Effect of Skewness on Different Design Parameters In Simply Supported RC T- Beam BridgesKamlesh Parihar [M.Tech (Structural Engg. student.), Civil Engg. Dept., IIT Roorkee]&Dr. N M Bhandari [Professor, Civil Engg. Dept, IIT Roorkee](1) ABSTRACTA very limited study has been carried out in the field of skew bridges and even that does not hold much relevance in Indian perspective due to difference in design live load standards and type of bridges being built there. Therefore it does not provide any help to designers regarding the quick estimation of design bending moments and shear forces which are of prime interest. In this paper an attempt has been made to study the effect of skewness directly on the design parameters i.e. B.M, Shear Force and Maximum Reaction in simply supported RC T-Beam 2 lane bridges. For this study bridges of practical dimensions and span range are considered. The paper present design factors for quick estimation of forces thus obviating the need of struggling with theories. Further to facilitate estimation of design forces i.e. BM, shear force and reaction, at critical locations design charts have been proposed.For this purpose a parametric study of Simply Supported 2-Lane T-Beam Bridge has been performed in STAAD PRO. The parameters varied were span and skew angle. The effect of same was observed on maximum live load bending moment, maximum live load shear force and maximum live load reaction at critical locations in terms of Moment Distribution Factor (MDF), Shear Coefficients and Reaction Coefficients. Live Load Class 70R Tracked, Class 70R Wheeled and Class A were applied as per IRC 6 guidelines. The spans used were 12 m, 15 m, 18 m and 21 m. The skew angles were taken at an interval of 100 starting from 00 up to a maximum of 400. Bridges with skew angle more than 400 are rare.From the study it was observed that as the skew angle increases from 00 to 400 there is a consistent reduction in Moment Distribution Factor (MDF) of the outer longitudinal girder of bridge. For 12 m span and class 70R wheeled loading the reduction in MDF of outer girder on eccentric side of loading was 17.5 % at a skew angle of 400 with respect to the straight bridge (i.e. no skew). For Class 70R Tracked, the reduction was 14.57 % where as it was 10.08 % for Class A loading. Similar trend of reduction in MDF were observed for 15m span, 18 m span and 21 m span. This suggests that skew bridges designed, ignoring the skew effect are conservative with respect to the bending moment. The effect of skew angle was also studied on the shear coefficients and reaction coefficients and the results were surprising. The shear coefficients and reaction coefficients increases almost linearly with skew angle and span. The increase in the reaction coefficient is as high as 61 % for Class A loading at a skew angle of 400 and span 12 m. For Class 70 R Tracked and 70 R Wheeled loading, the increase in reaction coefficients is around 40 % for all spans. Similarly increasing trends were obtained for shear coefficients. Hence it can be concluded that proper estimation should be made in the live load shear and live load reactions when designing skew bridges. Further, the forces estimated for a right bridge, ignoring skew angle would under estimate the same and hence could lead to failure.Keywords: Skew angle, distribution factor, T Beam Bridge, grillage analogy, bending moment, shear force, and support reaction(2) INTRODUCTIONMost of the bridges in older days were straight, and skew bridges were averted as far as possible. Lack of knowledge about the structural behavior and construction difficulties were obvious reasons contributing to the designers choice to favor straight bridges rather than skew bridges. But in the current scenario, with the increasing population, high cost of land acquisition for approach roads and other practical constraints, there is an increasing trend of providing skew bridges at oblique intersections. Also, in congested cities due to lack of space, bridges have to be skew in nature if the intersection is not orthogonal. Hence there is need to study the behavior of skew bridges so as to facilitate quick estimation of design BM, shear force and support reactions and thus obviating the need of a rigorous analysis. The results have been presented in the form of ready to use design charts. (3) METHODOLOGYWith the advancement in modeling and computing facilities world over, it has now become possible to perform a near exact analysis of any kind of bridge. The commercially available software packages like ANSYS, ABAQUS, SAP etc has made it possible to use the methods of Finite Element Analysis, etc with much ease. In spite of the fact that these methods are highly efficient and accurate, these methods are often criticized also for the reason that the efficiency is achieved at the cost of exorbitant computations and time requirement. Hence, care must be taken in selection of the appropriate method of analysis, appropriate to the type of bridge depending upon the required accuracy in the parameters under investigation. Grillage Analogy on the other hand presents a sufficiently accurate method to analyze slab-beam bridges for estimation of design bending moment, torsion, shear force etc. It is a comparatively simpler method to analyze the bridge decks and gives an excellent visualization of distribution