PPT: The Force Method of Analysis | Structural Analysis - Civil Engineering (CE) PDF Download

 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