STRUCTURAL ANALYSIS 1 1 STRUCTURAL ANALYSIS FUNDAMENTALS 2

STRUCTURAL ANALYSIS 1

1. STRUCTURAL ANALYSIS FUNDAMENTALS 2

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 load safely - 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 Factors 3

Various components carry different types of loads Figure 1. 2 a The human skeleton is a structure which maintains the shape of the body, keeps the various organs and muscles in the right place and transmits loads down to the ground 4

Figure 1. 2 b The spider’s web is a good example of a tension structure. The weight of the spider and its prey is supported by tensile strength of the web 5

Fig. 4 Figures 4 and 5 • • • Fig. 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 compressed or contracted near its lower surface by the weight of the monkey 6

Figure 1. 1 • A building structure safely transmits loads down to Earth 7

1. 1 INTRODUCTION (Cont’d) • Collapse or failure under applied extreme loads - Loads due to extreme environmental 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), Improper anchorage of roof, reinforcement, etc. (Roof blown off or beam collapsing), Lack of sufficient indeterminacy (collapse) 8

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 • Humbley’s 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 9

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 2 j, where m = number of members, j = number of joints and r = number of external constrains. 10

1. 3 ASSESSING THE DEGREE OF INDETERMINACY (Cont’d) • Three dimensional truss structure: m + r 3 j, where m = number of members, j = number of joints, and r = number of external constraints 11

1. 3 ASSESSING THE DEGREE OF INDETERMINACY (Cont’d) Two-dimensional framed structure: 3 m + r 3 j +ec 12

1. 3 ASSESSING THE DEGREE OF INDETERMINACY • Three-dimensional framed structure: (Cont’d) 6 m + r 6 j +ec 13

ASSESSING THE DEGREE OF INDETERMINACY (Cont’d) 14

ASSESSING THE DEGREE OF INDETERMINACY (Cont’d) 15