Advanced Methods of Structural Analysis

2.3 Indirect Load Application 33

P 1

P 1

P 1

P 1

P 1

P 2

2m

q

3m 6m 4m 3m

k

A B

Inf. line Mk (m)

2.4

−

+

0.6 1.8

1.6

1.2

Inf. line Qk

1

− 1

0.6

0.4 0.2

0.4

0.3

0.3

P 2

P 2

P 2

P 2

Fig. 2.14Design diagram of the beam, influence lines, and most unfavorable positions of two
connected loads

Action of the set of loadsP 1 D5kNandP 2 D8kN. Unfavorable locations
of two connected loads are shown in Fig.2.14. Critical load for bending moment at
sectionk(triangular influence line) is defined by graphical method; the loadP 2 is a
critical one and it should be placed over the vertex of influence line.

Qk.maxC/D 5 0:4C 8 0:2D3:6kNI

Qk.max/D.50:4C 8 0:6/D6:8kN;

Mk.maxC/D 5 1:6C 8 2:4D27:2kNmI

Mk.max/D.50:6C 8 1:8/D17:4kNm:

If a set of loadsP 1 andP 2 modeling a crane bridge then theorderof loads is fixed
and cannot be changed. If a set loadsP 1 andP 2 is a model of a moving car then we
need to consider case when a car moves in opposite direction. In this case the order
of forces from left to right becomesP 2 andP 1.

2.3 Indirect Load Application

So far, we have been considering cases when external loads were applied directly
to the beams. In practice, however, loads are often applied to secondary beams (or
stringers) and then are transmitted through them to the main beam (or girder) as
shown in Fig.2.15. Stringers are simply supported beams. Each stringer’s span is
called a paneldand each point where the stringer transmits its load onto the main
beam is called a panel point or a joint. The load is transmitted from the secondary
beams onto the main beam only at panel points.