This lecture discusses analysis of indeterminate beams. It begins with an introduction to structures, including what structures are, what they do, and how their performance is assessed. Structures must carry and transfer loads safely while maintaining equilibrium. The degree of indeterminacy, or whether a structure has enough equations to solve for its unknown forces, is then introduced. The document provides equations to assess the degree of indeterminacy in two-dimensional and three-dimensional truss and framed structures based on the number of members, joints, and external constraints. Various examples of determinate and indeterminate structures are shown.

1. Subject Name: Theory of
Structures
Topic Name:Analysis of Indeterminate
Beams
Lecture No: 17
Dr.Omprakash Netula
Professor & HOD
Department of Civil Engineering
09/28/17 Lecture Number, Unit Number 1

2. 2
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 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. 3
Figure 1.2a
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
Various components
carry different types
of loads

4. 4
Figure 1.2b
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. 5
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 compressed
or contracted near its lower surface by the weight of the monkey
Fig.4
Fig.5

6. 6
Figure 1.1
• A building structure safely transmits loads down to Earth

7. 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. 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
.0,0 == ∑∑ MF

9. 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 ≥ 2j, where m = number of
members, j = number of joints and r = number of external constrains.

10. 10
1.3 ASSESSING THE DEGREE OF INDETERMINACY (Cont’d)
• Three dimensional truss structure: m + r ≥ 3j, where m = number of
members, j = number of joints, and r = number of external constraints

11. 11
1.3 ASSESSING THE DEGREE OF INDETERMINACY (Cont’d)
Two-dimensional framed structure: 3m + r ≥ 3j +ec

12. 12
1.3 ASSESSING THE DEGREE OF INDETERMINACY (Cont’d)
• Three-dimensional framed structure: 6m + r ≥ 6j +ec

13. 13
ASSESSING THE
DEGREE OF
INDETERMINACY
(Cont’d)

14. 14
ASSESSING THE
THE DEGREE OF
INDETERMINACY
(Cont’d)