PPT: Influence Lines Notes | EduRev

Structural Analysis

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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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