOW SECTIONSPAN 3The ultimate limit state analysis is carried out by the AdSEC software for bending capacity check, whereas
combined shear and torsion design is done by using a spreadsheet. The figure below shows the
arrangement of bars in the box section at the mid span after the completion of the structure.
4.2.3.1 SUMMARY OF BEAM FORCESThe summary of the maximum element forces due to various ultimate load combinations is tabulated below
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002‐D‐DR‐EPW‐LTSE‐311050 Rev. A1
Table 4.4: Ultimate Load Combinations 1 - 5 (U1-U5) for span3
El L d A i l (kN)Moment-y
(kN )Moment-z
(kN )
The summary of the maximum element forces due to various ultimate load combinations is tabulated below. The 6 cases summarized below areCase 1 – Max & Min Axial Force + corresponding resultsCase 2 - Max & Min My + corresponding resultsCase 3 - Max & Min Mz + corresponding resultsNegative sign in axial force indicates compression and vice versa.
Elem Load Axial (kN) (kN·m) (kN·m)42 U3b(min) 310.39 1029.97 106.2543 U4(max) 397.83 703.1 595.635 U4(min) 83.11 5693.12 600.6340 U4(max) 35.43 5697.52 188.735 U3b(min) 37.81 19.89 617.7743 U3b(max) 270.66 1156.38 832.45
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002‐D‐DR‐EPW‐LTSE‐311050 Rev. A1
Page 34 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Specification
General Specification
Code of Practice BS5400
Country India
Bending Axes Biaxial
Section 1 Details
Definition
Name Mid-section
Type Concrete
Material C60
Perimeter
Section Area 1.407E+6mm2
Reinforcement Area 23710.mm2
Reinforcement 1.685%
Section Nodes
Node Y Z
[mm] [mm]
1 375.0 1100.
2 400.0 1075.
3 400.0 -1075.
4 375.0 -1100.
5 -375.0 -1100.
6 -400.0 -1075.
7 -400.0 1075.
8 -375.0 1100.
9 110.0 850.0
10 110.0 -750.0
11 -110.0 -750.0
12 -110.0 850.0
Page 35 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Bars
Bar Y Z Diameter Material Type Pre-stress Pre-stress Appl. loads
Force Strain include/exclude
pre-stress
[mm] [mm] [mm] [kN]
1 -326.0 -1026. 16.00 Fe 500 Steel
2 -217.3 -1026. 16.00 Fe 500 Steel
3 -108.7 -1026. 16.00 Fe 500 Steel
4 0.0 -1026. 16.00 Fe 500 Steel
5 108.7 -1026. 16.00 Fe 500 Steel
6 217.3 -1026. 16.00 Fe 500 Steel
7 326.0 -1026. 16.00 Fe 500 Steel
8 -326.0 1026. 16.00 Fe 500 Steel
9 -217.3 1026. 16.00 Fe 500 Steel
10 -108.7 1026. 16.00 Fe 500 Steel
11 0.0 1026. 16.00 Fe 500 Steel
12 108.7 1026. 16.00 Fe 500 Steel
13 217.3 1026. 16.00 Fe 500 Steel
14 326.0 1026. 16.00 Fe 500 Steel
15 -326.0 -1010. 16.00 Fe 500 Steel
16 326.0 -1010. 16.00 Fe 500 Steel
17 -326.0 -804.0 16.00 Fe 500 Steel
18 326.0 -804.0 16.00 Fe 500 Steel
19 -326.0 872.0 16.00 Fe 500 Steel
20 326.0 872.0 16.00 Fe 500 Steel
21 -326.0 1010. 16.00 Fe 500 Steel
22 326.0 1010. 16.00 Fe 500 Steel
23 -225.0 -200.0 42.22 Strands Steel -1860. exclude
24 -225.0 -925.0 42.22 Strands Steel -1530. exclude
25 -324.0 -899.0 20.00 Fe 500 Steel
26 -324.0 -699.0 20.00 Fe 500 Steel
27 -324.0 -499.0 20.00 Fe 500 Steel
28 -324.0 -299.0 20.00 Fe 500 Steel
29 -324.0 -99.00 20.00 Fe 500 Steel
30 -324.0 101.0 20.00 Fe 500 Steel
31 -324.0 301.0 20.00 Fe 500 Steel
32 -324.0 501.0 20.00 Fe 500 Steel
33 -324.0 701.0 20.00 Fe 500 Steel
34 326.0 -899.0 20.00 Fe 500 Steel
35 326.0 -699.0 20.00 Fe 500 Steel
36 326.0 -499.0 20.00 Fe 500 Steel
37 326.0 -299.0 20.00 Fe 500 Steel
38 326.0 -99.00 20.00 Fe 500 Steel
39 326.0 101.0 20.00 Fe 500 Steel
40 326.0 301.0 20.00 Fe 500 Steel
41 326.0 501.0 20.00 Fe 500 Steel
42 326.0 701.0 20.00 Fe 500 Steel
43 -148.0 -691.0 16.00 Fe 500 Steel
44 -148.0 -491.0 16.00 Fe 500 Steel
45 -148.0 -291.0 16.00 Fe 500 Steel
46 -148.0 -91.00 16.00 Fe 500 Steel
47 -148.0 109.0 16.00 Fe 500 Steel
48 -148.0 309.0 16.00 Fe 500 Steel
49 -148.0 509.0 16.00 Fe 500 Steel
50 -148.0 709.0 16.00 Fe 500 Steel
51 326.0 -788.0 16.00 Fe 500 Steel
52 148.0 -788.0 16.00 Fe 500 Steel
53 -326.0 -788.0 16.00 Fe 500 Steel
54 -148.0 -788.0 16.00 Fe 500 Steel
55 0.0 -788.0 16.00 Fe 500 Steel
56 326.0 888.0 16.00 Fe 500 Steel
57 148.0 888.0 16.00 Fe 500 Steel
58 -326.0 888.0 16.00 Fe 500 Steel
59 -148.0 888.0 16.00 Fe 500 Steel
60 0.0 888.0 16.00 Fe 500 Steel
Page 36 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
61 148.0 -691.0 16.00 Fe 500 Steel
62 148.0 -491.0 16.00 Fe 500 Steel
63 148.0 -291.0 16.00 Fe 500 Steel
64 148.0 -91.00 16.00 Fe 500 Steel
65 148.0 109.0 16.00 Fe 500 Steel
66 148.0 309.0 16.00 Fe 500 Steel
67 148.0 509.0 16.00 Fe 500 Steel
68 148.0 709.0 16.00 Fe 500 Steel
69 225.0 -200.0 42.22 Strands Steel -1860. exclude
70 225.0 -925.0 42.22 Strands Steel -1530. exclude
71 225.0 250.0 42.22 Strands Steel -1860. exclude
72 -225.0 250.0 42.22 Strands Steel -1860. exclude
Elastic Properties
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y 0.0mm
z -12.51mm
Area 1.407E+6mm2
Second Moments of Area Iyy 632.2E+9mm4
Izz 92.26E+9mm4
Iyz 33.06E-6mm4
Principal Second Moments of Area Iuu 632.2E+9mm4
Izz 92.26E+9mm4
Angle 0.0°
Shear Area Factor ky 0.0
kz 0.0
Torsion Constant 0.0mm4
Section Modulus Zy 568.2E+6mm3
Zz 230.6E+6mm3
Plastic Modulus Zpy 825.1E+6mm3
Zpz 332.2E+6mm3
Radius of Gyration Ry 670.4mm
Rz 256.1mm
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y 0.01648mm
z -8.317mm
EA 55.91E+6kN
EI EIyy 23.64E+6kNm2
EIzz 5.152E+6kNm2
EIyz -83.55kNm2
Principal EI EIuu 23.64E+6kNm2
EIzz 5.152E+6kNm2
Angle -259.0E-6°
Maximum compressive force Nu -16360.kN
Strain at Nmax 0.0[-]
Moment at ref. pt. for Nmax Myy 0.03479kNm
Mzz 59.75E-6kNm
Page 37 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Note: Nmax is the maximum compressive force which can be carried by the section.
This is calculated by applying a constant strain across the entire section, using
ultimate material properties.
Section Material Properties
Type Concrete
Name C60
Weight Normal Weight
Density 2.300t/m3 Cube Strength fcu 60000.kPa
Tensile Strength fct 3718.kPa
Elastic Modulus (short E 37.00E+6kPa
term)
Poisson's Ratio 0.2000
Coeff. Thermal Expansion 12.00E-6/°C
Partial Safety Factor mc,ULS 1.500
mc,SLS 1.000
Maximum Strain 0.003500[-]
ULS Compression Curve Recto-parabolic
ULS Tension Curve No-tension
SLS Compression Curve Linear
SLS Tension Curve No-tension
Aggregate Size 20.00mm
Reinforcement Properties
Name Fe 500
fy 500000.kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Name Strands
fy 1.857E+6kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Loading
Reference Point
All loading acts through the Reference Point.
