Load distribution factors for quick design and assessment in typical Australian bridges

Figures & data

Table 1. Finite element modelling verification.

		Natural frequency modes (Hz)
		1	2	3
Field measurement		4.49	6.78	11.32
Mesh size (mm)	800	4.21	7.06	9.81
	1200	4.19	7.52	10.02
	1600	4.14	8.15	10.28

Figure 1. Super-T girder bridge at Boronia Road (a) actual cross-section (b) FE model by CSiBridge.

Figure 2. LDF comparison between Yousif and Hindi (2007) and this study.

Figure 3. Studied Australian bridge geometries: (a) Super-T girder bridge (b) I-girder bridge.

Figure 4. Selected load cases (a) MS18 (b) T44 (c) M1600 (d) B-double truck (e) Road train (102t) (f) E-class tram.

Figure 5. Studied I-girder bridge to identify the critical load.

Table 2. The comparison LDFs of the different Australian loads.

Vehicle	Distribution factors				% different with T44 distribution factors
	Moment		Shear		Moment		Shear
	Ext	Int	Ext	Int	Ext	Int	Ext	Int
T44	0.64	0.72	0.79	0.88	0%	0%	0%	0%
MS18	0.65	0.73	0.79	0.88	1%	0%	0%	0%
M1600	0.66	0.71	0.62	0.88	3%	−2%	−21%	0%
E-class tram	0.65	0.72	0.63	0.93	1%	0%	−20%	7%
B-double (68t)	0.65	0.71	0.62	0.90	2%	−1%	−21%	3%
Road train (102t)	0.66	0.71	0.67	0.86	3%	−2%	−16%	−2%

Figure 6. Transverse vehicle positioning: (a) single-lane load (b) multiple-lane load.

Figure 7. Comparison of the different loading positions in transverse direction: (a) Super-T girder bridge (b) I-girder bridge.

Table 3. Selected load cased for single- and multiple-lane loads for I-girder and Super-T girder bridges.

Type of lane load	Girder	Highest LDF in the cases
		Bending moment	Shear
Single-lane load	Exterior	1L–1	1L–1
	Interior	1L–1	1L–2
Multiple-lane load	Exterior	2L–1	2L–1
	Interior	2L–1	2L–1

Table 4. Table National Association of Australian State Road Authorities (1976) LDF equations (National Association of Australian State Road Authorities, 1976).

Type of deck	Bridge designed for one lane load	Bridge designed for two or more traffic lanes
Concrete Deck (i) On steel I-beam stringers or prestressed concrete beams	S/2.1 (If S> 3m note 1 applies)	S/1.7 (If S>4.3m note 1 applies)

S = spacing between girder (m). Note 1 assumes the flooring between beams acts as a simple beam.

Table 5. Modification factor for Henry’s method to improve the accuracy (Huo, Conner, and Iqbal 2003.).

Structure Type	Moment modification factors	Shear modification factor
Precast spread box girder	1.00	1.15
Precast concrete I-girder	1.10
Cast-in-place concrete T-girder	1.05
Cast-in-place concrete box girder	1.05
Steel I-girder	1.10
Steel open box girder	1.00

Table 6. I-girder bridge LDF equations (AASHTO 2017.).

Type of load effects	Girders	Distribution factors
		One-lane load	Multiple-lane load
Moment	Int	$0.06+{\left(\frac{S}{4300}\right)}^{0.4}{\left(\frac{S}{L}\right)}^{0.3}{\left(\frac{K_g}{L{t}_s^3}\right)}^{0.1}$	$0.075+{\left(\frac{S}{2900}\right)}^{0.6}{\left(\frac{S}{L}\right)}^{0.2}{\left(\frac{K_g}{L{t}_s^3}\right)}^{0.1}$
	Ext	Use lever rule	$g=e{g}_{interior}$ $e=0.77+\frac{d_e}{2800}$
Shear	Int	$0.36+\frac{S}{7600}$	$0.36+\frac{S}{3600}-{\left(\frac{S}{10700}\right)}^2$
	Ext	Use lever rule	$g=e{g}_{interior}$ $e=0.6+\frac{d_e}{3000}$

Figure 8. Open precast concrete/steel box support typical cross-section according to AASHTO (2017).

