bridges 6 computations

8/10/2019 Bridges 6 Computations

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The bridge deck is designed as composite concrete construction, where pre-cast concrete

units used as permanent form works are combined with added in-situ concrete to resist

flexure.

The pre-cast unit is 75mm thick, and the in-situ concrete is 175mm thick, giving the deck

a combined thickness of 250mm.

2.1 THE PRECAST CONCRETE UNITSThe pre-cast concrete slab unit is cast in strips measuring 1.0m wide, and spanning from

one beam girder to the other.

They are designed to withstand their own weight, the dead load of the in-situ concrete part

of the slab being supported by the pre-cast unit during construction, and a conservative

imposed loading during construction works.

Two types of pre-cast slab are available, TYPE A & TYPE B.

2.1.1 LOADING

Precast Slab thickness = 75 mmIn-situ concrete thickness = 175 mm

1. Dead Load, Gk

a. Self Weight of Pre-cast unit = 1.80 KN/m2

b. Weight of In-situ Concrete = 4.20 KN/m2

S = 6.00 KN/m2

2. Imposed Loading, Qk

A nominal imposed loading is considered, purely for the movement of men and materials

during the laying of reinforcement and casting of the insitu concrete

Use an Imposed load, Qk = 2.00 KN/m2

3. Design Loading, w

Design udl = 1.6Qk +1.4Gk = 11.60 KN/m2

2.1.2 THE PRECAST CONCRETE SLAB TYPE A

Job No.

Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD Designed E

KABIR ASSOCIATES

Member Bridge Deck Date___december '04Checked

OUTPREF. CALCULATIONS

2.0 B RIDGE DECK

Page


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They are designed as simply supported, to span between girders.

Therefore Span Length = 2.40 Lm

Maximum Shear Force, V1 = 13.92 KN

Design Moment = 8.352 KNm

DESIGN FOR BENDINGDesign as a rectangular - beam

Design Moment = KNm

Span Length = mm

Depth of slab/deck = mm

a. CALCULATION OF EFFECTIVE DEPTH, d

beam depth, h = 75 mm

width of beam web, bw = 1000 mm m m

cover to reinforcement, d' = 25.0 mm 7 5

\ reinforcement size, f = 20.0 mmstirrup diameter, t = 6.0 mm 1000 mm

effective depth, d = h - (d' + f /2 + t)

= mm

effective width, b = bw

mm

b. LEVER ARM CALCULATIONS, Z

clause 3.4.4.4 assume moment redistribution < 10%. This implies that k' = 0.156

BS8110:PART1: i. k = M/bdfcu fcu = 40 N/mm

1997 therefore, k = 0.181

since k' = 0.156

it implies that compression steel required.

use z = d

c. TENSILE REINFORCEMENT

fy = 410 N/mm

As ' = (k-k')fcu bd/(0.87fy.(d-d')) = mm

Apply T 10 @ 200 mm centres

(As prov. = mm)

As = {k'fcubd/(0.87fy.Z)} + As' = mm

Apply T 20 @ 200 mm centres

(As prov. = mm)

DESIGN FOR SHEAR

393

1,000

0.775

1,122

1,571

355

8.352

2,400

75

34


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i. Design shear Force

Design Shear Force , V = KN

ii. Design Shear Stress, v = V/bd = N/mm

fcu = 40 N/mm

Checks: 0.8 (fcu) = 5.060 N/mm design okay with respect to shear

iii. Obtaining the design concrete shear stress, vc

a. Compute 100As/(bvd) (should be 3.00) = 4.620

b. compute 400/d (should not be < 1.00) = Use 400/d =

c. By interpolation, obtain the design concrete shear stress, vc

= 0.79(100As/(bvd)) 1/3(400/d) 0.25 /1.25 = 1.949 N/mm

iv. Obtain the form and area of shear reinforcement

a. if v < 0.5v c provide nominal links

b. if 0.5v c +v < (v c + 0.4) then A sv/S v = 0.4*b v/(0.87f yv)

c. if (vc +0.4) < v < 0.8 (fcu) then A sv/S v = b v(v - v c)/(0.87f yv)

for this design v = N/mm

vc = N/mm v c + 0.4 = N/mm

i.e. 0.5v c +v < (v c + 0.4)

A sv/S v = 0.4*b v/(0.87f yv) f yv = 410 N/mm

and Asv/Sv reqd = 1.121

Apply a 4 Leg stirrup

T 10 @ 250 mm centres

and Asv/Sv provided = 1.257

2.1.2 THE PRECAST CONCRETE SLAB TYPE BThey are designed to be simply supported, to span at the girders and to also have an overhang of 700mm.

Therefore Span Length = 2.40 Lm

Cantilever Span = 0.70 m

Maximum Shear Force, V1 = 22.04 KN

Design Span Moment = 8.352 KNm

Design Cantilever Moment = 2.842 KNm

DESIGN FOR BENDING (MAIN SPAN)

Design as a rectangular - beam

Design Moment = KNm

Span Length = mm

2.349

11.76

2,400

13.920

11.765

8.352

0.409

0.409

1.949


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= mm


mm





since k' = 0.156

it implies that compression steel required.

use z = d


fy = 410 N/mm


Apply T 10 @ 200 mm centres TOP

(As prov. = mm)


Apply T 20 @ 200 mm centres BOTTOM

(As prov. = mm)

DESIGN FOR SHEAR (TYPE B SLAB)

i. Design shear Force



fcu = 40 N/mm

Checks: 0.8 (fcu) = 5.060 N/mm design okay with respect to shear

22.040

0.648

1,122

1,571

75

34

1,000

0.775

355

393


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iii. Obtaining the design concrete shear stress, vc

a. Compute 100As/(bvd) (should be 3.00) = 4.620

b. compute 400/d (should not be < 1.00) = Use 400/d =

c. By interpolation, obtain the design concrete shear stress, vc

= 0.79(100As/(bvd)) 1/3(400/d) 0.25 /1.25 = 1.949 N/mm


a. if v < 0.5v c provide nominal links

b. if 0.5v c +v < (v c + 0.4) then A sv/S v = 0.4*b v/(0.87f yv)

c. if (vc +0.4) < v < 0.8 (fcu) then A sv/S v = b v(v - v c)/(0.87f yv)


vc = N/mm v c + 0.4 = N/mm

i.e. 0.5v c +v < (v c + 0.4)


and Asv/Sv reqd = 1.121




DESIGN FOR BENDING (CANTILEVERED PORTION)

Design as a rectangular - beam

Design Moment = KNm

Span Length = mm








= mm


34

2.842

700

75

11.76

2.349

11.765

0.648

1.949


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mm





since k' = 0.156

it implies that compression steel not required.

ii. z = d(0.5 + (0.25 - k/0.9)0.5

) = d

use z = d


fy = 410 N/mm

As = M/(0.87fy.Z) = mm


(As prov. = mm)

2.2.1 DECK GEOMETRY2.2.1 MEMBER SIZINGThe pier are braced and restrained at both ends

a. width of deck = carriageway width + walkway width

Effective Width , Le = + = 11.00m

b. Total Depth of deck-slab = 250 mm

c. Depth of in-situ component of slab-deck = 175 mm

d. Depth of pre-cast concrete section = 75 mm

2.2.2 STRUCTURAL SYSTEM OF DECKfig. 20.1;

L.S. Blake (ed), Cross - section of bridge structure is a multiple web system.

Civ. Engr's Ref This system consists of a concrete deck/slab supported on, and integral

253

2.2 DESIGN OF IN-SITU CONCRETECOMPONENT OF SLAB DECK

452

1,000

0.926

0.926

10,000mm 2 * 1,500


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Book (4th ed) with longitudinal concrete beams (girders).

2.2.3 SPACING OF GIRDERSSection 17.20, "Girder spacing ranges from 7 to 9 feet. A deck slab overhang of about 2ft

F.S.Merritt (ed) 6ins is economical".

Std H/bk for The girders which are designed as rectangular sections (inorder to ease

Civ. Engrs. pre cast construction) have equal centre - centre of girder spacing as 2.40m,

and the edge - edge of girder as 2.20m, while the deck overhang is 700mm.

Fig 1: Sketch of the deck x-section

700 2 400 2 400 2 400 2 400 700

2.2.4 LOAD ANALYSIS2.2.4.1 Dead loads, G k (udl)

i. Self weight of slab: 24kN/m3 * 0.175m = 4.20 kN/m

2

ii. Weight of asphalt overlay: = 1.15 kN/m 2

TOTAL Gk = 5.35 kN/m 2

Clause 5.4

BS 5400:Part II: Design dead load = 6.153 kN/m 2

2.2.4.2 Point Loads (dead) on cantilevered section: P ci. weight of walk ways/kerbs:

0.35m*0.70m*24KN/m3*1.15 = 6.76 KN

ii. Weight of concrete handrails

0.15m*1.50m*24KN/m*1.15 = 6.21 KN

TOTAL P c = 12.97 KN

KN 6.15 KN/m 2 KN

700 2 400 2 400 2 400 2 400 700

1978

12.97 12.97


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Live loads must be place where they will produce the most severe condition of loading.

The critical positions for placing live loads will not be the same for every member.

Influence lines are therefore used in determining the most severe condition for

loading. Influence lines are primarily used to determine where to place live loads to

cause the maximum effects.

An influence line for a particular response such as reactions, shear force, bending

moment axial force is defined as a diagram in which the ordinate at any point equals

the value of that response attributable to a unit load acting at that point on thestructure.

Influence lines provide a systematic procedure for determining how the force ( or

moment or shear force) in a given part of a structure varies as the applied load moves

about the structure.

2.2.5.1 Influence Lines for udlThis is used for plotting the influence lines for uniformly distributed loads such as

those due to dead loads, and for the udl portion of HA - live loads.

Influence lines for the bending moments at Support B (penultimate support) will be

first to be plotted.

2.2.5.1.1 Geometric Propertiesi. Stiffness Coefficients.

Assume a parabolic profile for the deck.

Chapter 5.7, r A = r E = 0

Design of r.c.bdg;

Aswani, et al. r B = r D = 1.3

r C = 1.5

Fig. 5.25 with the above r values, the stiffness coefficients obtained from standard

r Bhc r Ch c r Ch c

h AB C D E


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Design of r.c.bdg; charts for concrete bridges are:

Aswani, et al. kBA = = KDE

kBC = = KDC

ii. Carry - over factors

Fig. 5.24 Using the same r values, the carry-over factors are obtained by interpolation as

Design of r.c.bdg; shown below:

Aswani, et al. C AB = CBC = C CD =

C BA = CCB = C DC =

CDE = C ED =

However, since the end spans are discontinuous, the stiffness values are

modified inorder to make the applicable to the members.