All strain planes are defined relative to the Reference Point.
Definition Geometric
Centroid
Reference Point Coordinates y 0.0mm
z -12.51mm
Page 38 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Applied loads
Load Case N Myy Mzz
[kN] [kNm] [kNm]
Load Case 1 310.4 1030. 106.2
Load Case 2 397.8 703.1 595.6
Load Case 3 83.11 5693. 600.6
Load Case 4 35.43 5698. 188.7
Load Case 5 37.81 19.89 617.8
Load Case 6 270.7 1156. 832.4
Section 1 Details
1.69% reinforcement in section 1 (Mid-section). Check this against code requirements.
ULS Cases Analysed
Name Loading Pre-stress
Factor
Strength Analysis - Loads
Case N Myy Mzz M
[kN] [kNm] [kNm] [kNm] [°]
1 310.4 1030. 106.2 1035. -5.890
2 397.8 703.1 595.6 921.5 -40.27
3 83.11 5693. 600.6 5725. -6.022
4 35.43 5698. 188.7 5701. -1.897
5 37.81 19.89 617.8 618.1 -88.16
6 270.7 1156. 832.4 1425. -35.75
Strength Analysis - Summary
Governing conditions are defined as:
A - reinforcing steel tension strain limit
B - concrete compression strain limit
Effective centroid is reported relative to the reference point.
Case Eff. Eff. N M Mu M/Mu Governing Neutral Neutral
Centroid Centroid Condition Axis Axis
(y) (z) Angle Depth
[kN] [kNm] [kNm] [°] [mm]
Maxima 3 -2.437 29150. 83.11 5725. 15760. 0.3632 B: Node 2
Minima 1 -0.6666 7786. 310.4 1035. 15840. 0.06537 B: Node 2 From above it is observed that the Max. M/Mu ratio = 0.3632 which is less than unity. Hence section is safe.
Page 39 of 71
MUMBAI MONORAIL
______________________________________________________________________________
4.3 ULTIMATE LIMIT STATE DESIGN OF SOLID SECTIONS
4.3.1 ULTIMATE LIMIT STATE DESIGN OF SOLID SECTIONAt Pier 1The ultimate limit state analysis is carried out by the AdSEC software for bending capacity check, whereas
combined shear and torsion design is done by using a spreadsheet. The figure below shows the
arrangement of bars in the box section at the mid span after the completion of the structure.
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002‐D‐DR‐EPW‐LTSE‐311050 Rev. A1
4.3.1.1 SUMMARY OF BEAM FORCESThe summary of the maximum element forces due to various ultimate load combinations is tabulated below. The 6 cases summarized below areCase 1 – Max & Min Axial Force + corresponding resultsCase 2 - Max & Min My + corresponding resultsCase 3 - Max & Min Mz + corresponding resultsNegative sign in axial force indicates compression and vice versa.
Table 4.5: Ultimate Load Combinations 1 - 5 (U1-U5)
Elem Load Axial (kN)Moment-y
(kN·m)Moment-z
(kN·m)57 U3b(min) 466.14 -5816.81 371.8454 U4(max) 428.47 2251.52 399.0561 U4(min) 220.69 -8517.12 316.661 U4(min) 220.69 8517.12 316.654 U4(max) 298.11 4147.75 72.2157 U3b(min) 319.4 -5779.38 582.5461 U3b(max) 312.71 -6508.94 610.9
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002‐D‐DR‐EPW‐LTSE‐311050 Rev. A1
Page 40 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Specification
General Specification
Code of Practice BS5400
Country United Kingdom
Bending Axes Biaxial
Section 1 Details
Definition
Name 1C4end
Type Concrete
Material C60
Perimeter
Section Area 1.759E+6mm2
Reinforcement Area 23980.mm2
Reinforcement 1.364%
Section Nodes
Node Y Z
[mm] [mm]
1 375.0 1100.
2 400.0 1075.
3 400.0 -1075.
4 375.0 -1100.
5 -375.0 -1100.
6 -400.0 -1075.
7 -400.0 1075.
8 -375.0 1100.
Page 41 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Bars
Bar Y Z Diameter Material Type Pre-stress Pre-stress Appl. loads
Force Strain include/exclude
pre-stress
[mm] [mm] [mm] [kN]
1 -326.0 -1026. 25.00 Fe 500 Steel
2 -108.7 -1026. 25.00 Fe 500 Steel
3 108.7 -1026. 25.00 Fe 500 Steel
4 326.0 -1026. 25.00 Fe 500 Steel
5 -326.0 1026. 16.00 Fe 500 Steel
6 -244.5 1026. 16.00 Fe 500 Steel
7 -163.0 1026. 16.00 Fe 500 Steel
8 -81.50 1026. 16.00 Fe 500 Steel
9 0.0 1026. 16.00 Fe 500 Steel
10 81.50 1026. 16.00 Fe 500 Steel
11 163.0 1026. 16.00 Fe 500 Steel
12 244.5 1026. 16.00 Fe 500 Steel
13 326.0 1026. 16.00 Fe 500 Steel
14 -326.0 1010. 16.00 Fe 500 Steel
15 -244.5 1010. 16.00 Fe 500 Steel
16 -163.0 1010. 16.00 Fe 500 Steel
17 -81.50 1010. 16.00 Fe 500 Steel
18 0.0 1010. 16.00 Fe 500 Steel
19 81.50 1010. 16.00 Fe 500 Steel
20 163.0 1010. 16.00 Fe 500 Steel
21 244.5 1010. 16.00 Fe 500 Steel
22 326.0 1010. 16.00 Fe 500 Steel
23 -326.0 -907.0 16.00 Fe 500 Steel
24 -326.0 -891.0 16.00 Fe 500 Steel
25 -326.0 -707.2 16.00 Fe 500 Steel
26 -326.0 -691.2 16.00 Fe 500 Steel
27 -326.0 -507.4 16.00 Fe 500 Steel
28 -326.0 -491.4 16.00 Fe 500 Steel
29 -326.0 -307.7 16.00 Fe 500 Steel
30 -326.0 -291.7 16.00 Fe 500 Steel
31 -326.0 -107.9 16.00 Fe 500 Steel
32 -326.0 -91.89 16.00 Fe 500 Steel
33 -326.0 91.89 16.00 Fe 500 Steel
34 -326.0 107.9 16.00 Fe 500 Steel
35 -326.0 291.7 16.00 Fe 500 Steel
36 -326.0 307.7 16.00 Fe 500 Steel
37 -326.0 491.4 16.00 Fe 500 Steel
38 -326.0 507.4 16.00 Fe 500 Steel
39 -326.0 691.2 16.00 Fe 500 Steel
40 -326.0 707.2 16.00 Fe 500 Steel
41 -326.0 891.0 16.00 Fe 500 Steel
42 -326.0 907.0 16.00 Fe 500 Steel
43 326.0 -907.0 16.00 Fe 500 Steel
44 326.0 -891.0 16.00 Fe 500 Steel
45 326.0 -707.2 16.00 Fe 500 Steel
46 326.0 -691.2 16.00 Fe 500 Steel
47 326.0 -507.4 16.00 Fe 500 Steel
48 326.0 -491.4 16.00 Fe 500 Steel
49 326.0 -307.7 16.00 Fe 500 Steel
50 326.0 -291.7 16.00 Fe 500 Steel
51 326.0 -107.9 16.00 Fe 500 Steel
52 326.0 -91.89 16.00 Fe 500 Steel
53 326.0 91.89 16.00 Fe 500 Steel
54 326.0 107.9 16.00 Fe 500 Steel
55 326.0 291.7 16.00 Fe 500 Steel
56 326.0 307.7 16.00 Fe 500 Steel
57 326.0 491.4 16.00 Fe 500 Steel
58 326.0 507.4 16.00 Fe 500 Steel
59 326.0 691.2 16.00 Fe 500 Steel
60 326.0 707.2 16.00 Fe 500 Steel
Page 42 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
61 326.0 891.0 16.00 Fe 500 Steel
62 326.0 907.0 16.00 Fe 500 Steel
63 -165.0 -500.0 42.22 Strands Steel -1530. exclude
64 165.0 -500.0 42.22 Strands Steel -1530. exclude
65 -225.0 125.0 42.20 Strands Steel -1860. exclude
66 225.0 125.0 42.20 Strands Steel -1860. exclude
67 -225.0 650.0 42.20 Strands Steel -1860. exclude
68 225.0 650.0 42.20 Strands Steel -1860. exclude
69 -326.0 -969.0 25.00 Fe 500 Steel
70 -108.7 -969.0 25.00 Fe 500 Steel
71 108.7 -969.0 25.00 Fe 500 Steel
72 326.0 -969.0 25.00 Fe 500 Steel
Elastic Properties
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y 0.0mm
z 0.0mm
Area 1.759E+6mm2
Second Moments of Area Iyy 708.4E+9mm4
Izz 93.67E+9mm4
Iyz 37.64E-6mm4
Principal Second Moments of Area Iuu 708.4E+9mm4
Izz 93.67E+9mm4
Angle 0.0°
Shear Area Factor ky 0.0
kz 0.0
Torsion Constant 0.0mm4
Section Modulus Zy 644.0E+6mm3
Zz 234.2E+6mm3
Plastic Modulus Zpy 966.6E+6mm3
Zpz 351.5E+6mm3
Radius of Gyration Ry 634.6mm
Rz 230.8mm
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y -189.2E-9mm
z 1.264mm
EA 68.98E+6kN
EI EIyy 26.47E+6kNm2
EIzz 5.460E+6kNm2
EIyz 136.8E-6kNm2
Principal EI EIuu 26.47E+6kNm2
EIzz 5.460E+6kNm2
Angle 373.0E-12°
Maximum compressive force Nu 44510.kN
Strain at Nmax 0.0[-]
Moment at ref. pt. for Nmax Myy -0.04209kNm
Mzz -0.04327kNm
Page 43 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Note: Nmax is the maximum compressive force which can be carried by the section.