of forces among different longitudinal and transverse girders in a bridge. It can easily handle complicated geometric features of a bridge such as skew, edge stiffening, and deep haunches over support, continuous and isolated supports etc with ease. It is a versatile method and can also take into account the contribution of kerb beams, footpaths and the effect of differential sinking of girder ends over yielding supports. The method has proved to be reliable and versatile for a wide variety of bridge decks. It do possess some limitations such as inability to take into account the effects like shear lag, warping and distortional effects for which more sophisticated methods like FEM have to be used. Basically grillage analogy method uses stiffness approach for analyzing the bridge decks. The whole bridge deck is divided into no of longitudinal and transverse beams. The intersection of longitudinal and transverse beams is called as node. Each node has six degrees of freedom, namely 3 rotations and three translations. But if we assume the slab to be highly stiff in its own plane, which is actually the case in most of the bridges, the degrees of freedom are reduced to three i.e. 1- vertical translation and 2-rotations about the axes in plane of the bridge deck. The properties of cross-section such as beam moment of Inertia about their principal axes, Torsional constant, Effective Area etc are calculated and the grid is solved for the unknown degrees of freedom using the matrix stiffness method. After the nodal displacements are known, the forces in the grid members are calculated using the force displacement relationship. The overall equations of equilibrium are given below.{F} = [K]{ U} For Structural Level{f} = [k]{ u} For Member LevelWhere, F represents the unknown reaction/load vector (BM, Torsion, SF), K is the structure stiffness matrix and U is the vector of nodal displacement.Conceptually, grillage analogy method attempts to disretize the continuous or dispersed stiffness of bridge and concentrates it into discrete longitudinal and transverse members. The degree of structural similarity between the original bridge and grillage so formed depends on the fineness of the grid formed. But practically it is observed that after a certain degree of fineness in the grillage mesh, law of diminishing returns is followed and further reducing the size of grillage doesnt significantly add to the accuracy. The choice of the designer is the best judge to decide grid fineness.The solution of grillage mesh involves a large no. of equations, which is beyond the scope of the manual solution. Hence it becomes mandatory to take aid of computer programs in the grillage analogy method. Commercially available software package like Staad Pro, are very helpful in analyzing bridges with grillage analogy method considering all the 6-DOFs i.e. 3 translations and 3 rotations per node. The use of same has been made in this study.Gridlines, their locations, direction and properties:Gridlines are the beams representing the discretized stiffness and other structural properties of the slab portions which it replaces. Strictly speaking, gridlines represents the lines of strength. So they must be provided at all the locations where there is concentration of stiffness. Therefore gridlines must be provided at the centre of each longitudinal and transverse girder, running along them. Where isolated bearings are provided, gridlines should also be provided along the lines joining the bearings. Generally gridlines must coincide with the centre of gravity of the section but some shift may be permitted for the ease of calculation. A few guidelines for the Grillage Idealizations for slab T beam bridges are as follows.(a) Generally longitudinal gridlines are parallel to the free edge of Deck. (For straight bridges without skewness)(b) For skew Bridges with skew angle less than 15o the transverse girders are provided parallel to the support lines so the gridlines should also be parallel to the support lines. But for skew angles exceeding 15 degrees, where transverse diaphragms perpendicular to the longitudinal girders are provided as they are found to be more efficient in transverse load distribution amongst longitudinal Girders. Hence gridlines should be along the transverse diaphragms i.e perpendicular to the longitudinal beams.(c) End transverse gridlines must be provided along the center lines of bearings on each side of span.(d) For determining the sizes of gridlines aid form relevant IRC code can be taken. (4) Parametric study of RC T Beam BridgeA 2 lane RC T-Beam Bridge has been chosen for the study. Spans have been varied from 12m to 21 m with an increment of 3m. The no. of longitudinal girders has been kept as three. Cross Girders are hindrance in the speed of construction as they pose practical problems in construction. So their spacing is generally kept not less than 4 m and for this reason the spacing of cross girders is kept between 4.5 m to 6 m. For skew bridges of 00 and 100, the cross girders (& transverse gridlines) are parallel to the abutment, while for 200, 300, and 400, the cross girder (& transverse gridlines) are provided orthogonal to longitudinal girders for the reason explained in above section. The cross-section shown in Fig 1 has been chosen. The sizes of longitudinal and cross beams is given in Table 1

