The live load in the American Association of State Highway and Transportation Officials (AASHTO) is used in the design of bridges in Jordan. AASHTO LFD live loads is multiplied by 1.8 and used in Jordan to encounter the unexpected heavy live loads running on these bridges. The new code AASHTO LRFD for live loads is also used in the design of bridges. A Comparison between the bending moment obtained by 1.8 LFD live loads, and LRFD live loads were carried out to determine the coefficient which should the LRFD live loads be multiplied to give the same moment as 1.8 LFD live loads produced. A Comparison of 1.8 AASHTO LFD and AASHTO LRFD live loads for the bending moment of simply supported 30m bridge span with one lane in each direction showed that the LRFD HL–93 loadings should be multiplied by 1.35 to have the same moment as 1.8 multiplied by HS20–44 in LFD.

This result will be used for the design of highway bridges in Jordan, and it will be a reference number for the Arab Countries also for such subject.

Keywords: AASHTO specification, AASHTO LRFD, AASHTO LFD, loadings, bridges, highway

AASHTO LFD¹ live loads are used in Jordan, most of the Arab Countries and USA. In Jordan, the AASHTO LFD live load is increased to encounter the unexpected live loads. This increase is a multiplication factor of 1.8 to the live loads of AASHTO LFD. AASHTO LRFD² is the recent Code in designing bridges. Ministry of Public Works and Housing, and Ministry of Transportation^3,4 studied the axle weight in Jordan. Al foqaha'a⁵ studied the loading adopted for bridge design in Jordan in 1994. Qaqish⁶ presented load capacity evaluation of T – Beam bridges. Qaqish⁷ presented stress distribution at the corners of skew bridges. Qaqish⁸ illustrated a Comparison between one dimensional and three–dimensional models of one span box Girder Bridge. Qaqish⁹ illustrated a Comparison between one dimensional and three–dimensional models of two continuous spans of box, Girder Bridge. Qaqish¹⁰ illustrated the finite element analysis of two continuous skew spans of box Girder Bridge and the reaction distribution at the edges with 49 degrees skew angle. Campisi¹¹ illustrated the review of load rating highway bridges in accordance with load and resistance factor rating method. Deng¹² studied the numerical simulations to study the dynamic IFs of both simply supported and continuous bridges due to vehicle loading. Deng¹³ studied the impact factors for different bridge responses, including deflection, bending moment and shear. The results showed that the impact factors due to vehicle braking could be notably larger than those due to the vehicles moving at constant speeds and could exceed the impact factor specified in the AASHTO bridge design code. Leahy¹⁴ examined the HL–93 current bridge traffic load model in the United States. Li¹⁵ studied a three–dimensional nonlinear dynamic analysis framework for RC bridges based on the force analogy method (FAM).¹⁶

The live loads of the AASHTO specifications (LFD) consist of standards trucks or off– lane loads as shown in Figure 1. While the live loads of the AASHTO specifications (2) LRFD is HL–93 which consists of truck loading and distributed load of 9.3 KN/m as shown in Figure 2. The impact factor for LFD is calculated from:

Figure 1 Truck HS20–44 and equivalent.

Figure 2A Truck loading of HL–93.

Figure 2B Distributed HL–93 loading.

While the Dynamic load allowance is considered 33% for LRFD.

Figure 3 shows the plan of bridge, section A–A, and section B–B. The span of the bridges is 30m with two lanes, one lane in each direction. Box Type Bridge is considered with 7.8 m total width and 2.2 m total depth.

Figure 3 Plan and sections A–A and B–B of the Bridge.

Moment due to HS20–44

Maximum positive moment (Figure 4).

Figure 4 Truck Hs 20–44 location for Max moment.

$\text{ΣMB=0}\text{.0}$

${\text{R}}_{\text{A}}\times \text{30=35}\text{.7}\times \text{19}\text{.978}+\text{142}\text{.7}\times \text{142}\text{.7}\times \text{11}\text{.445}$
${\text{R}}_{\text{A}}\text{=(713}\text{.22}+\text{2241}\text{.817}+\text{1633}\text{.2)/30}$
${\text{R}}_{\text{A}}\text{=152}\text{.94KN}$
${\text{R}}_{\text{B}}\text{=168}\text{.16KN}$

Max. moment at C

${\text{M}}_{\text{C}}=\text{152}\text{.94}\times \text{14}\text{.29}-\text{35}\text{.7}\times \text{4}\text{.268}$
$=\text{2185}\text{.5}-\text{152}\text{.4}=\text{2033}\text{.1KN}\text{.m}$

Impact Factor      = $\frac{\text{50}}{\text{L}+\text{125}}$=$\frac{\text{50}}{\text{3}\text{.28}\times \text{30}+\text{125}}$= 22.4%

Total live load bending moment = 2 x 2033.1 x 1.224 =4977.029 kN.m

Equivalent uniform load (HS 20–44)

Figure 5 shows the maximum moment due to equivalent uniform loadings of HS 20–44.

Figure 5 Equivalent uniform load for HS 20–44.

Bending moment at C = $\frac{\text{W}{\text{L}}^{\text{2}}}{\text{8}}+\frac{\text{PL}}{\text{4}}$$\text{=}\frac{\text{9}\text{.37}\times \text{3}{\text{0}}^{\text{2}}}{\text{8}}+\frac{\text{80}\text{.345}\times \text{30}}{\text{4}}$$\text{=1054}\text{.125}+\text{602}\text{.59}$$\text{=165}\text{.7125}$

Total live equivalent bending moment = 2 x 1656.7125 x 1.224 = 4055.63 KN.m

So the bending moment due to the Truck Loading HS 20–44 governs and it's value 4977.029 KN.m.