The stiffness coefficient at the discontinuous end of the beam AB,which is

discontinuous at end A is

k = (1 - C ABC BA)KBA

C AB &CBA arecarryover factors of ends A & B of member AB, while K BA is the

k'BA = [ 1 - (-0.905 * - 0.415)] * 10.50 = 6.56 = k'DE

iii. Distribution factors

We now compute the distribution factors using the stiffness coefficient:

DBA = kBA = 6.56 / {6.56 + 16.00} = = DDE

SkB

DBC = 1 - D BA = = DDC

DCB = Kc B = 16.00 / {16.00 + 16.00} = = DDE

Sk c

DCD = 1 - D CB = = DDC

2.2.5.1.2 Final Support Moments due to udl.

10.50

16.00

-0.415 -0.905

-0.071

-0.415 -0.710 -0.076

-0.905 -0.760

0.5

0.709

0.500

0.291


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i. NotationsM AB, MBA, MBC , ... = Final moments at the support

M AB, MBA, MBC , ... = Fixed end moments

C AB, C BA, C BC, ... = Carry - over factors

D AB, D BA, D BC, ... = Distribution factors

M1 = MBA - C ABMBA

M2 = MBC - C CBMCB

M3 = MCD - C DCMDCM4 = MDE - C EDMED

V = C BCDBCDCD = -0.760 * 0.709 * 0.500 =

U = C BCCCBDBCDCB = -0.760 * -0.710 * 0.709 * 0.500 =

W = C CBDCBDBA = -0.710 * 0.500 * 0.291 =

ii. Numerical values of fixed end moments

Fig. 5.35 a. Load in span AB

Design of r.c.bdg; M AB = -0.060L Aswani, et al. MBA = -0.138L

b. Load in span BC

MBC = -0.101L

MCB = -0.111L

c. Load in span CD

MCD = -0.111L

MDC = -0.101L

d. Load in span DE

MCD = -0.138L

MDC = -0.060L

iii. Final support moments

-0.269

0.191

-0.103


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a. First span loaded (Span AB)

(1 - D BA) - (2 - D BA)U

1 - 2U

(1 - 0.291) - (2 -0.291)0.191

[1 - (2 * 0.191) ]

But M1 = MBA - C ABM AB

MB = 0.619 [-0.138 - (-0.905 * -0.060)]L

= -0.119L

b. Second span loaded (Span BC)

DBA(1 -U)M BC - WM CB

1 - 2U

0.291(1 - 0.191)M BC - - 0.103M CB

[1 - (2 * 0.191) ]

= 0.381M BC + 0.167M CB

Inserting the values for M BC & MCB ,MB = (0.381 * -0.101)L + (0.167 * -0.111)L

= -0.057L

c. Third span loaded (Span CD)

- UD DEMDC + WM CD (-0.191 * 0.291)M DC + (-0.103)M CD

1 - 2U [1 - (2 * 0.191) ]

= -0.090M DC - 0.167M CD

Inserting the values for M DC & MCD ,

MB = (0.090 * -0.101)L + (0.167 * -0.111)L

= -0.028L

d. Fourth span loaded (Span DE)

UD DE 0.191 * 0.291

1 - U [1 - (2 * 0.191) ]

= 0.090M 4

MB = M1

MB

MB

M1 = 0.619M 1

=

=

=

=

=MB =

M4 = M4


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But M4 = MDE - C EDMDC

MB = 0.090 [-0.138 - (-0.905 * -0.060)]L

= -0.017L

d. Value of M B when all spans are loaded

= ( -0.119 - 0.057 - 0.028 - 0.017)L = -0.114L

But L = 2.40m

MB = -0.114 * 2.40 = -0.657KNm

e Bending Moment at various sections due to the application of unit load.

after calculating the bending moment at support B, the bending moment

at various sections is now computed due to the application of unit load.

This is as tabulate below:

Calculations BM ordinates (KNm)

{(9/25) * (2.40/8)} - 0.0657

{(16/25) * (2.40/8)} - 0.1314

{(21/25) * (2.40/8)} - 0.1971

0.0

0.2 0.329

0.3 0.408

0.1

0.000

Section

0.194


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{(24/25) * (2.40/8)} - 0.2628

{(25/25) * (2.40/8)} - 0.3285

{(24/25) * (2.40/8)} - 0.3942

{(21/25) * (2.40/8)} - 0.4599

{(16/25) * (2.40/8)} - 0.5256

{(9/25) * (2.40/8)} - 0.5913

MB = -0.657

{(9/25) * (2.40/8)} - 0.6570

{(16/25) * (2.40/8)} - 0.6570{(21/25) * (2.40/8)} - 0.6570

{(24/25) * (2.40/8)} - 0.6570

{(25/25) * (2.40/8)} - 0.6570

{(24/25) * (2.40/8)} - 0.6570

{(21/25) * (2.40/8)} - 0.6570

{(16/25) * (2.40/8)} - 0.6570

{(9/25) * (2.40/8)} - 0.6570

2.5.2 HA - live loads udl moments.from sections 2.2.4 of this report,

the ultimate udl due to HA loading = KN/m2

Using this influence ordinate table above, we now compute the various moments

0.7

0.8

0.9

0.6 0.297

-0.398

0.5

0.4

-0.196

0.034

0.145

0.428

0.392

-0.398

0.000

0.063

0.034

-0.052

-0.196-0.052

-0.657

1.4

2.0

1.5

1.6

1.7

1.8

1.9

16.875

-0.065

-0.332

1.31.2

1.1

1.0

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

0.600

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

BM Influence Line Diagram For udl


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as below;

a. Support moments

influence line ordinate = KNm

design HA udl live load = KN/m2

\ HA udl support moments = KNm

b. Span momentsmaximum span moment occurs at 0.4L (1st span) and at 3.6L (4th span)


design HA udl live load = KN/m2

\ HA udl span moments = KNm

2.3.4 Dead load udl moments.from section 2.2.4 of this report,

the udl due to dead loading is = 6.15 KN/m

Using this influence ordinate table above, we now compute the various moments

as below;

a. Support moments


design dead load udl = KN/m2

\ dead load udl support moments = = KNm

b. Span momentsmaximum span moment occurs at 0.4L (1st span) and at 2.6L (3rd span)


design dead load udl = KN/m2

\ dead load udl span moments = = KNm

2.4 Influence Lines for Point Loads

7.22

-4.04

2.63

-0.657

6.1525

0.428

6.1525

-0.657

16.875

0.428

16.875

-11.09


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The point loads are due primarily to either HA live loads or the HB live loads.

The beam girder is designed to be continuous over three spans, and has a constant

moment of inertia over all the spans. We can therfore, plot the influence lines using

standard influence line tables for a three span continuous beam.

The following assumptions are made in the analysis of the continuous bridge girders

before using the standard influence tables:

* The girder is simply supported at the supports and monolithic with the

supports.

* Rocker or roller bearings are provided at all supports.

Find below the influence line tables and charts at sections 0.1L to 1.5L

We prepared the influence charts only upto 1.5L as the loading is symmetrical over

the three spans.

n uence ne or na es or a uppor B .

0.6L -0.0994 -0.2386

0.4L-0.2400

0.7L -0.0928 -0.2227

0.3L -0.0718 -0.17230.2L -0.0502 -0.12050.1L -0.0258 -0.0619

0.0 0.0 0.0

0.8L -0.0742 -0.1781

-0.20980.5L -0.1000

0.9L -0.0408 -0.09791.0L 0.0 0.0

-0.0874

-0.2

-0.1

-0.1

0.0

0.1

0.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 3

Influence Ordinate BMD @ 1st Internal Support


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n uence ne or na es or a uppor c .

1.1L -0.0341 -0.08181.2L -0.0612 -0.14691.3L -0.0738 -0.17711.4L -0.0764 -0.18341.5L -0.0740 -0.17761.6L -0.0614 -0.14741.7L -0.0474 -0.11381.8L -0.0306 -0.07341.9L -0.0150 -0.03602.0L 0.0 0.02.1L 0.0063 0.01512.2L 0.0126 0.03022.3L 0.0189 0.04542.4L 0.0206 0.04942.5L 0.0200 0.04802.6L 0.0170 0.04082.7L 0.0135 0.03242.8L 0.0090 0.02162.9L 0.0045 0.01083.0L 0.0 0.0

LoadPosition

Influenceline

coefficient

Influence lineordinates

3.9L4.0L 0.0

-0.0034-0.0067

0.0 0.0 0.0

-0.0067-0.0034

0.0

-0.0134-0.0168

0.1L 0.0072 0.01730.2L 0.0138 0.03310.3L 0.0192 0.04610.4L 0.0234 0.05620.5L 0.0270 0.06480.6L 0.0270 0.06480.7L 0.0252 0.06050.8L 0.0198 0.04750.9L 0.0108 0.02591.0L 0.0 0.0

3.1L3.2L3.3L3.4L3.5L3.6L3.7L3.8L

-0.0101

-0.0134-0.0101

-0.0028-0.0014

-0.0056-0.0070-0.0056-0.0042-0.0028

-0.0042

-0.0014

-0.3

-0.3

-0.2

-0.1

-0.1

0.0

0.1

0.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 3

Influence Ordinate BMD @ 2nd Internal Support


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Influence Line ordinates for BM at the section 0.1L(0.240m from support A)

1.1L -0.0167 -0.04011.2L -0.0340 -0.08161.3L -0.0520 -0.12481.4L -0.0668 -0.16031.5L -0.0800 -0.19201.6L -0.0830 -0.19921.7L -0.0802 -0.19251.8L -0.0658 -0.15791.9L -0.0366 -0.08782.0L 0.0 0.02.1L -0.0255 -0.06122.2L -0.0510 -0.12242.3L -0.0765 -0.18362.4L -0.0830 -0.1992

-0.1253-0.06682.6L

2.5L -0.0800 -0.1920-0.1603

0.02503.3L

-0.08352.9L -0.0174 -0.04182.8L -0.0348


0.0 0.0 0.0 0.0 0.0

LoadPosition

coeff.