This is calculated by applying a constant strain across the entire section, using
ultimate material properties.
Section Material Properties
Type Concrete
Name C60
Weight Normal Weight
Density 2.300t/m3 Cube Strength fcu 60000.kPa
Tensile Strength fct 3718.kPa
Elastic Modulus (short E 37.00E+6kPa
term)
Poisson's Ratio 0.2000
Coeff. Thermal Expansion 12.00E-6/°C
Partial Safety Factor mc,ULS 1.500
mc,SLS 1.000
Maximum Strain 0.003500[-]
ULS Compression Curve Recto-parabolic
ULS Tension Curve No-tension
SLS Compression Curve Linear
SLS Tension Curve No-tension
Aggregate Size 20.00mm
Reinforcement Properties
Name Fe 500
fy 500000.kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Name Strands
fy 1.857E+6kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Loading
Reference Point
All loading acts through the Reference Point.
All strain planes are defined relative to the Reference Point.
Definition Geometric
Centroid
Reference Point Coordinates y 0.0mm
z 0.0mm
Page 44 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Applied loads
Load Case N Myy Mzz
[kN] [kNm] [kNm]
Load Case 1 466.1 -5817. 371.8
Load Case 2 428.5 2252. 399.0
Load Case 3 220.7 -8517. 316.6
Load Case 4 298.1 4148. 72.21
Load Case 5 319.4 -5779. 582.5
Load Case 6 312.7 -6509. 610.9
Section 1 Details
1.36% reinforcement in section 1 (1C4end). Check this against code requirements.
ULS Cases Analysed
Name Loading Pre-stress
Factor
Strength Analysis - Loads
Case N Myy Mzz M
[kN] [kNm] [kNm] [kNm] [°]
1 466.1 -5817. 371.8 5829. -176.3
2 428.5 2252. 399.0 2287. -10.05
3 220.7 -8517. 316.6 8523. -177.9
4 298.1 4148. 72.21 4148. -0.9974
5 319.4 -5779. 582.5 5809. -174.2
6 312.7 -6509. 610.9 6538. -174.6
Strength Analysis - Summary
Governing conditions are defined as:
A - reinforcing steel tension strain limit
B - concrete compression strain limit
Effective centroid is reported relative to the reference point.
Case Eff. Eff. N M Mu M/Mu Governing Neutral Neutral
Centroid Centroid Condition Axis Axis
(y) (z) Angle Depth
[kN] [kNm] [kNm] [°] [mm]
Maxima 3 1.129E-6 -6250. 220.7 8523. 16470. 0.5176 B: Node 4
Minima 2 593.7E-9 -3220. 428.5 2287. 12230. 0.1870 B: Node 2
From above it is observed that the Max. M/Mu ratio = 0.5176 which is less than unity. Hence section is safe.
Page 45 of 71
MUMBAI MONORAIL
______________________________________________________________________________
At Pier 2The ultimate limit state analysis is carried out by the AdSEC software for bending capacity check, whereas
combined shear and torsion design is done by using a spreadsheet. The figure below shows the
arrangement of bars in the box section at the mid span after the completion of the structure.
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002‐D‐DR‐EPW‐LTSE‐311050 Rev. A1
4.3.2.1 SUMMARY OF BEAM FORCESThe summary of the maximum element forces due to various ultimate load combinations is tabulated below. The 6 cases summarized below areCase 1 – Max & Min Axial Force + corresponding resultsCase 2 - Max & Min My + corresponding resultsCase 3 - Max & Min Mz + corresponding resultsNegative sign in axial force indicates compression and vice versa.
Table 4.6: Ultimate Load Combinations 1 - 5 (U1-U5)
Elem Load Axial (kN)Moment-y
(kN·m)Moment-z
(kN·m)65 U4(min) 335.08 -7561.83 1071.4464 U4(max) 504.41 -1568.26 470.8465 U4(min) 228.05 -9045.02 1000.3560 U4(max) 329.31 146.61 123.9965 U3b(max) 7 83 2485 19 1197 9765 U3b(max) 7.83 -2485.19 1197.9768 U3b(max) 105.36 -2523.84 1350.99
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002‐D‐DR‐EPW‐LTSE‐311050 Rev. A1
Page 46 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Specification
General Specification
Code of Practice BS5400
Country United Kingdom
Bending Axes Biaxial
Section 1 Details
Definition
Name 1C4end
Type Concrete
Material C60
Perimeter
Section Area 1.759E+6mm2
Reinforcement Area 23680.mm2
Reinforcement 1.346%
Section Nodes
Node Y Z
[mm] [mm]
1 375.0 1100.
2 400.0 1075.
3 400.0 -1075.
4 375.0 -1100.
5 -375.0 -1100.
6 -400.0 -1075.
7 -400.0 1075.
8 -375.0 1100.
Page 47 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Bars
Bar Y Z Diameter Material Type Pre-stress Pre-stress Appl. loads
Force Strain include/exclude
pre-stress
[mm] [mm] [mm] [kN]
1 -326.0 -1026. 16.00 Fe 500 Steel
2 -244.5 -1026. 16.00 Fe 500 Steel
3 -163.0 -1026. 16.00 Fe 500 Steel
4 -81.50 -1026. 16.00 Fe 500 Steel
5 0.0 -1026. 16.00 Fe 500 Steel
6 81.50 -1026. 16.00 Fe 500 Steel
7 163.0 -1026. 16.00 Fe 500 Steel
8 244.5 -1026. 16.00 Fe 500 Steel
9 326.0 -1026. 16.00 Fe 500 Steel
10 -326.0 1026. 16.00 Fe 500 Steel
11 -244.5 1026. 16.00 Fe 500 Steel
12 -163.0 1026. 16.00 Fe 500 Steel
13 -81.50 1026. 16.00 Fe 500 Steel
14 0.0 1026. 16.00 Fe 500 Steel
15 81.50 1026. 16.00 Fe 500 Steel
16 163.0 1026. 16.00 Fe 500 Steel
17 244.5 1026. 16.00 Fe 500 Steel
18 326.0 1026. 16.00 Fe 500 Steel
19 -326.0 1010. 16.00 Fe 500 Steel
20 -244.5 1010. 16.00 Fe 500 Steel
21 -163.0 1010. 16.00 Fe 500 Steel
22 -81.50 1010. 16.00 Fe 500 Steel
23 0.0 1010. 16.00 Fe 500 Steel
24 81.50 1010. 16.00 Fe 500 Steel
25 163.0 1010. 16.00 Fe 500 Steel
26 244.5 1010. 16.00 Fe 500 Steel
27 326.0 1010. 16.00 Fe 500 Steel
28 -326.0 -907.0 16.00 Fe 500 Steel
29 -326.0 -891.0 16.00 Fe 500 Steel
30 -326.0 -707.2 16.00 Fe 500 Steel
31 -326.0 -691.2 16.00 Fe 500 Steel
32 -326.0 -507.4 16.00 Fe 500 Steel
33 -326.0 -491.4 16.00 Fe 500 Steel
34 -326.0 -307.7 16.00 Fe 500 Steel
35 -326.0 -291.7 16.00 Fe 500 Steel
36 -326.0 -107.9 16.00 Fe 500 Steel
37 -326.0 -91.89 16.00 Fe 500 Steel
38 -326.0 91.89 16.00 Fe 500 Steel
39 -326.0 107.9 16.00 Fe 500 Steel
40 -326.0 291.7 16.00 Fe 500 Steel
41 -326.0 307.7 16.00 Fe 500 Steel
42 -326.0 491.4 16.00 Fe 500 Steel
43 -326.0 507.4 16.00 Fe 500 Steel
44 -326.0 691.2 16.00 Fe 500 Steel
45 -326.0 707.2 16.00 Fe 500 Steel
46 -326.0 891.0 16.00 Fe 500 Steel
47 -326.0 907.0 16.00 Fe 500 Steel
48 326.0 -907.0 16.00 Fe 500 Steel
49 326.0 -891.0 16.00 Fe 500 Steel
50 326.0 -707.2 16.00 Fe 500 Steel
51 326.0 -691.2 16.00 Fe 500 Steel
