Module a Structural Analysis Suscos 2013 2014 l2 Wa
Transcript of Module a Structural Analysis Suscos 2013 2014 l2 Wa
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European Erasmus Mundus Master Course
Sustainable Constructionsunder Natural Hazards and Catastrophic Events520121-1-2011-1-CZ-ERA MUNDUS-EMMC
Conceptual Design of Buildings(Course unit code 1C2)
Module AStructural Analysis
Jean-Pierre Jaspart (University of Lige)
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L2 Global analysis of steel structures - Elastic analysis and plastic analysis.
European Erasmus Mundus
Master Course
Sustainable Constructions
under Natural Hazards
and Catastrophic Events
Conceptual Designof Buildings
2
Module A Structural Analysis
The structural analysis should take into account several effects, such as:
i) deformability and stiffness of the structure and supports;
ii) strength and stiffness of joints;iii) stability of the structure (global, members and local);
iv) behaviour of cross-sections (classif ication of sections);
v) imperfections (global and member imperfections).
Structural analysis Analytical process by which the response of
the structures (in terms stresses, internal forces and deformations) to
the acting loads is determined.
The understanding of the influence of all these effects is fundamental
for the designer, to make a suitable choice of the method of analysis
for a certain structure.
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
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L2 Global analysis of steel structures - Elastic analysis and plastic analysis.
European Erasmus Mundus
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Sustainable Constructions
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and Catastrophic Events
Conceptual Designof Buildings
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Module A Structural Analysis
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
Global elastic (linear) analysis
Global plastic (non-linear) analysis
Structural analysis
Steel behaviour
- Elastic global analysis should be based on the assumption that the stress-strainbehaviour of the material is linear. As a consequence, to perform a global elastic
analysis, the stresses applied in any cross section of any member, must be lower
than the yield strength of the material (fy in steel structures).
- Plastic global analysis allows the plastification of some cross-sections (ingeneral forming plastic hinges) and consequent redistribution of forces for othersections (with less forces). In this type of analysis the material is modelled by
constitutive relationships non-linear: rigid-plastic; elastic-perfectly plastic (structural
steel), elastic-plastic.
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L2 Global analysis of steel structures - Elastic analysis and plastic analysis.
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Conceptual Designof Buildings
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Module A Structural Analysis
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
- Plastic hinge is formed when in a bending section, all fibers reach the yieldstrength fy, in compression in one side of n.a. and in tension in the other side of
n.a.. The bending moment which can produce this stress diagram is called Plastic
Moment.
- The formation of a plastic hinge, and consequently the use of Structural Plastic
Analysis, require ductile materials and compact sections.
n.a.M
fy
fy
fy
fy
fy
fy
M=Mel Mel
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L2 Global analysis of steel structures - Elastic analysis and plastic analysis.
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Conceptual Designof Buildings
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Module A Structural Analysis
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
oad Linear elastic analysis
Elasto-plastic analysis
isplacement
Rigid-plastic analysis
Elasto-perfectly plastic
Structural analysis
Load-displacement curve for elastic and plastic analysis
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L2 Global analysis of steel structures - Elastic analysis and plastic analysis.
European Erasmus Mundus
Master Course
Sustainable Constructionsunder Natural Hazards
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Conceptual Designof Buildings
Module A Structural Analysis
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples Isostatic structures
6
- Isostatic structure A structure with a number of external supports (or
internal restrictions) equal to the minimum necessary to be in equilibrium forany set of acting loads (e.g. 2D structure with 3 supports). The distribution of
forces and moments can be obtained through conditions of static equilibrium
only.
V1 V2
H1
Statically
determinate frame
Statically
determinated beam
In terms ofnumber of support reactions (or internal restrictions), structuresmay be classified in:
Hyperstatic structures
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L2 Global analysis of steel structures - Elastic analysis and plastic analysis.
European Erasmus Mundus
Master Course
Sustainable Constructionsunder Natural Hazards
and Catastrophic Events
Conceptual Designof Buildings
Module A Structural Analysis
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
7
- Hyperstatic structure A structure with more than the minimum number of
external supports (or internal restrictions) necessary to be in equilibrium forany set of acting loads. In these structures, beyond the static conditions, it
must be used conditions of compatibility of deformations.