MB coeff. + M B

0.20980.2L 0.08 -0.0050 0.0750 0.18000.1L 0.09 -0.0026 0.0874

0.15080.4L 0.06 -0.0087 0.0513 0.12300.3L 0.07 -0.0072 0.0628

0.09600.6L 0.04 -0.0099 0.0301 0.07210.5L 0.05 -0.0100 0.0400

0.04970.8L 0.02 -0.0074 0.0126 0.03020.7L 0.03 -0.0093 0.0207

0.01421.0L 0.0 0.0 0.0 0.00.9L 0.01 -0.0041 0.0059

3.0L 0.0 0.0

2.7L -0.0522

0.0156 0.03743.4L 0.0208 0.0499

3.1L 0.0052 0.01253.2L 0.0104

3.5L 0.0260 0.06243.6L 0.0208 0.04993.7L 0.0156 0.03743.8L 0.0104 0.02503.9L 0.0052 0.01254.0L 0.0 0.0

-0.3

-0.2

-0.2

0.1

0.2

0.2

0.3Influence Ordinate BMD @ 0.1L


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-0.00821.2L -0.0061 -0.0061 -0.01471.1L -0.0034 -0.0034

-0.01771.4L -0.0076 -0.0076 -0.01831.3L -0.0074 -0.0074

-0.01781.6L -0.0061 -0.0061 -0.01471.5L -0.0074 -0.0074

-0.01141.8L -0.0031 -0.0031 -0.00731.7L -0.0047 -0.0047

-0.00362.0L 0.0 0.0 0.0 0.01.9L -0.0015 -0.0015

0.00152.2L 0.0013 0.0013 0.00302.1L 0.0006 0.0006

0.00452.4L 0.0021 0.0021 0.00492.3L 0.0019 0.0019

0.00482.6L 0.0017 0.0017 0.00412.5L 0.0020 0.0020

0.00322.8L 0.0009 0.0009 0.00222.7L 0.0014 0.0014

0.00113.0L 0.0 0.0 0.0 0.02.9L 0.0005 0.0005


0.0 0.0 0.0 0.0 0.0

LoadPosition

coeff.

MB coeff. + M B

0.17960.2L 0.16 -0.0100 0.1500 0.35990.1L 0.08 -0.0052 0.0748

0.30150.4L 0.12 -0.0175 0.1025 0.24600.3L 0.14 -0.0144 0.1256

0.19200.6L 0.08 -0.0199 0.0601 0.14430.5L 0.10 -0.0200 0.0800

0.09950.8L 0.04 -0.0148 0.0252 0.06040.7L 0.06 -0.0186 0.0414

0.02841.0L 0.0 0.0 0.0 0.00.9L 0.02 -0.0082 0.0118

3.1L -0.00013.2L3.3L

-0.0003-0.0004

3.4L3.5L3.6L3.7L3.8L3.9L4.0L

-0.0006-0.0004-0.0003-0.0001

0.0 0.0 0.0 0.0

-0.0001-0.0003-0.0004-0.0006-0.0007

-0.0007

-0.0006-0.0007-0.0006-0.0004

-0.0013-0.0017-0.0013-0.0010

-0.0003-0.0003-0.0001

-0.0003-0.0007-0.0010

-0.1

0.0

0.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

0.2

0.2

0.3

0.3

0.4



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0.0 0.0 0.0-0.0004 -0.0004

1.0L 0.0 0.0 0.0 0.0-0.0246

1.2L -0.0184 -0.0184 -0.04411.1L -0.0102 -0.0102

-0.05311.4L -0.0229 -0.0229 -0.05501.3L -0.0221 -0.0221

-0.05331.6L -0.0184 -0.0184 -0.04421.5L -0.0222 -0.0222

-0.03411.8L -0.0092 -0.0092 -0.02201.7L -0.0142 -0.0142

-0.01082.0L 0.0 0.0 0.0 0.01.9L -0.0045 -0.0045

0.00452.2L 0.0038 0.0038 0.00912.1L 0.0019 0.0019

0.01362.4L 0.0062 0.0062 0.01482.3L 0.0057 0.0057

0.01442.6L 0.0051 0.0051 0.01222.5L 0.0060 0.0060

0.00972.8L 0.0027 0.0027 0.00652.7L 0.0041 0.0041

0.00323.0L 0.0 0.0 0.0 0.02.9L 0.0014 0.0014


0.0 0.0 0.0 0.0 0.0

LoadPosition

coeff.

MB coeff. + M B

0.11920.2L 0.12 -0.0201 0.0999 0.23980.1L 0.06 -0.0103 0.0497

0.36310.4L 0.24 -0.0350 0.2050 0.49210.3L 0.18 -0.0287 0.1513

0.38400.6L 0.16 -0.0398 0.1202 0.28860.5L 0.20 -0.0400 0.1600

0.19890.8L 0.08 -0.0297 0.0503 0.12080.7L 0.12 -0.0371 0.0829

0.05680.9L 0.04 -0.0163 0.0237

3.1L

3.6L3.7L3.8L3.9L

3.2L3.3L3.4L3.5L

4.0L

-0.0050-0.0040-0.0030-0.0020

-0.0010-0.0020-0.0030-0.0040

-0.00100.0

-0.0004-0.0008-0.0013-0.0017-0.0021-0.0017-0.0013-0.0008

-0.0021-0.0017-0.0013-0.0008

-0.0004-0.0008-0.0013-0.0017

-0.1

0.0

0.1

0.2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 3

0.2

0.3

0.4

0.5

0.6

Influence Ordinate BMD @ 0.4L


22/221

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1.0L 0.0 0.0 0.0 0.0-0.0327

1.2L -0.0245 -0.0245 -0.05881.1L -0.0136 -0.0136

-0.07081.4L -0.0306 -0.0306 -0.07331.3L -0.0295 -0.0295

-0.07101.6L -0.0246 -0.0246 -0.05891.5L -0.0296 -0.0296

-0.04551.8L -0.0122 -0.0122 -0.02941.7L -0.0190 -0.0190

-0.01442.0L 0.0 0.0 0.0 0.01.9L -0.0060 -0.0060

0.00602.2L 0.0050 0.0050 0.01212.1L 0.0025 0.0025

0.01812.4L 0.0082 0.0082 0.01982.3L 0.0076 0.0076

0.01922.6L 0.0068 0.0068 0.01632.5L 0.0080 0.0080

0.01300.0036 0.0036 0.00860.0054 0.0054

0.0 0.0 0.00.0018 0.0018


0.0 0.0 0.0 0.0 0.0

LoadPosition

coeff.

MB coeff. + M B

0.08900.2L 0.10 -0.0251 0.0749 0.17980.1L 0.05 -0.0129 0.0371

0.27380.4L 0.20 -0.0437 0.1563 0.37510.3L 0.15 -0.0359 0.1141

0.48000.6L 0.20 -0.0497 0.1503 0.36070.5L 0.25 -0.0500 0.2000

0.24860.8L 0.10 -0.0371 0.0629 0.15100.7L 0.15 -0.0464 0.1036

0.07100.9L 0.05 -0.0204 0.0296

3.1L3.2L3.3L

3.0L2.9L2.8L2.7L

3.4L3.5L3.6L3.7L3.8L3.9L4.0L

-0.0054-0.0067-0.0054-0.0040

-0.0013-0.0027-0.0040

0.0043

-0.0027-0.0013

-0.0022

0.0

-0.0006

-0.0028-0.0022-0.0017-0.0011

0.0

-0.0006-0.0011-0.0017-0.0022-0.0028-0.0022-0.0017-0.0011-0.0006

0.0 0.00.0

-0.0011-0.0017

-0.0006

-0.2

-0.1

0.0

0.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

0.3

0.4

0.5



23/221

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1.0L 0.0 0.0 0.0 0.0-0.0409

1.2L -0.0306 -0.0306 -0.07341.1L -0.0171 -0.0171

-0.08861.4L -0.0382 -0.0382 -0.09171.3L -0.0369 -0.0369

-0.08881.6L -0.0307 -0.0307 -0.07371.5L -0.0370 -0.0370

-0.05691.8L -0.0153 -0.0153 -0.03671.7L -0.0237 -0.0237

0.01.9L -0.0075 -0.00752.0L 0.0 0.0 0.0

0.00760.01512.2L 0.0063 0.0063

2.1L 0.0032 0.0032

0.0103 0.0103 0.02470.0095 0.0095

0.02400.0085 0.0085 0.02040.0100

0.0045 0.0045 0.01080.0068 0.0068

0.00543.0L 0.0 0.0 0.0 0.02.9L 0.0023


0.0 0.0 0.0 0.0 0.0

LoadPosition

coeff.

MB coeff. + M B

0.05880.2L 0.08 -0.0301 0.0499 0.11970.1L 0.04 -0.0155 0.0245

0.18460.4L 0.16 -0.0524 0.1076 0.25810.3L 0.12 -0.0431 0.0769

0.33600.6L 0.24 -0.0596 0.1804 0.43290.5L 0.20 -0.0600 0.1400

0.29840.8L 0.12 -0.0445 0.0755 0.18120.7L 0.18 -0.0557 0.1243

0.08520.9L 0.06 -0.0245 0.0355

2.6L2.5L2.4L2.3L

3.2L3.3L3.4L3.5L

3.1L

2.8L2.7L

4.0L

3.6L3.7L3.8L3.9L

-0.0007 -0.0017

0.0023

0.0162

0.0100

0.0227

-0.0180

-0.0028-0.0021

-0.0014-0.0021-0.0028-0.0035

0.0 0.0

-0.0014-0.0007

0.0

-0.0007-0.0014-0.0021-0.0028-0.0035-0.0028-0.0021-0.0014-0.0007

-0.0067-0.0050-0.0034-0.0017

-0.0034-0.0050-0.0067-0.0084

0.0

-0.2

-0.1

0.0

0.1

0.2

1 4 7 10 13 16 19 22 25 28 31 34 37 4

0.2

0.3

0.4



24/221

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0.0 0.0 0.0 0.0

-0.0017 -0.0017 -0.0040-0.0008 -0.0008 -0.0020

-0.0034 -0.0034 -0.0081-0.0025 -0.0025 -0.0060

-0.0034 -0.0034 -0.0081-0.0042 -0.0042 -0.0101

-0.0017 -0.0017 -0.0040-0.0025 -0.0025 -0.0060

-0.0008 -0.0008 -0.0020

1.0L 0.0 0.0 0.0 0.0-0.0491

1.2L -0.0367 -0.0367 -0.08811.1L -0.0205 -0.0205

-0.10631.4L -0.0458 -0.0458 -0.11001.3L -0.0443 -0.0443

-0.10661.6L -0.0368 -0.0368 -0.08841.5L -0.0444 -0.0444

-0.06831.8L -0.0184 -0.0184 -0.04411.7L -0.0284 -0.0284

-0.02162.0L 0.0 0.0 0.0 0.01.9L -0.0090 -0.0090

0.00912.2L 0.0076 0.0076 0.01812.1L 0.0038 0.0038

0.02722.4L 0.0124 0.0124 0.02972.3L 0.0113 0.0113

0.02882.6L 0.0102 0.0102 0.02452.5L 0.0120 0.0120

0.01942.8L 0.0054 0.0054 0.01302.7L 0.0081 0.0081

0.00653.0L 0.0 0.0 0.0 0.02.9L 0.0027 0.0027


0.0 0.0 0.0 0.0 0.0

LoadPosition

coeff.