52 326.0 -507.4 16.00 Fe 500 Steel
53 326.0 -491.4 16.00 Fe 500 Steel
54 326.0 -307.7 16.00 Fe 500 Steel
55 326.0 -291.7 16.00 Fe 500 Steel
56 326.0 -107.9 16.00 Fe 500 Steel
57 326.0 -91.89 16.00 Fe 500 Steel
58 326.0 91.89 16.00 Fe 500 Steel
59 326.0 107.9 16.00 Fe 500 Steel
60 326.0 291.7 16.00 Fe 500 Steel
Page 48 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
61 326.0 307.7 16.00 Fe 500 Steel
62 326.0 491.4 16.00 Fe 500 Steel
63 326.0 507.4 16.00 Fe 500 Steel
64 326.0 691.2 16.00 Fe 500 Steel
65 326.0 707.2 16.00 Fe 500 Steel
66 326.0 891.0 16.00 Fe 500 Steel
67 326.0 907.0 16.00 Fe 500 Steel
68 -165.0 -500.0 42.22 Strands Steel -1530. exclude
69 165.0 -500.0 42.22 Strands Steel -1530. exclude
70 -225.0 250.0 42.20 Strands Steel -1860. exclude
71 225.0 250.0 42.20 Strands Steel -1860. exclude
72 -225.0 650.0 42.20 Strands Steel -1860. exclude
73 225.0 650.0 42.20 Strands Steel -1860. exclude
74 -326.0 -969.0 16.00 Fe 500 Steel
75 -244.5 -969.0 16.00 Fe 500 Steel
76 -163.0 -969.0 16.00 Fe 500 Steel
77 -81.50 -969.0 16.00 Fe 500 Steel
78 0.0 -969.0 16.00 Fe 500 Steel
79 81.50 -969.0 16.00 Fe 500 Steel
80 163.0 -969.0 16.00 Fe 500 Steel
81 244.5 -969.0 16.00 Fe 500 Steel
82 326.0 -969.0 16.00 Fe 500 Steel
Elastic Properties
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y 0.0mm
z 0.0mm
Area 1.759E+6mm2
Second Moments of Area Iyy 708.4E+9mm4
Izz 93.67E+9mm4
Iyz 37.64E-6mm4
Principal Second Moments of Area Iuu 708.4E+9mm4
Izz 93.67E+9mm4
Angle 0.0°
Shear Area Factor ky 0.0
kz 0.0
Torsion Constant 0.0mm4
Section Modulus Zy 644.0E+6mm3
Zz 234.2E+6mm3
Plastic Modulus Zpy 966.6E+6mm3
Zpz 351.5E+6mm3
Radius of Gyration Ry 634.6mm
Rz 230.8mm
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y -175.9E-9mm
z 2.818mm
EA 68.93E+6kN
EI EIyy 26.46E+6kNm2
EIzz 5.431E+6kNm2
EIyz -0.001529kNm2
Page 49 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Principal EI EIuu 26.46E+6kNm2
EIzz 5.431E+6kNm2
Angle -4.167E-9°
Maximum compressive force Nu 44210.kN
Strain at Nmax 0.0[-]
Moment at ref. pt. for Nmax Myy 0.08260kNm
Mzz 0.09794kNm
Note: Nmax is the maximum compressive force which can be carried by the section.
This is calculated by applying a constant strain across the entire section, using
ultimate material properties.
Section Material Properties
Type Concrete
Name C60
Weight Normal Weight
Density 2.300t/m3 Cube Strength fcu 60000.kPa
Tensile Strength fct 3718.kPa
Elastic Modulus (short E 37.00E+6kPa
term)
Poisson's Ratio 0.2000
Coeff. Thermal Expansion 12.00E-6/°C
Partial Safety Factor mc,ULS 1.500
mc,SLS 1.000
Maximum Strain 0.003500[-]
ULS Compression Curve Recto-parabolic
ULS Tension Curve No-tension
SLS Compression Curve Linear
SLS Tension Curve No-tension
Aggregate Size 20.00mm
Reinforcement Properties
Name Fe 500
fy 500000.kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Name Strands
fy 1.857E+6kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Page 50 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Loading
Applied loads
Load Case N Myy Mzz
[kN] [kNm] [kNm]
Load Case 1 335.1 -7562. 1071.
Load Case 2 504.4 -1568. 470.8
Load Case 3 228.0 -9045. 1000.
Load Case 4 329.3 146.6 124.0
Load Case 5 7.830 -2485. 1198.
Load Case 6 105.4 -2524. 1351.
Section 1 Details
1.35% reinforcement in section 1 (1C4end). Check this against code requirements.
ULS Cases Analysed
Name Loading Pre-stress
Factor
Strength Analysis - Loads
Case N Myy Mzz M
[kN] [kNm] [kNm] [kNm] [°]
1 335.1 -7562. 1071. 7637. -171.9
2 504.4 -1568. 470.8 1637. -163.3
3 228.0 -9045. 1000. 9100. -173.7
4 329.3 146.6 124.0 192.0 -40.22
5 7.830 -2485. 1198. 2759. -154.3
6 105.4 -2524. 1351. 2863. -151.8
Strength Analysis - Summary
Governing conditions are defined as:
A - reinforcing steel tension strain limit
B - concrete compression strain limit
Effective centroid is reported relative to the reference point.
Case Eff. Eff. N M Mu M/Mu Governing Neutral Neutral
Centroid Centroid Condition Axis Axis
(y) (z) Angle Depth
[kN] [kNm] [kNm] [°] [mm]
Maxima 3 -1.519E-6 -8034. 228.0 9100. 15740. 0.5780 B: Node 3
Minima 4 -1.062E-6 -5564. 329.3 192.0 6917. 0.02776 B: Node 2 From above it is observed that the Max. M/Mu ratio = 0.578 which is less than unity. Hence section is safe.
Page 51 of 71
MUMBAI MONORAIL
______________________________________________________________________________
At Pier 3The ultimate limit state analysis is carried out by the AdSEC software for bending capacity check, whereas
combined shear and torsion design is done by using a spreadsheet. The figure below shows the
arrangement of bars in the box section at the mid span after the completion of the structure.
4.3.2.1 SUMMARY OF BEAM FORCESThe summary of the maximum element forces due to various ultimate load combinations is tabulated below. The 6 cases summarized below are
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002‐D‐DR‐EPW‐LTSE‐311050 Rev. A1
Table 4.6: Ultimate Load Combinations 1 - 5 (U1-U5)
Elem Load Axial (kN)Moment-y
(kN·m)Moment-z
(kN·m)71 U3b( i ) 330 6 1023 3 229 79
Case 1 – Max & Min Axial Force + corresponding resultsCase 2 - Max & Min My + corresponding resultsCase 3 - Max & Min Mz + corresponding resultsNegative sign in axial force indicates compression and vice versa.
71 U3b(min) 330.6 -1023.3 229.7970 U4(max) 419.91 -2239.07 713.167 U4(min) 104.75 -9219.54 831.871 U4(max) 35.26 2871.36 174.2967 U3b(min) 50.46 -1420.91 941.6667 U3b(max) 60.32 -8310.88 1202.5
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002‐D‐DR‐EPW‐LTSE‐311050 Rev. A1
Page 52 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Specification
General Specification
Code of Practice BS5400
Country United Kingdom
Bending Axes Biaxial
Section 1 Details
Definition
Name 1C4end
Type Concrete
Material C60
Perimeter
Section Area 1.759E+6mm2
Reinforcement Area 23680.mm2
Reinforcement 1.346%
Section Nodes
Node Y Z
[mm] [mm]
1 375.0 1100.
2 400.0 1075.
3 400.0 -1075.
4 375.0 -1100.
5 -375.0 -1100.
6 -400.0 -1075.
7 -400.0 1075.
8 -375.0 1100.
