Civil Engineering Reference
In-Depth Information
MAXIMUM VALUES OF
S
K
AND
M
K
In determining maximum values of shear force and bending moment at a section of a
beam that is not in direct contact with the load, certain points are worthy of note.
1 When the section K coincides with a panel point (C or D, say) the
S
K
and
M
K
influence lines are identical in geometry to those for a beam that is in direct contact
with the moving load; the same rules governing maximum and minimum values
therefore apply.
2 The absolute maximum value of shear force will occur in an end panel, AE or
DB, when the
S
K
influence line will be identical in form to the bending moment
influence line for a section in a simply supported beam that is in direct contact with
the moving load. Therefore the same criteria for load positioning may be used for
determining the maximum shear force, i.e. the load per unit length of beam is equal
to the load per unit length to the left of E or D and the load per unit length to the
right of E or D.
3 To obtain maximum values of shear force and bending moment in a panel, a trial
and error method is the simplest approach remembering that, for concentrated
loads, a load must be placed at the point where the influence line changes slope.
20.5 F
ORCES IN THE
M
EMBERS OF A
T
RUSS
In some instances the main beams in a bridge are trusses, in which case the cross
beams are positioned at the joints of the truss. The shear force and bending moment
influence lines for a panel of the truss may then be used to determine the variation in
the truss member forces as moving loads cross the bridge.
Consider the simply supported Warren truss shown in Fig. 20.17(a) and suppose that
it carries cross beams at its upper chord joints which, in turn, support the bridge deck.
Alternatively, the truss could be inverted and the cross beams supported by the lower
chord joints; the bridge deck is then the
through
type. Suppose also that we wish to
determine the forces in the members CD, CE, DE and GE of the truss.
We have seen in Section 4.5 the mechanism by which a truss resists shear forces and
bending moments. Thus shear forces are resisted by diagonal members, while bending
moments are generally resisted by a combination of both diagonal and horizontal
members. Therefore, referring to Fig. 20.17(a), we see that the forces in the members
CE and DE may be determined from the shear force in the panel CD, while the forces
in the members CD and GE may be found from the bending moments at E and C,
respectively. Therefore we construct the influence lines for the shear force in the panel
CD and for the bending moment at E and C, as shown in Fig. 20.17(b), (c) and (d).
In Section 20.4 we saw that, for a given load position, the shear force in a panel such
as CD is constant at all sections in the panel; we will call this shear force
S
CD
. Then,
