Advanced Methods of Structural Analysis

2.4 Combining of Fixed and Moving Load Approaches 35

loadPwould be applied directly to the main beamAB. Influence line for bending
moment presents triangle with vertexab=lat the sectionk; influence line for shear
is bounded by two parallel lines with the jump at the sectionk. Then we need to
indicate the panel pointsmandn, which are nearest to the given sectionk,and
draw vertical lines passing through these points. These lines intersect the influ-
ence lines at the pointsm^0 andn^0. At last, these points should be connected by a
straight line.

Fig. 2.16 Influence lines in
case of indirect load
application

a

b

Inf. line Mk

m′ n′

Connecting line

1

1

Inf. line Qk

Connecting line

n′

m′

+

+

RA

A

l R

B

k

ab

B

P= 1

m n Main beam

Floor beam

Stringer

Pay attention, that if a floor beammwill be removed, then the influence line
forQkbecomes thepositive one-signfunction instead of a two-sign function, as
presented in Fig.2.16. If the floor beamnand all following ones (except floor beam
at the supportB) will be removed, then the influence line forQkbecomes theone-
signfunction too, but a negative one.

2.4 Combining of Fixed and Moving Load Approaches

So far we showed an application of influence linesZfor analysis of this particu-
lar functionZ. However, in structural analysis, the application of influence lines
is of great utility and we can use influence line forZ 1 for calculation of another
functionZ 2. For example, design diagram of the beam and influence line for re-
actionRAis shown in Fig.2.17. How we can calculate the bending moment at
sectionk?
Using fixed loads approach we need to calculate the reaction, which arises in right
stringer; transmit this reaction through floor beam to panel joint onto main beam;
determine reactionsRAandRBand, after that, calculateMKby definition using