Bars
Page 53 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Bar Y Z Diameter Material Type Pre-stress Pre-stress Appl. loads
Force Strain include/exclude
pre-stress
[mm] [mm] [mm] [kN]
1 -326.0 -1026. 16.00 Fe 500 Steel
2 -244.5 -1026. 16.00 Fe 500 Steel
3 -163.0 -1026. 16.00 Fe 500 Steel
4 -81.50 -1026. 16.00 Fe 500 Steel
5 0.0 -1026. 16.00 Fe 500 Steel
6 81.50 -1026. 16.00 Fe 500 Steel
7 163.0 -1026. 16.00 Fe 500 Steel
8 244.5 -1026. 16.00 Fe 500 Steel
9 326.0 -1026. 16.00 Fe 500 Steel
10 -326.0 1026. 16.00 Fe 500 Steel
11 -244.5 1026. 16.00 Fe 500 Steel
12 -163.0 1026. 16.00 Fe 500 Steel
13 -81.50 1026. 16.00 Fe 500 Steel
14 0.0 1026. 16.00 Fe 500 Steel
15 81.50 1026. 16.00 Fe 500 Steel
16 163.0 1026. 16.00 Fe 500 Steel
17 244.5 1026. 16.00 Fe 500 Steel
18 326.0 1026. 16.00 Fe 500 Steel
19 -326.0 1010. 16.00 Fe 500 Steel
20 -244.5 1010. 16.00 Fe 500 Steel
21 -163.0 1010. 16.00 Fe 500 Steel
22 -81.50 1010. 16.00 Fe 500 Steel
23 0.0 1010. 16.00 Fe 500 Steel
24 81.50 1010. 16.00 Fe 500 Steel
25 163.0 1010. 16.00 Fe 500 Steel
26 244.5 1010. 16.00 Fe 500 Steel
27 326.0 1010. 16.00 Fe 500 Steel
28 -326.0 -907.0 16.00 Fe 500 Steel
29 -326.0 -891.0 16.00 Fe 500 Steel
30 -326.0 -707.2 16.00 Fe 500 Steel
31 -326.0 -691.2 16.00 Fe 500 Steel
32 -326.0 -507.4 16.00 Fe 500 Steel
33 -326.0 -491.4 16.00 Fe 500 Steel
34 -326.0 -307.7 16.00 Fe 500 Steel
35 -326.0 -291.7 16.00 Fe 500 Steel
36 -326.0 -107.9 16.00 Fe 500 Steel
37 -326.0 -91.89 16.00 Fe 500 Steel
38 -326.0 91.89 16.00 Fe 500 Steel
39 -326.0 107.9 16.00 Fe 500 Steel
40 -326.0 291.7 16.00 Fe 500 Steel
41 -326.0 307.7 16.00 Fe 500 Steel
42 -326.0 491.4 16.00 Fe 500 Steel
43 -326.0 507.4 16.00 Fe 500 Steel
44 -326.0 691.2 16.00 Fe 500 Steel
45 -326.0 707.2 16.00 Fe 500 Steel
46 -326.0 891.0 16.00 Fe 500 Steel
47 -326.0 907.0 16.00 Fe 500 Steel
48 326.0 -907.0 16.00 Fe 500 Steel
49 326.0 -891.0 16.00 Fe 500 Steel
50 326.0 -707.2 16.00 Fe 500 Steel
51 326.0 -691.2 16.00 Fe 500 Steel
52 326.0 -507.4 16.00 Fe 500 Steel
53 326.0 -491.4 16.00 Fe 500 Steel
54 326.0 -307.7 16.00 Fe 500 Steel
55 326.0 -291.7 16.00 Fe 500 Steel
56 326.0 -107.9 16.00 Fe 500 Steel
57 326.0 -91.89 16.00 Fe 500 Steel
58 326.0 91.89 16.00 Fe 500 Steel
59 326.0 107.9 16.00 Fe 500 Steel
60 326.0 291.7 16.00 Fe 500 Steel
61 326.0 307.7 16.00 Fe 500 Steel
62 326.0 491.4 16.00 Fe 500 Steel
Page 54 of 71
MUMBAI MONORAIL PROJECT
Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
63 326.0 507.4 16.00 Fe 500 Steel
64 326.0 691.2 16.00 Fe 500 Steel
65 326.0 707.2 16.00 Fe 500 Steel
66 326.0 891.0 16.00 Fe 500 Steel
67 326.0 907.0 16.00 Fe 500 Steel
68 -165.0 -500.0 42.22 Strands Steel -1530. exclude
69 165.0 -500.0 42.22 Strands Steel -1530. exclude
70 -225.0 550.0 42.20 Strands Steel -1860. exclude
71 225.0 550.0 42.20 Strands Steel -1860. exclude
72 -225.0 850.0 42.20 Strands Steel -1860. exclude
73 225.0 850.0 42.20 Strands Steel -1860. exclude
74 -326.0 -969.0 16.00 Fe 500 Steel
75 -244.5 -969.0 16.00 Fe 500 Steel
76 -163.0 -969.0 16.00 Fe 500 Steel
77 -81.50 -969.0 16.00 Fe 500 Steel
78 0.0 -969.0 16.00 Fe 500 Steel
79 81.50 -969.0 16.00 Fe 500 Steel
80 163.0 -969.0 16.00 Fe 500 Steel
81 244.5 -969.0 16.00 Fe 500 Steel
82 326.0 -969.0 16.00 Fe 500 Steel
Elastic Properties
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y 0.0mm
z 0.0mm
Area 1.759E+6mm2
Second Moments of Area Iyy 708.4E+9mm4
Izz 93.67E+9mm4
Iyz 37.64E-6mm4
Principal Second Moments of Area Iuu 708.4E+9mm4
Izz 93.67E+9mm4
Angle 0.0°
Shear Area Factor ky 0.0
kz 0.0
Torsion Constant 0.0mm4
Section Modulus Zy 644.0E+6mm3
Zz 234.2E+6mm3
Plastic Modulus Zpy 966.6E+6mm3
Zpz 351.5E+6mm3
Radius of Gyration Ry 634.6mm
Rz 230.8mm
Properties of the untransformed section, ignoring reinforcement.
Geometric Centroid y -175.9E-9mm
z 6.125mm
EA 68.93E+6kN
EI EIyy 26.46E+6kNm2
EIzz 5.675E+6kNm2
EIyz -0.003643kNm2
Principal EI EIuu 26.46E+6kNm2
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EIzz 5.675E+6kNm2
Angle -10.04E-9°
Maximum compressive force Nu 43310.kN
Strain at Nmax 0.0[-]
Moment at ref. pt. for Nmax Myy 0.02029kNm
Mzz -0.01669kNm
Note: Nmax is the maximum compressive force which can be carried by the section.
This is calculated by applying a constant strain across the entire section, using
ultimate material properties.
Section Material Properties
Type Concrete
Name C60
Weight Normal Weight
Density 2.300t/m3 Cube Strength fcu 60000.kPa
Tensile Strength fct 3718.kPa
Elastic Modulus (short E 37.00E+6kPa
term)
Poisson's Ratio 0.2000
Coeff. Thermal Expansion 12.00E-6/°C
Partial Safety Factor mc,ULS 1.500
mc,SLS 1.000
Maximum Strain 0.003500[-]
ULS Compression Curve Recto-parabolic
ULS Tension Curve No-tension
SLS Compression Curve Linear
SLS Tension Curve No-tension
Aggregate Size 20.00mm
Reinforcement Properties
Name Fe 500
fy 500000.kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
Name Strands
fy 1.857E+6kPa
Modulus 200.0E+6kPa
Partial Safety Factor ms,ULS 1.150
ms,SLS 1.000
Maximum Strain 0.05000[-]
Stress/Strain Curve Fig 2
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Definitive Design Review – Design Calculations of Frame 17
MM001-D-DR-VSP-LTSE-311050 Rev A1
10-April-2013
Loading
Applied loads
Load Case N Myy Mzz
[kN] [kNm] [kNm]
Load Case 1 330.6 -1023. 229.8
Load Case 2 419.9 -2239. 713.1
Load Case 3 104.7 -9220. 831.8
Load Case 4 35.26 2871. 174.3
Load Case 5 50.46 -1421. 941.7
Load Case 6 60.32 -8311. 1202.
Section 1 Details
1.35% reinforcement in section 1 (1C4end). Check this against code requirements.
ULS Cases Analysed
Name Loading Pre-stress
Factor
Strength Analysis - Loads
Case N Myy Mzz M
[kN] [kNm] [kNm] [kNm] [°]
1 330.6 -1023. 229.8 1049. -167.3
2 419.9 -2239. 713.1 2350. -162.3
3 104.7 -9220. 831.8 9257. -174.8
4 35.26 2871. 174.3 2877. -3.474
5 50.46 -1421. 941.7 1705. -146.5
6 60.32 -8311. 1202. 8397. -171.8
Strength Analysis - Summary
Governing conditions are defined as:
A - reinforcing steel tension strain limit
B - concrete compression strain limit
Effective centroid is reported relative to the reference point.
Case Eff. Eff. N M Mu M/Mu Governing Neutral Neutral
Centroid Centroid Condition Axis Axis
(y) (z) Angle Depth
[kN] [kNm] [kNm] [°] [mm]
Maxima 3 -3.266E-6 -35120. 104.7 9257. 18200. 0.5085 B: Node 3
Minima 1 -1.058E-6 -11130. 330.6 1049. 15080. 0.06953 B: Node 3 From above it is observed that the Max. M/Mu ratio = 0.5085 which is less than unity. Hence section is safe.
