Aluminium Design and Construction John Dwight

Figure 10.11 Some other forms of section reinforcement.
Figure 10.10 shows a selection of junction details and also two quasibulbs.
For any of these the contribution �� may be found using a
general expression:
��=[(p+qN+r)t] 4 (10.19)
where N=geometric factor (see Figure 10.10), t=adjacent plate thickness,
and p,q,r=quantities given in Table 10.2, valid over the ranges indicated.
Note that for each detail equation (10.19) covers the area shown
hatched in Figure 10.10, with the adjacent plate element or elements
terminated a distance t or T from the start of the actual reinforcement.
This treatment is based on results due to Palmer [28] before the days
of computers, using Redshaw’s electrical analogue.
Figure 10.11 shows some other kinds of reinforcement, in the form of
an added circle or square. For these, it is acceptable to put dI equal to
the simple value below, adjacent plate elements being now taken right
up to the circle or square:
Circle ��=0.10d 4 Square ��=0.14a 4 (10.20)
where d is the circle diameter, and a the side of the square.
10.4.4 Polar inertia
The polar inertia I p is defined as the polar second moment of area of the
section about its shear centre S. S is also the centre of twist, the point
about which the section rotates under pure torsion. I p may be calculated
as follows:
I p =I xx +I yy +Ag 2 =I uu +I vv +Ag 2 (10.21)
where: I xx , I yy =inertias about any orthogonal axes Gx, Gy
I uu , I vv =principal inertias (Section 10.3.2);
A=section area;
g=distance of S from the centroid G.
For sections that are bisymmetric, radial-symmetric or skew-symmetric
S coincides with G and g=0. For sections entirely composed of radiating
outstand elements, such as angles and tees (‘type-R’ sections, Figure 9.7),
S lies at the point of concurrence of the median lines of the elements. For
all others (monosymmetric, asymmetric), a special calculation is generally
needed to locate S, involving consideration of warping (Section 10.5).
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