MB coeff. + M B

0.02870.2L 0.06 -0.0351 0.0249 0.05970.1L 0.03 -0.0181 0.0119

0.09540.4L 0.12 -0.0612 0.0588 0.14120.3L 0.09 -0.0503 0.0397

0.19200.6L 0.18 -0.0696 0.1104 0.26500.5L 0.15 -0.0700 0.0800

0.34810.8L 0.14 -0.0519 0.0881 0.21130.7L 0.21 -0.0650 0.1450

0.09950.9L 0.07 -0.0286 0.0414

3.1L3.2L3.3L

3.8L3.9L4.0L

3.4L3.5L3.6L3.7L

-0.2

-0.1

0.0

0.1

1 4 7 10 13 16 19 22 25 28 31 34 37 4

0.2

0.3



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0.00.0

+ M B

-0.0002


-0.0015

0.0

-0.0029-0.0039

-0.0071-0.0047

-0.0024-0.0047-0.0071-0.0094

-0.0010-0.0010 -0.0024

-0.0049-0.0039-0.0029-0.0020

-0.0118-0.0094

-0.0029-0.0039-0.0049-0.0039-0.0029-0.0020

-0.0010-0.0020

-0.0010-0.0020

1.0L 0.0 0.0 0.0 0.0-0.0573

1.2L -0.0428 -0.0428 -0.10281.1L -0.0239 -0.0239

-0.12401.4L -0.0535 -0.0535 -0.12841.3L -0.0517 -0.0517

-0.12431.6L -0.0430 -0.0430 -0.10321.5L -0.0518 -0.0518

-0.07961.8L -0.0214 -0.0214 -0.05141.7L -0.0332 -0.0332

-0.02522.0L 0.0 0.0 0.0 0.01.9L -0.0105 -0.0105

0.01062.2L 0.0088 0.0088 0.02122.1L 0.0044 0.0044

0.03182.4L 0.0144 0.0144 0.03462.3L 0.0132 0.0132

0.03362.6L 0.0119 0.0119 0.02862.5L 0.0140 0.0140

0.02272.8L 0.0063 0.0063 0.01512.7L 0.0095 0.0095

0.00763.0L 0.0 0.0 0.0 0.02.9L 0.0032 0.0032

MB coeff.

0.0101

0.0 0.02 -0.0206 -0.0006-0.0004

0.2L 0.06 -0.0574 0.0026 0.00610.1L 0.04 -0.0402

0.02420.4L 0.10 -0.0800 0.0200 0.04800.3L 0.08 -0.0699

0.09720.6L 0.14 -0.0742 0.0658 0.15780.5L 0.12 -0.0795 0.0405

0.24150.8L 0.08 -0.0326 0.0474 0.11370.7L 0.16 -0.0594 0.1006

0.00.9L 0.0 0.0 0.0

3.1L

3.6L3.7L3.8L3.9L

3.2L3.3L3.4L3.5L

4.0L

LoadPosition

0.0

coeff.

-0.2

-0.1

0.0

0.1

1 4 7 10 13 16 19 22 25 28 31 34 37 4

0.1000

0.1500

0.2000

0.2500



26/221

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0.0 0.0 0.0

0.0


-0.0960

0.0132

-0.0707-0.0324

-0.0022 -0.0022 -0.0054-0.0011 -0.0011 -0.0027

-0.0056 -0.0056 -0.0134-0.0045 -0.0108

-0.0034 -0.0034 -0.0081

-0.0022 -0.0054-0.0034 -0.0034 -0.0081

-0.0045 -0.0108

-0.0011 -0.0011 -0.0027

1.0L -0.0273 -0.0273 -0.0655-0.1175

1.2L -0.0590 -0.0590 -0.14171.1L -0.0490 -0.0490

-0.14671.4L -0.0592 -0.0592 -0.14211.3L -0.0611 -0.0611

-0.11791.6L -0.0379 -0.0379 -0.09101.5L -0.0491 -0.0491

-0.05881.8L -0.0120 -0.0120 -0.02881.7L -0.0245 -0.0245

0.02.0L 0.0050 0.0050 0.01211.9L 0.0 0.0 0.0

0.02422.2L 0.0151 0.0151 0.03632.1L 0.0101 0.0101

0.03962.4L 0.0160 0.0160 0.03842.3L 0.0165 0.0165

0.03262.6L 0.0108 0.0108 0.02592.5L 0.0136 0.0136

0.0

0.01730.0036 0.0036 0.00860.0072 0.0072

0.0

3.6L

0.0 0.0

-0.0022

-0.0045

-0.0045

3.3L

-0.03170.0

LoadPosition

coeff.

MB coeff. + M B

-0.0604-0.0831-0.0928-0.0787

3.4L3.5L

-0.0252

0.00.1L 0.01

0.3L 0.03 -0.0646 -0.0346

0.0

-0.0387

-0.0232 -0.01320.2L 0.02 -0.0452

-0.02950.5L 0.05 -0.0900 -0.04000.4L 0.04

0.6L 0.06 -0.08950.7L 0.07 -0.0835 -0.0135

0.03170.9L 0.09 -0.0367 0.0533 0.12790.8L 0.08 -0.0668

3.0L3.1L3.2L

2.9L2.8L2.7L

3.7L3.8L3.9L4.0L

0.0

0.0

-0.2000

-0.1500

-0.1000

-0.0500

0.0000

0.0500

1 4 7 10 13 16 19 22 25 28 31 34 37 4

0.0

0.1

0.1

0.2Influence Line Ordinate BMD @ 0.9L


27/221

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Influence Line ordinates for BM at the section 1.1L (0.240m from support B)

-0.0091-0.0060

-0.0038-0.0025-0.0013

-0.0030-0.0060-0.0091-0.0121-0.0151-0.0121

0.0 0.0

-0.0013-0.0025-0.0038-0.0050

-0.0030

-0.0063-0.0050

-0.0063-0.0050-0.0038-0.0025-0.0013

0.0 0.0

-0.0013

0.0

-0.0551

0.01.1L -0.0307 -0.0307 -0.07371.0L 0.0 0.0

-0.0688

-0.13221.3L -0.0664 -0.0664 -0.15941.2L -0.0551

-0.0553

-0.16501.5L -0.0666 -0.0666 -0.15981.4L -0.0688

-0.0275

-0.13261.7L -0.0427 -0.0427 -0.10241.6L -0.0553

0.0

-0.06611.9L -0.0135 -0.0135 -0.03241.8L -0.0275

0.0113

0.02.1L 0.0057 0.0057 0.01362.0L 0.0 0.0

0.0185

0.02722.3L 0.0170 0.0170 0.04082.2L 0.0113

0.0153

0.04452.5L 0.0180 0.0180 0.04322.4L 0.0185

0.0081

0.03672.7L 0.0122 0.0122 0.02922.6L 0.0153

0.0

0.01942.9L 0.0041 0.0041 0.00972.8L 0.0081

3.0L 0.0

-0.0025-0.0038-0.0050

-0.0225 -0.0540

0.0

LoadPosition

coeff.

MB coeff. MC coeff. + M B +

MC

3.1L3.2L


0.0 0.0 0.0 0.0 0.0 0.0

-0.0438 -0.10510.1L -0.02320.2L -0.0452 0.0014

0.0007

0.4L -0.0787 0.00230.3L -0.0646 0.0019 -0.0627 -0.1505

-0.0763 -0.1832-0.0873 -0.2095-0.0868 -0.2082

0.5L0.6L -0.0895 0.0027

-0.0900 0.0027

0.8L -0.0668 0.00200.7L -0.0835 0.0025 -0.0810 -0.1944

-0.0648 -0.1555-0.0356 -0.08550.9L -0.0367 0.0011

3.5L3.6L3.7L3.8L

3.3L3.4L

3.9L4.0L

0.0

-0.2

-0.2

-0.1

-0.1

0.0

0.1

0.1

0.2

0.2

1 4 7 10 13 16 19 22 25 28 31 34 37

Influence Line Ordinate BMD @ 1.1L


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Influence Line ordinates for BM at the section 1.2L (0.480m from support B)

0.0005 -0.00070.0 0.0 0.0

-0.0089-0.0071-0.0053-0.0036-0.0018

-0.0007-0.0015-0.0022-0.0030

-0.0018-0.0036-0.0053-0.0071

0.00260.00210.00160.0010

-0.0037-0.0030-0.0022-0.0015

-0.0013-0.0025-0.0038-0.0050-0.0063-0.0050-0.0038-0.0025-0.0013

0.0 0.0 0.0 0.00.00050.00100.00160.0021

0.0

0.0

0.0

1.0L 0.0 0.0 0.01.1L 0.09 -0.0307 -0.0017

0.0 0.00.0576 0.1383

0.0516-0.0016 -0.0039

0.08 -0.0551 -0.0034 0.02151.3L 0.071.4L 0.06 -0.0688 -0.0067

-0.0664 -0.0052

-0.05651.5L 0.05 -0.0666

-0.0154 -0.0371

-0.0080

-0.0246-0.0080

-0.0207

-0.05901.6L 0.04 -0.0553 -0.0083 -0.0236

-0.0496-0.0339

-0.0072 -0.01720.02 -0.0275 -0.0066 -0.01410.03 -0.0427

1.9L 0.012.0L 0.0 0.0 0.0

-0.0135 -0.0037

0.01502.1L 0.0057

0.0 0.0

-0.0077

0.0031-0.0026

0.0094

0.00752.2L 0.0113 -0.0051 0.0062

0.02250.0246

0.0100 0.02400.0185 -0.0083 0.01020.0170

0.0086 0.02072.5L2.6L 0.0153 -0.0067

0.0180 -0.0080

0.01662.8L 0.0081 -0.0035 0.0046 0.01112.7L 0.0122

0.0041 -0.0017

0.0069-0.0052

0.0023 0.0055

LoadPosition

coeff.


