Civil Engineering Reference
In-Depth Information
so that
M
K
=
27
.
8
×
10
.
105
−
9
×
4
.
3
−
15
×
2
.
3
=
207
.
7kNm
It is possible that in some load systems theremay bemore than one load position which
satisfies both criteria for maximum bending moment but the corresponding bending
moments have different values. Generally the absolute maximum bending moment
will occur under one of the loads between which the centre of gravity of the system
lies. If the larger of these two loads is closer to the centre of gravity than the other,
then this load will be the critical load; if not then both cases must be analysed.
20.4 I
NFLUENCE
L
INES FOR
B
EAMS NOT IN
C
ONTACT WITH THE
L
OAD
Inmany practical situations, such as bridge construction for example, themoving loads
are not in direct contact with the main beam or girder. Figure 20.15 shows a typical
bridge construction in which the deck is supported by stringers that are mounted on
cross beams which, in turn, are carried by themain beams or girders. The deck loads are
therefore transmitted via the stringers and cross beams to the main beams. Generally,
in the analysis, we assume that the segments of the stringers are simply supported at
each of the cross beams. In Fig. 20.15 the portion of the main beam between the cross
beams, for example FG, is called a
panel
and the points F and G are called
panel points.
Figure 20.16 shows a simply supportedmain beamABwhich supports a bridge deck via
an arrangement of cross beams and stringers. Let us suppose that we wish to construct
shear force and bending moment influence lines for the section K of the main beam
within the panel CD. As before we consider the passage of a unit load; in this case,
however, it crosses the bridge deck.
S
K
influence line
With the unit load outside and to the left of the panel CD (position 1) the shear force,
S
K
, at K is given by
x
1
L
S
K
=
R
B
=
(20.19)
S
K
therefore varies linearly as the load moves from A to C. Thus, from Eq. (20.19),
when
x
1
=
0,
S
K
=
0 and when
x
1
=
a
,
S
K
=
a
/
L
, the ordinate cf in the
S
K
influence
Stringers
Cross beams
F
IGURE
20.15
Typical bridge
construction
Main beam
F
G
