Civil Engineering Reference
In-Depth Information
Angle thickness to allow deformation
:
From Equations 9.12 and 9.13 the deformation of the connection angles is
12
Pel
3
d
2
Et
3
12
(
52
)(
4.5
)(
4
)
3
(
12
)
2
(
29000
)t
3
0.0430
t
3
Δ =
=
=
in.
If the beam is uniformly loaded with distributed load,
w
,
2
P
L
=
2
(
52
)
20
(
12
)
=
w
=
0.433 k/in.,
the end rotation,
Y
b
,is
wL
3
24
EI
=
0.433
(
240
)
3
24
(
29000
)I
=
8.60
I
θ
b
=
rad.
The rotation occurs about the bottom of the angle so that the deformation
at the top of the angle,
Δ
,is
103.2
I
Δ =
12
θ
b
=
so that
0.0747
(I)
1
/
3
.
t
≤
1200 in.
4
,
For a beam with
I
=
0.0747
(
1200
)
1
/
3
0.79 in.
The angle thickness should be based on the requirement for transmitting
shear or the minimum element thickness recommended by AREMA (2008),
but should not be greater than about 3/4 in. thick (note the calculation of
0.79 in is approximate) to ensure adequate flexibility for consideration as a
flexible beam framing connection.
t
≤
≤
Shear and torsion on welds in side elevation
:
The shear stress on the welds is
P
2
t
e
(
2
b
1.35
t
e
τ =
d)
=
ksi.
+
6
(P
e)y
0.203
y
t
e
σ
t
x
=
t
e
8
b
3
d
3
=
ksi
6
bd
2
+
+
0.203
x
t
e
σ
t
y
=
ksi.
The stress resultant,
f
2
, at any location on the weld described by locations
x
and
y
is
(
1.35
(
τ + σ
t
y
)
2
+
0.203
y
2
.
1
t
e
t
x
=
0.203
x)
2
f
2
=
+ σ
+
