course 1 - statics 1
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Ruxandra Enache
Structural Analysis
Contact information:
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