Staged Construction Analysis

While the importance of 3D finite element based analysis in studying lateral actions, like wind loadings, on high rise and/or irregular tall structures is well recognized, the inherited problem of general finite element analysis in getting the right member resultant forces under gravitational loading is some time overlooked.

Take the simple plane frame problem as shown in Fig. 1 for example. The 20-story 3-bay frame is loaded with uniform span loads of 10 kN/m per bay (the self-weight of the structural members is neglected for simplicity). The column reactions at the support can be conveniently computed by hand (tabulated as method (i) in Table 1).

Fig 1. Simple Plane Frame

Using the manual-like calculation method of PMCAD module in PTC SE CAD ( www.ptcsecad.com ), the same set of values was found in 100% agreement (method (ii) in Table 1). In PTC SE CAD, the member resultant forces computed using PMCAD method can also be further combined with 3D finite element lateral analysis result obtained from SATWE module for structural member design.

Table 1: Comparison of column resultant forces
Method	column reaction (kN)		% deviation
	outer	inner	outer	inner
(i) Manual	500	1000	--	--
(ii) PTC SE CAD's      PMCAD method	500	1000	0%	0%

Many of the general purpose finite element based structural software lack the capability of running staged construction analysis, an analysis that simulates the effects of (a) incremental floor-by-floor addition of self-weight (as well as other dead loadings); and (b) incremental structural stiffness; to the load paths and resultant member forces of a multi-storey building.

Analyze the above problem with any general finite element software that does not support staged construction analysis, one can easily find that the column reactions are different from the expected values, as well as the bending moment of the beams at the 20 th floor level seems odd (Fig. 2). For comparison, user of PTC SE CAD can also obtain the similar result by selecting "Loading at Same Time" option under SATWE "Define Design Parameters" menu.

Detailed staged construction analysis, which different stiffness matrixes are generated n-time and loaded incrementally on floor-by-floor basis for n-storey building, can be performed to correct this, provided the right formulation and assumptions are properly considered.

Fig 2. Beam Bending moment of 1 st and 20 th level beam after a finite element analysis without staged construction analysis.

However, such computational intensive approach is very time consuming and impractical sometime for deadline driven real world design projects. Therefore, an alternative fast staged construction analysis is also available in PTC SE CAD. Using this approach, good results can be obtained quickly in a single run (Fig 3).

Fig 3. Fast staged construction analysis option in PTC SE CAD gives good solution for 1 st and 20 th storey beam bending moment in a single run.

With the above features, one can then be assured that all the complete structural drawings produced on the fly by PTC SE CAD is in good order based on the reasonably good gravitational and 3D lateral analysis results.