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4.4 Check for Shear at Hollow section (As per IRC concrete bridge code)
Location Elem Load Part Component Axial (kN)Shear-y (kN)
Shear-z (kN)
Torsion (kN·m)
Moment-y (kN·m)
Moment-z (kN·m)
1st span 88 U4(max) J[23] Shear-z 129.78 -63.55 1638.82 234.42 -4270.29 47.9695 U3b(max) J[24] Torsion -234.66 -115.42 1013.07 419.09 -2966.69 255.9483 U4(max) J[72] Moment-y 230.73 16.45 -110.72 113.33 7177.02 -246.22
2nd span 26 U4(max) J[27] Shear-z -208.75 -128.5 1181.73 576.27 -4871.91 722.9534 U3b(min) J[28] Torsion -268.4 142.45 1067.51 -854.75 -3838.51 -839.9326 U4(min) J[27] Moment-y -215.35 -125.62 1165.87 441.82 -6264.1 693.31
3rd span 35 U4(min) I[29] Shear-z 83.01 104.35 -1547.42 -789.06 -5603.39 593.6843 U3b(min) I[30] Torsion 142.71 143.12 -1302.33 -1102.55 -2280.86 828.2240 U4(max) I[55] Moment-y 35.43 20.87 -208.44 -116.89 5697.52 -188.7
The Guideway beam hollow section is checked for shear capacity at a location of max. shear & corresponding moment &torsion and then at a location of max. torsion & corresponding shear & moment. The locations are based on sorted resultsobtained from MIDAS analysis, as tabulated below:
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Element No.(refer above table & MIDAS model) 88 83
Node end J[23] J[72]fck = MPa 60 60fy = MPa 415 415Duct diameter= m 0.085 0.085B m 0.8 0.8D m 2.2 2.2Depth of hollow box inside beam m 1.6 1.6Width of hollow box inside beam m 0.22 0.22Eff. Depth of beam d (m) 2.20 2.20Eff. Width of beam b(m) 0.4667 0.4667dist of T1, T2 from top(m) 1.7 1.7dist of T3, T4(m) 0.9 0.9dist of T5,T6(m) 0.5 0.5Area of T1,T2(mm2) 1400 1400Area of T3,T4(mm2) 1680 1680Area of T5,T6(mm2) 1680 1260Factored PS T1,T2(KN) 1538 1538Factored PS T3,T4(KN) 1935 1935Factored PS T5,T6(KN) 1910 1910Area of beam in section A (m2) 0.280 0.280Dist. of c.g of beam from comp. fibre y (m) 1.1 1.1Moment of inertia of beam I(m4) 0.63 0.63Ecc. of tendon T1,T2 e1(T1,T2) (m) -0.5710 -0.5710 (-ve indicates below c.g of beam)Ecc. of tendon T3,T4 e2(T3,T4) (m) 0.2064 0.2064 (+ve indicates above c.g of beam)Ecc. of tendon T5,T6 e3(T5,T6) (m) 0.5728 0.5728 (+ve indicates above c.g of beam)Prestress on beam P/A (Mpa) 38.5 38.5
Pe1*y/I (Mpa) -3.0 -3.0Pe2*y/II (Mpa) 1.4 1.4Pe3*y/II (Mpa) 3.8 3.8fp-comp (Mpa) 40.6 40.6
fp-tension(Mpa) 36.3 36.3CG of Tendons (m) 1.2 1.2
Cracking Moment of beam Mcr(KN-m) 22611.6 22611.6ft(Mpa) 1.9 1.9
Vco(KN) 5954.55 5954.55From above tables, M at Max V (kNm) 4270.00 5852.00
Max V (kN) 1639.00 563.00Shear at Max Mn(kN) 1471.00 111.00
Max M (kNm) 4545.00 7177.00Governing Shear (Max V) 1639.00 563.00
Shear stress (Mpa) 1.6 0.5Vcr 1 (KN) 8840.7 2330.8Vcr 2 (KN) 7479.7 505.1
Min Vcr (IRC 16.4.4.3) (KN) 795.3 795.3V limiting (KN) 5954.5 795.3
Dia of stirrups 16 16Number of stirrups 2 2Dia of links 12 12Number of links 2 2Area of links provided Asv 628.3 628.3Dia of Longi bars 16 16Cover (mm) 50 50Eff.depth of beam dt 2126 2126Spacing of stirrups reqd. Sv req(mm) 450 450
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4.4.1 Check for Max. Torsion at Hollow section
Element 43
Max Torsion (KN-m) 1102.60 kNmCorresponding shear (kN) 1302.30 kNB (mm) 800 mmD (mm) 2200 mmThickness of web (mm) 290 mmThickness of top flange (mm) 250 mmThickness of bottom flange (mm) 250 mmAo (mm2) 994500 mm2
Torsional stress v (Mpa) 1.9 N/mm2
V min (Mpa) 0.42 N/mm2
Ast required Reqd.
V+Vt (Mpa) 2.7 N/mm2
Max allowable stress (Mpa) 5.80 N/mm2
Status OK
dia of stirrups (mm) 16.0 mmspacing of stirrups (mm) 100.0 mmNumber of outer legs 2 no.Ast (mm2) 201.06 mm2
T/(2*Ao*.87*fyv) 1.54Ast/Sv 2.01Status OK
Dia of longi bars 16.0 mmNumber of bars in bundle 2 no.AsL 402.12 mm2
(Ast/Sv)*(fyv/fyL) 1.27Minimum spacing req.(mm) 315.5 mmSpacing provided(mm) 200.0 mmStatus OK
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4.5 Check for Shear at Solid section (As per IRC concrete bridge code)
Location Elem Load Part Component Axial (kN)Shear-y (kN)
Shear-z (kN)
Torsion (kN·m)
Moment-y (kN·m)
Moment-z (kN·m)
1st span 61 U4(max) J[18] Shear-z -214.78 -88.93 1840.59 157.81 -8437.13 331.9957 U3b(max) J[17] Torsion 17.89 -133.1 1347.27 417.45 -5386.02 462.9461 U4(min) J[18] Moment-y -220.69 -87.89 1722.21 132.84 -8517.12 316.6
2nd span 65 U4(max) J[13] Shear-z -222.21 -150.63 1503.23 382.71 -7640.89 1032.6368 U3b(min) J[14] Axial -295.85 155.33 1184.66 -1012.87 -6270.28 -1163.0665 U4(min) J[13] Moment-y -228.05 -148.11 1436.11 197.64 -9045.0 1000.35
3rd span 67 U4(min) I[15] Shear-z 108.44 112.55 -1797.62 -571.81 -9011.4 805.4570 U4(min) I[16] Torsion 94.9 123.37 -1362.57 -1071.78 -4073.85 943.4767 U4(min) I[15] Moment-y 104.75 114.88 -1683.88 -584.86 -9219.54 831.8
The Guideway beam hollow section is checked for shear capacity at a location of max. shear & corresponding moment & torsion andthen at a location of max. torsion & corresponding shear & moment. The locations are based on sorted results obtained from MIDASanalysis, as tabulated below:
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Element No.(refer above table & MIDAS model) 61 67
Node end J[18] I[15]fck = MPa 60 60fy = MPa 415 415Duct diameter= m 0.085 0.085B m 0.8 0.8D m 2.2 2.2Depth of hollow box inside beam m 0 0Width of hollow box inside beam m 0 0Eff. Depth of beam d (m) 2.20 2.20Eff. Width of beam b(m) 0.6867 0.6867dist of T1, T2 from top(m) 1.6 1.6dist of T3, T4(m) 0.8 0.6dist of T5,T6(m) 0.4 0.3Area of T1,T2(mm2) 1400 1400Area of T3,T4(mm2) 1680 1680Area of T5,T6(mm2) 1680 1260Factored PS T1,T2(KN) 1519 1491Factored PS T3,T4(KN) 1920 1832Factored PS T5,T6(KN) 1884 1848Area of beam in section A (m2) 1.511 1.511Dist. of c.g of beam from comp. fibre y (m) 1.1 1.1Moment of inertia of beam I(m4) 0.71 0.71Ecc. of tendon T1,T2 e1(T1,T2) (m) -0.5000 -0.5000 (-ve indicates below c.g of beam)Ecc. of tendon T3,T4 e2(T3,T4) (m) 0.2506 0.5472 (+ve indicates above c.g of beam)Ecc. of tendon T5,T6 e3(T5,T6) (m) 0.6511 0.8478 (+ve indicates above c.g of beam)Prestress on beam P/A (Mpa) 7.0 6.8
Pe1*y/I (Mpa) -2.4 -2.3Pe2*y/II (Mpa) 1.5 3.1Pe3*y/II (Mpa) 3.8 4.9fp-comp (Mpa) 10.0 12.5
fp-tension(Mpa) 4.1 1.2CG of Tendons (m) 1.3 1.4
Cracking Moment of beam Mcr(KN-m) 4500.69 2620.06ft(Mpa) 1.9 1.9
Vco(KN) 4118.46 4071.66From above tables, M at Max V (kNm) 8437.00 9011.00
Max V (kN) 1841.00 1798.00Shear at Max Mn(kN) 1722.00 1684.00
Max M (kNm) 8517.00 9220.00Governing Shear (Max V) 1841.00 1798.00
Shear stress (Mpa) 1.2 1.2Vcr 1 (KN) 1232.2 797.7Vcr 2 (KN) 1160.1 753.4
Min Vcr (IRC 16.4.4.3) (KN) 1170.2 1170.2V limiting (KN) 1170.2 1170.2
Dia of stirrups 16 16Number of stirrups 2 2Dia of links 16 16Number of links 2 2Area of links provided Asv 804.2 804.2Dia of Longi bars 16 16Cover (mm) 50 50Eff.depth of beam dt 2126 2126Spacing of stirrups reqd. Sv req(mm) 450 450
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4.5.1 Check for Max. Torsion at Hollow section
Element 70
Max Torsion (KN-m) 1072.000 kNmCorresponding shear (kN) 1363.000 kNB (mm) 800 mmD (mm) 2200 mmThickness of web (mm) 290 mmThickness of top flange (mm) 250 mmThickness of bottom flange (mm) 250 mmAo (mm2) 994500.0 mm2
Torsional stress v (Mpa) 1.9 N/mm2
V min (Mpa) 0.42 N/mm2
Ast required Reqd.
