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# PPT: The Force Method of Analysis Civil Engineering (CE) Notes | EduRev

## Civil Engineering (CE) : PPT: The Force Method of Analysis Civil Engineering (CE) Notes | EduRev

``` Page 1

ANALYSIS OF INDETERMINATE
STRUCTURES BY FORCE METHOD
Page 2

ANALYSIS OF INDETERMINATE
STRUCTURES BY FORCE METHOD
5.1 ANALYSIS OF INDETERMINATE STRUCTURES
BY FORCE METHOD - AN OVERVIEW
 5.1 ANALYSIS OF INDETERMINATE STRUCTURES BY FORCE
METHOD - AN OVERVIEW
 5.2 INTRODUCTION
 5.3 METHOD OF CONSISTENT DEFORMATION
 5.4 INDETERMINATE BEAMS
 5.5 INDETRMINATE BEAMS WITH MULTIPLE DEGREES OF
INDETERMINACY
 5.6 TRUSS STRUCTURES
 5.7 TEMPERATURE CHANGES AND FABRICATION ERRORS
Page 3

ANALYSIS OF INDETERMINATE
STRUCTURES BY FORCE METHOD
5.1 ANALYSIS OF INDETERMINATE STRUCTURES
BY FORCE METHOD - AN OVERVIEW
 5.1 ANALYSIS OF INDETERMINATE STRUCTURES BY FORCE
METHOD - AN OVERVIEW
 5.2 INTRODUCTION
 5.3 METHOD OF CONSISTENT DEFORMATION
 5.4 INDETERMINATE BEAMS
 5.5 INDETRMINATE BEAMS WITH MULTIPLE DEGREES OF
INDETERMINACY
 5.6 TRUSS STRUCTURES
 5.7 TEMPERATURE CHANGES AND FABRICATION ERRORS
5.2 INTRODUCTION
5.2 Introduction
 While analyzing indeterminate structures, it is necessary to satisfy (force)
equilibrium, (displacement) compatibility and force-displacement relationships
 (a) Force equilibrium is satisfied when the reactive forces hold the structure in
stable equilibrium, as the structure is subjected to external loads
 (b) Displacement compatibility is satisfied when the various segments of the
structure fit together without intentional breaks, or overlaps
 (c) Force-displacement requirements depend on the manner the material of the
structure responds to the applied loads, which can be linear/nonlinear/viscous
and elastic/inelastic; for our study the behavior is assumed to be linear and elastic
Page 4

ANALYSIS OF INDETERMINATE
STRUCTURES BY FORCE METHOD
5.1 ANALYSIS OF INDETERMINATE STRUCTURES
BY FORCE METHOD - AN OVERVIEW
 5.1 ANALYSIS OF INDETERMINATE STRUCTURES BY FORCE
METHOD - AN OVERVIEW
 5.2 INTRODUCTION
 5.3 METHOD OF CONSISTENT DEFORMATION
 5.4 INDETERMINATE BEAMS
 5.5 INDETRMINATE BEAMS WITH MULTIPLE DEGREES OF
INDETERMINACY
 5.6 TRUSS STRUCTURES
 5.7 TEMPERATURE CHANGES AND FABRICATION ERRORS
5.2 INTRODUCTION
5.2 Introduction
 While analyzing indeterminate structures, it is necessary to satisfy (force)
equilibrium, (displacement) compatibility and force-displacement relationships
 (a) Force equilibrium is satisfied when the reactive forces hold the structure in
stable equilibrium, as the structure is subjected to external loads
 (b) Displacement compatibility is satisfied when the various segments of the
structure fit together without intentional breaks, or overlaps
 (c) Force-displacement requirements depend on the manner the material of the
structure responds to the applied loads, which can be linear/nonlinear/viscous
and elastic/inelastic; for our study the behavior is assumed to be linear and elastic
5.2 INTRODUCTION (Cont’d)
 Two methods are available to analyze indeterminate structures, depending on
whether we satisfy force equilibrium or displacement compatibility conditions -
They are: Force method and Displacement Method
 Force Method satisfies displacement compatibility and force-displacement
relationships; it treats the forces as unknowns - Two methods which we will be
studying are Method of Consistent Deformation and (Iterative Method of)
Moment Distribution
 Displacement Method satisfies force equilibrium and force-displacement
relationships; it treats the displacements as unknowns - Two available methods
are Slope Deflection Method and Stiffness (Matrix) method
Page 5

ANALYSIS OF INDETERMINATE
STRUCTURES BY FORCE METHOD
5.1 ANALYSIS OF INDETERMINATE STRUCTURES
BY FORCE METHOD - AN OVERVIEW
 5.1 ANALYSIS OF INDETERMINATE STRUCTURES BY FORCE
METHOD - AN OVERVIEW
 5.2 INTRODUCTION
 5.3 METHOD OF CONSISTENT DEFORMATION
 5.4 INDETERMINATE BEAMS
 5.5 INDETRMINATE BEAMS WITH MULTIPLE DEGREES OF
INDETERMINACY
 5.6 TRUSS STRUCTURES
 5.7 TEMPERATURE CHANGES AND FABRICATION ERRORS
5.2 INTRODUCTION
5.2 Introduction
 While analyzing indeterminate structures, it is necessary to satisfy (force)
equilibrium, (displacement) compatibility and force-displacement relationships
 (a) Force equilibrium is satisfied when the reactive forces hold the structure in
stable equilibrium, as the structure is subjected to external loads
 (b) Displacement compatibility is satisfied when the various segments of the
structure fit together without intentional breaks, or overlaps
 (c) Force-displacement requirements depend on the manner the material of the
structure responds to the applied loads, which can be linear/nonlinear/viscous
and elastic/inelastic; for our study the behavior is assumed to be linear and elastic
5.2 INTRODUCTION (Cont’d)
 Two methods are available to analyze indeterminate structures, depending on
whether we satisfy force equilibrium or displacement compatibility conditions -
They are: Force method and Displacement Method
 Force Method satisfies displacement compatibility and force-displacement
relationships; it treats the forces as unknowns - Two methods which we will be
studying are Method of Consistent Deformation and (Iterative Method of)
Moment Distribution
 Displacement Method satisfies force equilibrium and force-displacement
relationships; it treats the displacements as unknowns - Two available methods
are Slope Deflection Method and Stiffness (Matrix) method
5.3 METHOD OF CONSISTENT DEFORMATION
 Solution Procedure:
 (i) Make the structure determinate, by releasing the extra forces constraining
the structure in space
 (ii) Determine the displacements (or rotations) at the locations of released
(constraining) forces
 (iii) Apply the released (constraining) forces back on the structure (To
standardize the procedure, only a unit load of the constraining force is applied
in  the +ve direction) to produce the same deformation(s) on the structure as
in (ii)
 (iv) Sum up the deformations and equate them to zero at the position(s) of
the released (constraining) forces, and calculate  the unknown restraining
forces
Types of Problems to be dealt: (a) Indeterminate beams; (b) Indeterminate
trusses; and (c) Influence lines for indeterminate structures
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## Structural Analysis

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