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Analysis of Models with Diaphragms

Diaphragms are horizontal structural components, which constitutes primary load transferring path for story shears and torsional moments to vertical force-resisting members like columns or walls. The way in which story shears and torsional moments are distributed to the vertical members depends on relative stiffness of diaphragms with respect to vertical members in the building. Diaphragms are also primary components to transfer gravity loads to vertical members through its one-way or two-way load distribution action.

Regarding diaphragm's in-plane (membrane) stiffness, a diaphragm can be assumed rigid if it is relatively stiffer than vertical members. The salient characteristics for a rigid diaphragm can be summarized as follows:

  • It is assumed that the diaphragm is rigid enough so that no axial, bending and shear deformations are expected in the plane of the diaphragm. Thus, the diaphragm is displaced as one rigid component under applied lateral loads.
  • Diaphragm deformation characteristics can be uniquely defined with three degrees of freedom: two lateral displacements in the plane of the diaphragm (i.e., one along global X-direction, and one along global Y-direction) and one rotation perpendicular to the diaphragm (i.e., rotation around global Z-axis). These three degrees of freedom uniquely define the kinematics of the diaphragm's behavior.
  • Diaphragm mass is similarly lumped at diaphragm's mass center and it has three components: mass in X and Y direction and around Z-axis (i.e., rotational inertia of diaphragm mass)
  • All members connected to the diaphragm are forced to be moved with the same displacements of the diaphragm (compatibility requirement). Thus, all these connected members experience the same lateral displacements in global X- and Y-directions. Plus, additional displacements are imposed due to the diaphragm' rotation around the global Z-axis.
  • It is interesting to know that it may be possible to see horizontal shear reversal in the diaphragm and this behavior can be attributed primarily to the nature of structural configuration, relatively irregular stiffness distribution of vertical members and finally due to the compatibility requirement for rigid diaphragms.
  • Story shears are distributed to supporting vertical members based on their relative rigidities. Thus, stiffer members attract more story shears.
  • Diaphragm masses can be concentrated at the diaphragm mass centers. And analysis is carried out based on the assumption that applied loads are imposed through the center of mass of the diaphragm but they are resisted through diaphragm' center of rigidity. Thus, if diaphragm's center of rigidity and center of mass are not coincident, an inherit torsional moment is imposed on the diaphragm and it is further transmitted to vertical members through the rigid diaphragm.

A diaphragm can be assumed to be flexible (also referred to as pseudo-flexible or semirigid) if it is relatively less stiffer than vertical members. For the discussion followed below, a flexible diaphragm is defined as a diaphragm that is not capable of transmitting torsional moments and it is relatively more flexible than the vertical members. Important salient characteristics of a flexible diaphragm are summarized below:

  • A flexible diaphragm can be viewed as a deep beam where lateral forces are applied through its web. Thus, the diaphragm experiences flexural deformations in its own plane. Collectors and chords are used to transmit shear and flexural forces to the vertical members (deep beam flanges can be viewed as collectors or chords).
  • It can be assumed that story shears are transmitted to the vertical resisting members based on tributary areas of the frames.
  • The diaphragm is not capable of transmitting torsional moments.

In RAM Frame, a diaphragm can be modeled either as rigid, pseudo-flexible or semirigid. This can be defined for each diaphragm in Story Diaphragm dialog. Note that there can be multiple diaphragms at a story and the user can assign rigid or flexible for each diaphragm.

Gravity loads are distributed to vertical members through diaphragms by means of two methods: one-way load distribution and two-way load distribution. Each diaphragm can be composed of one or more decks and each deck type (one-way or two-way deck) is assigned in the Modeler. One-way load distribution is well known tributary area load distribution so that gravity loads are projected to beams, walls and columns based on one-way deck orientation and load tributary areas. Two-way load distribution is carried out through diaphragm's out-of-plane (bending) stiffness. For this reason, the diaphragm should be meshed (the program meshes the diaphragm automatically if a two-way system is detected). See Analysis with Two-way Slabs: Out-of-Plane Stiffness (Bending) for two-way load distribution.