Figure 1Table 1. Dimensions of Longitudinal and Transverse girdersLongitudinal BeamTransverse Beams

S.NoSpan(m)B (mm)D (m)Intermediate Cross BeamEnd Cross Beam

B (mm)D(m)B(mm)D(m)

1123501.2 3000.963001.2

215 3501.53001.23001.5

318 4001.83001.443001.8

421 4002.13001.683002.1

GRILLAGE IDEALIZATION OF BRIDGE:In grillage analogy method, the continuous bridge deck is discretized into a no of longitudinal and transverse beams. Since the distribution of bending stress in the flange of the T-Beam bridge is not uniform as suggested by the simple bending theory, so the effective width concept is used to define the flange of the T-section. For this purpose assistance from IRC 21: 2000 clause 305.15 was sought in the selection of sizes of T-Beam. It suggests be = bw + lo / 5IRC 21: 2000 clause 305.15be is effective width of T-Beam; bw is width of T-Beamlo is distance between the points of contraflexure.Exact modeling of bridge is difficult so some approximations were made in grillage idealizations and the slab was assumed to be of uniform thickness taking partially into account the effect of kerbs. Figure 2 shows the grillage idealization of the bridge in longitudinal direction. Same method was used for discretizing the bridge in transverse direction also.

Figure 2 Grillage idealization in Longitudinal Direction All dimensions in mm(5) LIVE LOAD (LL) APPLICATION ON THE BIRDGEThe Bridge deck was analyzed for Class A, Class 70R Tracked and Class 70R Wheeled vehicles. As per IRC 6: 2000 Table 2, a two lane bridge should be loaded with either one lane of Class 70R or two lanes of Class A. For the transverse placement of the vehicle, guidelines of IRC 6: 2000 clause 207 were followed which suggests that the minimum spacing of vehicle form the face of the kerb is 1.2 m for Class 70R and 0.15 m for Class A loading. Many other trials of the transverse placement of vehicles were also made to obtain the maximum LL moments and maximum LL shear force and maximum LL reactions in the bridges. Following observations were made during these trials.(a) For Class A, Class 70R Wheeled and 70R Tracked the maximum bending moment in the bridge is always obtained in the outer girder when the vehicle is placed at minimum spacing from the kerb.(b) For maximum bending moment in the middle girder the vehicle is placed both eccentrically and centrally as it does not always occur for same transverse placement loads.(c) For all Class of loading, the maximum LL shear occurs in the outer girder, near the obtuse corner.(d) For Class 70R Wheeled and 70R Tracked the maximum LL support reaction occurs in the middle girder when the vehicle is placed centrally.(e) For Class A the maximum LL support reaction is obtained in the outer girder when the vehicle is placed at minimum spacing form the kerb.The loads were placed accordingly to obtain maximum bending moment, maximum shear and reaction in the bridge.Idealization of VehicleThe details of vehicles have been given in IRC 6: 2000. The Class 70 R Tracked vehicle has been simulated as train of 20 equal point loads as shown below in figure 3. The load values shown in the longitudinal details are the axle loads and since there are two wheels on each axle, so the values are halved when seen in the transverse view.

