Let's consider the following example: we have a bridge with many members and we want to calculate maximum axial force in a member due to moving loads. The procedure for influence-based analysis follows the following steps
The following example, which demonstrates the implementation of influence-based moving-load analysis, considers a bridge system which will be subjected to a moving load such that a maximum response quantity may be resolved. Influence-based analysis proceeds as follows:
Step 1: Obtain
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deflected shape
CSI Software first generates lane-load points along and across each lane according to lane discretization. Deflected shapes are then obtained by placing a unit load at each lane-load point along the gravity direction. These unit loads are then transferred from the lane surface to joints within the structural system according to their tributary distribution. The lane-to-object connections which govern this transfer of load path may be reviewed through Display > Show Lanes > Show Structural Connection For Selected Point" you can display the connections between the lane loading point and the joints in the model. So if our . If, for example, the model contains 1000 lane loading -load points, the program would calculate 1000 deflected shapes , each corresponding to a unit load at each lane loading point. These deflected shapes are then used to determine all response quantitieswill be calculated, from which response quantities are determined.
Step 2: Obtain
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influence surfaces for response quantities of interest
For each response quantity (such as reaction or , member axial force in a member). The value of , etc.), the influence surface is then derived from the deflected shapes previously calculated. Values are exact at the lane loading points and linear interpolation is used to obtain values on the influence surface between the lane loading lane-load point locations, and linearly interpolated between points.
Step 3: Find minimum and maximum response quantities
Once the influence surface is known, the program runs an algorithm that places the vehicular loading to a location in which causes maximum effect.
So there are two parts to the analysis – solving for the response (deflected shape) to the unit influence loads, then for each response quantity calculating the influence surface and moving the vehicles along it. The first part must always be done once and completely. The second part needs only be done for the requested response quantities.
Depending on the parameters of the model – generated, a software algorithm locates vehicular loading such that minimum and maximum effect is induced. Response is enveloped to obtain the maximum absolute value.
Summary
In summary, deflected shapes are first resolved for each unit influence load, then the influence surface is calculated for each response quantity as vehicle loads move along the structure. Since the first step provides for analysis, it must be done in its entirety, then the second and third steps may be done selectively for the response quantities desired.
Computational time for each phase of analysis may vary depending on model parameters, including the number of degrees of freedom, number of lane-load points, number of vehicles and axles, and number of response quantities requested – the relative time taken by these two parts may differ. Please read the section "Computation Considerations" at the end of Chapter "Bridge Analysis" of the CSI Analysis Reference Manualresponse measures, etc. Additional information is available in the CSI Analysis Reference Manual (Computation Considerations, page 467).