MCInfluence line

ordinates

3.2L3.3L3.4L

0.1L -0.0206 0.00140.0 0.0 0.0 0.0 0.0 0.0

-0.0192 -0.0461-0.0374 -0.0898-0.0536 -0.1286

0.2L0.3L -0.0574 0.0038

-0.0402 0.0028

0.5L -0.0800 0.00540.4L -0.0699 0.0047 -0.0652 -0.1566

-0.0746 -0.1790-0.0741 -0.1779-0.0692 -0.1661

0.6L0.7L -0.0742 0.0050

-0.0795 0.0054

-0.0326 0.00220.8L -0.0594 0.0040 -0.0554 -0.1330

-0.0305 -0.0732

3.0L3.1L

2.9L

2.4L2.3L

1.8L1.7L

1.2L

3.5L3.6L3.7L3.8L

0.9L

3.9L4.0L

-0.3

-0.2

-0.2

-0.1

-0.1

0.1

0.2

0.2

0.3



29/221


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Page

Influence Line ordinates for BM at the section1.4L (0.960m from support B)

0.00140.0 0.0 0.0 0.0

-0.0010 0.0016 0.0006

0.0042-0.0020 0.0031 0.0012 0.0028-0.0029 0.0047 0.0017

0.0070-0.0039 0.0062 0.0023 0.0056-0.0049 0.0078 0.0029

0.0042-0.0039 0.0062 0.0023 0.0056-0.0029 0.0047 0.0017

0.0014-0.0020 0.0031 0.0012 0.0028-0.0010 0.0016 0.0006

0.0 0.0 0.0 0.0

-0.01020.04110.0870

0.09871.0L 0.01.1L 0.07 -0.0239 -0.0050

0.20870.3426

0.1065 0.25560.21 -0.0517 -0.0156 0.14270.14 -0.0428

1.4L 0.181.5L 0.15 -0.0518 -0.0240

-0.0535 -0.0200

0.07861.6L 0.12 -0.0430

0.0742 0.1781

-0.0197

0.0521-0.0249

0.0188

0.12511.7L 0.09 -0.0332 -0.0241 0.0328

0.04520.0204

0.0 0.00.03 -0.0105 -0.0110 0.00850.06 -0.0214

-0.0032 -0.00782.0L 0.02.1L 0.0044 -0.0077

0.0 0.0

-0.01562.3L 0.0132 -0.0230 -0.0097 -0.02332.2L 0.0088

0.0144 -0.0249

-0.0065-0.0153

-0.0105

-0.01570.0119 -0.0200

-0.0252-0.0240

-0.0081 -0.01950.0140 -0.0240 -0.0100

2.8L 0.0063-0.0062 -0.0149

2.6L2.7L 0.0095

2.9L 0.0032 -0.0052 -0.0021 -0.00500.0 0.0

-0.0041-0.0104

0.0

-0.0099

0.0

LoadPosition

coeff.


MCInfluence line

ordinates

3.2L3.3L3.4L

0.1L -0.0155 0.00290.0 0.0 0.0 0.0 0.0 0.0

-0.0126 -0.0302-0.0246 -0.0590-0.0354 -0.0850

0.2L0.3L -0.0431 0.0077

-0.0301 0.0055

0.5L -0.0600 0.01080.4L -0.0524 0.0094 -0.0431 -0.1034

-0.0492 -0.1181-0.0488 -0.1172-0.0456 -0.1094

0.6L0.7L -0.0557 0.0101

-0.0596 0.0108

-0.0245 0.00430.8L -0.0445 0.0079 -0.0366 -0.0878

-0.0202 -0.0484

3.1L3.0L

2.5L2.4L

1.9L1.8L

1.3L1.2L

3.5L3.6L3.7L3.8L

0.9L

3.9L4.0L 0.0

0.0

-0.2

-0.1

0.0

0.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 3

0.2

0.3

0.4



31/221

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0.00890.0060

0.01490.0119

0.00300.0

-0.0008 0.0021 0.00120.0 0.0 0.0 0.0

-0.0025 0.0062 0.0037-0.0017 0.0042 0.0025

-0.0042 0.0104 0.0062-0.0034 0.0083 0.0050

0.0089-0.0034 0.0083 0.0050 0.0119-0.0025 0.0062 0.0037

0.0030-0.0017 0.0042 0.0025 0.0060-0.0008 0.0021 0.0012

0.0 0.00.01.1L 0.06 -0.0205 -0.0067

0.0 0.0

0.12 -0.0367 -0.01360.03290.0697

0.0789

-0.0320-0.0458 -0.0267

0.16720.2758

0.1674 0.4019-0.0443 -0.0208 0.1149

-0.03680.12360.0900-0.0332

0.29661.4L 0.241.5L 0.20 -0.0444

0.21590.0595 0.1428

0.08481.7L 0.12 -0.0284 -0.03211.6L 0.16

-0.0154

-0.0090 -0.0146 0.01640.08 -0.0184 -0.0263 0.0353

0.0 0.02.0L 0.00.0393

0.0 0.0-0.0064-0.0128-0.0204

0.0038 -0.01022.1L

2.3L 0.0113 -0.03062.2L 0.0076

0.0124 -0.0332 -0.0208

-0.0308-0.0193 -0.0462

-0.0500-0.0480

-0.0165 -0.0396-0.0128 -0.0307

0.0120 -0.0320 -0.0200

2.8L 0.00540.0081 -0.02090.0102 -0.02672.6L

2.7L

2.9L 0.0027 -0.0070 -0.0043 -0.01020.0 0.0

-0.0085-0.0139

0.0

-0.0204

0.0

LoadPosition

coeff.


MCInfluence line

ordinates

3.2L3.3L3.4L

0.1L -0.0129 0.00360.0 0.0 0.0 0.0 0.0 0.0

-0.0093 -0.0223-0.0182 -0.0437-0.0263 -0.0631

0.2L0.3L -0.0359 0.0096

-0.0251 0.0069

0.5L -0.0500 0.01350.4L -0.0437 0.0117 -0.0320 -0.0768

-0.0365 -0.0876-0.0362 -0.0869-0.0338 -0.0811

0.6L0.7L -0.0464 0.0126

-0.0497 0.0135

0.9L -0.0204 0.00540.8L -0.0371 0.0099 -0.0272 -0.0653

-0.0150 -0.0360

1.9L1.8L

1.3L1.2L

1.0L

3.5L3.6L3.7L3.8L

3.1L3.0L

2.5L2.4L

3.9L4.0L

0.04

0.18

0.0

-0.2

-0.1

0.0

0.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 3

0.2

0.3

0.4



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0.12580.2090

0.0581

-0.0720

-0.0310

0.3067

0.0 0.01.0L 0.01.1L 0.05 -0.0171 -0.0084

0.0 0.0

-0.0306 -0.01700.15

0.02460.0524

0.0590

-0.0370 -0.0400-0.0382-0.0369 -0.0260 0.0871

-0.0334

1.6L 0.20 -0.0307

0.1284 0.30820.4152

1.4L 0.201.5L

0.0518

0.1730

1.7L 0.15 -0.0237 -0.04010.1278-0.04150.0862

0.25

0.0

0.10 -0.0153 -0.03290.05

0.20690.1243

-0.0075 -0.0183 0.02420.0

2.2L 0.0063

0.0 0.0-0.0230

2.0L 0.02.1L -0.0096

2.3L 0.0095 -0.0383-0.0192-0.0255

0.0032 -0.0128

0.0103 -0.0415 -0.0312

-0.0461-0.0288 -0.0691

-0.0749

-0.0249 -0.0598-0.0194 -0.0464

0.0100 -0.0400 -0.0300

0.0068 -0.02610.0085 -0.03342.6L

2.7L

-0.01552.8L 0.00452.9L 0.0023 -0.0087

0.0 0.0

-0.0129-0.0174

0.0-0.0065

0.0

2.5L2.4L

1.9L1.8L

1.3L1.2L

3.8L3.9L

3.2L3.3L3.4L3.5L3.6L3.7L

3.1L3.0L

4.0L

0.0046-0.0014 0.0052 0.0038 0.0091-0.0007 0.0026 0.0019

0.0137-0.0028 0.0104 0.0076 0.0182-0.0021 0.0078 0.0057

0.0228-0.0028 0.0104 0.0076 0.0182-0.0035 0.0130 0.0095

0.0137-0.0014 0.0052 0.0038 0.0091-0.0021 0.0078 0.0057

0.0 0.0 0.0 0.0-0.0007 0.0026 0.0019

0.0 0.0 0.0 0.0

LoadPosition

coeff.


MCInfluence line

ordinates

0.0 0.0-0.0060 -0.0144-0.0118 -0.0283

0.1L0.2L -0.0201 0.0083

-0.0103 0.0043

0.4L -0.0350 0.01400.3L -0.0287 0.0115 -0.0172 -0.0413

-0.0209 -0.0502-0.0238 -0.0571-0.0236 -0.0565

0.5L0.6L -0.0398 0.0162

-0.0400 0.0162

0.8L -0.0297 0.01190.7L -0.0371 0.0151 -0.0220 -0.0528

-0.0178 -0.0427-0.0098 -0.02360.9L -0.0163 0.0065

0.0

0.0

0.10

0.0046

-0.2

-0.1

0.0

0.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 3

0.2

0.3

0.4



33/221

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0.0 0.01.0L 0.0 0.0 0.0

1.2L 0.08 -0.0245 -0.02041.1L 0.04 -0.0136 -0.0100 0.0163 0.0392

0.0351 0.08430.0593 0.14230.0894 0.2145

1.3L 0.121.4L 0.16 -0.0306 -0.0401

-0.0295 -0.0312

1.6L 0.24 -0.0246 -0.04981.5L 0.20 -0.0296 -0.0480 0.1224 0.2938

0.1656 0.39750.1129 0.27100.0683 0.1639

1.7L 0.181.8L 0.12 -0.0122 -0.0395

-0.0190 -0.0481

2.0L 0.0 0.0 0.01.9L 0.06 -0.0060 -0.0220 0.0320 0.0769

0.0 0.0-0.0128 -0.0307-0.0256 -0.0613

2.1L2.2L 0.0050 -0.0306

0.0025 -0.0153

2.4L 0.0082 -0.04982.3L 0.0076 -0.0459 -0.0383 -0.0920

-0.0416 -0.0997-0.0400 -0.0960-0.0333 -0.0799

2.5L2.6L 0.0068 -0.0401

0.0080 -0.0480

2.8L 0.0036 -0.02092.7L 0.0054 -0.0313 -0.0259 -0.0622

-0.0173 -0.0415-0.0086 -0.0207

0.0 0.02.9L3.0L 0.0 0.0 0.0

0.0018 -0.0104

3.2L -0.0011 0.00623.1L -0.0006 0.0031 0.0026 0.0061

0.0051 0.01230.0077 0.01840.0102 0.0246

3.3L3.4L -0.0022 0.0125

-0.0017 0.0094

3.6L -0.0022 0.01253.5L -0.0028 0.0156 0.0128 0.0307

0.0102 0.02460.0077 0.01840.0051 0.0123

3.7L3.8L -0.0011 0.0062

-0.0017 0.0094

4.0L 0.0 0.0 0.03.9L -0.0006 0.0031 0.0026 0.0061

0.0 0.0

+ M B +MC


0.0 0.0

LoadPosition

coeff.