Figure 3 Idealized 70R Tracked(6) Results and Discussion: Bridges of span 12 m, 15 m, 18 m and 21 m were analyzed for skew angles 00, 100, 200, 300 and 400. The vehicles were placed as explained section 5 and maximum moment and maximum shear forces were obtained in G1, G2 and G3, whereG1 is the outer longitudinal girder on the eccentric side near to live load vehicle.G2 is the middle longitudinal girderG3 is also the outer longitudinal girder on the other side of eccentrically placed load.The moments, shear force and reactions so obtained are converted into MDF, shear coefficients, and reaction coefficients as explained below.The Moment Distribution Factor (MDF) has been defined as

The maximum moment in the girder is the maximum live load moment in that girder due to specified vehicle.The maximum span moment of right bridge can be obtained by carrying out a simple beam analysis of same span and running the specified IRC vehicle over it.The SHEAR COEFFICIENTS and REACTION COEFFICIENTS are obtained by dividing the maximum LL shear and maximum LL reaction with total load of the respective vehicle. For 70 R Tracked and 70 R Wheeled vehicles the maximum shear and reactions are divided by 700 kN and 1000 kN respectively, while for class A loading it is to be divided by 2x 554 kN = 1108 kN as two Class A trains can be accommodated in the bridge.12 m span Effect of Skew on MDFFigure 4, Figure 5 and Figure 6 shows the variation of MDF of G1, G2 and G3 with skewness. The MDF for G1 and G3 are obtained by placing the vehicle eccentrically, while For G2 it is obtained by picking the severe values of eccentric and central placement of load. It is observed that for G1 the MDF falls consistently in a non linear fashion for all class of loading, while the MDF of G2 remains nearly constant for 70 R Tracked and Wheeled loading. For G3 there is a marginal increment with skew angle. At 400 skew the MDF in G1 due to 70 R tracked vehicle decreases from 0.482 to 0.412 which is 14.5 % while for 70 R wheeled it decreases from 0.491 to 0.405 which is 17.5 %. For Class A loading the reduction was 10 % at 400 skew. Figure 4: Variation of MDF with Skew Angle (12m span 70 R TR) Figure 5: Variation of MDF with Skew Angle (12m span 70 R WH)

Figure 6: Variation of MDF with Skew Angle (12m span Class A)Effect of Skew on Shear Coefficients and Reactions CoefficientsThere is a increase in shear coefficient and reaction coefficient with skewness as depicted in the figure7 and figure 8. The maximum increases in reaction coefficient is observed in class A 61 % while for 70 TR and 70 Wheeled it is around 40 % at a skew of 400. For Class A, Class 70 Tracked and Class 70 R wheeled the increase in shear coefficients is 38.3 %, 30.66% and 27.6%. Figure 7: Variation of shear coefficient with Skew Angle (12m) Figure 8: Variation of reaction coefficient with Skew Angle (12m) 15 m spanEffect of Skew on MDFThe placement of live load is similar to 12 m span (also explained in section 5). The MDF in G1 falls consistently in a non-linearly manner with skew while for G2 it is almost constant up to 300 skew and at 400 skew a decrease is observed for 70 R Tracked and 70 R wheeled. The MDF in G2 falls in similar manner to G1 for Class A loading. The reduction in MDF for G1 at 400 skew is 10.1% for 70 R Tracked, 12.36 % for 70 R Wheeled and 7.69 % for Class A vehicle. There is a increase in MDF of G3 with skew. Figure 9: Variation of MDF with Skew Angle (15m span 70 R TR) Figure 10: Variation of MDF with Skew Angle (15m span 70 R WH)

