CALCULATIONS

EPCof Metro Rail Transit System on the Orange Line in Lahore FORMAT OF THE BID

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METRO RAIL ON THE ORANGE LINE IN PAKISTAN LAHORE PROJECT

20M STANDARD SPAN OF METRO RAILWAY CURVED BRIDGE

CALCULATIONS

Project manager: YIN, Delan

Project engineer: RAN,Wei

Engineers: LI LEI

JUL , 2014


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Structure General List: Bridge function Standard span of metro railway curved bridge

Governing

Features

Bridge length 20 m

Curve radius 250m

Track number Double

Track gauge 5000 mm

Derailment protection Inside Guide rails and outside protect wood

Vertical clearance at

roadway overpass

>5.0 m

Design

Load

Live load Double track (Type B metro train)

Design

speed

Vmax = 80 km/H

Secondary

dead load

28.9 KN/m

Temperature

load

0 25

Wind speed 44.77m/s(100mph)

Earthquake 70.16g (Pakistani Building Code)

Super-structure Simple support curved beam girders with two U-shaped

cross-section

Sub-structure Reinforced concrete columns supported by drilled shafts

Materials

Concrete

(Eurocode)

GIRDER: GRADE C55

PIER CAP: GRADE C40

PIER COLUMN: GRADE C40

ABUTMENT: GRADE C30

PILE: GRADE C30

Reinforcing Steel:

(Eurocode)

CLASS A, CHARECTERISTIC STRENGH = 400 MPa

Structural Steel :

(Eurocode)

Y1860S7(15.2mm) =1860 MPa

Govening

Structural

Features

Super-structure Maximum deflection by live load: 6.5mm

Bending moment of main girder:6942 kN-m

Bearing Capacity of Bending moment : 17522kN-m

The maximum compressive stress value :8.3MPa

The minimum compressive stress value :2.0MPa

The maximum Principal compressive stress value :

16.9MPa

The maximum Principal tensile stress value : 2.2MPa

Sub-structure The structure end reaction value :1664kN

Bearing reaction of side pier :6622kN

Maximum axial force of single drilled shaft:2555 kN


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CONTENT

1.SUMMARIZE ..................................................................................... - 4 -

2. CALCULATION MODULE AND DATA ............................................. - 5 -

2.1 Calculation module ................................................................ - 5 -

2.2 Calculation load ..................................................................... - 5 -

3. ANALYSIS RESULT OF STATIC FORCE ............................................ - 7 -

3.1 Displacement calculation ....................................................... - 7 -

3.2 The support reaction ............................................................. - 7 -

3.3 Internal force of main girder ................................................. - 8 -

3.4 Conclusion of Internal force calculation ............................... - 10 -

3.5 stress calculation results of Main girder .............................. - 10 -

3.6 Conclusion of stress calculation ........................................... - 12 -

4. SUB-STRUCTURAL DESIGN ......................................................... - 13 -

4.1 Pier ...................................................................................... - 13 -

4.2 Footing ................................................................................ - 15 -

4.3 Foundation .......................................................................... - 17 -

5. SEISMIC ANALYSIS ..................................................................... - 19 -

5.1 Seismic load ........................................................................ - 19 -

5.2 Character value analysis model ........................................... - 19 -

5.3 Character value analysis result ............................................ - 20 -

5.4 Seismic load check .............................................................. - 21 -


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20M Standard SPAN OF METRO RAILWAY

Curved BRIDGE

DESIGN CALCULATION REPORT

1. SUMMARIZE

The curved bridge is 20m long with one span, and the radius of curvature is 250m. The

detailed span layout please sees the figure 1-1 and figure 1-2. Double concrete U deck supporting

one track each; it will be constructed using the Full Precast Span Method (FPSM), the deck is

precast and pre-tensioned at pre-casting yard. The calculation is designed according to the Limit

state method.

Fig 1-1 Bridge Configuration Layout (Unit: mm)

Fig 1-2Bridge Configuration Layout (Unit: mm)


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Fig 1-3 Bridge Configuration Layout (Unit: cm)

2. CALCULATION MODULE AND DATA

2.1 Calculation module

Predigest the structure at first and calculate with the special design program of the bridge, the

bridge dispersed result is as follows: 21 nodes and 20 girder units. The disperse drawing see

figure 2.1.

