## Panel Zone Effects

Structural engineers involved in the design of high-rise structures are confronted with many uncertainties when calculating lateral drifts. For example, they must decide the magnitude of appropriate wind loads and the limit of allowable lateral deflections and accelerations. Even assuming that these are well defined, another question that often comes up in modeling of building frames is whether or not one should consider the panel zones at the beam-column intersections as rigid.

The panel zone can be defined as that portion of the frame whose boundaries are within the rigid connection of two or more members with webs lying in a common plane.

Figure 8.31a. Typical frame element: (1) free-body diagram; (2) bending moments due to shear in beam and columns.

It is the entire assemblage of the joint at the intersection of moment-connected beams and columns. It could consist of just two orthogonal members as at the intersection of a roof girder and an exterior column, or it may consist of several members coming together as at an interior joint, or any other valid combination. In all of these cases, the panel zone can be looked upon as a link for transferring loads from horizontal members to vertical members, and vice versa. For example, consider the free-body diagram of a frame element consisting of an assemblage of two identical beams and columns with points of zero moment at the ends (Fig. 8.31a). These zero-moment ends are, in fact, representative of points of inflection in the members.

Consider the frame element subjected to lateral loads. It is easy to see that, because of these loads, the columns are subjected to horizontal shear forces and corresponding bending moments, as shown in Fig. 8.31a(2). Equilibrium considerations result in vertical shear forces in the beams at the inflection points and corresponding bending moments in the beams. The panel zone thus acts as a device for transferring the moments and forces between columns and beams. In providing for this mechanism, the panel zone itself is subjected to large shear stresses.

The presence of high shear forces in a panel zone is best explained with reference to the connection shown in Fig. 8.31b(1). The bending moment in the beam can be considered as being carried as tensile forces in the top flange and compressive forces in the bottom flange, and the shear stresses can be assumed as being carried by the column web. In the panel zone, the tensile force in the top flange is carried into the web by horizontal shear forces and, by a similar action, is converted back into a tensile force in the outer flange of the column. The distribution of the actual state of stress in the panel zone is highly indeterminate, but a reasonable approximation can be obtained by assuming that the tensile stresses are reduced linearly from a maximum at the edge of the corner B or D to zero at the external corner. If members AB and CD are assumed as stiffeners, a distinct load path can be visualized for the compressive and tensile forces in the beam flange. Consideration of equilibrium of forces within the panel zone results in shear stress and a corresponding shear deformation as shown in Fig. 8.31b(4). It is this deformation that is of considerable interest in the calculation of drift of multistory buildings.

Before proceeding with an explanation of the behavior of panel zones and their influence on building drift, it is instructive to discuss some of the assumptions commonly made in the analysis of building frames. Prior to the availability of commercial analysis

Figure 8.31b. Panel zone behavior: (1) corner panel; (2) schematic representation of shear forces in panel zone; (3) linear distribution of tensile stresses; (4) shear deformation of panel zone.

programs with built-in capability of treating panel zones as rigid joints, it was common practice to ignore their effects; the frame was usually modeled using actual properties along the centerlines of beams and columns.

If the size and number of joints in a frame were relatively large, an effort was made to include the effect of joint rigidity by artificially increasing the moments of inertia of beams and columns; the actual properties were usually multiplied by a square of the ratio of centerline dimensions to clear-span dimensions.

It is now relatively easy to model the panel zone as a rigid element because of the availability of a large number of computer programs which include this feature. Flexibility of panel zones can also be considered in some of these programs, although somewhat awkwardly, by artificially decreasing the size of panel zones.

Computations of beam, column, and panel zone contributions to frame drift can be carried out by hand calculation using a virtual work method. For this purpose consider again the typical frame element subjected to horizontal shear forces Pc and vertical shear forces Pb at the inflection points (Fig. 8.31c(1)).

The notations used in the development of the method are as follows:

db = depth of panel zone dc = width of panel zone

Figure 8.31c. Typical frame segment: (1) geometry; (2) bending moment diagram with rigid panel zone; (3) bending moment diagram without panel zone; (4) bending moment diagram with flexible panel zone; (5) shear force diagram; (6-9) unit load diagrams.

Figure 8.31c. Typical frame segment: (1) geometry; (2) bending moment diagram with rigid panel zone; (3) bending moment diagram without panel zone; (4) bending moment diagram with flexible panel zone; (5) shear force diagram; (6-9) unit load diagrams.

hc = clear height of column Lc = clear span of beam L = center-to-center span of beam h = center-to-center height of column Ic = moment of inertia of column Ib = moment of inertia of beam E = modulus of elasticity

G = shear modules

Ab = frame drift due to beam bending

Ac = frame drift due to column bending

Ap = frame drift due to panel zone shear deformation

The bending moment diagrams for the typical frame element can be obtained under three different assumptions.

1. The first assumption corresponds to ignoring the rigidity of panel zone; the bending moment diagrams for the external and unit loads can be assumed as shown in Figs. 8.31c(3) and (7). The bending moments increase linearly from the point of contraflexure to the centerline of the joint. By integrating the moment diagrams shown in Figs. 8.31c(3) and (7), the column- and beam-bending contributions to the frame drift are given by:

A PL

b 12 EIb

2. In the second case, which corresponds to assuming that the panel zone is completely rigid, we get bending moment diagrams for external and unit loads as shown in Figs. 8.31c(2) and (6). The bending moments increase linearly from the points of contraflexure but stop at the face of beams and columns. Integration of moment diagrams gives the expressions for Ac and Ab as follows:

12 EIC

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