Fig 11 Variation of MDF with Skew Angle (15m span Class A)Effect of Skew on Shear Coefficients and Reactions CoefficientsBoth shear and reaction coefficients increases with skew in a linear fashion. The increase in shear coefficients is 25.2 %, 28.4% and 21.65% at a skew angle of 400 for class 70 R tracked, class A and Class 70 R wheeled vehicles. For reaction coefficients the increase is 40.6 % for 70 R Tracked, 49.9 % for Class A and 43.1 % for Class 70 R loading. Figure 12: Variation of shear coefficient with Skew Angle (15m) Figure 13: Variation of reaction coefficient with Skew Angle (15m) 18 m spanEffect of Skew on MDFSimilar trends have been observed as in 15 m span. The MDF of G1 for all class loadings decreases with increasing skew with a maximum fall of 10.5 % for class 70 R Wheeled vehicle. For G2, the MDF almost remains constant for 70 R Tracked and 70 R Wheeled loading. For class A loading the MDF for G2 starts falling steeply after 200. Figure 14: Variation of MDF with Skew Angle (18m span 70 R TR) Figure15: Variation of MDF with Skew Angle (18m span 70 R WH)

Figure 16: Variation of MDF with Skew Angle (18m span Class A)Effect of Skew on Shear Coefficients and Reactions CoefficientsThe shear coefficients and reaction coefficients shows similar increasing trend as of other spans. The maximum increase in reaction coefficients is 44.2 % for 70 R wheeled loading and for shear coefficient it is 26.5% for class A loading. Figure 17: Variation of shear coefficient with Skew Angle (18m) Figure18: Variation of reaction coefficient with Skew Angle (18m) 21 m spanEffect of Skew on MDFThe effect of skew on MDF is less as compared to 12 m span. The fall in MDF for G1 is small and its maximum value is 9.9% for 70 R wheeled loading at a skew of 400. For G2 the MDF almost remains constant for 70 R tracked and 70 R wheeled vehicle. For class A it shows a fall after 300. The reduction in MDF is higher at higher skew. Figure 19: Variation of MDF with Skew Angle (21m span 70 R TR) Figure 20: Variation of MDF with Skew Angle (21m span 70 R WH)

Figure 21: Variation of MDF with Skew Angle (21m span Class A)Effect of Skew on Shear Coefficients and Reactions CoefficientsHere also the shear and reaction coefficients increase linearly. The maximum increase in shear coefficient and reaction coefficient is 27.5 % and 38.8 % for class 70 R Wheeled loading. Figure 22: Variation of shear coefficient with Skew Angle (21m) Figure 23: Variation of reaction coefficient with Skew Angle (21m) 6.1 Variation of Span Moment with spanTo know the behavior of bending moment with span, the span moment are plotted against the span. The span moments are used to normalize the girder moment and convert to MDF. It is obtained by carrying out simple beam analyses of same span with specified vehicle and observing the maximum moment. The spans moments are calculated for at 12m, 15m, 18m and 21m spans and plotted below (Figure 24). Figure shows that the variation of moment with respect to span is linear.

Figure 246.2 Variation of Shear coefficients and Reactions coefficient with spanShear coefficients and reaction coefficients have a linearly increasing trend with span also. A typical plot has been given in figure 25 and 26 to substantiate this. Table 3 gives the values of shear and reaction coefficients for all spans and skew angle. Figure 25: Variation of shear coefficient with span (70 R wheeled) Figure 26: Variation of reaction coefficient with Span (Class A) 6.3 Variation of percentage reduction in MDF with spanAs the span increases the percentage reduction in MDF (between 00 skew and 400 skew) for G1 also reduces. Table 2 gives the values of percentage reduction in MDF for different class loadings with span.SpanClass A70 R TR70 R WH

