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OMPARITIVE STUDY OF SKEW DECK SLABS&ITH ORTHOGONAL PARALLELOGRAMESHES OF GRILLAGE ANALOGY

ACHUTHA.oll No 05011D 2002

GUIDED BY.MRS P SRI LAKSHMI

DEPT OF CIVIL ENGINEERING,JNTU HYDERABAD


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YPES OF BRIDGE DECKS

hallow type bridge decks Slab type

Beam and slab type

Voided slab bridge

ellular type bridge decks Single cell bridge

Multiple cell bridge

Multispan bridge with steel boxesMultispan bridge with concrete boxes


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OADING ON BRIDGE:ead Loads ( , ,Permanent stationary loads wearing coat kerb parapets

.,)etc :ive Loads IRC Class A Loading single Lane and Two Lanes

IRC Class 70R Loading

,0R train loading weighing 100 tones through seven axles one,xle of 8 tones two axles of 12 tones each and four axles of

.7 tones each:mpact loading

Value of impact load is a percent of live load depending upon

the material used in the construction of the deck of the

,bridge type of loading and bridge span

, , :oot Way Kerb Railing and Parapet Live Load .For effective span of 7 5 m or less the foot way live load

considered is 400 kg m-2


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TEPS FOLLOWED IN THEETHOD OF GRILLAGE ANALYSISIdealisation of physical deck into equivalent

grillage

Evaluation of equivalent elastic inertia of members

of grillage

Application and transfer of loads to various nodes

of grillage

Determination of force responses and design

envelopes and

Interpretation of results


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DEALIZATION OF PHYSICAL DECK INTOQUIVALENT GRILLAGE.1 Direction of longitudinal grid line is parallel to free edge of

.deck

.2 .Longitudinal grid lines at either edge placed 0 3 D from the edge

, .for slab bridges where D is the depth of the deck

.3 .Longitudinal gird lines are placed along the centre of each bearing

.4 .Minimum of five grid lines are adopted in each direction

.5 .Grid lines are taken at right angles

.6 .Grid lines in general should coincide with the CG of the section

, , .Some shift if it simplifies the idealisation can be made

.7 ,For better results the ratio of the grid spacing in the

.longitudinal and transverse directions should lie between 1 0 to

. .2 0


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b/d 1 1.2 1.5 2 2.5 3 4 5 10 0.141 0.166 0.196 0.229 0.249 0.263 0.281 0.291 0.312 0.333

or rectangular sections = bd >here b d


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UMERICAL ANALYSISNPUT DATAridge data

