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# PPT: Influence Lines Notes | EduRev

## GATE : PPT: Influence Lines Notes | EduRev

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Definition of Influence Line
INFLUENCE LINES
Variation of Reaction, Shear, Moment or Deflection at a SPECIFIC POINT due to a
concentrated force moving on beam or frames.

?Applying a deformation to a statically determinate beam or frame will not
cause the beam or frame to bend. The deflected shape due to the unit deformation
will be composed of straight lines and can be used to locate the movable loads to
cause maximum effect, and to calculate the magnitude of the force. Such an
influence diagram is called a quantitative influence line for a determinate structure.

?Applying a deformation to a statically indeterminate beam or frame
will cause the structure to bend and can only be used to locate the position of

Page 2

Definition of Influence Line
INFLUENCE LINES
Variation of Reaction, Shear, Moment or Deflection at a SPECIFIC POINT due to a
concentrated force moving on beam or frames.

?Applying a deformation to a statically determinate beam or frame will not
cause the beam or frame to bend. The deflected shape due to the unit deformation
will be composed of straight lines and can be used to locate the movable loads to
cause maximum effect, and to calculate the magnitude of the force. Such an
influence diagram is called a quantitative influence line for a determinate structure.

?Applying a deformation to a statically indeterminate beam or frame
will cause the structure to bend and can only be used to locate the position of

Page 3

Definition of Influence Line
INFLUENCE LINES
Variation of Reaction, Shear, Moment or Deflection at a SPECIFIC POINT due to a
concentrated force moving on beam or frames.

?Applying a deformation to a statically determinate beam or frame will not
cause the beam or frame to bend. The deflected shape due to the unit deformation
will be composed of straight lines and can be used to locate the movable loads to
cause maximum effect, and to calculate the magnitude of the force. Such an
influence diagram is called a quantitative influence line for a determinate structure.

?Applying a deformation to a statically indeterminate beam or frame
will cause the structure to bend and can only be used to locate the position of

Comparison Between Indeterminate and Determinate Beams

Indeterminate Beam Determinate Beam
Page 4

Definition of Influence Line
INFLUENCE LINES
Variation of Reaction, Shear, Moment or Deflection at a SPECIFIC POINT due to a
concentrated force moving on beam or frames.

?Applying a deformation to a statically determinate beam or frame will not
cause the beam or frame to bend. The deflected shape due to the unit deformation
will be composed of straight lines and can be used to locate the movable loads to
cause maximum effect, and to calculate the magnitude of the force. Such an
influence diagram is called a quantitative influence line for a determinate structure.

?Applying a deformation to a statically indeterminate beam or frame
will cause the structure to bend and can only be used to locate the position of

Comparison Between Indeterminate and Determinate Beams

Indeterminate Beam Determinate Beam
Comparison Between Indeterminate and Determinate Beams

Page 5

Definition of Influence Line
INFLUENCE LINES
Variation of Reaction, Shear, Moment or Deflection at a SPECIFIC POINT due to a
concentrated force moving on beam or frames.

?Applying a deformation to a statically determinate beam or frame will not
cause the beam or frame to bend. The deflected shape due to the unit deformation
will be composed of straight lines and can be used to locate the movable loads to
cause maximum effect, and to calculate the magnitude of the force. Such an
influence diagram is called a quantitative influence line for a determinate structure.

?Applying a deformation to a statically indeterminate beam or frame
will cause the structure to bend and can only be used to locate the position of

Comparison Between Indeterminate and Determinate Beams

Indeterminate Beam Determinate Beam
Comparison Between Indeterminate and Determinate Beams

Qualitative Influence Lines
Müller-Breslau Principle
The Müller-Breslau principle is a method to determine influence
lines. The derivation of the principle comes from the theory
of Virtual work.
Statement:
The influence line for a  response function (reaction, shear,
moment or deflection) is given by the deflected shape of the
released structure by removing the displacement constraint
corresponding to the response function of interest from the original
structure and giving a unit displacement or rotation at the location
and in the direction of the response function.
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## Structural Analysis

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