ENGI 6705: STRUCTURAL ANALYSIS

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1. STRUCTURAL ANALYSIS -FUNDAMENTALS

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1.1 INTRODUCTION

1.1 INTRODUCTION What is a structure? - General Types: Based on deformation and type of

primary load carried [Axial (tensile, compressive), flexure, shear and torsion]; combinations of various types - How to determine? Strip it down to its basic skeleton

What does a structure do? - Carries the load - Loads acting on the structure: Dead & Live (people, equipment, wind, wave, seismic)- Superposition Principle - Keeps the structure in static and dynamic equilibrium -Transfers the load to contiguous structural components - Transfers the loadsafely - Transfers the loads to the foundation

How do you assess the safe performance of a structure? - How does a structure become unsafe? - Collapse or failure - Unserviceable - Unsafe due to unexpected design scenario or shall we say unwise design

Structural Design Principles - Load Factors3

Figure 1.2aThe human skeleton is a structure which maintains the shape of the body,keeps the various organs and muscles in the right place and transmitsloads down to the ground

Various components carry different types of loads

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Figure 1.2bThe spiders web isa good exampleof a tensionstructure. Theweight of the spiderand its prey issupported by tensilestrength of the web

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Figures 4 and 5 All materials and structures deflect, to greatly varying extents, when they are loaded. The science of elasticity is about the interactions between forces and

deflections. The material of the bough is stretched near its upper surface and compressedor contracted near its lower surface by the weight of the monkey

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Fig.5

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Figure 1.1 A building structure safely transmits loads down to Earth7

1.1 INTRODUCTION (Contd)

Collapse or failure under applied extreme loads - Loads due to extremeenvironmental loads (acting, earthquake, wind) - Modes of failure: Plastic deformation(ductile, yielding), Brittle fracture, Buckling (elastic or inelastic), Fatigue, Vibration(resonance), foundation settlement and failure.

Unserviceability: Excessive deformation, acoustic deformation Unexpected load scenario or unwise design: Lack of or faulty sprinkler (fire

damage), Inadequate sealing and paint protection (leakage and corrosion), Improperanchorage of roof, reinforcement, etc. (Roof blown off or beam collapsing), Lack of sufficientindeterminacy (collapse)

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1.2. DETERMINACY AND INDETERMINACY

What do we understand by determinate and indeterminate structures?Determinate: Forces and Moments are determined by statical equations of equilibrium

Humbleys problem: Stool with three or four legs on irregular floor Indeterminate structures: Less equations are available than the number of

unknown forces that constrain the body in space. Extra conditions of deformation compatibility have to be introduced to solve the problem. These conditions will give the extra number of equations required to solve the problem, which will indicate the degree of indeterminacy

Determinacy and indeterminacy - Stable and unstable structures Unstable: When more equations are available than the number of forces that

constrain the body in space, then the structure is unstable

.0,0 == MF

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1.3 ASSESSING THE DEGREE OF INDETERMINACY

Easy to deal with by specifying simple types of structures - Truss structures:2-D, 3-D, - Framed structures: 2-D, 3-D

Two-dimensional truss structures: m + r 2j, where m = number of members, j = number of joints and r = number of external constrains.

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1.3 ASSESSING THE DEGREE OF INDETERMINACY (Contd)

Three dimensional truss structure: m + r 3j, where m = number of members, j = number of joints, and r = number of external constraints

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1.3 ASSESSING THE DEGREE OF INDETERMINACY (Contd)

Two-dimensional framed structure: 3m + r 3j +ec

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1.3 ASSESSING THE DEGREE OF INDETERMINACY (Contd)

Three-dimensional framed structure: 6m + r 6j +ec

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ASSESSING THE DEGREE OF INDETERMINACY(Contd)

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ASSESSING THETHE DEGREE OF INDETERMINACY(Contd)

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ENGI 6705: STRUCTURAL ANALYSIS1. STRUCTURAL ANALYSIS - FUNDAMENTALS1.1 INTRODUCTIONSlide Number 4Slide Number 5Slide Number 6Slide Number 71.1 INTRODUCTION (Contd)1.2. DETERMINACY AND INDETERMINACY1.3 ASSESSING THE DEGREE OF INDETERMINACY1.3 ASSESSING THE DEGREE OF INDETERMINACY (Contd)1.3 ASSESSING THE DEGREE OF INDETERMINACY (Contd)1.3 ASSESSING THE DEGREE OF INDETERMINACY (Contd)Slide Number 14Slide Number 15