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h1. Overview and purpose

This test problem demonstrates the formulation of [staged-construction|kb:Staged construction] analysis, as applied using various [modeling|kb:Modeling techniques] procedures. Time-dependent behavior is considered, new [joints|kb:Joint] are placed within deformed and undeformed locations, and a description of how users may interpret output is included.

A five-story column is modeled with five construction stages which ascend vertically. At each stage, a [frame|kb:Frame] object is assigned to represent a 3.7m column segment. A load of 500kN is applied in the gravity direction at the top of each segment. Five load cases are defined to illustrate the process and to evaluate construction scenario. These load cases include:

* LOAD: new joints placed in *undeformed* position; load applied without considering [creep|kb:Creep].

* (DEF) LOAD: new joints placed in *deformed* position using the [ghost structure|kb:Accounting for deformed shape in staged construction#The concept of Ghost Structure] concept; load applied without considering creep.

* LOAD+CR: new joints placed in *undeformed* position; load applied and *creep is considered*.

* (DEF2) LOAD+CR: new joints placed in *deformed* position using a ghost structure with change modifiers; load applied and *creep is considered*.

* (DEF2) LOAD+CR: new joints placed in *deformed* position using a parallel ghost structure with change modifiers; load applied and *creep is considered*.

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Each [load case|kb:Load case] is described more fully in the sections below. Further, the attached PDF provides additional sketches. Results for each load case are independently verified by the spreadsheet calculations in the attached Excel file.


h1. Modeling and staged-construction sequences

A sketch of the construction sequence and associated loading is presented in Figure 1:

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!Sketch.jpg|align=center,border=0!

{center-text}Figure 1 - Column model and sequence{center-text}

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A high resolution image of Figure 1 is presented in the attached [PDF |Staged construction of a five-story column^Hand_calculations_and_sketches.pdf].


h1. Summary of deflection results

Analysis generates the deflection results which follow:

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!SAP2000_deflections_summary.png|align=center,border=0!

{center-text}Figure 2 - Deflection summary{center-text}

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!final joint displacements.png|align=center,border=0!

{center-text}Figure 3 - Graph of final joint deflections{center-text}

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A full resolution image of Figure 2 is attached in the Excel [spreadsheet |Staged construction of a five-story column^Tabulated summary of SAP2000 results.zip].


h1. Discussion of modeling and results for individual load cases

Modeling and results for individual load cases are discussed as follows:


h2. LOAD

* Following the default procedure, newly added joints are placed in undeformed locations. This corresponds to a situation where concrete is cast-in-place up to the desired elevation.
* Leaving the Time-Dependent Material Properties option unchecked in the Nonlinear Parameters menu keeps [creep|kb:Creep] from being considered in analysis.
* In each construction stage, one story is added, and then loaded.


h2. (DEF) LOAD - using ghost structure

* An auxiliary [ghost structure|kb:Accounting for deformed shape in staged construction#The concept of Ghost Structure] is used to add new joints to deformed locations. This is a manual staged-construction process which requires additional stages to setup and utilize the ghost structure. This method may be applicable when fixed-length precast-column segments are erected one by one.
* Creep is not considered.
* Staged construction consists of the following stages:
** To create the ghost structure, the entire structure is first added.
** Frame property modifiers equal to 0.0001 are applied to the entire structure to make it very flexible.
** Stories are added one-by-one in subsequent stages by first assigning unit property modifiers to the story that is being erected. This effectively assigns the actual stiffness and activates the member before load is then applied.


h2. LOAD+CR

* Newly added [joints|kb:Joint] are placed in undeformed locations.
* Creep is considered.
* Construction stages are similar to those of the LOAD load case. Please note that nonzero stage duration causes creep deformation.


h2. (DEF1) LOAD+CR - using ghost structure

* Newly added joints are placed in deformed locations.
* Creep is considered.
* Construction stages are similar to those of the (DEF) LOAD load case, but nonzero stage duration leads to creep deformation in this case.
* Please note that the *age of all elements is counted from the time the entire (ghost) structure is added* in the first step. The upper-story columns are activated, by changing their modifiers from GHOST to FULL, at an older age than the lower-story columns. This may underestimate the creep deformation when compared to the case where all members are activated at the same (young) age of seven days.


h2. (DEF2) LOAD+CR - using parallel ghost structure

* Newly added joints are placed in deformed locations.
* Creep is considered.
* Staged construction is slightly modified from the (DEF1) LOAD+CR load case to model *all elements being activated at the age of seven days*. This is achieved by first adding the entire ghost structure and then by then adding the real structure, story-by-story, with an actual age of seven days.
* Another approach which simulates the activation of elements at the age of seven days is to remove the ghost elements and then add the real elements in a subsequent stage. This procedure is illustrated in the DEF3 LOAD+CR [load case|kb:Load case] within the model.


h1. See Also

* [tp:Staged construction in buildings] test problem


h1. Attachments

* [SAP2000 V12.0.2 model |Staged construction of a five-story column^SAP2000 V12.0.2 model.zip] (zipped SDB file)
* [Hand calculations and sketches |Staged construction of a five-story column^Hand_calculations_and_sketches.pdf] (PDF)
* [Spreadsheet calculations to verify SAP2000 results |Staged construction of a five-story column^Verification using spreadsheet.zip] (zipped Excel file)
* [Tabulated summary of SAP2000 results |Staged construction of a five-story column^Tabulated summary of SAP2000 results.zip] (zipped Excel file)