Page 87 - Handbook of Structural Steel Connection Design and Details

Design of Connections for Axial, Moment, and Shear Forces

72 Chapter Two

of the gusset, the column, and the beam with axial forces only. Such a
set of forces is said to be “admissible.” But equilibrium is not the only
requirement that must be satisfied to establish the true distribution of
forces in a structure or connection. Two additional requirements are the
constitutive equations that relate forces to deformations and the com-
patibility equations that relate deformations to displacements.
If it is assumed that the structure and connection behave elastically
( an assumption as to constitutive equations) and that the beam and the
column remain perpendicular to each other (an assumption as to defor-
mation–displacement equations), then an estimate of the moment in the
beam due to distortion of the frame (frame action) (Thornton, 1991) is
given by

2
2
P I I c sb 1 c d
b
M 6
D Abc I b 2I c bc
a 1 b
b c
where D distortion
I moment of inertia of beam 2370 in 4
b
I moment of inertia of column 3840 in 4
c
P brace force 855 kips
A brace area 26.4 in 2
b length of beam to inflection point (assumed at beam
midpoint) 175 in
c length of columns to inflection points (assumed at column
midlengths) 96 in

I
2I c b
With 5 80 and 5 13.5
c b
2
6 3 855 3 2370 3 3840 175 1 96 2
M 5 2670 kips-in
D 26.4 3 175 3 96 3 s13.5 1 80d s175 3 96d

This moment M is only an estimate of the actual moment that will
D
exist between the beam and column. The actual moment will depend on
the strength of the beam-to-column connection. The strength of the
beam-to-column connection can be assessed by considering the forces
induced in the connection by the moment M as shown in Fig. 2.12. The
D
distortional force F is assumed to act as shown through the gusset
D
edge connection centroids. If the brace force P is a tension, the angle
between the beam and column tends to decrease, compressing the gusset
between them, so F is a compression. If the brace force P is a com-
D
pression, the angle between the beam and column tends to increase
and F is a tension. Figure 2.12 shows how the distortional force F is
D D

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