Analysis of Stage Construction: The Hidden Mechanics of Section Changes
In CSI software, the operation of changing sections (known as Change Section in Staged Construction analyses) is often interpreted as a simple stiffness update in the model. However, numerical results reveal a much more complex mechanical reality: an element introduced in an already deformed state inherits a "geometric memory" that invisibly conditions its entire in‑service behavior.
Understanding what the finite element software does internally is crucial to avoid underestimating accumulated deformations or misjudging the assessment of internal forces.
The Computational Mechanics of Replacement
When we instruct the software to replace a beam that is already loaded, the algorithm ensures static equilibrium of the model through a rigorous sequence:
Initial Deformed State (Step 1):
The original beam deforms under a distributed load, causing translations and rotations at the end joints.
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Removal and Blocking:
The original beam is removed. The software applies equivalent forces and moments at the joints to ensure that the remaining structure remains in equilibrium.
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Introduction of the New Section:
The new beam is introduced into the model with no initial stress state (zero internal forces). The fundamental aspect is that its initial geometry is generated to exactly match the current rotation of the joints. The member is already introduced with deformation.
Force Rebalancing (Step 2):
The blocking forces are removed. The structure seeks a new static equilibrium. The columns, which were bent, attempt to recover their verticality (elastic recovery or springback effect). The new beam resists this movement, forcing the joints to assume an intermediate rotation. Since the new beam undergoes imposed rotations at its ends without any span load applied, it develops a constant bending moment diagram along its entire length.
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Load Reapplication (Step 3):
Span loads must always be reapplied by the user after the Change Section operation. After this reapplication, the results are as follows:
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Step-by-Step Numerical Evolution
To illustrate this phenomenon, we numerically analyze the frame in which an IPE 200 beam is replaced by an IPE 400 beam. The vertical displacements (Dz) and rotations (Ry) at the column head and the mid‑span displacement, together with the bending moments (M), quantify the exact behavior of the structure.
Table of Forces and Deformations Evolution
Below, only as an example, the expected moments and displacements are presented for a simple frame with an IPE400 beam subjected to a distributed load.
| Description of the Operation | Mid‑Span Displacement Dz (m) | Column Head Moment (kNm) | Span Moment (kNm) | |
|---|---|---|---|---|
| Frame with IPE 400 | Initial load on IPE 400 | -0.00251 | -17.94 | 44.55 |
Next is the table with the results of the multiple steps of the Change Section operation:
| Analysis Phase | Description of the Operation | Column Head Displacement Dz (m) | Column Head Rotation Ry (rad) | Mid‑Span Displacement Dz (m) | Column Head Moment (kNm) | Span Moment (kNm) |
|---|---|---|---|---|---|---|
| Step 1 | Initial load on IPE 200 | -0.000091 | -0.002574 | -0.01198 | -37.80 | 24.70 |
| Step 2 | Replacement with IPE 400 | 0.000000 | -0.001481 | -0.01052 | +21.20 | +21.20 |
| Step 3 | Load reapplied on IPE 400 | -0.000091 | -0.002703 | -0.01303 | -39.17 | 23.33 |
Elastic Recovery (Springback)
In Step 2, the joint rotation changes from -0.002574 rad to -0.001481 rad. This positive variation DeltaRy 0.001093 rad represents the frame attempting to straighten after removal of the original beam.
The Constant Moment Diagram
The new IPE 400 beam appears in Step 2 and is immediately subjected to this Delta Ry at its ends. According to elasticity theory, a member subjected to pure rotations at its supports/end connections develops a constant moment, approximated by its flexural rigidity M = 2EI/L Delta R. This explains why Step 2 records a positive moment of +21.20 kNm both at the end joints and at mid‑span.
Accumulated Deformation
In Step 3, the end moment of -39.17 kNm closely matches the results of a linear analysis of a frame with an IPE400 beam. The nuance lies in the deformation: the final rotation -0.002703 rad is more than double that which an IPE 400 beam would experience in an undeformed frame (which would be generated only by the increment of Step 3).
As for the mid‑span displacement, it is evident that the deformation is significantly larger in the case of staged construction, 0.01303 m versus -0.00251 m.
Conclusion for Engineering Practice
The most sensitive aspect of the Change Section operation does not relate to structural strength, since the final bending moments tend to present adequate or even conservative distributions due to the stiffness history.
The main analytical nuance lies in the evaluation of deformations. As the new structure passively inherits the bent geometry of the original system, in a practical rehabilitation scenario the new beam will easily satisfy Ultimate Limit States. However, it may exceed Serviceability Limit State limits, with potential impact on the behavior of non‑structural elements that experience the total accumulated deformation of the structure.
To ensure rigor and full control of the model, it is recommended that the engineer systematically monitors the absolute displacement values at each stage and ensures the explicit reapplication of the original span loads after the section change.
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