V+Vt (Mpa) 2.6 N/mm2
Max allowable stress (Mpa) 5.80 N/mm2
Status OK
dia of stirrups (mm) 16.0 mmspacing of stirrups (mm) 100.0 mmNumber of outer legs 2 no.Ast (mm2) 201.06 mm2
T/(2*Ao*.87*fyv) 1.49Ast/Sv 2.0Status OK
Dia of longi bars 16.0 mmNumber of bars in bundle 2 no.AsL 402.12 mm2
(Ast/Sv)*(fyv/fyL) 1.24Minimum spacing req.(mm) 324.6 mmSpacing provided(mm) 200.0 mmStatus OK
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4.6 END BLOCK DESIGN
4.6.1 GEOMETRY AND PRESTRESS LOADS
The cross-sectional geometry at the expansion joint end of the PC Guideway beam is as
shown in the following figure. The six tendons are stressed to the following forces and the
anchorages are 265mm square
Anchorage Data
X(mm) Y(mm) X Dim (mm)Y Dim
(mm)
Nos of
strands
Jacking
Force per
Strand
Jacking
Force of
Anchor
1 -165 550 275 275 10 195 1950
2 -165 550 275 275 10 195 1950
3 -165 975 275 275 12 195 2340
4 -165 975 275 275 12 195 2340
5 -165 1600 275 275 12 195 2340
6 -165 1600 275 275 12 195 2340
4.6.2 PRIMARY REINFORCEMENT
Provide reinforcement around each anchorage to resist the bursting forces. The magnitude of
these forces depends on the size of the anchorage and dimensions of the theoretical prism
surrounding the anchorage as tabulated below
Vertically Laterally Vertically Laterally Vertically Laterally Vertically Laterally
1 425 330 0.65 0.83 0.126 0.11 1227 1073
2 425 330 0.65 0.83 0.126 0.11 1227 1073
3 675 330 0.41 0.83 0.198 0.11 2314 1287
4 675 330 0.41 0.83 0.198 0.11 2314 1287
5 675 330 0.41 0.83 0.198 0.11 2314 1287
6 675 330 0.41 0.83 0.198 0.11 2314 1287
Maximum reinforcement = 2314 mm2
Provide 12 dia helical upto 330 mm from face
nos of rounds = 8
Anchor
Location Anchor Size Jacking Force(KN)
CablePrism Dimensions Ypo / Yo Fbst / Pk Area of Steel required
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4.6.3 SECONDARY OR EQUILIBRIUM REINFORCEMENT
As well as providing primary reinforcement in the immediate vicinity of the anchorages, it is
necessary to consider the overall equilibrium of the anchor block and to determine any outof-
balance forces and moments that may be set up by the anchorages acting individually or
together. Check for the following stressing sequence.
Case
1 1
2 1 2
3 1 2 3
4 1 2 3 4
5 1 2 3 4 5
6 1 2 3 4 5 6
Transverse Out-Of-balance Moments In Vertical Plane
Transverse out-of-balance moments in vertical plane are as tabulated below
Due to
distribution
Due to
anchorages
Net Vertical
Moment
(KNm)
Due to
distributio
n
Due to
anchorages
Net
Vertical
Moment
(KNm)
0 0 0.00 0.00 0.00 0.00 0.00
110 13.14 0.00 13.14 26.28 0.00 26.28
220 51.48 0.00 51.48 102.96 0.00 102.96
330 113.42 0.00 113.42 226.85 0.00 226.85
440 197.36 -2.68 194.68 394.71 -5.36 389.35
550 301.67 -67.03 234.64 603.35 -134.06 469.29
660 424.77 -217.18 207.59 849.54 -434.36 415.17
770 565.03 -429.00 136.03 1130.06 -858.00 272.06
880 720.86 -643.50 77.36 1441.71 -1287.00 154.71
990 890.64 -858.00 32.64 1781.28 -1716.00 65.28
1100 1072.77 -1072.50 0.27 2145.54 -2145.00 0.54
1210 1265.64 -1287.00 -21.36 2531.28 -2574.00 -42.72
1320 1467.64 -1501.50 -33.86 2935.29 -3003.00 -67.71
1430 1677.17 -1716.00 -38.83 3354.35 -3432.00 -77.65
1540 1892.63 -1930.50 -37.87 3785.25 -3861.00 -75.75
1650 2112.39 -2145.00 -32.61 4224.78 -4290.00 -65.22
1760 2334.86 -2359.50 -24.64 4669.72 -4719.00 -49.28
1870 2558.43 -2574.00 -15.57 5116.85 -5148.00 -31.15
1980 2781.48 -2788.50 -7.02 5562.97 -5577.00 -14.03
2090 3002.43 -3003.00 -0.57 6004.85 -6006.00 -1.15
2200 3219.65 -3217.50 2.15 6439.29 -6435.00 4.29
MAX 234.64 MAX 469.29
MIN -38.83 MIN -77.65
Dimension
from
Bottom
Case-1 Case-2
Stressed cables/ Tendons
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Due to
distribution
Due to
anchorages
Net Vertical
Moment
(KNm)
Due to
distributio
n
Due to
anchorages
Net
Vertical
Moment
(KNm)
0 0.00 0.00 0.00 0.00 0.00 0.00
110 21.69 0.00 21.69 43.39 0.00 43.39
220 85.41 0.00 85.41 170.83 0.00 170.83
330 189.11 0.00 189.11 378.22 0.00 378.22
440 330.74 -2.68 328.06 661.48 -5.36 656.12
550 508.26 -67.03 441.23 1016.52 -134.06 882.46
660 719.62 -217.18 502.44 1439.25 -434.36 1004.88
770 962.78 -429.00 533.78 1925.57 -858.00 1067.57
880 1235.69 -651.18 584.51 2471.39 -1302.37 1169.02
990 1536.31 -956.94 579.37 3072.63 -1913.89 1158.74
1100 1862.59 -1365.66 496.93 3725.18 -2731.33 993.85
1210 2212.49 -1836.90 375.59 4424.97 -3673.80 751.17
1320 2583.95 -2308.80 275.15 5167.90 -4617.60 550.30
1430 2974.94 -2780.70 194.24 5949.88 -5561.40 388.48
1540 3383.41 -3252.60 130.81 6766.81 -6505.20 261.61
1650 3807.31 -3724.50 82.81 7614.62 -7449.00 165.62
1760 4244.60 -4196.40 48.20 8489.20 -8392.80 96.40
1870 4693.23 -4668.30 24.93 9386.46 -9336.60 49.86
1980 5151.16 -5140.20 10.96 10302.32 -10280.40 21.92
2090 5616.34 -5612.10 4.24 11232.68 -11224.20 8.48
2200 6086.73 -6084.00 2.73 12173.46 -12168.00 5.46
MAX 584.51 MAX 1169.02
MIN 0.00 MIN 0.00
Dimension
from
Bottom
Case-4 Case-5
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Due to
distribution
Due to
anchorages
Net Vertical
Moment
(KNm)
Due to
distributio
n
Due to
anchorages
Net
Vertical
Moment
(KNm)
0 0.00 0.00 0.00 0.00 0.00 0.00
110 19.65 0.00 19.65 39.29 0.00 39.29
220 78.39 0.00 78.39 156.78 0.00 156.78
330 175.94 0.00 175.94 351.88 0.00 351.88
440 312.00 -2.68 309.32 624.01 -5.36 618.64
550 486.29 -67.03 419.26 972.57 -134.06 838.51
660 698.50 -217.18 481.32 1397.00 -434.36 962.64
770 948.35 -429.00 519.35 1896.70 -858.00 1038.70
880 1235.54 -651.18 584.36 2471.09 -1302.37 1168.72
990 1559.79 -956.94 602.85 3119.58 -1913.89 1205.69
1100 1920.80 -1365.66 555.13 3841.60 -2731.33 1110.27
1210 2318.27 -1836.90 481.37 4636.55 -3673.80 962.75