Deck slab thickness 200 mm

- -Girder to girder spacing .1 875 m

Road width .7 5 m

Effective span 20 m


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Longitudinal Girders1880

800 200

70 150

70

250 1500

760

70

250

300

S.NO AREA B H K KBH3 IZZ Y AY AY2

1 120000 800 150 0.294 7.937E+08 2.250E+08 75 9000000 675000000

2 4900 70 70 0.123 2.961E+06 1.334E+06 173 849333.3333 147217777.8

3 225000 250 900 0.275 3.867E+09 1.519E+10 600 135000000 81000000000

4 1750 25 70 0.258 2.826E+05 4.764E+05 1027 1796666.667 1844577778

5 75000 300 250 0.158 7.422E+08 3.906E+08 1175 88125000 1.03547E+11

426650 IXX= 5.406E+09 1.580E+10 3050 234771000 1.87214E+11

YC=A*Z/A = 550 mm Ig=Iself+A*Y2 = 0.2030m4

Y_TOP = 550 mm IN.A(ZZ) =IG-A*YC2 = 0.0738m4

Y_BOTTOM = 750 mm Ixx = 0.0054m4

I = 0.0738m4

Z_TOP = 0.1342m3

Z_BOTTOM= 0.0985m3

PROPERTIES FOR GRILLAGE ANALYSIS

COMPONENT

800x 150

70x 70

250x 900

25x 70

300x 250

1880

800

70

70

70

1500

150

760

250

200

300

250


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Composite section

S.NO AREA B H K KBH3 IZZ Y AY AY2

1 376000 1880 200 0.311 4.677E+09 1.253E+09 100 37600000 3760000000

2 120000 800 150 0.294 7.937E+08 2.250E+08 275 33000000 9075000000

3 4900 70 70 0.123 2.961E+06 1.334E+06 373 1829333.333 682951111.1

4 225000 250 900 0.275 3.867E+09 1.519E+10 800 180000000 1.44E+11

5 1750 25 70 0.258 2.826E+05 4.764E+05 1227 2146666.667 2633244444

6 75000 300 250 0.158 7.422E+08 3.906E+08 1375 103125000 1.41797E+11

802650 IXX= 1.008E+10 1.706E+10 4150 357701000 3.01948E+11

YC=A*Z/A = 446 mm Ig=Iself+A*Y2 = 0.3190 m4

YTS 446 mm IN.A(ZZ) =IG-A*YC2 = 0.1596 m4 Y_TOP = 246 mm Ixx = 0.0101 m4

Y_BOTTOM 1054 mm

I C = 0.1596 m4

Z_TS= 0.3581 m3

Z_TOP = 0.6497 m3

Z_BOTTOM= 0.1514 m3

Intermediate slab members

1.8800

A = 0.3760 m2 0.200

Iz = 1.8800 x 0.2003 =

0.00125m412

Ix = 2 x 0.00125 = 0.00251 m4


300x 250

COMPONENT

1880x 200

800x 150

70x 70

250x 900

25x 70


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End slab members0.940

A = 0.1880 m2 0.200

Iz = 0.9400 x 0.200 3 = 0.00063 m4

12

Ix = 2 x 0.00063 = 0.00125 m4

Transverse Members

End Crossgirder 1.000

0.200

A Yt Ayt Ayt2 Iself

0.2000 0.1000 0.0200 0.0020 0.0007 1.050

0.3150 0.7250 0.2284 0.1656 0.0289

0.5150 0.2484 0.1676 0.0296

0.300

Yt = 0.2484 = 0.4823 m

0.5150

Iz = 0.0296 + 0.1676 - 0.2484 x 0.4823 = 0.0774 m4

Ix = 0.276 x 1.000 x 0.200 3

+ 0.294 x 1.050 x 0.300 3

= 0.0105 m4



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Intermediate Crossgirder 2.0000.200

A Yt Ayt Ayt2 Iself

0.4000 0.1000 0.0400 0.0040 0.0013 1.0500.3150 0.7250 0.2284 0.1656 0.0289

0.7150 0.2684 0.1696 0.0303

0.300

Yt = 0.2684 = 0.3753 m

0.7150

Iz = 0.0303 + 0.1696 - 0.2684 x 0.3753

= 0.0991 m4

Ix = 0.276 x 2.000 x 0.200 3

+ 0.294 x 1.050 x 0.300 3

= 0.0128 m4

Slab members

2.000

A = 0.400 m2 0.200

Iz = 2.000 x 0.200 3 = 0.00133 m4

12

Ix = 2 x 0.00133 = 0.00267 m4



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LASSIFICATION OF GRILLAGEMODELLING

15 degree skew parallelogram mesh 15 degree skew orthogonal mesh

30 degree skew parallelogram mesh30 degree skew orthogonal mesh

45 degree skew parallelogram mesh 45 degree skew orthogonal mesh

arallelogram mesh rthogonal meshOADING DATA CONSIDERED

RC Class 70 R train loading weighing 000 KN wo lanes of IRC Class A loading each weighing 54 KN


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OUTPUT ( ), ( )Decks are evaluated for bending moment BM shear force SF and

( )torsional moment TM for parallelogram and orthogonal meshes

, ,Variation of BM SF TM for skew angles 00, 50 , 150 , 300, 45 0

studied


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ESULTS ANDDISCUSSION


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DENTIFICATION OF CRITICALGIRDER

. ( ) :Fig 5 0 i Variation of Bending Moment values as a function of span fordifferent Girders for skew angle 00 in parallelogram mesh with IRC Class

70R wheel loading


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70R wheel loading


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70R wheel loading


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70R wheel loading


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70R wheel loading


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. ( ) :Fig 5 0 ii Variation of Shear Force as a function of span for differentGirders for skew angle 00 in parallelogram mesh with IRC Class 70R wheel

loading


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. ( ) :Fig 5 1 ii Variation of Shear Force as a function of span for differentGirders for skew angle 50in parallelogram mesh with IRC Class 70R wheel

loading


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. ( ) :Fig 5 2 ii Variation of Shear Force as a function of span for differentGirders for skew angle 150in parallelogram mesh with IRC Class 70R wheel

loading


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loading


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loading


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. ( ) :Fig 5 0 iii Variation of TorsoinalMoment as a function of span fordifferent Girders for skew angle 00 in parallelogram mesh with IRC Class