V1 V2
H1
M1M2
H1
2D indeterminate
frame =3
Indeterminated
beam =1
Global elastic analysis
Global plastic analysis
Isostatic structures
Hyperstatic structures
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L2 Global analysis of steel structures - Elastic analysis and plastic analysis.
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Sustainable Constructionsunder Natural Hazards
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Conceptual Designof Buildings
8
Module A Structural Analysis
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
- How to perform a global linear elastic analysis of a structure?
- It is easy, even by hand calculation, in isostatic structures, because it is
needed only equilibrium equations.
- In hyperstatic structures, it is needed more complex methods such asthe well-know force method, displacement method, among others.However, in general we use automatic calculation. There are lots of
programs available in the market to perform elastic analysis of structures;
in this course we will use the software OSSA2D.
- The bending stiffness is a fundamental parameter in the analysis ofhyperstatic framed structures (axial stiffness and shear stiffness are in
general neglected in this type of structures). This is defined by EI, being E
the modulus of elasticity of the material (E = 210 GPa for steel) and I thesecond moment of area of cross section around the bending axis.
- In an elastic analysis the distribution of internal forces isproportional to the stiffness (in general the bending stiffness) of themembers. So, stiffer members support higher forces.
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Module A Structural Analysis
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
- Influence of bending stiffness in the elastic analysis of a hyperstatic frame
Bending moment diagram
Columns HEA 260 in both models (EI = 210x106x10450x10-8=21945 kN/m2)
Bending moment diagram
Beams IPE 300
(EI= 210x106x8356x10-8=17547.6 kN/m2)
Beams IPE 600
(EI= 210x106x92080x10-8=193368 kN/m2)
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Module A Structural Analysis
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
- How to perform an global plastic (non-linear) analysis of a structure?
- It is more complex. By hand calculation this is possible only for 2D
structures, with a low degree of indetermination. In more complex structures,this type of analysis requires the use of sophisticated softwares.
- Global plastic analysis may be performed by one of the two
following methods:
Static method (also designated by incremental method) the load isincremented stepwise until the collapse of the structure, which happen
(unless a partial mechanism is formed) when the number of sequential
plastic hinges reach +1, being the degree of indetermination of the
structure. This method is not suitable for perform plastic analysis by hand
calculations. Cinematic method (also designated by mechanism method) comprise three
conditions:
- Firstly, it is assumed a collapse mechanism which comprise +1 plastic
hinges (in general in beam-columns joints, mid-span sections of beams or
sections with point loads) mechanism condition;
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Module A Structural Analysis
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
Cinematic method (continuation):
- Then, it is established the equilibrium equations, considering that in cross
sections where were assumed the formation of a plastic hinge, the bendingmoment equals the plastic bending moment of the cross section
equilibrium condition, from which it is obtained the collapse load (if thestructure and consequently the plastic bending moment of cross section is
known) or the plastic bending moment for a given load (to be used in a pre-
design of a structure).- Finally it must be necessary to check if the bending moments in all other
sections are lower than the plastic moment evaluated for the present
mechanism - plasticity condition.
If this condition is not verified, this means that the present mechanism is not
the correct and it must be necessary to repeat the analysis for others, until to
find the correct one (which correspond the highest plastic bending moment
or the minimum collapse load, depending of which one are being evaluated).
Note: This type of analysis is valid provided that any significant decrease in the fullplastic moment due to axial forces are accounted for.
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L2 Global analysis of steel structures - Elastic analysis and plastic analysis.
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Module A Structural Analysis
EXAMPLE 1
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
Pre-design a cont inuous beam (S 275).
a) global elastic analysis;b) global plastic analysis.
42 kN/m 100 kN100 kN
3 m
A
BC E
F
G
3 m 3 m 3 m6 m
D
D
89.7 kNm
A
C
F
120.6 kNm
68.4 kNm
B
E
G
120.6 kNm
89.7 kNm
a) Elastic global analysis
Elastic bending moment diagram
Hyperstatic structure
= 2
12
Pre-design bending momentMEd = 120.6 kNm.