Table 7. Open precast concrete box bridge LDF equations (AASHTO 2017).

Type of load effects	Girders	Distribution factors
		One-lane load	Multiple-lane load
Moment	Int	${\left(\frac{S}{910}\right)}^{0.35}{\left(\frac{Sd}{L^2}\right)}^{0.25}$	${\left(\frac{S}{1900}\right)}^{0.6}{\left(\frac{Sd}{L^2}\right)}^{0.125}$
	Ext	Lever rule	$g=e{g}_{interior}$ $e=0.97+\frac{d_e}{8700}$
Shear	Int	${\left(\frac{S}{3050}\right)}^{0.6}{\left(\frac{d}{L}\right)}^{0.1}$	${\left(\frac{S}{2250}\right)}^{0.8}{\left(\frac{d}{L}\right)}^{0.1}$
	Ext	Lever rule	$g=e{g}_{interior}$ $e=0.8+\frac{d_e}{3050}$

Table 8. Range of parametric study (Super-T girder bridges).

Parametric study	Value
Span length (L)	15–35 m
Girder spacing (S)	1300 – 3000 mm.
Girder depth (d)	750–1800 mm

Table 9. Range of parametric study (I-girder bridges).

Parametric study	Value
Span length (L)	5–35 m
Girder spacing (S)	1300–3000 mm.
Girder depth (d)	750–1400 mm

Figure 9. LDF of I-girder (span length) with different LDF standards – red is single lane and blue is multiple lanes (a) bending moment – exterior girder (b) bending moment – interior girder (c) shear – exterior girder (d) shear – interior girder.

Figure 10. LDF of I-girder (girder spacing) with different LDF standards – red is single lane and blue is multiple lanes (a) bending moment – exterior girder (b) bending moment – interior girder (c) shear – exterior girder (d) shear – interior girder.

Figure 11. LDF of I-girder (girder depth) with different LDF standards – red is single lane and blue is multiple lanes (a) bending moment – exterior girder (b) bending moment – interior girder (c) shear – exterior girder (d) shear – interior girder.

Figure 12. LDF of Super-T bridges (span length) with different LDF standards – red is single lane and blue is multiple lanes (a) bending moment – exterior girder (b) bending moment – interior girder (c) shear – exterior girder (d) shear – interior girder.

Figure 13. LDF of Super-T bridges (girder spacing) with different LDF standards – red is single lane and blue is multiple lanes (a) bending moment – exterior girder (b) bending moment – interior girder (c) shear – exterior girder (d) shear – interior girder.

Figure 14. LDF of Super-T bridges (girder depth) with different LDF standards – red is single lane and blue is multiple lanes (a) bending moment – exterior girder (b) bending moment – interior girder (c) shear – exterior girder (d) shear – interior girder.

Table

$A$	=	area of girder $(m{m}^2$)
$d$	=	depth of girder (mm)
$d_e$	=	distance from exterior web of exterior to the interior edge of curb (mm)
$E_B$	=	elastic modulus of beam material (MPa)
$E_D$	=	elastic modulus of deck material (MPa)
$e_g$	=	distance between the centres of gravity of the basic beam and deck (mm)
$I$	=	moment of inertia of beam $(m{m}^4)$
$K_g$	=	longitudinal stiffness parameter $(m{m}^4)$
$L$	=	span length of deck (mm)
$N_b$	=	number of girders
$S$	=	spacing of beams or webs (mm)
$t_s$	=	depth of concrete slab (mm)

Yousif, Z., and R. Hindi. 2007. “AASHTO-LRFD Live Load Distribution for Beam-And-Slab Bridges: Limitations and Applicability.” Journal of Bridge Engineering 12 (6): 765–773. https://doi.org/10.1061/(ASCE)1084-0702(2007)12:6(765).

 Web of Science ®Google Scholar

National Association of Australian State Road Authorities 1976. “NAASRA Bridge Design Specification.” Accessed October 29, 2021.

 Google Scholar

Huo, X. S., S. O. Conner, and R. Iqbal. 2003. “Re-Examination of the Simplified Method (Henry’s Method) of Distribution Factors for Live Load Moment and shear.“ TNSPR-RES 1218.

 Google Scholar

AASHTO 2017. “AASHTO LRFD Bridge Design Specifications.”

 Google Scholar