52 3 Multispan Beams and Trusses1.When unit loadPis to therightof the sectioned panel, it is more convenient to
consider the equilibrium of the left-hand part of the truss
O 46!X
M 7 leftD 0 !O 46 rCRA3dD 0 !O 46 D3d
rRA:The last equation for forceO 46 should be transformed into the equation of in-
fluence line forO 46. When loadPhas a fixed position, then reactionRAis a
specified number andO 46 is a number as well. However, if loadPis changing
its position, then reactionRAis changing its value as well, so it becomes afunc-
tion(influence line) and therefore internal forceO 46 becomes a function as well.
Thus, equation of influence line forO 46 may be expressed in term of influence
line of reactionRA
IL.O 46 /D3d
rIL.RA/:Thus, to construct influence line forO 4 - 6 , the following steps are necessary:(a)Show the influence line forRA
(b)Multiply all ordinates by factor3d=r
(c)Draw a shaded region, which corresponds tolocationof the loadP(to the
right of the sectioned panel), but not part of the truss, which is considered as
a free body for equilibrium (!).2.Similar discussions are applied for the construction of influence line when the
unit loadPis to theleftof joint 5. In this case, it is more convenient to consider
the equilibrium of the right-hand part of the truss
O 46!X
M 7 rightD 0 !O 46 rCRB3dD 0 !O 46 D3d
rRB:The last equation should be transformed in the equation of influence line. When
loadPhas a fixed position, then reactionRBis a number andO 46 is a number
as well. However, if loadPhas various positions, then reactionRBbecomes a
function(influence line) and thus, internal forceO 46 becomes a function as well.
Therefore,
IL.O 46 /D3d
rIL.RB/:Thus, influence line forO 46 is obtained from influence line forRBby multiply-
ing its ordinates by corresponding value (3d=r). Hatching shows region 1-5,
which correspond to the position of the load.
Note, that the point of intersection of the left-hand portion and right-hand one
is always located under the Ritter’s point. If the Ritter’s point is in the infinity,
then the left-hand and right-hand portions are parallel.
3.LoadPD 1 is locatedwithin the sectioned panel5-7; since external load should
be applied at joints only, then this case corresponds to indirect load application.
Therefore, the influence line connects ordinates of influence lines at points 5