Civil Engineering Reference
In-Depth Information
Furthermore, we see that
S
DC
changes sign at the point j (Fig. 20.18(b)) where jd,
from similar triangles, is 0
.
4
.
Themember ECwill be in compressionwhen the shear force in the panel DC is positive
and its maximum value will occur when the head of the load is at j, thereby completely
covering the length aj in the
S
DC
influence line. Therefore
1
2
×
F
EC
sin 45
◦
=
S
DC
=
2
.
5
×
3
.
2
×
0
.
25
from which
F
EC
=
1
.
41 kN (compression)
The force in the member EC will be tensile when the shear force in the panel DC is
negative. Therefore to find the maximum tensile value of
F
EC
we must position the
load within the part jb of the
S
DC
influence line such that the maximum value of
S
DC
occurs. Since the positive portion of the
S
DC
influence line is triangular, we may use
the criterion previously established for maximum bending moment. Thus the load per
unit length over jb must be equal to the load per unit length over jc and the load per
unit length over cb. In other words, c divides the load in the same ratio that it divides jb,
i.e. 1 : 7. Therefore 0
.
5m of the load is to the left of c, 3
.
5m to the right. The ordinates
under the extremities of the load in the
S
DC
influence line are then both 0
.
3125m.
Hence the maximum negative shear force in the panel CD is
2
.
5
1
0
.
3125)3
.
5
1
2
(0
.
625
S
CD
( max
−
ve)
=
2
(0
.
3125
+
0
.
625)0
.
5
+
+
which gives
S
CD
(max
−
ve)
=
4
.
69 kN
Then, since
F
EC
sin 45
◦
=
S
CD
F
EC
=
6
.
63 kN
which is the maximum tensile force in the member EC.
COUNTERBRACING
A diagonal member of a Pratt truss will, as we saw for the member EC in Ex. 20.7, be in
tension or compression depending on the sign of the shear force in the particular panel
in which the member is placed. The exceptions are the diagonals in the end panels
where, in the Pratt truss of Fig. 20.18(a), construction of the shear force influence
lines for the panels AH and MB shows that the shear force in the panel AH is always
negative and that the shear force in the panel MB is always positive; the diagonals in
these panels are therefore always in tension.