0.0 0.0 0.0 0.0

MB coeff. MC coeff.

0.2L -0.0151 0.00970.1L -0.0077 0.0050 -0.0027 -0.0065

-0.0054 -0.0130-0.0081 -0.0194-0.0098 -0.0236

0.3L0.4L -0.0262 0.0164

-0.0215 0.0134

0.6L -0.0298 0.01890.5L -0.0300 0.0189 -0.0111 -0.0266

-0.0109 -0.0262-0.0102 -0.0245-0.0084 -0.0202

0.7L0.8L -0.0223 0.0139

-0.0278 0.0176

0.9L -0.0122 0.0076 -0.0047 -0.0112

-0.2

-0.1

0.0

0.1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 3

0.1

0.2

0.3



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1.0L 0.0 0.0 0.0 0.0 0.00.0081 0.01940.0178 0.0428

1.1L 0.031.2L 0.06 -0.0184 -0.0238

-0.0102 -0.0117

1.4L 0.12 -0.0229 -0.04681.3L 0.09 -0.0221 -0.0364 0.0315 0.0755

0.0503 0.12080.0718 0.17230.1035 0.2484

1.5L 0.151.6L 0.18 -0.0184 -0.0581

-0.0222 -0.0560

1.8L 0.14 -0.0092 -0.04611.7L 0.21 -0.0142 -0.0561 0.1396 0.3351

0.0848 0.20340.0399 0.0957

0.0 0.01.9L 0.072.0L 0.0 0.0 0.0

-0.0045 -0.0256

2.2L 0.0038 -0.03572.1L 0.0019 -0.0179 -0.0160 -0.0383

-0.0319 -0.0766-0.0479 -0.1149-0.0519 -0.1246

2.3L2.4L 0.0062 -0.0581

0.0057 -0.0536

2.6L 0.0051 -0.04682.5L 0.0060 -0.0560 -0.0500 -0.1200

-0.0417 -0.1000-0.0325 -0.0780-0.0217 -0.0520

2.7L2.8L 0.0027 -0.0244

0.0041 -0.0365

3.0L 0.0 0.0 0.02.9L 0.0014 -0.0122 -0.0108 -0.0260

0.0 0.00.0032 0.00770.0064 0.0155

3.1L3.2L -0.0008 0.0073

-0.0004 0.0036

3.4L -0.0017 0.01463.3L -0.0013 0.0109 0.0097 0.0232

0.0129 0.03090.0161 0.03860.0129 0.0309

3.5L3.6L -0.0017 0.0146

-0.0021 0.0182

3.8L -0.0008 0.00733.7L -0.0013 0.0109 0.0097 0.0232

0.0064 0.01550.0032 0.0077

0.0 0.03.9L4.0L 0.0 0.0 0.0

-0.0004 0.0036

0.0 0.0 0.0 0.0

LoadPosition

coeff.


MCInfluence line

ordinates

0.0 0.00.0006 0.00140.0010 0.0024

0.1L0.2L -0.0100 0.0110

-0.0052 0.0058

0.4L -0.0175 0.01870.3L -0.0144 0.0154 0.0010 0.0024

0.0012 0.00300.0016 0.00380.0017 0.0041

0.5L0.6L -0.0199 0.0216

-0.0200 0.0216

0.8L -0.0148 0.01580.7L -0.0186 0.0202 0.0016 0.0038

0.0010 0.00240.0005 0.00120.9L -0.0082 0.0086

-0.2

-0.1

0.01 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 3

0.1

0.1

0.2

0.2

0.3


`


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0.0 0.01.0L 0.0 0.0 0.0

1.2L 0.04 -0.0122 -0.02721.1L 0.02 -0.0068 -0.0134 -0.0002 -0.0004

0.0006 0.00130.0036 0.00870.0113 0.0271

1.3L 0.061.4L 0.08 -0.0153 -0.0534

-0.0148 -0.0416

1.6L 0.12 -0.0123 -0.06641.5L 0.10 -0.0148 -0.0640 0.0212 0.0509

0.0413 0.09920.0664 0.15930.1012 0.2430

1.7L 0.141.8L 0.16 -0.0061 -0.0526

-0.0095 -0.0642

2.0L 0.0 0.0 0.01.9L 0.08 -0.0030 -0.0293 0.0477 0.1145

0.0 0.0-0.0191 -0.0459-0.0383 -0.0919

2.1L2.2L 0.0025 -0.0408

0.0013 -0.0204

2.4L 0.0041 -0.06642.3L 0.0038 -0.0612 -0.0574 -0.1378

-0.0623 -0.1495-0.0600 -0.1440-0.0500 -0.1201

2.5L2.6L 0.0034 -0.0534

0.0040 -0.0640

2.8L 0.0018 -0.02782.7L 0.0027 -0.0418 -0.0391 -0.0937

-0.0260 -0.0625-0.0130 -0.0312

0.0 0.02.9L3.0L 0.0 0.0 0.0

0.0009 -0.0139

3.2L -0.0006 0.00833.1L -0.0003 0.0042 0.0039 0.0093

0.0078 0.01860.0116 0.02790.0155 0.0372

3.3L3.4L -0.0011 0.0166

-0.0008 0.0125

3.6L -0.0011 0.01663.5L -0.0014 0.0208 0.0194 0.0466

0.0155 0.03720.0116 0.02790.0078 0.0186

3.7L3.8L -0.0006 0.0083

-0.0008 0.0125

4.0L 0.0 0.0 0.03.9L -0.0003 0.0042 0.0039 0.0093

0.0 0.0

+ M B +MC


0.0 0.0

LoadPosition

coeff.

0.0 0.0 0.0 0.0

MB coeff. MC coeff.

0.2L -0.0050 0.01240.1L -0.0026 0.0065 0.0039 0.0094

0.0074 0.01780.0101 0.02420.0123 0.0296

0.3L0.4L -0.0087 0.0211

-0.0072 0.0173

0.6L -0.0099 0.02430.5L -0.0100 0.0243 0.0143 0.0343

0.0144 0.03450.0134 0.03220.0104 0.0250

0.7L0.8L -0.0074 0.0178

-0.0093 0.0227

0.9L -0.0041 0.0097 0.0056 0.0135

-0.2

-0.2

-0.1

-0.1

0.01 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 3

0.0

0.1

0.1

0.2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 3

Influence Line Ordinate BMD @ 1.9L


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Since the structure is symmetrical, influence lines are only drawn for load positionsupto 2.0L (i.e. Support C)

. en ng momen s ue oHA live loads (point loads)

Sections 1.2 The point loads due to HA live loads is the HA Knife - Edge load (KEL).of this report With reference to Clause 6.2.2 of BS 5400: Part II: 1978, 120KN of KEL is

recommended per notional lane.Based on this, the ultimate KEL per deck span is computed as 67.32KN/m.

a. Support moments

1.0L 0.0 0.0 0.0 0.0 0.0-0.0084 -0.0203-0.0167 -0.0401

1.1L 0.011.2L 0.02 -0.0061 -0.0306

-0.0034 -0.0150

1.4L 0.04 -0.0076 -0.06011.3L 0.03 -0.0074 -0.0468 -0.0242 -0.0580

-0.0278 -0.0666-0.0294 -0.0706-0.0208 -0.0500

1.5L 0.051.6L 0.06 -0.0061 -0.0747

-0.0074 -0.0720

1.8L 0.08 -0.0031 -0.05921.7L 0.07 -0.0047 -0.0722 -0.0069 -0.0166

0.0177 0.04250.0556 0.1333

0.0 0.01.9L 0.092.0L 0.0 0.0 0.0

-0.0015 -0.0329

2.2L 0.0013 -0.04592.1L 0.0006 -0.0230 -0.0223 -0.0536

-0.0446 -0.1071-0.0670 -0.1607-0.0726 -0.1743

2.3L2.4L 0.0021 -0.0747

0.0019 -0.0689

2.6L 0.0017 -0.06012.5L 0.0020 -0.0720 -0.0700 -0.1680

-0.0584 -0.1402-0.0456 -0.1095-0.0304 -0.0730

2.7L2.8L 0.0009 -0.0313

0.0014 -0.0470

3.0L 0.0 0.0 0.02.9L 0.0005 -0.0157 -0.0152 -0.0365

0.0 0.00.0045 0.01090.0091 0.0218

3.1L3.2L -0.0003 0.0094

-0.0001 0.0047

3.4L -0.0006 0.01873.3L -0.0004 0.0140 0.0136 0.0327

0.0182 0.04360.0227 0.05450.0182 0.0436

3.5L3.6L -0.0006 0.0187

-0.0007 0.0234

3.8L -0.0003 0.00943.7L -0.0004 0.0140

0.0-0.0001 0.0047

0.0136 0.03270.0091 0.02180.0045 0.0109

0.0 0.03.9L4.0L 0.0 0.0

-0.2

-0.2

-0.1

-0.1


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i. when first span loaded; apply KEL at 0.5L: = Pii. when second span loaded; apply KEL at 1.4L: = Piii. when third span loaded; apply KEL at 2.4L: = Piv. when fourth span loaded; apply KEL at 3.5L: = Pv. when all four spans are loaded = P

where P = design KEL = 67.5 KN/mTherefore M = KNm

b. Span momentsi. when first span loaded; apply KEL at 0.4L: = Pii. when second span loaded; apply KEL at 1.5L: = Piii. when third span loaded; apply KEL at 2.5L: = Piv. when fourth span loaded; apply KEL at 3.6L: = Pv. when all four spans are loaded = P

where P = design KEL = 67.5 KN/mTherefore M = KNm

2.6 Total Bending moments due toHA live loads + Dead loads

a. Support momentsSections 3.2.1.3 moments due to HA point loads = KNm HA + Gk 3.2.1.4 & 3.2.2.1 moments due to HA udl loads = KNm support mmts

of this report moments due to dead loads = KNm =Design HA + Dead loads = KNm -44.38KN/m

b. Span momentsmoments due to HA point loads = KNmmoments due to HA udl loads = KNm HA + Gkmoments due to dead loads = KNm support mmtsDesign HA + Dead loads = KNm =