70R wheel loading


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70R wheel loading


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70R wheel loading


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. ( ) :Fig 5 3 iii Variation of TorsoinalMoment as a function of span for differentGirders for skew angle 300 in parallelogram mesh with IRC Class 70R wheel

loading


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70R wheel loading


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DENTIFICATION OF LOADS

. . ( ) :Fig 5 5 i Shows Bending Moment values for two lanes of IRC Class A loadingand IRC Class 70R wheel loading for skew angle 00 parallelogram mesh


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. . ( ) :Fig 5 6 i Shows Bending Moment values for two lanes of IRC Class A loadingand IRC Class 70R wheel loading for skew angle 50parallelogram mesh


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. . ( ) :Fig 5 8 i Shows Bending Moment values for two lanes of IRC Class A loadingand IRC Class 70R wheel loading for skew angle 150 parallelogram mesh


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. ( ) :Fig 5 5 ii Shows the variation of Shear Force for IRC Class 70R wheelloading and two lanes of IRC Class A loading for skew angle 00parallelogram

mesh


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mesh


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mesh


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mesh


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mesh


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. . ( ) :Fig 5 5 iii Shows the variation of Shear Force for two lanes of IRC Class Aloading and IRC Class 70R wheel loading for skew angle 00parallelogram mesh


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. . ( ) :Fig 5 6 iii Shows the variation of Shear Force for two lanes of IRC ClassA loading and IRC Class 70R wheel loading for skew angle 50parallelogram

mesh


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. . ( ) :Fig 5 7 iii Shows the variation of Shear Force for two lanes of IRC Class Aloading and IRC Class 70R wheel loading for skew angle 150parallelogram

mesh


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mesh


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mesh


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UANTITATIVE COMPARISON SHEAR FORCEOR PARALLOGRAM MESH AND ORTHOGONALMESH

. ( ):Fig 5 10 ii Shows the variation of Shear Force for parallogrammesh andorthogonal mesh for skew angle

50


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UANTITATIVE COMPARISON TORSIONALOMENT FOR PARALLOGRAM MESH ANDRTHOGONAL MESH

. ( ):Fig 5 10 ii Shows the Variation of TorsionalMoment for parallogram mesh andorthogonal mesh for skew angle 50


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UANTITATIVE COMPARISON BENDINGOMENT FOR PARALLOGRAM MESH ANDRTHOGONAL MESH

. ( ):Fig 5 10 i Shows variation of the Bending Moment for parallogram mesh andorthogonal mesh for skew angle 50


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. ( ):Fig 5 11 ii Shows the variation of Shear Force for parallogram mesh andorthogonal mesh for skew angle 150


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. ( ):Fig 5 11 iii Shows the variation of TorsionalMoment for parallogram mesh andorthogonal mesh for skew angle 150



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. ( ):Fig 5 11 i Shows the variation of Bending Moment for parallogram mesh andorthogonal mesh for skew angle 150



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. ( ):Fig 5 12 ii Shows the variation of Shear Force for parallogram mesh andorthogonal mesh for skew angle 300


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. ( ):Fig 5 13 ii Shows the variation of Shear Force for parallogrammesh andorthogonal mesh for skew angle 450


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, ,UANTITATIVE COMPARISON OF BM TM SFOR PARALLELOGRAM AND ORTHOGONALMESHES

. ( ):Table 5 15 ii Values of Shear Force with respect to skew angels fororthogonal mesh


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. ( ):Table 5 15 iii Values of Torsional Moment with respect to skew angels fororthogonal mesh



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. ( ):Fig 5 15 i Shows the variation of Bending Moment with respect to skew angles for IRC70R wheel loading



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UMMARY AND CONCLUSIONS

Girder 1 closest to the kerb is the critical girder

Amongst the two loads considered IRC 70R wheel loading is

chosen for further analysis

, , ( %)Values of BM TM SF are same within 2 to 3 for skew angles

less than 150 .both for parallelogram and orthogonal meshesHence parallogram mesh should be considered for further

.analysis

For skew angles greater than 150 orthogonal mesh should be

, ,chosen for further analysis since the values for BM TM SF are( %) .higher 8 to 30 for parallogrammesh Such choice ensures

.safety and economy

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