Lesson 1. Introduction to Structural Analysis.pdf

Teora de Estructuras y Construcciones Industriales. 2014-2015

CHAPTER 1. Introduction to Structural Analysis


Lesson 1. Introduction to Structural Analysis

1.1. Objectives of structural analysis.

1.2. Structural models.

1.3. Structural forms.

1.4. Simplified structural models.

1.5. Types of internal forces.

1.6. Types of external loading.

1.7. Types of supports and reactions.

1.8. Determinacy and freedom degrees.

1.9. Design hypothesis: first and second order theories.


3

Structure could be a load-bearing element or a group of load-bearing elements with functional requirements.

The main objective of structural analysis is to determine how a structure responds to specified loads and actions.

1.1. Objectives of structural analysis


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Conceptual and preliminary stages (types of structure,

materials and loading),

Calculation stage (internal forces and displacements),

Final stage (design drawings with written

specifications of materials and

pertinent codes to be

employed),

Construction stage.

The structural design process:



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Structural model

(elements, materials,

supports)

Loading analysis

Calculation of

stresses and strains

Checking limit states

(design codes)

Final design

New structural

design

Calculation of

displacements

Calculatin of

internal forces

YES

NO



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1.2. Simplified structural models

(Idealization)

Variables to define:

Materials,

Structural forms,

Elements types,

Joints (connections) types,

Supports,

External loading,

Type of calculation (static,

dynamic, etc.)

Type of structural analysis


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1.3. Structural forms

Clasification by structural funtion:

Houses, offices and industrial buildings.


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Industrial equipment (cranes,

pressure vessels, silos)


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Gateways, bridges and slabs.


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Classification of structures: Rigid and pin joint structures.

Rigid joint: same angle before and after deformation.

2D and 3D Rigid joint structures (Frames)

Before

deformation

After

deformation


- 11 - 2D Pin joint structures (Trusses)

Pin Joint: free rotation (hinge)



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Element types:

1D elements (bar elements)

2D elements:

- Membranes,

- Plates,

- Shells,

- Shear walls.

3D elements.



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1.5. Types of internal forces

b)

1D elements: bars elements

2D and 3D Rigid elements

(Axial and Shear Forces and

Bending and Torsion Moments)

Cables

(Axial Force: Tension)

Pin joint elements

(Axial Force: Tension and Compression)


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2D elements: Membranes


Membranes examples


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2D elements: Plates


Plates examples


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2D elements: Shells


placamembranaMembrane Plate

Shells examples


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2D elements: Shear walls


Shear wall example


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3D elements


Dam example


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1.6. Types of external loading

Classification (actions):

Surface and volume loads. Static and dynamic loads. Permanent and variable loads.

Point and distributed loads. Thermal load. Enforced displacements. Fitting defects.

Classification (actions): own weight load snow load

wind load


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Support clasification:

Pin and roller (rocker) supports

Fixed or clamped (encastre) support

Guide

Spring supports: linear ad torsional springs.

1.7. Types of supports and reactions

Pin support

Spring support

Roller support

Fixed support


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3 linear displacements (u, v, w )

3 rotations (Fx, Fy, Fz)

3D element section

(6 degrees of freedom)

Fixed: Restriction of 6 FD 6 Reactions (Unknowns)

Pin: Restriction of 3 FD 3 Reactions (Unknowns)



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1 rotation (Fz)

2D element section

(3 degrees of freedom)

2 linear displacements (u, v)

Pin support Roller support Fixed support Guide

Schematic representation


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Spring supports: partially limitation of linear and rotation

displacements. The reactions depend on the rigid constant (k = sm).

RV

Linear spring support Torsional spring support


RH


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1.8. Determinacy grade: DG ( = GH) = r - 3

If DG < 0 Unstable structures (mechanisms) (No. unknowns < No. available equilibrium equations)

If DG = 0 Statically determinate structures (No. unknowns = No. available equilibrium equations)

If DG > 0 Statically indeterminate structures

(No. unknowns > No. available equilibrium equations)

DG=1 DG=3


Rigid joint open structures:

DG = DGext + DGint = r - 3 ao

DGext = r 3 ao

DGint = 0

r = No. reactions

ao = bo 1 = hinge equations (open contours)

Rigid joint closed structures:

DG = DGext + DGint = r + 3 cc - 3 (ao + ac)

DGext = r 3 - aa

DGint = 3 cc ac

r = No. reactions,

cc = No. closed contours,

ao = bo - 1= hinge equations (open contours)

ac = bc 1 = hinge equations (closed contours)

DG = DGext = 3 DG = DGext = 2

DG = 3+3=6

DGext = 3

DGint = 3

DG = 3+2=5

DGext = 3

DGint = 2

1.8.a) Statically indeterminate rigid joint structures.


DG = DGext + DGint = r + b 2n

DGext = r - 3

DGint = DG - DGext = b 2n + 3

b = No. bars, r = No. reactions, n = No. joints

b = 17

r = 3

n = 10

b = 17

r = 3

n = 10

b = 18

r = 3

n = 10 A

Sm

50kN

50kN

4m 4m

3m

C

D

B

b = 5

r = 4

n = 4 d)

DG=0 DG=0

DG=DGint=1 DG=DGext=1

1.8.b) Statically indeterminate pin joint structures.


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Structures without sidesway: If AE = (axial deformations, e = 0), kinematic unknowns

(freedom degrees) are rotation of joints (NR) only, because bar rotation are cero (BR = 0).

A B C DA B C D

jB jC

CIR

1.8.c) Kinematically indeterminate structures:

Degrees of freedom FD (= GL) = NR + BR

FD = NR = 2 (jB , jC)

Structures with sidesway: If AE= (axial

deformations, e = 0), kinematic unknowns

(freedom degrees) are both joint rotations (NR)

and bar rotations (BR).

A

B C

D

UB UC

VB VCjB

jC

q q

yAB yDC

yBC

FD = NR + BR = 3 (jB , jC , yAB)

yBC = f (yAB)

yDC = f (yAB)


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Requirements of first order theory:

Linear-elastic material behaviour.

Small strain and displacements

These conditions permit:

Equilibrium applied to undeformed structure geometry.

Linear equation systems solution.

Superposition principle.

1.9. Design hypothesis: First and second order theories


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First order theory:



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Second order theory:


Documents

Lesson 1. Introduction to Structural Analysis.pdf