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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
movable loads (like Live load ) to cause maximum response.
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
movable loads (like Live load ) to cause maximum response.
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
movable loads (like Live load ) to cause maximum response.
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
movable loads (like Live load ) to cause maximum response.
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
movable loads (like Live load ) to cause maximum response.
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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FAQs on PPT: Influence Lines - Structural Analysis - Civil Engineering (CE)
| 1. What are influence lines in structural analysis? |  |
Ans. Influence lines in structural analysis represent the variation of a specific response (such as a force, moment, or displacement) at a particular point in a structure due to the movement of a unit load along the structure. They are used to determine the maximum or minimum values of the response at different locations in the structure.
| 2. How are influence lines used in bridge engineering? | |
Ans. Influence lines are extensively used in bridge engineering to analyze the effect of moving loads on bridge structures. By placing a unit load at different positions along the bridge, the corresponding influence line can be obtained, which helps in determining the maximum or minimum forces and moments experienced by the bridge components.
| 3. What is the significance of influence lines in structural design? | |
Ans. Influence lines play a crucial role in structural design as they provide a graphical representation of the internal forces and displacements in a structure due to the movement of a load. By analyzing the influence lines, engineers can determine the critical locations where the structure is subjected to maximum or minimum forces, enabling them to design the structure accordingly.
| 4. How are influence lines helpful in determining the critical load positions? | |
Ans. Influence lines help in determining the critical load positions by showing the variation of a specific response at different points in a structure when a unit load moves along it. The maximum or minimum values of the response occur when the unit load is placed at the position where the influence line reaches its peak or trough. These critical load positions are important for assessing the structural integrity and designing the structure to withstand the maximum loads.
| 5. Can influence lines be used for other types of structures apart from bridges? | |
Ans. Yes, influence lines can be used for other types of structures apart from bridges. They are applicable to any structure where the response to moving loads needs to be analyzed, such as beams, trusses, frames, and even complex structures like buildings or industrial facilities. The principles of influence lines remain the same, regardless of the type of structure, making them a valuable tool in structural analysis and design.
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