A three-span curved bridge is loaded according to AASHTO LFD's live load specifications using influence lines. This example illustrates the use of bridge paths and span break makers.

Model Setup

This model consists of a 200-foot bridge in three spans of length 60, 80, and 60 feet. The bridge is divided into members of 20 feet each (span 1: members 1-3; span 2: members 4-7; span 3: members 8-10). The end joints are fully supported. The intermediate supports are simply supported, supported in translation but not rotation.

The bridge is curved using Bridge Paths. A bridge path coordinate system is defined as follows:

With the bridge coordinate system set as the active coordinate system, the coordinates of the joints are simply spaced 20-feet along the station axis.

The lane and moving load case setup are identical as in the previous sample: INF01: AASHTO LFD Simple Span.

Span Break Markers

AASHTO LFD Section 3.11.3 provides that for the determination of maximum negative moments, two concentrated loads on different spans must be considered. It is possible to specify that two point loads be applied using influence lines, but a special feature has been added that ensures 1) that a second load is only considered for negative moments, and 2) that the second concentrated load is applied on a different span than the first concentrated load.

LARSA cannot automatically determine where one span ends and another span begins. In complex bridge models, the locations of supports at spans are not located near the deck where the influence lines are considered but at the base of piers. So LARSA needs to be informed where one span ends and another begins on the lane path definition.

The lane path definition is amended by inserting Span Break markers after the last geometry point of each span. In this example, the first span ends after the third member, member 3. However, the last geomety point on the span is the geometry point at the start of member 4. A span break marker goes after this row to indicate that the first span contains member 3. If a marker were placed after the geometry point at the start of member 3, the first span would go only as far as the beginning of member 3, not to its end.

The second span break marker is placed four rows later, after the row for the geometry point at the start of member 8. This makes the middle span contain members 4, 5, 6, and 7.

Result Case Setup

The result case setup for the vehicle load pattern and the 26 kip concentrated load for shear using influence-based results is identical to the previous sample: INF01: AASHTO LFD Simple Span.

The setup for the 18 kip concentrated load for negative moment is slightly different. The load is set with Max # to 2, since there can be at most two loads applied. In addition, the AASHTO LFD Point Loading option is checked.

The AASHTO LFD Point Loading option has two effects. The first is to ensure that the two concentrated loads are placed in separate spans. The other effect is to ensure that the second load is only applied in certain circumstances. But, LARSA cannot simply apply the load only when the engineer is investigating envelope minimums for member forces. "Negative moments" as intended by the AASHTO LFD specification may not mean negatively-signed moments as outputted by LARSA. The orientation of the model and LARSA's sign conventions may result in positively-signed moments being the ones intended to be considered "negative" for the purposes of AASHTO LFD.

The second concentrated load is applied when enveloping member end forces or member sectional forces for local y or z moments. It is applied in either the y or z direction, and either for enveloped minimums (negatives) or enveloped maximums (positives), depending on the orientation angle of the member. The following table indicates when the second concentrated load will be applied. It is dependent on the sign convention for the results. Member sectional forces, stresses, and member end forces at the end joint have the same sign convention. This is also the sign convention used in graphical diagrams of member forces and stresses. Member end forces at the start joint has the opposite sign convention.

Orientation Angle	Sectional Forces (and End Forces at End)	End Forces at Start
0° (-45 to 45)	positive y moments	negative y moments
90° (45 to 135)	negative z moments	positive z moments
180° (135 to 225)	negative y moments	positive y moments
270° (225 to 315)	positive z moments	negative z moments

The engineer should confirm that the conditions in which the second concentrated load is applied corresponds with the intentions of the specification for each model.

The AASHTO LFD Point Loading option should only be used when the elevation axis is the global z-axis.

Accessing Results

See the previous sample (INF01: AASHTO LFD Simple Span) for an overview of accessing influence line results.

To verify the application of the second concentrated load for moments, select the LL Lane/AASHTO Point 18kip (moment)[x2]/Lane Load for negative moments only case in the Analysis Results Explorer. Then turn on graphical moment diagrams and select the direction Moment My.

Next activate graphical influence coefficient view. Using the pointer tool, click member 3 and when prompted enter station 0. LARSA will display the influence line coefficients with the locations of the two concentrated loads applied. In this model, the members were created with orientation angle 0. As a result, the concentrated loads are applied for positive y moments in sectional forces and in graphical diagrams. This is shown below:

Influence coefficients view always shows two diagrams: above the bridge are positive moments, below the bridge are negative moments. Two concentrated loads were applied for positive moments, and, appropriately, one concentrated load for negative moments, following the sign convention of LARSA. The solid bars above and below represent the application of the uniform lane load.

This diagram shows that the first concentrated load was placed directly above member 3's start, where it produced the maximum positive y-moment at the start of member 3. The second concentrated load was placed in the third span, at the next worst position for positive y moments.

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