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in load and resistance factor design according to LRFD-F2. In this inequality
φ
is
the resistance factor for flexure which is given as 0.9,
M
is the nominal moment
strength and
u
M
is the factored service load moment for member
r
.
Eq. 18 represents the shear strength requirement in the load and resistance factor
design according to LRFD-F2. In this inequality
v
nr
represents the resistance factor
for shear given as 0.9,
n
V
is the nominal strength in shear and
u
V
is the factored
service load shear for member
r
. The details of obtaining nominal moment strength
and nominal shear strength of a W-section according to LRFD are given in [27].
φ
4.2 Design Example
The grillage system shown in Figure 3 is used to cover the area of 12m×12m. The
grillage system is planned to carry 15kN/m
2
uniformly distributed load covering the
whole area total of which is 2,160kN. This total load can be applied to the system as
86.4kN of point load acting at each joint. The grillage system has 60 members alto-
gether that are collected in two groups. The vertical displacements of joints 8, 13, 14
and 18 are restricted to 25 mm. A36 mild steel is selected for the design which has the
yield stress of 250MPa, the modulus of elasticity of 205kN/mm
2
and shear modulus
of 81kN/mm
2
respectively. The discrete set from which the design algorithm selects
the sectional designations for grillage members is considered to be the complete set of
33
31
32
34
35
2
86.4 kN
2
86.4 kN
86.4 kN
2
86.4 kN
86.4 kN
2
2
40
5
20
25
1
45
1
1
10
1
15
1
1
86.4 kN
2
86.4 kN
86.4 kN
2
86.4 kN
2
86.4 kN
2
2
39
1
4
1
9
1
14
19
1
24
1
44
1
2
2
2
86.4 kN
86.4 kN
86.4 kN
86.4 kN
2
86.4 kN
2
38
1
3
23
1
8
1
13
18
1
1
43
1
2
2
2
2
2
86.4 kN
86.4 kN
86.4 kN
86.4 kN
86.4 kN
37
2
7
12
17
22
42
1
1
1
1
1
1
2
2
2
86.4 kN
86.4 kN
86.4 kN
2
2
86.4 kN
86.4 kN
36
1
1
1
6
1
11
16
1
21
1
41
1
2
2
2
2
2
29
30
26
27
28
2 m
2 m
2 m
2 m
2 m
2 m
Fig. 3.
60-member grillage system
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