Advanced Methods of Structural Analysis

362 10 Influence Lines Method

P= 1

1452 3

n k

× ×

FL FR

Inf. line R 1

R 1

(^1) +
Inf. line M 3
− −
Inf. line Qk
1
Qk
Qk

• −
  Inf. line Q 3 R
  Inf. line Mn
  − Mn


• 
  

  Inf. line MFR

  
  


• 
  

  1

  
  


• 
  

  −
  Inf. line Q 3 L
  1

  
  


• 
  

  − −
  Inf. line Mk

  
  


• 
  

  1
  M 3 =1
  Mk
  Fig. 10.19 Continuous beam. Design diagram and models of influence lines for reactions and
  internal forces
  influence line at this support equals to 1. If load is located on portions 1-2 and 3-4,
  then ordinates of influence lines forR 1 are positive, i.e., the vertical reactionR 1 is
  directed upward.
  Influence line for bending moment at the supportM 3 In this case we need to in-
  clude the hinge at the support 3, to apply two positive unit couplesM 3 ,andshow
  the corresponding elastic curve which is a model of required influence line. If a load