1st order & 2nd order analysis

7/26/2019 1st Order & 2nd Order Analysis

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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

J.P. Jaspart (University of Lige)


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L3 Structural analysis - First order analysis and second order analysis.

European Erasmus Mundus

Master Course

Sustainable Constructions

under Natural Hazards

and Catastrophic Events

Conceptual Designof Buildings

2

Module A Structural Analysis

List of contents

1st order analysis

2nd order analysis

Examples

In a f irst 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) areproportional to the applied loads, and as a consequence the principle of

superposition of effects can be used to simplify the analysis.

Undeformed structure

Load

Displacement

2nd order elastic analysis

1st order elastic analysis


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Master Course

Sustainable Constructions

under Natural Hazards



3


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

effects) is considered in the evaluation ofinternal forces (and displacements).

P- effects (local effects).

P- effects (global effects).

P P

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 2Dsteel frames) there are simplified 2nd order processes.

In accordance with this type of analysis the deformations (and internal forces)

are not proportional to the applied loads.


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Master Course

Sustainable Constructionsunder Natural Hazards



4


List of contents

1st order analysis

2nd order analysis

Examples

(elastic analysis)10 Edcrcr FF

15Edcrcr

FF (plastic analysis)

FEd: design loading for a given load combination;

Fcr: elastic critical load.

Need to consider 2a order analysis in steel structures clause 5.2.1 (3)

of EC3-1-1:

Load

Displacement

1st order elastic analysis

1st order plastic analysis

2nd order elastic analysis

2nd order plastic analysis

(advanced analysis)


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Master Course





EXAMPLE 1

5

Consider a structure composed of a series of frames with 10 m spacing. Assume that the

structure is laterally rigid in the longitudinal direction (perpendicular to the main frames).

3D View of a module with 2 frames Plan View of a module with 2 frames

Typical frame

For the given load combinat ion 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 .

List of contents

1st order analysis

2nd order analysis

Examples


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Master Course





EXAMPLE 1

6

List of contents

1st order analysis

2nd order analysis

Examples

Frame loading

Pinned supports

Rigid joints

Beams: Levels 1 and 2 IPE 450Level 3 IPE 360

Columns: External HEB 220

Internal HEB 260

Material: S 235

i) Pre-design solution 1.


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7

List of contents

1st order analysis

2nd order analysis

Examples

Axial force diagrams (1st order elastic)

i) Internal forces using a 1st order elastic versus 2nd order elastic analysis

Axial force diagrams (2nd order elastic)

EXAMPLE 1


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Master Course





EXAMPLE 1

8

List of contents

1st order analysis

2nd order analysis

Examples


Shear force diagrams (1st order elastic)

Shear force diagrams (2nd order elastic)


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Master Course





EXAMPLE 1

9

List of contents

1st order analysis

2nd order analysis

Examples


Bending moment diagrams (1st order elastic)

Bending moment diagrams (2nd order elastic)

Higher difference in columns 27.7% increasing of the bending moment


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Master Course





EXAMPLE 1

10

List of contents

1st order analysis

2nd order analysis

Examples

Frame loading

Pinned supports

Rigid joints


Columns: External HEB 300Internal HEB 360

Material: S 235

i i) Pre-design solution 2.

Column cross sections increased.


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Master Course





EXAMPLE 1

11

List of contents

1st order analysis

2nd order analysis

Examplesii) Internal forces using a 1st order elastic versus 2nd order elastic analysis

Axial force diagrams (1st order elastic)

Axial force diagrams (2nd order elastic)


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Master Course





EXAMPLE 1

12

List of contents

1st order analysis

2nd order analysis

Examplesii) Internal forces using a 1st order elastic versus 2nd order elastic analysis

Shear force diagrams (1st order elastic)

Shear force diagrams (2nd order elastic)


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Master Course





EXAMPLE 1

13

List of contents

1st order analysis

2nd order analysis

Examples



Higher difference in columns 10.3% increasing of the bending moment


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Master Course





EXAMPLE 1

14

List of contents

1st order analysis

2nd order analysis

Examples

Frame loading

i i i) Pre-design solution 3.

Initial cross sections but introducingbracing members.

Pinned supports

Beam-column joints pinned


Columns: External HEB 220

Internal HEB 260

Bracing members CHS 60x5Material: S 235


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Master Course





EXAMPLE 1

15

List of contents

1st order analysis

2nd order analysis

Examplesiii) Internal forces using a 1st order elastic versus 2nd order elastic analysis



All differences in the bending moments (and also in other internal forces) can be neglected


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Master Course





EXAMPLE 2

16

List of contents

1st order analysis

2nd order analysis

ExamplesConsider 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;

b) 2nd order elastic analysis.

33.6 kN/m

204.0 kN 204.0 kN

10 m

5 m

5 m

45.0 kN/m

18.2 kN

14.8 kN

253.5 kN 253.5 kN


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Master Course





EXAMPLE 2

17

List of contents

1st order analysis

2nd order analysis

Examples

10 m

5 m

5 m

3

45

5

6

6

7

8

8

33

1 2

5

Bending moment at indicated sections.

1stOrder 2ndOrder

My(kNm) My(kNm)

1 11.0 2.9

2 -109.3 -115.1

3 -256.4 -244.0

3 -86.4 -78.33 170.0 165.8

4 253.5 257.2

5 -360.9 -363.6

5 153.1 156.4

5 -207.8 -207.2

6 -174.1 -168.76 -174.1 -168.7

7 219.0 225.3

8 -227.3 -227.9

8 227.3 227.9

Note: This values of bending moments were

obtained by a 2nd order elastic analysis


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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

1st order & 2nd order analysis

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