Civil Engineering Reference
In-Depth Information
W
W
a
b
a
(a)
W
ve
Shear force diagram
ve
W
(b)
F
IGURE
8.2
Bending test on a
beam, 'two-point'
load
Wa
ve
Wa
Bending moment diagram
(c)
subjected to a 'two-point' loading system as shown in Fig. 8.2(a). Two concentrated
loads are applied symmetrically to the beam, producing zero shear force and constant
bending moment in the central span of the beam (Fig. 8.2(b) and (c)). The condition
of pure bending is therefore achieved in the central span (see Section 9.1).
The second form of loading system consists of a single concentrated load at mid-span
(Fig. 8.3(a)) which produces the shear force and bending moment diagrams shown in
Fig. 8.3(b) and (c).
The loads may be applied manually by hanging weights on the beam or by a testing
machine. Deflections aremeasured by a dial gauge placed underneath the beam. From
the recorded results a load-deflection diagram is plotted.
For most ductile materials the test beams continue to deform without failure and
fracture does not occur. Thus plastic properties, e.g. the ultimate strength in bending,
cannot be determined for such materials. In the case of brittle materials, including
cast iron, timber and various plastics, failure does occur, so that plastic properties can
be evaluated. For such materials the ultimate strength in bending is defined by the
modulus of rupture.
This is taken to be the maximum direct stress in bending,
σ
x,u
,
corresponding to the ultimate moment
M
u
, and is assumed to be related to
M
u
by the
elastic relationship
M
u
I
σ
x,u
=
y
max
(see Eq. 9.9)
Other bending tests are designed to measure the ductility of a material and involve
the bending of a bar round a pin. The angle of bending at which the bar starts to crack
is then taken as an indication of its ductility.