Fig 2-1 Structural Finite element disperse figure

2.2 Calculation load

The permanent load

the selfweight

Including the deadweight of the main girder member, and the plane longitudinal lateral brace,

transverse lateral brace and deck system should be supposed as concentrated load imposed on

the main girder.

the secondary dead load


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The weight of concrete deck, asphalt layer, handrail ,crash barrier and sound barrier are the

secondary dead load. Considering the stressing of concrete bridge deck, the carriageway of main

bridge will be taken stress analysis together with longitudinal beams according to combined

structure.

The total secondary dead load exclude carriageway concrete deck is 28.9 KN/m. The

carriageway concrete deck is designed according to combined beam units dead weight.

Live load

Vertical Train Loads

The standard vehicle is defined in the Rolling Stock Design Criteria System specification: 2

lanes

Fig 2-2 automobile load figure

Centrifugal load

The centrifugal load shall be calculated from the following formula:

Where

P -the static equivalent uniformly distributed load(kN/m); r-the radius if curvature(m); V-the

greatest speed(km/h);

Temperature load

Consider temperate load in scope of 0 25 for the whole structure .

Wind load

According to reference wind speed of 44.77m/s(100mph) at the structure position,

considering the influence on structure under wind load. Under operating condition, calculate load

according to wind speed of 25m/s55.9mphand combine with other load.

Combination load

Considering the following 2 combinations in this calculation:


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Basic combinationComb1Dead load+ Vertical Train Loads+ Centrifugal load

Addition combinationComb2: Dead load+ Vertical Train Loads + Centrifugal load+ wind

load + temperature load

3. ANALYSIS RESULT OF STATIC FORCE

According to structure calculation analysis, the static force calculation result is as following:

3.1 Displacement calculation

The structure deflection value under related calculated load is as following:

Fig 3-1 Bottom edge dead load displacement in verticalunit: mm

Fig 3-2 Bottom edge live load displacement in vertical (unit: mm)

On the middle position of the span, the total deflection is 6.5mm under dead load.The total

deflection of middle span is 4.0mm under the live load; the deflection-span ratio is 1/5000. the

deflection-span ratio is less than 1/2000, which satisfies the design standard request.

3.2 The support reaction

The structure support reaction under dead load, live load, combination 1 and combination 2 is

as following:

Table 3-1 the structure end reaction value (Unit: KN)

Position Dead

load

Live load COMB1

Min Max Min Max


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The end pivot -910 -754 0 -1664 -910

The above table shows that the max. Bearing reaction of side pier is 1664kN under COMB1,

which all satisfy the requirements.

3.3 Internal force of main girder

The envelope diagram of main girder are as following:

Fig 3-3 Bending moment Diagram of Plate Girder under Dead load (Unit: KNm)

Fig 3-4 Shear Diagram of Plate Girder under Dead load (Unit: Unit: KN)

Fig 3-5 Torsion Diagram of Plate Girder under Dead load (Unit: KNm)

Fig 3-6 Bending moment Diagram of Plate Girder under Vertical Train Loads (Unit: KNm)


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Fig 3-7 Shear Diagram of Plate Girder under Vertical Train Loads (Unit: KN)

Fig 3-8 Torsion Diagram of Plate Girder under Live load (Unit: KNm)

Fig 3-9 Bending moment Diagram of Plate Girder under combination 1(Unit: KNm)

Fig 3-10 Shear Diagram of Plate Girder under combination 1(Unit: KN)

Fig 3-11 Torsion Diagram of Plate Girder under combination 1(Unit: KN)


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3.4 Conclusion of Internal force calculation

Fig 3-12 Bearing Capacity of Bending moment of Plate Girder under combination 1(Unit: KNm)

Fig 3-13 Bearing Capacity of Shear Diagram of Plate Girder under combination 1(Unit: KN)

Fig 3-14 Bearing Capacity of Torsion of Plate Girder under combination 1(Unit: KNm)

According to above envelop diagram,The maximum calculated Bending moment value of

bridge under COMB1 is 6942 KN-m. According to allowable Bending moment, the allowable

Bending moment is 17522 KN-m. The bearing capacity of Bending moment satisfies requirements.

Meanwhile, The maximum calculated Shear value of bridge under COMB1 is 1665 KN. According

to allowable Bending moment, the allowable Bending moment is 1879 KN. The bearing capacity

of Shear satisfies requirements. The maximum calculated Torsion value of bridge under COMB1

is 350 KN. According to allowable Torsion value, the allowable Torsion is 5790 KN. The bearing

capacity of Torsion satisfies requirements.

