Information Technology Reference
In-Depth Information
where
W
is the weight of the cellular beam,
is density of
steel,
A
is total area of the profile selected,
NH
is number of holes,
H
and
L
are the
overall depth and the span of the cellular beam and
S
is the distance between centers
of holes.
D
is hole diameter,
ρ
M
is the maximum moment under the applied loading,
M
is plastic
U
P
moment capacity,
V
is the maximum shear at support,
V
is the maximum
max
sup
max
shear at the opening,
V
is the maximum horizontal shear,
M
is the
max
A
−
A
max
maximum moment at A-A section shown in Figure 10,
M
is the maximum al-
w
max
lowable web post moment,
Tee
V
is vertical shear on tee,
P
,
M
forces on the section
and
ma
y
maximum deflection of the cellular beam.
Although the diameter of holes and spacing between their centers are left to de-
signer to select, this selection has to satisfy the limitations given in constraints Eqs.
25-28. Inequality (Eq. 29) represents overall beam flexural capacity constraint. Under
unfavourable applied load combinations the cellular beam should have sufficient
flexural capacity to be able to resist the external loading.
M
=
A
p
h
where
p
tee
y
tee
A
is the area of lower tee,
p
is the design strength of steel and
h
is the distance
between centrals of upper tee and lower tee.
Inequalities (Eqs. 30-32) represent shear capacity checks. There are three shear
checks in the design of cellular beams. The first one is the shear check at the support.
Constraint (Eq. 30) makes sure that shear at the support does not exceed the shear ca-
pacity of the section where
.0
Area of web at supports
). It is also
necessary to check two more shear failure modes additionally. The first shear failure
mode check (Eq. 31) is the vertical shear capacity check of the beam. The sum of the
shear capacities of the upper and lower tees gives the vertical shear capacity of the
beam. The factored shear force in the beam should not exceed
×
P
=
0
.
6
×
p
×
(
×
v
y
vy
pP
Area of web at upper and lower tees
). The other (Eq. 32) is the
horizontal shear check. The horizontal shear is developed in the web post due the
change in axial forces in the tee as shown in Figure 10. The horizontal shear capacity
in the web post of the beam should not exceed
=
0
.
6
×
×
(
0
.
9
y
vh
pP Minimum
area of web post
). The details of the computations of shear force and bending moment
at a section of cellular beam is given in [34].
The flexural capacity of the upper and lower tees under bending is critical in cellu-
lar beams. The transfer of shear forces across a single opening causes secondary
bending stresses. Inequalities (Eqs. 33-35) are required for the flexural and buckling
strength of web post. The details of the computation of the maximum moment
max
=
0
.
6
×
×
(
0
.
9
×
y
M
at section A-A shown in Figure 10 and the maximum allowable web post
A
−
A
moment
w
M
are given in [34]. The last constraint is the serviceability require-
ment that the cellular beam has to satisfy. This constraint requires that the maximum
deflection of the beam should not be more than its span over 360.
max
Search WWH ::
Custom Search