1320 2751.92 -2308.80 443.12 5503.85 -4617.60 886.25
1430 3221.46 -2780.70 440.76 6442.92 -5561.40 881.52
1540 3726.58 -3278.15 448.43 7453.17 -6556.31 896.86
1650 4267.01 -3874.07 392.93 8534.02 -7748.15 785.87
1760 4842.44 -4570.80 271.64 9684.88 -9141.60 543.28
1870 5452.59 -5300.10 152.49 10905.17 -10600.20 304.97
1980 6097.15 -6029.40 67.75 12194.31 -12058.80 135.51
2090 6775.85 -6758.70 17.15 13551.71 -13517.40 34.31
2200 7488.39 -7488.00 0.39 14976.78 -14976.00 0.78
MAX 602.85 MAX 1205.69
MIN 0.00 MIN 0.00
Dimension
from
Bottom
Case-5 Case-6
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Maximum moment = 1205.69 KNm
lever arm = 1.1 m
Fy = 240 Mpa
Area of steel required = 4567.02285 mm2
Provide
2 nos 2 T 16 @ 100 mm c/c for 1.1 m from
face
Area provided = 8846.72 mm2 OK
-200.00
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1400.00
0 500 1000 1500 2000 2500
Net Transverese Moment in Vertical Plane
Case1
Case2
Case3
Case4
Series5
Case5
Case6
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002-D-DR-EPW-LTSE-311050 Rev. A1 Page 68 of 71
MUMBAI MONORAIL
_____________________________________________________________________________________
Transverse Out-Of-balance Moments In Horizontal Plane
Transverse out-of-balance moments in vertical plane are as tabulated below
Due to
distribution
Due to
anchorages
Net Vertical
Moment
(KNm)
Due to
distributio
n
Due to
anchorages
Net
Vertical
Moment
(KNm)
0 0 0.00 0.00 0.00 0.00 0.00
110 11.19 0.00 11.19 22.38 0.00 22.38
220 43.88 0.00 43.88 87.75 0.00 87.75
330 96.75 0.00 96.75 193.50 0.00 193.50
440 168.49 0.00 168.49 336.99 0.00 336.99
550 257.79 -22.54 235.26 515.59 -45.08 470.51
660 363.33 -122.71 240.63 726.66 -245.41 481.25
770 483.80 -298.35 185.45 967.59 -596.70 370.89
880 617.87 -491.40 126.47 1235.74 -982.80 252.94
990 764.24 -684.45 79.79 1528.49 -1368.90 159.59
1100 921.59 -877.50 44.09 1843.19 -1755.00 88.19
1210 1088.61 -1070.55 18.06 2177.22 -2141.10 36.12
1320 1263.98 -1263.60 0.38 2527.96 -2527.20 0.76
1430 1446.38 -1456.65 -10.27 2892.77 -2913.30 -20.53
1540 1634.51 -1649.70 -15.19 3269.01 -3299.40 -30.39
1650 1827.04 -1842.75 -15.71 3654.07 -3685.50 -31.43
1760 2022.66 -2035.80 -13.14 4045.32 -4071.60 -26.28
1870 2220.06 -2228.85 -8.79 4440.11 -4457.70 -17.59
1980 2417.91 -2421.90 -3.99 4835.83 -4843.80 -7.97
2090 2614.92 -2614.95 -0.03 5229.84 -5229.90 -0.06
2200 2809.76 -2808.00 1.76 5619.51 -5616.00 3.51
MAX 240.63 MAX 481.25
MIN -15.71 MIN -31.43
Dimension
from
Bottom
Case-1 Case-2
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002-D-DR-EPW-LTSE-311050 Rev. A1 Page 69 of 71
MUMBAI MONORAIL
_____________________________________________________________________________________
Due to
distribution
Due to
anchorages
Net Vertical
Moment
(KNm)
Due to
distributio
n
Due to
anchorages
Net
Vertical
Moment
(KNm)
0 0.00 0.00 0.00 0.00 0.00 0.00
110 15.50 0.00 15.50 31.01 0.00 31.01
220 61.43 0.00 61.43 122.85 0.00 122.85
330 136.89 0.00 136.89 273.79 0.00 273.79
440 241.03 0.00 241.03 482.06 0.00 482.06
550 372.96 -22.54 350.42 745.91 -45.08 700.84
660 531.80 -122.71 409.09 1063.59 -245.41 818.18
770 716.68 -298.35 418.33 1433.35 -596.70 836.65
880 926.71 -491.40 435.31 1853.43 -982.80 870.63
990 1161.04 -684.45 476.59 2322.08 -1368.90 953.18
1100 1418.77 -877.75 541.02 2837.54 -1755.50 1082.05
1210 1699.03 -1131.51 567.53 3398.07 -2263.01 1135.06
1320 2000.95 -1492.11 508.84 4001.91 -2984.22 1017.69
1430 2323.65 -1936.35 387.30 4647.30 -3872.70 774.60
1540 2666.25 -2386.80 279.45 5332.49 -4773.60 558.89
1650 3027.87 -2837.25 190.62 6055.74 -5674.50 381.24
1760 3407.64 -3287.70 119.94 6815.28 -6575.40 239.88
1870 3804.68 -3738.15 66.53 7609.36 -7476.30 133.06
1980 4218.12 -4188.60 29.52 8436.24 -8377.20 59.04
2090 4647.07 -4639.05 8.02 9294.15 -9278.10 16.05
2200 5090.67 -5089.50 1.17 10181.34 -10179.00 2.34
MAX 567.53 MAX 1135.06
MIN 0.00 MIN 0.00
Due to
distribution
Due to
anchorages
Net Vertical
Moment
(KNm)
Due to
distributio
n
Due to
anchorages
Net
Vertical
Moment
(KNm)
0 0.00 0.00 0.00 0.00 0.00 0.00
110 10.49 0.00 10.49 20.97 0.00 20.97
220 42.94 0.00 42.94 85.87 0.00 85.87
330 98.84 0.00 98.84 197.69 0.00 197.69
440 179.70 0.00 179.70 359.39 0.00 359.39
550 286.98 -22.54 264.45 573.97 -45.08 528.89
660 422.20 -122.71 299.49 844.40 -245.41 598.99
770 586.83 -298.35 288.48 1173.66 -596.70 576.96
880 782.37 -491.40 290.97 1564.74 -982.80 581.94
990 1010.30 -684.45 325.85 2020.61 -1368.90 651.71
1100 1272.13 -877.75 394.38 2544.25 -1755.50 788.76
1210 1569.33 -1131.51 437.82 3138.65 -2263.01 875.64
1320 1903.39 -1492.11 411.29 3806.79 -2984.22 822.57
1430 2275.82 -1936.35 339.47 4551.64 -3872.70 678.94
1540 2688.09 -2386.80 301.29 5376.19 -4773.60 602.59
1650 3141.71 -2837.50 304.21 6283.42 -5675.00 608.42
1760 3638.15 -3348.66 289.49 7276.30 -6697.31 578.99
1870 4178.91 -3966.66 212.25 8357.82 -7933.32 424.50
1980 4765.48 -4668.30 97.18 9530.96 -9336.60 194.36
2090 5399.35 -5376.15 23.20 10798.70 -10752.30 46.40
2200 6082.01 -6084.00 -1.99 12164.02 -12168.00 -3.98
MAX 437.82 MAX 875.64
MIN -1.99 MIN -3.98
Dimension
from
Bottom
Case-5 Case-6
Dimension
from
Bottom
Case-4 Case-5
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002-D-DR-EPW-LTSE-311050 Rev. A1 Page 70 of 71
MUMBAI MONORAIL
_____________________________________________________________________________________
Maximum moment = 1135.06 KNm
lever arm = 1.1 m
Fy = 200 Mpa
Area of steel required = 5159.35239 mm2
Provide
2 nos 2 T 16 @ 100 mm c/c for 1.1 m from face
Area provided = 8846.72491 mm2 OK
LTSEDefinitive Design Review
Design Calculation for Frame 17
MM002-D-DR-EPW-LTSE-311050 Rev. A1 Page 71 of 71