HL-93 Highway Bridge Loading Models — Worked Examples

Example

Example 1: Build the Governing Vehicular Load Alternatives

A simply supported highway bridge is being analyzed for positive midspan moment.

Task: State the minimum loading alternatives that must be generated before comparing the governing live-load effect.

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Example

Example 2: Dynamic Load Allowance Without Double Counting

A girder analysis gives a static truck moment of 520 kN⋅m520\text{ kN}\cdot\text{m} and a lane-load moment of 280 kN⋅m280\text{ kN}\cdot\text{m}. The applicable dynamic allowance for the concentrated vehicle component is IM=0.33IM=0.33.

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Common error: multiplying the entire 800 kN⋅m800\text{ kN}\cdot\text{m} static sum by 1.331.33 would incorrectly amplify the lane-load contribution.

Example

Example 3: Watch an Axle Enter the Span — Left Reaction

A 30 m30\text{ m} simply supported span carries the nominal design truck. The front axle is at x=8.00 mx=8.00\text{ m} from the left support, the front-to-second spacing is 4.27 m4.27\text{ m}, and the rear spacing is 4.27 m4.27\text{ m}. Ignore lane load first.

The axle locations are

x1=8.00 m,x2=3.73 m,x3=−0.54 m.x_1=8.00\text{ m},\qquad x_2=3.73\text{ m},\qquad x_3=-0.54\text{ m}.

For the left reaction, the influence ordinate is

yR(x)=1−xL,0≤x≤L,y_R(x)=1-\frac{x}{L},\qquad 0\le x\le L,

and it is zero for an axle outside the span.

Therefore,

Rtruck=35.6(1−8.0030)+142.3(1−3.7330)+0≈150.7 kN.R_{truck} = 35.6\left(1-\frac{8.00}{30}\right) + 142.3\left(1-\frac{3.73}{30}\right) + 0 \approx 150.7\text{ kN}.

For the common general dynamic-load-allowance illustration used in the simulator,

Rtruck+IM=150.7(1.33)≈200.4 kN.R_{truck+IM}=150.7(1.33)\approx 200.4\text{ kN}.

If the full-span nominal lane load is then turned on,

Rlane=wL2=9.34(30)2=140.1 kN,R_{lane}=\frac{wL}{2} =\frac{9.34(30)}{2}=140.1\text{ kN},

so the displayed combined result is approximately

R≈200.4+140.1=340.5 kN.R\approx 200.4+140.1=340.5\text{ kN}.

Visualization point

The third axle is still visible before it reaches the bridge, but its influence ordinate is zero. This is why a moving-load model must distinguish vehicle geometry from the portion of the vehicle currently acting on the structure.

Example

Example 4: Compare One-Lane and Two-Lane Girder Effects

An interior girder receives a live-load distribution effect of 410 kN⋅m410\text{ kN}\cdot\text{m} from one loaded design lane and 650 kN⋅m650\text{ kN}\cdot\text{m} from two loaded lanes before the applicable multiple-presence treatment.

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Example

Example 5: Separate Strength and Fatigue Models

A steel bridge is being checked for both Strength I and fatigue.

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Engineering conclusion: Strength and fatigue may use related vehicle concepts, but they answer different failure questions and should remain separate in the model and reporting workflow.

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