12 m10.0814.5717.5

15 m7.6910.112.36

18 m7.439.410.49

21 m6.348.169.93

Table 2 Percentage Reduction in MDF (in G1) b/w 00 & 400 skew

6.4 Design Procedure to Estimate maximum LL moment in girder, maximum LL shear and maximum LL reaction in skew Bridges.In the design of any skew bridge, analyses are done for dead loads and live loads. Skew angle has little effect on dead load analyses, and hence it can be carried out in the routine way as for right bridges. For live load analyses the study conducted above can be used to directly estimate the key parameters i.e. maximum live load moment, maximum live load shear and maximum live load reaction in bridge of same configuration and cross section, span in between 12 to 21 m and skew angle between 00 and 400. This is explained below.Suppose in a bridge of skew angle say and span L, the maximum LL moment in G1 and G2, and maximum LL shear and maximum LL reaction is to be obtained. Following steps are to be followed.(1)From Figure 4 to 21, obtain values of MDF at required skew angle and for specified vehicle class at control points (i.e. 12 m, 15m, 18m and 21m) between which L lies.(2) Multiply the MDF of control points with respective span moment given in Fig 24.(3) From the values at control points, interpolate the value of maximum LL moment at span L.(4) To obtain the maximum LL shear and maximum LL reaction perform double interpolation at required span and skew angle form the values of shear coefficients and reactions coefficients given in table 4.To substantiate the validity of the proposed distribution factors three bridges were taken whose span and skew angles were different from those considered in the parametric study. They were analyzed in STAAD PRO using grillage analogy method and the results were compared with those obtained from charts and tables proposed in the study (Kamlesh, 2011). A linear interpolation of coefficients has been done within the two nearest values for which the distribution factors are given in the charts. Comparisons of results are given below.

Table 3: Comparison of Analytical and Predicted Values of Design Forces.Case 1Span = 20, Skew angle = 20

70 R TrackedClass A70 R Wheeled

ParameterStaad AnalysisCharts & Tables% ErrorStaad AnalysisCharts & Tables% ErrorStaad AnalysisCharts & Tables% Error

Moment (kN-m)14711462.6-0.57126512710.4716211613.6-0.46

Shear (kN)308310.80.91301306.91.96369.13710.51

Reaction (kN)460.4453.6-1.48380384.51.18460450-2.17

Case 2Span = 19, Skew angle = 35

70 R TrackedClass A70 R Wheeled

ParameterStaad AnalysisCharts & Tables% ErrorStaad AnalysisCharts & Tables% ErrorStaad AnalysisCharts & Tables% Error

Moment (kN-m)1345.81321-1.841143.41136-0.6514491413.2-2.47

Shear (kN)3383380.00334.4331-1.02408.3400-2.03

Reaction (kN)505.25503.3-0.39415.8433.34.21508.95090.02

Case 3Span = 13.5, Skew angle = 25

70 R TrackedClass A70 R Wheeled

ParameterStaad AnalysisCharts & Tables% ErrorStaad AnalysisCharts & Tables% ErrorStaad AnalysisCharts & Tables% Error

Moment (kN-m)896.8905.40.96678.8688.61.44845.8849.90.48

Shear (kN)293.9294.70.27257.5251.5-2.33307.5307-0.16

Reaction (kN)475.9473-0.61346.2356.83.06440.7434-1.52

Design SF/ Reaction = Appropriate coefficient x Total Live Load of the train without impact.The above results are in good agreement and the maximum error is 4.2 % for 19 m span and 350 skew and that also in the safer side. But if we observe the governing forces, the error is further reduced within 2.5%.