3.5 stress calculation results of Main girder

The stress envelope diagrams of components under different combination are as following:


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Fig 3-15 Stress diagram of top edge under Dead load (Unit: N/mm2)

Fig 3-16 Stress diagram of bottom edge under Dead load (Unit: N/mm2)

Fig 3-17 Stress diagram of top edge under live load(Unit: N/mm2)

Fig 3-18 Stress diagram of bottom edge under live load(Unit: N/mm2)

Fig 3-19 Stress diagram of top edge under under combination 1(Unit: N/mm2)


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Fig 3-20 Stress diagram of bottom edge under under combination 1(Unit: N/mm2)

Fig 3-21 Min Principal Stress under combination 1(Unit: N/mm2)

Fig 3-22 Max Principal Stress under combination 1(Unit: N/mm2)

3.6 Conclusion of stress calculation

Table 3-2 Control stress of main rods under dead load and related combination Unit: MPa)

components Dead load

Vertical Train

Loads COMB1

Min Min Max Min Max

Chord Top edge -4.2 -4.1 0 -8.3 -4.2

Bottom edge -4.1 0 2.1 -4.1 -2.0

*+-tensile stress;--compressive stress.

According to above envelop diagram,The maximum calculated stress value of bridge under

COMB1 (additional combination) is -8.3MPa. According to allowable stress calculation, the

allowable stress of C55 is -18.5MPa. The minimum calculated stress value of bridge under

COMB1 (additional combination) is -2.0MPa. According to allowable stress calculation, the

allowable stress is 0MPa. The bearing capacity of stress satisfies requirements.

According to above envelop diagram,The maximum calculated Principal stress value of

bridge under COMB1 (additional combination) is -8.2MPa. According to allowable stress


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calculation, the allowable stress of C55 is -22.2MPa. The minimum calculated Principal stress

value of bridge under COMB1 (additional combination) is 2.2MPa. According to allowable stress

calculation, the allowable stress is 3.3MPa. The bearing capacity of Principal stress satisfies

requirements.

As the above table shows, the stress of components and concrete bridge deck is in the

allowable range under construction stage, which is safety.

4. SUB-STRUCTURAL DESIGN

4.1 Pier


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4.2 Footing


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4.3 Foundation


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As the above table shows, the internal force of sub-structural components is less than the

allowable capacity, , which satisfies requirements for safety.


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5. SEISMIC ANALYSIS

5.1 Seismic load

The earthquake acceleration is 0.16g. Field coefficient takes the secondary site for

consideration which is 1.2. The curve of corresponding response spectrum is as following:

Fig 5-1 the response spectrum

The seismic effect of finished bridge will be calculated in dynamic analysis of structure.

5.2 Character value analysis model

Analyze the dynamic property of structure and work out its calculation result of character

value. Meanwhile, take a response spectrum analysis to finished bridge according to seismic load

on structure. The following report is centered on introducing dynamic character and seismic

response analyzing results.

Model:

Fig 5-2 the structure model


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5.3 Character value analysis result

Carry out the character value analysis to structure according to current load; the character

value calculation result is as following:

Table 5-1 results of character value analysis

Stage number Frequency (HZ) Buckling mode

1 0.964523 First stage longitudinal direction move

2 1.061830 First stage right lateral bend

3 1.235035 First stage right lateral anti-symmetric bend

Fig 5-3 The first stage vibration mode

Fig 5-4 The second stage vibration mode


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Fig 5-5 The third stage vibration mode

5.4 Seismic load check

According to the description of seismic response spectrum , take a seismic load check to

bridge structure at finished bridge phase.

Fig 5-6 Pier section Fig 5-7 Moment-Curvature picture

Table 5-3 seismic load check

Seismic

direction

Dead

load(kN)

Seismic axial

force(kN)

Check axial

force(kN)

Seismic

moment

(kN*m)

Bending

capacity(kN*m)

X-Z 6622 300.1 10989.2 3702 1.53E+04 Ok

Y-Z 6622 320.2 10989.2 4488 1.53E+04 Ok


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After seismic load check of finished bridge, the structure component force is all in a

reasonable range, which ensures the structure safety.

According to calculation result, the Characters of the bridge satisfies requirements.the

structure is all in a reasonable range, safe and reliable.

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