133.93KN/m

2.7 HB Live loading2.7.1 Wheel Loads

This is done using a 45 - unit HB loading. A 45 - unit HB vehicle has 4 axles, carrying 4 wheels each.weight of each axle = 10KNTotal axle weight = 10KN /axle * 4Axles = 40KNFor a 45 - unit HB loading, wheel load = 45 * 40KN = 1,800KNTotal No. of wheels supported = 16No.Therefore, load exerted by each wheel = 1,800/16 = 112.50KN

Alternative method of calculating Load exerted by each wheel: = 2,500j Newtons (where j = no of units of HB load )

-41.51

122.167.222.63

132.01

-11.09

-4.04

122.159

-26.38

-0.2400-0.18340.0494

-0.0168

0.41520.49211.8146

-0.3908

0.49210.4152

-26.379


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= 2,500 * 45 / 1,000 = 112.5KN

Fig 3: Dimensions of a HB vehicle

Table 9,

R.C. H/Bk,

Reynolds & Stee-

dman. (10th ed)

AXLE AXLE AXLE AXLE Fig 4 : A unit of HB - vehicle configuration

2.7.2 DISPERSION OF WHEEL LOADSSect. 1.17(11)

Design of

R.C. Bridges F = Wheel load

a x = Contact length (varies: 0 - 380mm)by = width of tyre (varies: 75 - 450mm)

wheel load dispersal = A * B

The dispersal is carried out at an angle of 45 o through the concrete.The dispersal is treated separately between the concrete and the surfacing.

a. Load Dispersal Through Asphalt

1 , 0 0 0

1 , 0 0 0

1 , 0 0 0

3 7

5

75

DIRECTION OF TRAVEL

6,100 1,8001,800

1,8001,800 6,100

F

REINFORCEMENT

da x

a xb y

B=

b y+ 2

d

A = a x + 2d

B

A

Load = 1.1N/mm


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where, f = pressure in N/mm j = No. of units of HB loading = 45

h' = depth below surface at which load is acting

b. Load Dispersal Through Concrete

Use f = 1.1N/mm

2.7.3 MOMENTS DUE TO HB LIVE LOADSThe tyres of a HB vehicle are spaced at 1,000mm as shown in the sketch above.

a. SupportsThe point loads are placed at critical positions to produce maximum effect.

i. when 1st span only is loadedThe tyres of a HB vehicle are spaced at 1,000mm as shown in the sketch above.

Load Position BM ordinate BM But P = 112.5KNm0.5L P KNm0.9L P KNm

KNm

ii. when only 2nd span is loadedThe influence values are as tabulated below.Load Position BM ordinate BM But P = 112.5KNm

1.3L P KNm

1.7L P KNm KNm

ii. when only 3rd span is loadedThe influence values are as tabulated below.Load Position BM ordinate BM But P = 112.5KNm

2.4 P KNm2.8L P KNm

KNm

ii. when only 4th span is loaded

-0.2400 -27.00-0.0979 -11.01

0.0216 2.43

-0.1771 -19.92375

7.99

-0.1138 -12.8025-32.73

0.0494 5.5575

-38.01

f = 2,500j[ (2,500j/1.1) 0.5 + h' ]

f = 2,500 * 45[ (2,500 * 45/1.1) 0.5 + 0 ]

= 1.1N/mm

2

1

f = 2,500j[ (2,500j/1.1) 0.5 + 2h' ]

=2,500 * 45

[ (2,500 * 45/1.1) 0.5 + (2 * 0.05) ]= 0.97


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The influence values are as tabulated below.Load Position BM ordinate BM But P = 112.5KNm

3.2L P KNm3.6L P KNm

KNm

iii. When all four spans are loaded:Total moments due to HB load = -38.01KNm -32.73KNm + 7.99KNm -1.89KNm = KNm

. pan momenThe point loads are placed at critical positions to produce maximum effect.

i. when 1st span only is loadedThe tyres of a HB vehicle are spaced at 1,000mm as shown in the sketch above.

Load Position BM ordinate BM But P = 112.5KNm0.5L P KNm0.9L P KNm

KNm

ii. when only 2nd span is loadedThe influence values are as tabulated below.Load Position BM ordinate BM But P = 112.5KNm


KNm

ii. when only 3rd span is loadedThe influence values are as tabulated below.Load Position BM ordinate BM But P = 112.5KNm


KNm

ii. when only 4th span is loadedThe influence values are as tabulated below.Load Position BM ordinate BM But P = 112.5KNm


KNm

iii. When all four spans are loaded:

15.19875

-1.89

0.2425 27.280.1079 12.14

0.1920 21.60.1351

40.25

0.1715 19.293750.1863 20.95875

36.80

37.64

-0.0134 -1.5075

-64.64

0.1916 21.5550.1430 16.0875

39.42

-0.0034 -0.3825


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Total moments due to HB load = KNm

2.7.4 Total Bending moments due toHB live loads + Dead loads

a. Support momentsSections 3.2.1.4 moments due to HB point loads = KNm& 3.3.3 moments due to dead loads = KNm DesignHof this report support

Design HB + Dead loads = KNm = 71.64

b. Span momentsmoments due to HB point loads = KNmmoments due to dead loads = KNm design H

span mm

Design HB + Dead loads = KNm = 304.29

2.8 Design MomentsThe design moment is obtained by comparing the HA + Dead load momentswith those of the HB + Dead load moments.

a. Support MomentsHA + Dead Load Moments = KNmHB + Dead Load Moments = KNmDesign moment is that due to HB + Dead load moment = KNm

b. Span MomentsHA + Dead Load Moments = KNmHB + Dead Load Moments = KNmDesign moment is that due to HB + Dead load moment = KNm

DESIGN MOMENTSDesign support moments = KNm (Hogging)

Design span mmts = KNm (Sagging)

2.9 DESIGN FOR BENDING

DESIGN OF SPANDesign as a rectangular - beam

Design Moment = KNm

-68.68

154.112.63

156.75

-64.64-4.04

154.11

156.747122.159

-26.379-68.685-68.685

156.747

68.685

156.747

156.747


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Span Length = mm




width of beam web, bw = 1000 mm

Flange depth, hf = 175 mm m m

cover to reinforcement, d' = 0.0 mm 1 7 5



= mm


mm




1997 therefore, k =

since k' =


use z = d


fy = 410 N/mm



(As prov. = mm)


Apply T 25 @ 125 mm centres BOTTOM

(As prov. = mm)

Table A.7 Checks for minimum steel:

Mosley, Bungay As min = 0.13Ac/100 = mm

Hulse: r.c. design, 5th ed. Apply T 12 @ 250 mm centres as distribution bars

(As prov. = mm)

3.4.2 CHECKS FOR DEFLECTION

Table 3.10 a. Basic span - effective depth ratio =

BS8110:PART1: 1997 To avoid damages to finishes, modified ratio =

670

3,927

452

20.00

16.67

0.775

52

157

1,000

0.159

0.156

175

3,596

227.50

2,400


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and Asv/Sv provided =

CHECK FOR INTER-PHASE SHEAR

There's need to compute the shear force at the inter phase between the precast and insitu concrete.

Shear connectors will be required to prevent slippage between the insitu concrete and the

precast concrete sections to enable them act as a single composite unit.The slippage that occurs is a maximum at the supported end of the slabs, where the shear,V

and the rate of change of moment dm/dx are a maximum. This slippage to zero at midspan

where moments is at a maximum, and shear force, SF, V = 0 for a udl.

The shear connectors are the shear reinforcement for the maximum inter-phase shear force.

Since the inter-phase between the precast concrete and the in-situ concrete is located in the

horizontal direction, it implies that the maximum interphase shear under consideration is in

the vertical direction.Section 2.1.2 & Shear due to Precast Slab = KN

of this report Therefore, the design inter phase shear, V1 = KN

CHECKS:

clause 7.4.2.3 V1 must not exceed the lesser of

BS 5400:Part 4:1990 a. k 1 .f cu .Ls

b. v 1 .Ls + 0.7Ae.fy

where,

k1 is a constant depending on the concrete bond,obtained from Table 31, BS 5400:Part 4

fcu is the characteristic cube strenght of concrete

Ls is the length of theshear plane under consideration

v1 is the ultimate longitudinal shear stress in the concrete for shear plane under consideration

taken from Table 31, BS5400:Part 4

Ae is the area of fully anchored reinforcement per unit length crossing the shear plane under consideration

fy is the characteristic strenght of the reinforcement.

Table 31 k1 = 0.15 Ae = 314 mm

13.92

1.257

13.92


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3.0 DIAPHRAGM/TRANSVERSE BEAMS3.1 INTRODUCTION

For the purpose of this designs, diaphragm beams are used only at supportsas end beams to the various spans.They act as stiffeners, distribute concentrated loads, reduce local deflections,act as chords for the lateral system, and secure the aerodynamic stability of the structure.During construction, they are cast in two parts; one part as thte pre castpier cap and the second part is cast in-situ and integral with the pier cap beams.

A sketch of the slab/ deck, showing the location of diaphragm beams is asshown below:

DiaphragmBeams

Slab areasupportedby diaph -

ragm beam

BeamGirder

1 Area of slab - deck supported by intermediate diaphragm beam: = 2 * (0.5 * 1.40 * 0.70 ) + { 8 * (0.5 * 2.4 * 1.2)} = 12.50m 2

Designed E ra

Job No.