Table 4: Reaction and Shear Coefficients in skew BridgesSpan(m)Skew AngleDegreeDesign IRC Loads

70 R TRCLASS A70 R WH

ReactionShearReactionShearReactionShear

1200.5370.3460.2310.1740.3520.240

100.6030.3540.2600.1780.3890.244

200.6360.4050.2860.2080.3980.281

300.7030.4200.3290.2300.4340.293

400.7390.4520.3720.2410.4980.306

1500.5290.3800.2600.2030.3620.291

100.5950.3890.2880.2070.3960.296

200.6540.4190.3160.2280.4320.320

300.7090.4360.3530.2400.4700.333

400.7450.4760.3900.2610.5190.354

1800.5160.4060.2870.2350.3710.328

100.5820.4140.3110.2380.4020.332

200.6430.4400.3390.2600.4350.355

300.7000.4640.3710.2820.4750.377

400.7380.4940.4010.2970.5350.400

2100.5400.4090.3070.2550.3930.346

100.5980.4170.3280.2590.4230.352

200.6500.4460.3510.2850.4570.379

300.6990.4700.3800.3020.4910.400

400.7360.5140.4190.3230.5450.441

(7) Conclusions: Following conclusions can be drawn from the above parametric study.1) With the increase in skew angle, the maximum Bending moment in the girder G1 reduces for all class of loadings. The reason is that with the increasing skew angle the rectangular bridge takes the shape of parallelogram and load follows the shorter path along the shorter diagonal. This can also be called as reduction of effective span. Hence simply supported T-Beam skew bridges are found to be conservative with respect to the moments even if the skew angle is ignored.2) For class 70 R Tracked and Wheeled vehicle the maximum BM in girder G2 nearly remains constant irrespective of skew. For Class A there is fall in maximum LL BM.3) The reduction in maximum LL BM is parabolic in nature. At higher skew angle more reduction is observed.4) The maximum support reactions and shear increases significantly with the increase in skew angle, and thus the design based upon right bridge analysis is unsafe. The increase can be as high as 60% at about 400 of skew. The increase in support reaction approximately follows a linear trend.5) With the increase in span the maximum BM increases linearly. 6) With the increase in span there is a fall in the percentage reduction in maximum BM of the Bridge, yet no co-relation could be established.(8)References:

Trilok Gupta and Anurag Misra (2007) Effect of Support Reaction of T-Beam Skew Bridges ARPN Journal of Engineering and Applied Sciences, Vol 2, No.1, Feb (2007) C. Menassa, M. Mabsout, K. Tarhini, and G. Frederick, Influence of Skew Angle on Reinforced Concrete Slab Bridges Journal of Bridge Engineering(ASCE) Vol. 12 (2007) S. Maleki and V Bisadi, Orthogonal effects in seismic analysis of skew bridges. Journal of Bridge Engineering(ASCE) Vol. 9 (2006) Haoxiong H., Shenton, H. W and Chajes M. J., Load Distribution for a Highly Skewed Bridge: Testing and Analysis Journal of Bridge Engineering(ASCE) Vol. 9 No.6, Nov1(2004) Khalo, A.R., and Mirzabozorg H Load Distribution Factors in Simply Supported Skew Bridges. Journal of Bridge Engineering (ASCE), Vol. 8, No.4, July 1(2003). Bakht B. Analysis of some skew bridges as right bridges, Journal of Structural Engineering, Vol (10) (1998) IRC 21-2000 Standard Specification and Code of Practice for Bridges, Section III-Cement Concrete (Plain and Reinforced). Indian Road Congress, New Delhi IRC 6-2000 Standard Specification and Code of Practice for Bridges, Section II-Loads and Stresses. Indian Road Congress, New Delhi Harrop J, Ultimate Load Design of Skew Slabs by the Strip Method Building Science Vol. 5 pp 117-121 (1970) Alfred G. Bishara, Wheel Load Distribution on simply supported Skew I Beam composite Bridges, Journal of Structural Engineering,(1993) Ajit Singh, Analysis of skew effects on slab bridges, M.Tech Dissertation (2006) IIT Roorkee. Kamlesh Parihar, Effect of Skewness on Simply Supported Girder Bridges, M.Tech Dissertation (2011) IIT Roorkee. Surana, C.S. and Aggarwal, R. 1998. Grillage Analogy in Bridges Deck Analysis, Narosa Publishing House, New Delhi, First Edition.17