Technical
26 NSC
Feb 20
The quantities are defined in Table 2, taken from the example
in P398.
Item Description Value
AVC shear area of column 3810 mm2
β transformation parameter (Table 5.4) 1.0
zeq lever arm 498 mm
beff , leff effective width or length various
t component thickness 12.8, 20.5, 25 mm
dc clear depth of web 200.3 mm
m distance of bolt centre to root radius
or weld toe
The first challenge in calculating the stiffness components
appears to be the determination of the equivalent lever arm for
the column web stiffness coefficient k1. However, the parameter
depends on the effective stiffness for each bolt row r, and the
height of the bolt row relative to the centre of compression of the
beam flange so the calculation of the effective stiffnesses is in
fact the real task. The effective stiffness for each bolt row must be
calculated from the stiffness components ki for that bolt row,
given by:
keff,j = 1
1
k,r
The equivalent lever arm is given by:
zeq =
rkeff,rhr
rkeff,rhr
To complete the list of expressions for stiffness, the equivalent
stiffness is given by:
keq =
rkeff,rhr
zeq
Using the data from Examples C1 and C2 in P398, the relevant
effective widths of plate or lengths of T-stub can be determined.
The value corresponds to the effective width or length which
gives the lowest resistance for that component in the
determination of the resistance of the joint. Where the lowest
resistance is for several bolt rows acting as a group, the value for
each bolt row is the total length divided by the number of bolt
rows in the group, leading to the stiffnesses corresponding to
each bolt row. The values are given in Table 3
As an example calculation for the first bolt row,
keff,1 = 1
1
6.3
+ 1
6.3
+ 1
30.6
+ 1
8.01
= 2.10
The heights of the bolt rows above the centre of compression
are shown in Figure 1 and finally the value of zeq can be
determined. The value is:
1.439 × 106
zeq =
2994 = 498
The value for the equivalent stiffness is then:
keq =
2994
498 = 6.01
The remaining stiffnesses can also be calculated and the values
are k1 = 2.91 and k2 = ∞ because of the presence of the
compression stiffener.
The joint stiffness can now be calculated as follows:
Sj = 210 × (533.1 – 15.6)
( = 1
+ 0 + 1
2.91
6.01
)
102
MNm/radian
The effect of the stiffness ratio μ is shown in Figure 2. For the
bolted joint being considered, the value of ψ from Table 6.8 is 2.7.
If the design bending moment is greater than two thirds of the
bending resistance of the joint, the stiffness is reduced as
indicated, to a value of about one third of the maximum stiffness
when the applied moment approaches the joint resistance. It
should be noted that UK practice is often to optimise the design,
so a high utilisation might be expected.
24
Table 2: Values of parameters
various
As Tensile area of bolt 353 mm2
Lb Bolt length 70.5 mm
Stiffness minimum
beff , leff (mm)
beff , leff
(mm)
ki,1 ki,2 ki,3
k3,r r1 + r2 + r3 422/3 6.3 6.3 6.3
k4,r r1 + r2 + r3 422/3 6.3 6.3 6.3
k5,1 r1 125 30.6 - -
k5,r r2 + r3 379/2 - 46.5 46.5
k10 - - 8.01 8.01 8.01
keff,r - - 2.10 2.15 2.15
Table 3: Stiffness values