9. Specified Displacement

Specified displacements are used to analyse the structural behaviour under the displacement condition when the amount of displacement in the direction of a certain degree of freedom is known at a specific point.

In general, specified displacement analysis is used in the following cases:

1. When an existing structure is deformed and precise safety diagnosis is required
2. If you want to precisely analyze the behavior of a specific part using a detailed model
3. When the analysis of the entire model of the structure is performed and the displacement value of the corresponding part is used as the boundary condition of the detailed model
4. If you want to perform an analysis that considers point settlement in an existing structure
5. When performing an analysis considering the settlement of a bridge structure

Specified displacement is the concept of forcibly moving a certain node.

That is, instead of applying a load, a displacement of a specific value is generated and a corresponding load value is calculated.
Figure 9.2 shows the case where settlement (Specified displacement) occurs at the central point of a two-span continuous beam.
In Figure 9.2, it is assumed that the load and settlement are in the downward direction and the reaction force is in the upward direction.

From the previous figure, the formula can be formulated with the concept that the role of the reaction force (concentrated load) 𝑋 remains when the effect of the vertical load 𝑞 is excluded from the forced displacement ∆.

As a result, if the specified displacement value is given, the support reaction force can be calculated.
Figure 9.3 shows a graph of the reaction force ratio to the settlement ratio at point B.
The settlement ratio is the value obtained by dividing the amount of settlement by the length of the span, and the reaction force ratio is the value obtained by dividing the X value by the reaction force value when there is no point settlement.

Figure 9.3 shows the settlement ratio-reaction force ratio relationship in the case of three types of vertical loads 𝑞 ( 10𝑘𝑁/𝑚, 0𝑘𝑁/𝑚, -10𝑘𝑁/𝑚).
When the vertical load 𝑞 is in the downward direction (10𝑘𝑁/𝑚), the small value of 𝑋 means that the reaction force at point B decreases when the load is in the downward direction.
However, when the direction of the load is upward (-10𝑘𝑁/𝑚), the reason why the 𝑋 value appears large is that settlement must occur while offsetting the load.