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subject to
(
δ
−
δ
)
/
h
≤
δ
,
j
=
1
,....,
nsy
(6)
j
j
−
1
j
ju
δ
≤ δ
i
=
1
,....,
nd
(7)
i
iu
F
M
xk
+
≤
1
(8)
A
Py
M
gk
cxk
F
m
M
xk
or
,
k
=
1
,....,
nc
(9)
+
≤
1
A
P
M
gk
ck
bk
(10)
M
≤
M
,
n
=
1
,....,
nb
xn
cxn
where Eq. 5 defines the weight of the frame,
m
is the unit weight of the steel section
selected from the standard steel sections table that is to be adopted for group
r
.
t
is
the total number of members in group
r
and
ng
is the total number of groups in the
frame.
l
is the length of member
s
which belongs to group
r
.
Eq. 6 represents the inter-storey drift of the multi-storey frame.
are
lateral deflections of two adjacent storey levels and
h
is the storey height.
nsy
is the
total number of storeys in the frame. Eq. 7 defines the displacement restrictions that
may be required to include other than drift constraints such as deflections in beams.
nd
is the total number of restricted displacements in the frame.
δ
and
δ
j
j
−
1
is the allowable
lateral displacement. BS 5950 limits the horizontal deflection of columns due to un-
factored imposed load and wind loads to height of column / 300 in each storey of a
building with more than one storey.
δ
ju
is the upper bound on the deflection of beams
which is given as span / 360 if they carry plaster or other brittle finish.
Eq. 8 defines the local capacity check for beam-columns.
F
and
x
M
are respec-
tively the applied axial load and moment about the major axis at the critical region of
member
k
.
g
A
is the gross cross sectional area, and
p
is the design strength of the
steel.
c
M
is the moment capacity about major axis.
nc
is the total number of beam-
columns in the frame. Eq. 9 represents the simplified approach for the overall buck-
ling check for beam-columns.
m
is the equivalent uniform moment factor given in
BS 5950.
b
M
is the buckling resistance moment capacity for member
k
about its
major axis computed from clause 4.3.7 of the code.
c
p
is the compression strength
obtained from the solution of quadratic Perry-Robertson formula given in appendix
C.1 of BS 5950. It is apparent that computation of compressive strength of a compres-
sion member requires its effective length. This can be automated by using Jackson
and Moreland monograph for frame buckling [23]. The relationship for the effective
length of a column in a swaying frame is given as:
δ
iu
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