Page 71 - Handbook of Structural Steel Connection Design and Details

Design of Connections for Axial, Moment, and Shear Forces

56 Chapter Two

section. Note that this can be done because M of Fig. 2.4, although shown
at the centroid of the section, is actually a free vector that can be applied
anywhere on the section or indeed anywhere on the free-body diagram.
This being the case, there is no reason to assume that the bending stress
distribution is symmetrical about the center of the section. Considering
the distribution shown in Fig. 2.6, because the stress from A to the center
is too high, the zero point of the distribution can be allowed to move
down the amount e toward B. Equating the couple M of Fig. 2.4 to the
statically equivalent stress distribution of Fig. 2.6 and taking moments
about point D,
t 2 2
M 5 [f sa 1 ed 1 f sa 2 ed ]
2
1
2
where t is the gusset thickness. Also, from equilibrium
f (a e) t f (a e)t
1 2
The above two equations permit a solution for f and f as
1 2
M
f 5
1
atsa 1 ed
M
f 5
2
atsa 2 ed
For a uniform distribution of normal stress,
f f f f
1 a 2 a
from which e can be obtained as

1 M 2 M
2
e 5 c a b 1 4a 2 d
2 B at f a at f a
Substituting numerical values,

1 7280 2 2 7280
e 5 c a b 1 4s21d 2 d 5 8.10 in
2 B s21ds0.75ds9.97d s21ds0.75ds9.97d

Thus,
7280
f 5 5 15.9 ksi
1
s21ds0.75ds21 1 8.10d
7280
f 5 5 35.8 ksi
2
s21ds0.75ds21 2 8.10d

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