Advanced Methods of Structural Analysis

10.1 Construction of Influence Lines by the Force Method 329

Influence line for shear forceQk

Should be constructed using formula (10.6). Reaction at supportAin primary sys-
tem caused by primary unknownX 1 D 1 equalsRAD1= l ."/(Fig.10.2a), so
the shear in primary system at sectionkdue to primary unknownX 1 D 1 is
QkDRAD1= l. Therefore

IL.Qk/D

1

l

IL.X 1 /CIL



Qk^0



: (10.11)

Construction of IL.Qk/step by step is presented in Fig.10.4.

k

P= 1

1345268910711

0.6

(^1) ILX
l^1
0.0480.0840.0960.072 0.0720.0960.0840.048
−− −−
a

• 0.2 Inf. line Qk 0
  0.4 0.2
  0.4
  b
  Inf. line Qk


• 
  

  − −
  0.248
  0.484
  0.3040.128
  0.0720.0960.0840.480
  0.516
  (^1) IL(X 0
  IL(Qk) =l 1 )+IL(Qk)
  c
  Fig. 10.4 Construction of influence lines for shear force at sectionk
  The first term of (10.11) is the influence line forX 1 scaled by1= l, so ordinates of
  this graph (Fig.10.4a) are dimensionless. The second term IL
  
  Qk^0
  
  is the influence
  line of shear force at sectionkin the primary system. If loadPD 1 is located in
  the left span, then influence line of shear force for simply supported beam is shown
  in Fig.10.4b. If loadP D 1 is located in the right span, then shear at sectionk
  does not arise, and influence line has zeros ordinates. Summation of two graphs
  .1= l /IL.X 1 /and IL
  
  Q^0 k
  
  leads to the required influence line for shear force at
  sectionk; this influence line is presented in Fig.10.4c.