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363 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
S. J. P. J. MARQUES FILHO | B. HOROWITZ
ample observe from Figure 6(a) that the reaction obtained from
the finite element model is 74kN, corresponding to an imposed
displacement of 1cm at the top of the column. For a bar model with
rigid links inside the joint the reaction force is 92,1kN. Figure 6(b),
which shows a section through the symmetry plane of the joint,
depicts again the concentration of shear stresses inside the joint. If
no rigid links are specified the required force is 69,7kN.
Despite beams and columns having the same moment of inertia,
the joint of the second example has less stiffness than that of the
first example. Among various factors, one of the largest contribu-
tors to the increase of the flexibility of the connection is the addi-
tional torsional deformation that exists in the column. This subject
will be discussed in detail in section 4.1.
From the above discussion it can be concluded that in usual situations,
errors in joint modeling can result in lateral displacement errors in the
order of 20%. Experimental results from Shin and LaFave [3] show that
joint flexibility contribute with 24% of total lateral displacement for drifts
of 1% of story height and 53% for drifts of 6% of story height.
are specified, with all bars having constant properties throughout
their lengths, completely neglecting the stiffness of the joint region,
the corresponding force would be 68,3kN. Computing the ratios of
those different values of required forces to the finite element result
one concludes that the stiffness of the subassemblage is either
overestimated by 23% or underestimated by 16%.
Figure 4(a) shows color-filled contours of shear stresses. It can
be seen that there exists a high concentration of shear stress in
the joint zone. These stresses result from the combined action of
normal stresses due to bending moments of same sense applied
by beams and columns to the joint. Figure 5(a) shows a represen-
tation of the moments applied by the beams to the joint. Figure
5(b) shows the normal stresses resulting from the applied bending
moments and the required shear stresses inside the joint to main-
tain equilibrium. Joint shown in Figure 5(a) also suggests that the
largest contribution to joint deformation is due to shear distortion,
and not bending in the interior of the joint.
For the second case, shown in Figure 3(b), of the illustrative ex-
Figure 5 – (a) Joint deformed configuration; (b) Shear and normal stresses
Figure 6 – (a) Interior frame joint substructure; (b) Concentration of shear stress inside the frame joint
B A