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Received: 2012-04-15

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Journal of Zhejiang University SCIENCE A 2012 Vol.13 No.12 P.915-925


Development of the applicability of simplified Henry’s method for skewed multicell box-girder bridges under traffic loading conditions

Author(s):  Iman Mohseni, A. R. Khalim Rashid

Affiliation(s):  Department of Civil Engineering, Universiti Kebangsaan Malaysia (National University of Malaysia), UKM Bangi, Selangor 43600, Malaysia

Corresponding email(s):   mohseni@eng.ukm.my, khalim@eng.ukm.my

Key Words:  Distribution factor, Live loads, Skewed bridges, Grillage analysis

Iman Mohseni, A. R. Khalim Rashid. Development of the applicability of simplified Henry’s method for skewed multicell box-girder bridges under traffic loading conditions[J]. Journal of Zhejiang University Science A, 2012, 13(12): 915-925.

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%A A. R. Khalim Rashid
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1200098

T1 - Development of the applicability of simplified Henry’s method for skewed multicell box-girder bridges under traffic loading conditions
A1 - Iman Mohseni
A1 - A. R. Khalim Rashid
J0 - Journal of Zhejiang University Science A
VL - 13
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SP - 915
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%@ 1673-565X
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A1200098

Concrete precast multicell box-girder (MCB) bridges combine aesthetics with torsional stiffness perfectly. Previous analytical studies indicate that currently available specifications are unable to consider the effect of the twisting moment (torsional moment) on bridge actions. In straight bridges the effect of torsion is negligible and the transverse reinforced design is governed by other requirements. However, in the case of skewed bridges the effect of the twisting moment should be considered. Therefore, an in-depth study was performed on 90 concrete MCB bridges with skew angles ranging from 0° to 60°. For each girder the bridge actions were determined under the American Association of State Highway and Transportation Officials (AASHTO) live load conditions. The analytical results show that torsional stiffness and live load positions greatly affected the bridges’ responses. In addition, based on a statistical analysis of the obtained results, several skew correction factors are proposed to improve the precision of the simplified Henry’s method, which is widely used by bridge engineers to predict bridge actions. The relationship between the bending moment and secondary moments was also investigated and it was concluded that all secondary actions increase with an increase in skewness.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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[32]Appendix A: Non-Orthogonal grillage method

[33]The same procedure as recommended by Hambly (1991) was used to obtain the grillage layout and properties. The grid mesh is chosen with longitudinal members coincident with webs. Two nominal members are located along the edges of the cantilevers. The section is divided in such a way that each internal longitudinal member has half of the top and bottom slabs. The torsion constant and shear area in the longitudinal direction can be determined by the following equations, respectively:

[34] (A1)

[35]As=W·h, (A2)

[36]where h and W stand for depth and width of deck, and d' and d" are the top and bottom thicknesses, respectively.

[37]The transverse member represents the top and bottom slab and is perpendicular to the longitudinal members. The maximum spacing of transverse members is taken as one-quarter of the contra-flexure point’s distance but the spacing is chosen to be shorter near the intermediate supports to give greater detail.

[38]Hambly (1991) indicated that the moment of inertia (is) per unit width in the transverse direction is half of the torsional constant (cs) and their equivalent shear area can be obtained by



[41]where dw, E and G are the thickness of web, the modulus of elasticity and shear modulus of bridge, respectively.

[42]Appendix B: Simplified Henry’s EDF method

[43]Henry’s EDF method requires only the roadway width (Wroadway), number of beams (Nbeam) and an intensity factor (IF) based on a linear interpolation to determine the total number of traffic lanes considered as live load on the bridge. From the AASHTO Standard, the intensity factor of live load equals 100% for a two-lane bridge, 90% for a three-lane bridge, or 75% for a four-line or more lane bridge. Henry’s EDF method for interior and exterior beams

[44]is as follows:


[46]The multicell box is considered as a group of equivalent I-beams based on the centre-to-centre distance between the webs. The number of equivalent I-beams is counted as the number of beams in the calculation.

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