Civil Engineering Reference
In-Depth Information
Figure5.39bindicatesthatinthiscase,themaximummomentoccurstotheright
of mid-span, and is greater than
M
p
, so that the solution above is an upper bound.
A more accurate solution can be obtained by trial and error, by increasing the
slope of the reactant moment diagram until the moment of the left-hand support
is equal to the interior maximum moment, as indicated by the dashed line in
Figure 5.39b.
5.11.3.4 Virtual work solution
For the first mechanism for the propped cantilever shown in Figure 5.31c, for
virtual rotations
δ
θ
,
δ
W
=
qL
2
δ
θ/
4
δ
U
=
3
M
p
δ
θ
and
q
ult
≤
12
M
p
/
L
2
as before.
5.12 Worked examples
5.12.1 Example1-properties of a plated UB section
Problem
. The610
×
229UB125sectionshowninFigure5.40aisstrengthenedby
weldinga300mm
×
20mmplatetoeachflange.Determinethesectionproperties
I
y
and
W
el
,
y
.
Solution
. Because of the symmetry of the section, the centroid of the plated UB
is at the web centre.Adapting equation 5.58,
I
y
=
98610
+
2
×
300
×
20
×[
(
612.2
+
20
)/
2
]
2
/
10
4
=
218500cm
4
W
el
,
y
=
218500
/
[
(
612.2
+
2
×
20
)/(
2
×
10
)
]=
6701cm
3
5.12.2 Example2-properties of a tee-section
Problem
. Determine the section properties
I
y
and
W
el
,
y
of the welded tee-section
shown in Figure 5.40b.
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