LRFD

Bending moment due to truck loading

Figure 6 shows the location of HL– 93 Truck loading to give maximum moment at point O.

Figure 6 Truck HL–93 location for max. moment.

${\text{R}}_{\text{A}}\times \text{30}=\text{35}\times \text{20}\text{.01}+\text{145}\times \text{15}\text{.71}+\text{145}\times \text{11}\text{.41}$$=\text{700}\text{.35}+\text{2277}\text{.95}+\text{1654}\text{.45}$

 ${\text{R}}_{\text{A}}=\text{154}\text{.425K}$

$$\text{Moment at O }=\text{ 154}\text{.425}\times \text{ 14}\text{.29 – 35 }\times \text{ 4}\text{.3}$$
$$\begin{array}{l}=\text{2206}\text{.73 }-\text{150}\text{.5}\hfill \\ =\text{2056}\text{.23 KN}\text{.m}\text{.}\hfill \end{array}$$

Bending moment due to distributed load

Figure 7 shows the maximum moment due to uniform loading of HL–93 loading.

Figure 7 Moment due to additional uniform loading of HL–93.

$\text{Bending moment at O }=\text{ 1043}\text{.67 KN}\text{. m}\text{.}$ 

Total live bending moment

$$\left(\text{2056}\text{.23}+\text{ 1043}\text{.67}\right)\times \text{ 2 }\times \text{1}\text{.33 }=\text{ 8245}\text{.734 KN}\text{. m}\text{.}$$ 

Where 33% is the impact factor, and it is calculated for two lanes.

Dead load

Bending moment due to own weight of the bridge

$\text{Own weight of bridge}=\text{ 7}\text{.8 }\times \text{ 0}\text{.2 }\times \text{ 25 }+\text{ 0}\text{.6 }\times \text{ 0}\text{.3 }\times \text{2 }\times \text{ 25}+\text{2}\text{.24 }\times \text{ 0}\text{.3 }\times \text{ 25}\times \text{ 2 }+\text{3}\text{.2 }\times \text{ 0}\text{.2 }\times \text{ 25 = 97}\text{.6 KN/m}$ 

$\text{Own weight of wearing surface}=\text{ 3}\text{.6 }\times \text{ 2 }\times \text{ 0}\text{.05 }\times \text{21}=\text{ 7}\text{.56 KN}\text{. m}$

Total Bending moment due to Dead load + Live load

LFD

B. M. due to own weight of the bridge

$$\frac{\text{97}\text{.6}\times \text{3}{\text{0}}^{\text{2}}}{\text{8}}\text{=10980KN}\text{.m}$$

B.M. due to wearing surface

$$\frac{\text{7}\text{.56}\times \text{3}{\text{0}}^{\text{2}}}{\text{8}}\text{=850}\text{.5KN}\text{.m}$$

The truck loading is multiplied by 1.8 to encounter the unexpected traffic loading:

$$\text{Total B}\text{.M}=\text{1}\text{.3 }\left(\text{Moment D}\text{.L}+\text{Moment L}\text{.L}\text{. }\times \text{ 1}\text{.67}\right)$$
$=\text{1}\text{.3 }\left(\text{11830}\text{.5}+\text{1}\text{.67}\times \text{1}\text{.8}\times \text{4977}\text{.029}\right)$
$=\text{34828}\text{.89 KN}\text{. m}\text{.}$Total B.M=1.3

LRFD

$$\text{Total B}\text{. M}\text{. }=\text{ 1}\text{.25 }\times \text{ M}\text{. D}\text{. L}\text{. }+\text{ 1}\text{.5 x M W}\text{.S}\text{. }+\text{ 1}\text{.35 }\times \text{ ML}\text{.L}$$
$=\text{1}\text{.25 }\times \text{ 10980 + 1}\text{.5 }\times \text{ 850}\text{.5 }+\text{ 1}\text{.35 }\times \text{ 8245}\text{.734}$
$=\text{13725 }+\text{ 1275}\text{.75 }+\text{ 11131}\text{.74}$
$=\text{26132}\text{.49 KN}\text{. m}\text{.}$

So the factor to make the bending moment due to LFD equal to LRFD is:

$\text{Factor Equal=}\frac{\text{34828}\text{.89}}{\text{26132}\text{.49}}\text{=1}\text{.33}$ 

So the live loads for LRFD should be multiplied by 1.33 to make the bending moment due to 1.8 HS 20–44 equal to the moment due to LRFD loadings.

Finite element analysis was carried out for the bridge using CSi bridge software (16), and the results are:

Total B. M. (LFD)                36332 KN. m.
Total B. M. (LRFD)             27995 KN. m.

$\text{Factor=}\frac{\text{36332}}{\text{27995}}\text{=1}\text{.3}$

So it can be noticed that the factor from the structural calculations and the Csibridge is almost identical, and it is recommended to use 1.35 as a factor.

The live loads for LRFD designated as HL–93 which consist of design truck or design tandem and design lane load should be multiplied by 1.35 to encounter the unexpected traffic loading in Jordan and to be equivalent to 1.8 HS 20–44 LFD which is adopted in design bridges in Jordan to get the same bending moment for LFD and LRFD. This result will be used in Jordan for designing bridges after will be adopted in the Ministry of Public works and Housing.

None.

The authors declare no conflict of interest.

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