Advanced Methods of Structural Analysis

70 3 Multispan Beams and Trusses

For each condition, the force in the substituted bar can be found in two steps: first,

compute the forceN 1 in the memberLC(using section 1-1) and then find required

force in substitute bar, considering jointC. This procedure is presented in Table3.1.

According to (3.3), the unknown reaction of supportCequals

XCD

FP

F

D

0:672P

0:328

D2:048P: (3.4)

After this, the calculation of reactionsRAandRBpresents no further difficulty. As

soon as all the reactions are known, the calculation of the internal forces in all the

members can be carried out as usual.

Discussion

1.For the given Wichert truss, loaded by vertical forcePdirected downward, the
vertical reaction of the intermediate support is also directed downward. This
surprising result can be easily explained. Imagine that supportCis removed.
Obviously, pointKwould be displaced downward, rigid discAKLwould rotate
clockwise around supportAand rigid discKBRwould rotate counterclockwise
around supportB. Therefore, supportCwould be displaced upward, so the re-
action of supportCis directed downward.
2.If the substituted member is a horizontal bar (between jointsLandR), then

FP D

3

4

P;FD

p

3

2



1

2

D0:366and for reactionXCwe obtain the same
result.
3.A Wichert truss is a very sensitive structure with respect to angle ̨. Indeed, if

angle ̨D 45 ı,thenFPD0:707PandFD 0 ,soXCD

0:707P

0

. This means
that the system is simultaneously changeable. If angle ̨D 30 ı, then reactionXC
is positive and equals 3.55P.

3.5.4 Summary......................................................

Analysis of any truss can be performed using two different analytical methods: the

fixed and moving load approaches.

The fixed load approach (methods of joints and through sections) allows us to

calculate the internal force in any selected member of a truss.

The moving load approach requires the construction of influence lines. The

following approach for the construction of influence lines may be used: the mov-

ing load,P D 1 , is placed at each successive joint of the loading chord and

foreachsuch loading the required internal force is calculated by the method

of joints or method of cuts. This procedure leads to a correct picture of the