Ruxandra Enache

Structural Analysis

Contact information:

enacheruxandra@msn.com

Office hours:

Thursday: 12-14 FILS Dean Office

Ruxandra Enache Structural Analysis

Course 1

How I earn points in order to pass the Structural Analysis exam?

Homeworks (10) = 10 points

Problem 1 (C 7 ) = 20 points

Problem 2 (C10) = 5 points

Problem 3(C12) = 5 points

Problem 4(exam) = 20 points

• Problem 1+Problem 4 are mandatory

• Minimum 35 points for getting theory

Theory Test (exam) = 40 points

Minimum 45 points for passing the exam

Ruxandra Enache Structural Analysis

Course 1

Bibliography• Ifrim M., Macavei F., Vlad I. - Statica, stabilitatea şi dinamica

construcţiilor. Structuri static determinate, UTCB, 1987

• Gheorghiu, Al .- Statica, stabilitatea şi dinamica construcţiilor, Editura didactică şi pedagogică, Bucureşti, 1974 .

• Harry H. West, Fundamentals of Structural Analysis, John Wiley & Sons, Inc., 2002

• Keneth Leet et al., Fundamentals of Structural Analysis, Mc Graw Hill, 2008

• L.Gabor, M.Zanfir, E.Albotă, R.Enache – Statica construcţiilor, Aplicaţii, Bucureşti, Conspress, 2003.

Ruxandra Enache Structural Analysis

Course 1

Chapter 1 :FUNDAMENTAL CONCEPTS IN STRUCTURAL ANALYSIS

Content

Structural Mechanics Disciplines

Structural Analysis Objectives

Modelling actions

Modelling system

Modellins response

Objectivs of chapter 1

• Knowledge and competences refering to modelling actions, system and response

• Define and classify actions

• Accept assumptions for defining structural linear model

• Understand the consequences of accepting theseassumptions

• Define the types of structures to be studied.

Objectivs of Structural Analysis

• Correct designing of the structural form

• Determination of internal forces diagrams

• Computation of elastic displacements in different points of the structure

Disciplines of Structural Mechanisc

• Theoretical Mechanics

• Strength of Materials

• Structural Analysis

• Stability of structures

• Dynamics of structures

• Earthquake Engineering

• Plastic Analysis of structures

• Elasticity Theory

Action System Response

Models

Modelling action

• Clasifying actions

• Types of actions

Clasifying actions

• :By their variability in time

static

dynamic

By the variability of their point of application

fixed

moving

By the variability of their existencepermanent

temporary

By the manner they act on the structure

direct

indirect

By the law of defining actiondeterminist

random

Clasifying actions

Types of actions

• Exterior forces

The exterior force concept must be understand in a generalised form, which consists of:

oConcentrated forces

oDistributed forces

oConcentrated moments

• Temperature changes

• Support settlements

• Imposed displacements

• Execution errors

Modelling system

• Types of structural elements

• Assumptions

• Principles

• Types of structures

Types of structural elements

Line type elements (bars) Surface type elements

Block type elements

B

S

H

B

L

H

B,H<<LB,H<<S

ab

Figura 1

B

L

H

S

L

H

H<<B,L H<<S,L

a b

Figura 2

BL

H

Figura 3

Types of structural elements

Line type elements

B

S

H

B

L

H

B,H<<LB,H<<S

ab

Figura 1

Structural Analysis deals only with line type elements

Assumptions

• “Small displacements” assumption

• Elements should be considered by their axes

• Axial indeformability assumption

• Neglecting the effect of the element curving on the displacement of its ends

• The assumption of a perfect elastic, continous, homogeneous and isotropic material

Geometricallylinear model

Physicallylinear model

Assumptions

Structural Analysis deals with solving linear systems, therefore it is also named Linear Structural Analysis

(or Linear Statics) or First Order Analysis.

Geometricallylinear model

Physicallylinear model

Model withlinear behaviour

Principles

In Linear Structural Analysis the following two principles are valid:

• The superposition principle

• The proportionality principle

Giving up to some assumptions

• If we give up to axial indeformability assumption there is available a joint displacement generalisation which basis the Matrix Analysis of structures

• If we give up to small displacement asumption, the static equilibrium is no longer expressed by reporting it to the undeflected structure. This is The second order Analysis and the Stability of structures domain.

• If we give up to the elastic material assumption, there is no proportionality between forces and displacements. This is Plastic Analysis of structures.

Types of structuresBeams

Simple beams

Figura 9

a b

c d

Gerber beamsFigura 10

Continous beamsFigura 11

Types of structures

Frames

a

Figura 12

b

c

d

Types of structures

Arches

a b

dc

Figura 13

Types of structures

Trusses

Figura 14

c

a b

d

Modelling response

• Internal forces diagrams (N-axial force diagram, T-shear force diagram, M- bending moment diagram);

• Displacement in a point (translations și rotations ).

Self evaluation test1. The concept of force refers to:

a. Only concentrated forces

b. Concentrated, distribuited forces and moments

c. Concentrated, distribuited forces, moments and support settlements

2. Structural Analysis deals with:

a. Structures made up by straight line elements

b. Structures made up by straight and curved line elements

c. Structures made up by line and surface elements

3. The displacements of a structure can be neglected :

a. In absolute value

b. Only by reporting them to the structure dimensions

4. In the Second order Analysis there are valid:

a. Small displacement assumption

b. Axial indeformability assumption

c. Elastic material assumption

5. The response resulting from structural analysis consists of:

a. Internal forces

b. Stresses

c. Reinforce dimensioning

d. Displacement computation

Ruxandra Enache Structural Analysis

Course 1

Chapter 2 : ASSEMBLING ELEMENTS TO FORM STRUCTURAL SYSTEMS

ObjectivesDesign correctly the structural form

Content• Supports and Internal Connections

• Static determinancy

• Geometrical invariability

• Static determinate structures made up by structural units

• Critical systems

Supports and Internal Connections

Axiom of the restraints

Supports Internal connections

The roller (the simple support/the link)

The simple interior connection (the link)

The pin ( or the external hinge) The simple hinge

The fixed end The multiple hinge

The simple rigid connection

The multiple rigid connection