Determination of Stress-Strain State Taking into Account Genetic Nonlinearity (“Erection” Mode)

Objective: Comparison of the results of the calculations of the stress-strain state of a bar structure taking into account genetic nonlinearity performed by SCAD and the analytical solution.

Initial data file: Truss.MPR

Problem formulation:

References: A.V.Perelmuter, Control of the Behavior of Load-Bearing Structures (2-nd edition revised and supplemented) , Moscow: ASV, 2011, § 5.2.

Initial data:

The final model of the analyzed structure is given in the figure (linear dimensions in meters), and some additional information is given in the table. Element 11 shown with a dotted line in this figure was added temporarily and was not included in the final configuration.

Bar	Stiffness
numbers	ЕА, t
1	10
2	10
3	10
4	10
5	10
6	2
7	2
8	4
9	5
10	5
11	25
12	10
13	10

The sequence of operations for achieving the prestressing is shown in the figure below.

Finite element model:

The structure is modeled by bar elements of general type 1.
The dimension of the complete model is 8 nodes and 13 finite elements.
Modeling of the building erection process consists of the following stages:

Stage	Description of operations
1	Forced shortening of the bar 6 (dislocation d₆= 0,001 m) and suspension of the ballast weight G₆=10 t in the node 6.
2	Attachment of the bar 12 to the system
3	Removal of the bar 11 performed by the program in two stages: replacement of the effect of the bar by forces S₁₁, which it transfers to the rest of the system (see. 3а), and application of the “compensating” load to the system ̶ S₁₁ (see. 3b). Installation of the ballast weight G₁=10 t in the node 1.
4	Attachment of the bar 13 to the system
Working	Removal of the ballast weights G1 and G6 and loading the system by the live load Q₁=Q₃=Q₅=2.

Comparison of solutions:

Parameter	Results		Deviations, %
Parameter	Theory	SCAD	Deviations, %
Stage 1: Vertical displacement of the node 6, cm	-17,078	-17,042	0,21
Force in the element 2, t	-2,510	-2,500	0,40
Stage 2: Vertical displacement of the node 6, cm	-17,078	-17,042	0,21
Force in the element 2, t	-2,510	-2,500	0,40
Stage 3: Vertical displacement of the node 6, cm	-28,220	-28,185	0,12
Force in the element 2, t	4,990	5,000	-0,20
Stage 4: Vertical displacement of the node 6, cm	-28,220	-28,185	0,12
Force in the element 2, t	4,990	5,000	-0,20
Working stage Vertical displacement of the node 6, cm	1,257	1,293	0,21
Force in the element 2, t	5,559	5,61	0,91

Note: There are arithmetic errors in the source. The comparison of solutions was made on the basis of the corrected calculations reported by the author.