The simplified model and stages are shown below:

• Beams at each level are the same size

• A single point load is applied in each stage - same value (100kN) at all levels

  (all other loading, including selfweight, is excluded)

• Stage durations are set to zero to eliminate creep effects.

Focussing on the first floor beam, as expected:

• In stage 1:

  

  • Beam carries 100% of the load at level 1 and deflects 5.75mm

• In stage 2:

  

  • 2 beams share the load applied at level 2 - approx 50:50

  • Level 2 beam deflects 2.44mm

  • The level 1 beam sees additional deflection of a similar amount, so total deflection is now 8.16mm

  • This deflected shape tends to be perceived as reasonable. If you are thinking of a concrete structure it seems imaginable that the column between the two beams would be constructed slightly longer, but this is discussed further in the next section.

  • Also note that the column is in compression (as shown below), even though viewed in isolation it looks like the column between the level 1 and 2 beams has lengthened.

    

• In stage 3:

  

  • 3 beams share the load applied at level 3 - approx ⅓ each

  • Level 3 beam deflects 1.6mm

  • The level 1 beams sees additional deflection of a similar amount, so total deflection is now 9.71mm

  • Once again the deflections can be viewed as seeming reasonable

In practice there is just one analysis model with information for each stage about which elements are active. The view below shows the active elements in stages 1 to 3.

Note that:

• There is no deformed geometry introduced in stage 2 as a result of deformations from stage 1.

• The start and end positions (and hence the length) of any member are the same for every stage in which a member exists.

• Section and material properties for a member can change from stage to stage.

Referring back to the deflections shown for each stage.

The deflection shown represents the total deflection since that node/member was first introduced. There are actually 2 real world scenarios to consider:

• Scenario 1 - Insitu construction:

  • It is imaginable that a concrete column between levels 1 and 2 would be cast 5.75mm longer so that the top lies exactly in the target level 2.

  • When load is applied to stage 2 it then deflects 2.44 mm out of plane.

    

• Scenario 2 - Pre-fabricated construction

  • A steel column is prefabricated taking no account of the deflection of the supported beam.

  • When it is introduced to the deflected beam the top of the column will be 5.75 mm below the target level and the beams connected to it will be sloping slightly.

  • When load is applied to stage 2 it then deflects 2.44 mm from the position at which it started.

  • Of course, the column could be prefabricated with some extended length (not necessarily 5.75mm)

• It's a subtle point but it is not considered significant to the analysis results to know which of these scenarios applies - we just know that wherever it started, the top of the column deflects 2.44mm by the end of stage 2 and 4.01mm by the end of stage 3.

For the same model the stage loading is changed so that the only load applied is horizontal load in stage 1 (no additional load is applied in stages 2 and 3), the views below show that:

• As expected there is horizontal displacement in stage 1

  

• When stage 2 is introduced without any loading nothing in that stage moves - the deflections are all 0.00

  

  • The diagram shows the stage 2 members undeformed from the original analysis model positions

  • At level 1 you see some horizontal offsets connecting the bottoms of the undeformed stage 2 columns to the tops of the stage 1 columns in their deformed positions which can look strange - this may not seem/feel correct, but it is following exactly the same display principle shown for vertical deflection in the previous example.

  • The deflection shown represents the total deflection since that node/member was first introduced.

The example is now adjusted to apply the same load to the newly introduced level in each stage

• Now we see the sort of step backs shown at each level as were shown for the “realistic” model.

  

• Hopefully now the reasoning behind this display makes sense

  REMINDER - The deflection shown represents the total deflection since that node/member was first introduced.

• The view below shows results for an analysis without SCA on the left and with SCA on the right

  

  • In the analysis without SCA the loads applied at 1st and 2nd floor level cause deflection at the top level. If the top structure did not exist at the time the load was applied then this is not logical.

  • SCA predicts that the deflection at the top level is 0.66mm subsequent to the introduction of that level.

    • REMINDER - The deflection shown represents the total deflection since that node/member was first introduced.

    • The same sort of discussion about construction scenarios applies. The member may have been introduced in an offset location as a result of the offset that develops in previous stages. This is not considered significant to the analysis.