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L2 Global analysis of steel structures - Elastic analysis and plastic analysis.
European Erasmus Mundus
Master Course
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Module A Structural Analysis
EXAMPLE 1
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
VA
42 kN/m 100 kN100 kN
3 m
A
BC E
F
G
3 m 3 m 3 m6 m
D
Mpl
A
C
D F
Mpl
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Module A Structural Analysis
EXAMPLE 2
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
14
50 kN
280 kN
4 m
4 m 4 m
A
B
C
D
E
189.9 kNm
A
B
C
D
E
247.0 kNm
341.6 kNm
142.9 kNm
Pre-design of a frame (S 275).
a) Elastic global analysis;b) Plastic global analysis.
a) Elastic global analysis
Elastic bending moment diagram
Pre-design bending moment
MEd = 341.6 kNm.
Hyperstatic structure
= 2
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50 kN
280 kN
pl
Mpl
Mpl
HE
VEVA
HA
MA
Plastic hinges
A
B
C
D
E
Conceptual Designof Buildings
Module A Structural Analysis
EXAMPLE 2
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
15
50 kN
280 kN
4 m
4 m 4 m
A
B
C
D
E
b) Plastic global analysis
Plastic bending moment diagram
pl
ri ght
B
pl
right
C
pl
right
D
MM
MM
MM
plEE
plEE
plE
MVH
MVH
M
428084
44
4
kNm280
kN140
kN70
pl
E
E
M
V
H
correct mechanism
Pre-design
bending moment
MEd = 280.0 kNm.
= 2, so it is required 3 plastic hinges
to form a collapse mechanism. It is
assumed a mechanism with plastic
hinges in sections B, C, D.
kNmMkNmM
kNV
kNH
VM
V
H
M
F
F
plA
A
A
AA
A
A
E
Vert
Horiz
280200
140
120
0.045042808
0.0280140
0.07050
0.0
0.0
0.0
.
.
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European Erasmus Mundus
Master Course
Sustainable Constructionsunder Natural Hazards
and Catastrophic Events
Conceptual Designof Buildings
Module A Structural Analysis
EXAMPLE 3
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
16
Calculate the collapse load (load multipl ierp)
of the frame with = 2 (S 275).
80 kN
5 m
6 m 6 m
1
3 4 5
5 m
40 kN
10 kN
20 kN2
Column 152x152 UC 37 (Mpl = 84.92 kNm);
Beam 305x165 UB 40 (Mpl = 171.35 kNm).
Hyperstatic structure
= 2
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L2 Global analysis of steel structures - Elastic analysis and plastic analysis.
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Master Course
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Conceptual Designof Buildings
Module A Structural Analysis
EXAMPLE 3
List of contents
Structural analysis
Elastic analysis
Plastic analysis
Examples
17
px 80
Mpl
Mpl
H5
V5
V1
H1
Mpl
Plastic hinges
1
2
3
4
5
px 40
px 10
px 20
M5
M5
Mechanism 1 Hinges in section 2, 3 and 4.
35.1716
92.8420510
92.845
0.0101268010105200.0
0.010200.0
0.080400
554
13
12
5551
51
51
MVMM
HMM
xHMM
MHVM
HHF
VVF
pl
right
ppl
l eft
pll eft
ppp
gl obal
ppH
ppv
kNmkNmMkNHkNVkNVkNH plp 35.17194.794;43.59;05.161;59.144;98.16;547.2 55511
So, this is not the correct mechanism
80 kN
5 m
6 m 6 m
1
3 4 5
5 m
40 kN
10 kN
20 kN2
Column (Mpl = 84.92 kNm);
Beam (Mpl = 171.35 kNm).
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This lecture was prepared for the Edition 1 of SUSCOS
(2012/14) by RUI SIMES (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 exclusiveuse by the SUSCOS teachers in the framework of this Erasmus Mundus Master.
They may be improved by the various teachers throughout the different editions.
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Thank you
for your attention
http://steel.fsv.cvut.cz/suscos