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Conceptual onceptual Design sig n of Buildin Buil dings gs (Cour (Course se unit uni t code c ode 1C2) 1C2)
Modu odule le A Struc tructural tural Analys Analysis is J.P. Jaspart (University of Liège)
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents
1st order analysis 2nd order analysis Examples
In a first order analysis the internal forces (and displacements) are evaluated in relation to the undeformed structure (clause 5.2.1(1) of EC3-1-1).
This is the method most used in the analysis of current structures. The internal forces (and displacements) may be obtained using the well-know methods (force method, displacement method, among others). In general, any commercial software performs this type of analysis (e.g. OSSA2D).
In the case of 1st order elastic analysis, the deformations (and internal forces) are proportional to the applied loads, and as a consequence the principle of
superposition of effects can be used to simplify the analysis. Load
1st order elastic analysis 2nd order elastic analysis
European Erasmus Mundus Master Course
Undeformed structure Sustainable Constructions under Natural Hazards and Catastrophic Events
L3 – Structural analysis - First order analysis and second order analysis.
Displacement
2
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
In a second order analysis the deformation
of the structure (the so-called 2nd order
P
P
effects) is considered in the evaluation of internal forces (and displacements).
P-
effects (local effects).
P-
effects (global effects).
Structures more sensitive to 2nd order effects are structures with high compressed members and structures with low stiffness.
This type of analysis is performed through iterative processes, only practicable by using computer programs. In the case of simple 2D structures (such as 2D steel frames) there are simplified 2nd order processes.
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
In accordance with this type of analysis the deformations (and internal forces) are not proportional to the applied loads.
L3 – Structural analysis - First order analysis and second order analysis.
3
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
1st order elastic analysis
Load
2nd order elastic analysis 1st order plastic analysis 2nd order plastic analysis (advanced analysis)
Displacement
Need to consider 2a order analysis in steel structures – clause 5.2.1 (3) of EC3-1-1: cr
cr European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
F cr F Ed
F cr F Ed
10
15
(elastic analysis) (plastic analysis)
FEd:
design loading for a given load combination;
Fcr :
elastic critical load.
L3 – Structural analysis - First order analysis and second order analysis.
4
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1 Consider a structure composed of a series of frames with 10 m spacing. Assume that the structure is laterally rigid in the longitudi nal direction (perpendicular to the main frames). For the given load combination and 3 pre-design solutions, obtain the internal forces using a computer program, considering a 1st order elastic analysis versus a 2nd order elastic analysis.
Typical frame
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3D View of a module with 2 frames L3 – Structural analysis - First order analysis and second order analysis.
Plan View of a module with 2 frames 5
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1 i) Pre-design solution 1.
Pinned supports Rigid joints Beams: Levels 1 and 2 – IPE 450 Level 3 – IPE 360 Columns: External – HEB 220 Internal – HEB 260 Material: S 235
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
Frame loading L3 – Structural analysis - First order analysis and second order analysis.
6
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1 i) Internal forces using a 1st order elastic versus 2nd order elastic analysis
Axial force diagrams (1st order elastic)
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
Axial force diagrams (2nd order elastic) L3 – Structural analysis - First order analysis and second order analysis.
7
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1 i) Internal forces using a 1st order elastic versus 2nd order elastic analysis
Shear force diagrams (1st order elastic)
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
Shear force diagrams (2nd order elastic) L3 – Structural analysis - First order analysis and second order analysis.
8
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1 i) Internal forces using a 1st order elastic versus 2nd order elastic analysis
Bending moment diagrams (1st order elastic )
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
Bending moment diagrams (2nd order elastic)
Higher difference in columns – 27.7% increasing of the bending moment L3 – Structural analysis - First order analysis and second order analysis.
9
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1 ii) Pre-design solution 2. Column cross sections increased.
Pinned supports Rigid joints Beams: Levels 1 and 2 – IPE 450 Level 3 – IPE 360 Columns: External – HEB 300 Internal – HEB 360 Material: S 235
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
Frame loading L3 – Structural analysis - First order analysis and second order analysis.
10
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1 ii) Internal forces using a 1st order elastic versus 2nd order elastic analysis
Axial force diagrams (1st order elastic)
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
Axial force diagrams (2nd order elastic) L3 – Structural analysis - First order analysis and second order analysis.
11
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1 ii) Internal forces using a 1st order elastic versus 2nd order elastic analysis
Shear force diagrams (1st order elastic)
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
Shear force diagrams (2nd order elastic) L3 – Structural analysis - First order analysis and second order analysis.
12
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1
Bending moment diagrams (1st order elastic )
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
Bending moment diagrams (2nd order elastic)
Higher difference in columns – 10.3% increasing of the bending moment L3 – Structural analysis - First order analysis and second order analysis.
13
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1 iii) Pre-design solution 3.
Pinned supports
Initial cross sections but introducing bracing members.
Beams:
Beam-column joints pinned Levels 1 and 2 – IPE 450 Level 3 – IPE 360 Columns: External – HEB 220 Internal – HEB 260
Bracing members – CHS 60x5 Material: S 235
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
Frame loading L3 – Structural analysis - First order analysis and second order analysis.
14
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 1 iii) Internal forces using a 1st order elastic versus 2nd order elastic analysis
Bending moment diagrams (1st order elastic )
Bending moment diagrams (2nd order elastic) European Erasmus Mundus Master Course
All differences in the bending moments (and also in other internal forces) can be neglected Sustainable Constructions under Natural Hazards and Catastrophic Events
L3 – Structural analysis - First order analysis and second order analysis.
15
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
EXAMPLE 2 Consider the following steel frame with fixed bases, composed by columns HEA 260 and beams IPE 400 submitted to the shown load combination. Calculate the internal forces using a computer program (OSSA2D), considering: a) 1st order elastic analysis;
204.0 kN
204.0 kN 33.6 kN/m 18.2 kN
b) 2 nd order elastic analysis. 253.5 kN
45.0 kN/m
253.5 kN
5m
14.8 kN
5m
10 m
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
L3 – Structural analysis - First order analysis and second order analysis.
16
Conceptual Design of Buildings
Module A – Structural Analysis
List of contents 1st order analysis 2nd order analysis Examples
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
EXAMPLE 2 Bending moment at indicated sections. 6
1 2 3 3’ 3’’ 4 5 5’ 5’’ 6 6’ 7 8 8’
1st Order M y (kNm) 11.0 -109.3 -256.4 -86.4 170.0 253.5 -360.9 153.1 -207.8 -174.1 -174.1 219.0 -227.3 227.3
2 nd Order M y (kNm ) 2.9 -115.1 -244.0 -78.3 165.8 257.2 -363.6 156.4 -207.2 -168.7 -168.7 225.3 -227.9 227.9
7
6’
8 8’
5m 3’’
3
4
5
3’
5’’ 5’
5m
1
2
10 m
Note: This values of bending moments were obtained by a 2nd order elastic analysis
L3 – Structural analysis - First order analysis and second order analysis.
17
•
This lecture was prepared for the Edition 1 of SUSCOS (2012/14) by RUI SIMÕES (UC) and FLOREA DINU (UPT). Adaptations brought by J.P. Jaspart (Ulg) for Edition 2 of SUSCOS The SUSCOS powerpoints are covered by copyright and are for the exclusive use by the SUSCOS teachers in the framework of this Erasmus Mundus Master. They may be improved by the various teachers throughout the different editions.
Thank you for your attention http://steel.fsv.cvut.cz/suscos