Checked

OUTPUT

KABIR ASSOCIATES

REF. CALCULATIONS

Project: Bridge No. 6; DABAI - MAHUTA - BABBAN DADA ROAD

Member: Diaphragm/Transverse Beam Date___december '04

1 7 . 8

0 m

1 7 . 8

0 m

11.0m

0.70m 0.70m2.40m 2.40m2.40m 2.40m

1 7 .

8 0 m

Page No.


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Member: Diaphragm/Transverse Beam Date___december '04 Page No.

3.2 LOAD ANALYSISa. Dead Loads, G ki. Self weight of beam = 24 * 0.45 * 1.00 * 11 = 118.80KN

Section 2.2 of ii. Dead loads from slab deck;this report 10.65KN/m 2 * 12.50m 2 = 133.13KN

TOTAL Gk = 251.93KN

b Live Loads, Q kTable 11; i. HA udlReynolds & Ste- Bridge span = 17.50medman : R.C Equivalent udl load = 10.5KN/m 2

Designer's H/bk And load per beam = 10.50 * 8.0 * 0.5 = 42.0KN/mwhere 8.0m = c/way width,

and 0.5 used because there are 2No.diaphragm beams per span.

Table 9 ; ii Foot path live load = 4.2KN/m 2

Reynolds & Ste- = 4.2KN/m 2 * 2No. = 5.6KN/medman : R.CDesigner's H/bk Total udl Live Loads = 47.6KN/m

Clause 6.2.2 iii. HA KELBS 5400: Part II 120KN is recommended as KEL per notional lane.

Total KEL = 360KN, since we have 3 notional lanes.

There fore Total KEL per beam = 360KN * 0.5 = 180KNEach beam has 4No spans.There fore Total KEL per span = 180KN/4 = 45KN

c. LOAD COMBINATIONSi. Design dead load = 1.50 * 251.93KN = 377.90KN

dead udl = 377.90KN/11m = 34.35KN/m

ii Design live loads(udl) = 1.50 * 47.60 = 71.40KN/mTOTAL UDL = 105.75KN/m

iii. Design concentrated live loads (KEL)

= 1.50 * 45.0 = 67.50KN

iv. LOADING DIAGRAMS

d. MOMENTS

216.01216.01 297.73 297.73 297.73

67.50KN 67.50KN 67.50KN 67.50KN

105.75KN/m


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I. Cantilever mmts (Negative)Mcant = 105.75 * 0.50 *0.70 2 = KNm

ii. Max Span mmtsTake mmts about the middle od the 2nd internal slab:Mspan = - (105.75 * 4.3 * 0.5) + (216.01 * 3.6 )

+ (297.73 * 1.2 ) - (67.50 * 2.4 ) = KNm

ii. Max Support mmtsTake mmts about the 3rd internal support,Msupp = (105.75 * 5.5 * 0.5) + 67.50 * ( 1.2 + 3.6 )

- ( 216.01 * 4.8 ) - ( 297.73 * 2.4 )

= KNm

1,069.55

25.91

2,366.21


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REF. CALCULATIONS



DESIGN FOR BENDING & SHEAR3.3.1 DESIGN FOR BENDING (MID - SPAN)Design as a rectangular - beam

Design Moment = KNm

Span Length = mm

Depth of slab/deck = mma. CALCULATION OF EFFECTIVE DEPTH, d




cover to reinforcement, d' = 30.0 mm


effective depth, d = h - (d' + f /2 + t) = mm

effective width, b = bw+(0.7L/5)mm




1997 therefore, k =since k' =


ii. z = d(0.5 + (0.25 - k/0.9)0.5

) = duse z = d


fy = 410 N/mm

As = M/(0.87fy.Z) = mm

Apply 6 T 25 Bottom

(As prov. = mm)Table A.7 Checks for minimum steel:


Hulse: r.c. design, 5th ed. Apply 4 T 16 Top (A's prov. mm )

3.3.2 CHECKS FOR DEFLECTIONTable 3.10 a. Basic span - effective depth ratio =

BS8110:PART1: 1997 To avoid damages to finishes, modified ratio =

b. Tensile reinforcement modification factor:

Table 3.11 i. M/bd = 1.86BS8110:PART1: ii. service stress, f s = 5f y As req. /8As prov. )*1/bb = N/mm1997 Note: iii. By interpolation, Modification Factor, MF

MF should not = 0.55 + (477 - fs)/(120(0.9+(M/bd)) = 1.22

be greater than 2 Use MF = 1.22

c. Modified span - effective depth ratio = MF * Basic span - effective ratio =

d. Actual span - effective depth ratio = L/d = 2.00

Since Modified L/d > Actual L/d,

Design okay w.r.t deflection.

16.67

20.33

400

255.49

2,945

650.00

804.25

20.00

1,069.550

2,400

250

2,643

0.9450.945

0.046

0.156

1 2 5 0

1,200


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REF. CALCULATIONS



3.3.3 DESIGN FOR SHEARi. Design shear Force



fcu = 40 N/mm

Checks: 0.8 (fcu) = N/mm design okay with respect to shear

iii. Obtaining the design concrete shear stress, vca. Compute 100As/(bvd) (should be 3.00 =

b. compute 400/d (should not be < 1.00) = Use 400/d = 1.00

c. By interpolation, obtain the design concrete shear stress, vc = 0.79(100As/(bvd)) 1/3 (400/d) 0.25 /1.25 = N/mm


a. if v < 0.5v c provide nominal linksb. if 0.5v c +v < (v c + 0.4) then A sv/S v = 0.4*b v/(0.87f yv)

c. if ( vc +0.4) < v < 0.8 (fcu) then A sv/S v = b v(v - v c)/(0.87f yv)


vc = N/mm v c + 0.4 = N/mm

i.e. 0.5v c +v < (v c + 0.4)


and Asv/Sv reqd =



and Asv/Sv provided =

3.4.1 DESIGN FOR BENDING (SUPPORTS)Design as a rectangular - beam

Design Moment = KNm

Span Length = mm






fire resistance = 2.0 hrs

cover to reinforcement, d' = 30.0 mm


effective depth, d = h - (d' + f /2 + t) = mm

effective width, b = bw+(0.7L/5)

mm




1997 therefore, k =since k' =


ii. z = d(0.5 + (0.25 - k/0.9) 0.5 ) = d

use z = d

1,200

400

0.869

0.869

0.103

0.156

2,366.213

2,400

250

1 2 5 0

0.524

0.937

0.620

0.537

0.449

0.537

298

0.620

5.060

0.614

0.333


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fy = 410 N/mm

As = M/(0.87fy.Z) = mm

Apply 8 T 32 TOP

(As prov. = mm)

Table A.7 Checks for minimum steel:


Hulse: r.c. design, 5th ed. Apply 4 T 16 BOTTOM

(A's prov. mm )

3.4.2 CHECKS FOR DEFLECTIONTable 3.10 a. Basic span - effective depth ratio =BS8110:PART1: 1997 To avoid damages to finishes, modified ratio =

b. Tensile reinforcement modification factor:

Table 3.11 i. M/bd = 4.11

BS8110:PART1: ii. service stress, f s = 5f y As req. /8As prov. )*1/bb = N/mm1997 Note: iii. By interpolation, Modification Factor, MF

MF should not = 0.55 + (477 - fs)/(120(0.9+(M/bd)) = 0.88

be greater than 2 Use MF = 0.88

c. Modified span - effective depth ratio = MF * Basic span - effective ratio =

d. Actual span - effective depth ratio = L/d = 2.00

Since Modified L/d > Actual L/d,

Design okay w.r.t deflection.

3.4.3 DESIGN FOR SHEARi. Design shear Force



fcu = 40 N/mm

Checks: 0.8 (fcu) = N/mm design okay with respect to shear

iii. Obtaining the design concrete shear stress, vca. Compute 100As/(bvd) (should be 3.00 =

b. compute 400/d (should not be < 1.00) = Use 400/d = 1.00

c. By interpolation, obtain the design concrete shear stress, vc = 0.79(100As/(bvd)) 1/3 (400/d) 0.25 /1.25 = N/mm


a. if v < 0.5v c provide nominal linksb. if 0.5v c +v < (v c + 0.4) then A sv/S v = 0.4*b v/(0.87f yv)

c. if (v c +0.4) < v < 0.8 (fcu) then A sv/S v = b v(v - v c)/(0.87f yv)


vc = N/mm v c + 0.4 = N/mm

i.e. 0.5v c +v < (v c + 0.4)


and Asv/Sv reqd =




0.620

0.697

650.00

804.25

281.63

14.58

298

0.620

1.097

0.449

5.060

1.340

0.333

0.697

20.0016.67

6,364

6,434


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OUTP


REF. CALCULATIONS

Job No.

Designed EChecked

Member: Bridge Beam/Girder Date___december '04

KABIR ASSOCIATES

Page

edman : R.C Equivalent HA udl is = 10.50KN/m 2

Designer's H/bk ie load per beam = 10.50 * 8.0/5 = 16.8KN/m8.0 used above represents the c/way width.

Total udl = 5.6KN/m + 16.8KN/m 2

= 22.40KN/m

4.1.4 Load combinations: (HA live Loads + Dead Loads) I. Table 1BS 5400:Part II: Loads factors: Dead = 1.15

Live = 1.50

ii. Clause 5.1.2 a. Design dead loads, udl, G k

BS 5400:Part II: = 28.24KN/m * 1.15 = 32.48KN/m ( per beam)

b. Design concentrated dead loads per beam, P D = 93.80KN * 1.15 = 107.87KN

c. Design live loads , udl, Q k = 22.40KN/m * 1.50 = 33.60KN/m

d. Design concentrated live loads ( KEL) = 72KN * 1.50 = 108KN

Loading diagram : HA + Dead Load

4.2 DESIGN MOMENTS & SHEARThe bridge deck and girders are required to support both static and moving loads.Each element of the bridge must therefore, be designed for the most severe conditions

1978

1978

740.07KN 2*740.07KN 2*740.07KN

66.08KN/m

107.87 2*107.87

2*107.87

108 108 2*107.87 108 2*107.87

2*740.07KN


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REF. CALCULATIONS

Job No.

Designed EChecked

Member: Bridge Beam/Girder Date___december '04

KABIR ASSOCIATES

Page

C AB &CBA arecarryover factors of ends A & B of member AB, while K BA is the

k'BA = [ 1 - (-0.905 * - 0.415)] * 10.50 = 6.56 = k'DE

iii. Distribution

bridges 6 computations

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