In-Plane Stiffness

The in-plane stiffness of the floor systems of most building structures are very high compared to the stiffness of framing members. As a result, the in-plane deformations can be neglected, assuming that it is infinitely stiff for axial deformations. Furthermore, columns and walls connected to a rigid diaphragm will have the same lateral displacements. Based on this assumption, forces on rigid diaphragms are distributed to connected members according to their relative stiffness. RAM Frame uses this assumption to reduce the size of the system equations of buildings with such floor types. If the Rigid Diaphragm option is selected, the program automatically carries out the necessary transformation for all the elements to arrive at a system equation that allocates only three in-plane degrees of freedom for each diaphragm.

The equations that govern the transformation of the in-plane lateral displacements of each member to that of the lateral displacements at the center of mass are:

u = u^{m} + Δ y θ_{z}^{m}

(6.15)

v = v^{m} - Δ x θ_{z}^{m}

(6.16)

θ_{z} = θ_{z}^{m}

(6.17)

where

u^m, v^m, and θ^z_m	=	the lateral displacements at the center of mass of a diaphragm
Δ_y and Δ_x	=	the distances from the point of interest to the center of mass of the diaphragm

For dynamics, the predominant masses in such buildings are the ones that correspond to the three degrees of freedom per story (translation in X and Y direction and rotation around Z-axis). In the dynamic analysis of buildings with rigid diaphragms, RAM Frame evaluates corresponding stiffness and mass coefficients in these three degrees of freedom.

When all nodes on a beam are connected to the diaphragm, the rigidity of the diaphragm prevents any axial deformations of the beam from being considered; there are no relative in-plane displacements between any two points on the diaphragm. This means that there will be no axial load attributed to the beam. However, if any node along a beam is disconnected from the diaphragm, the beam will receive axial load.

For Chevron type and eccentric braces, RAM Frame automatically disconnects the interior nodes of the beam from the diaphragms. As a result, the link beams in such braces will have axial forces. However, note that for each disconnected node in the building three additional degrees of freedom are introduced in the system equations. Disconnecting these nodes from diaphragms not only increases the degrees of freedom of the structure and hence the size of the system equation to be solved, but also results in a "softer" structure.

Columns can also be disconnected from the diaphragms. This is done in the RAM Modeler where you define the slab edges. Columns outside the region bounded by the slab edges will be automatically disconnected from the diaphragm. When columns are supported by a beam, the node at the base of the column is automatically disconnected from the diaphragm. Specifying penetrations or slab openings around a column also disconnects the column from a diaphragm. When columns are supported by a beam, the node at the base of the column is automatically disconnected from the diaphragm. Nodes can also be disconnected (or connected) in RAM Frame by using the Disconnect option in the Assign > Nodes > Diaphragm Connection command.

The Rigid Diaphragm option can be specified using Criteria > Diaphragm. When the Rigid Diaphragm option is selected, lateral forces are typically input as story forces, either user-specified or generated, applied to the diaphragm. Lateral nodal loads can also be applied at any node in the structure. The diaphragm acts as the mechanism by which the story forces are distributed to the individual frame members.

When the Rigid Diaphragm option is selected, story displacements and story drift outputs are available. For stories with all columns and braces disconnected from the diaphragm, RAM Frame assumes that there is no diaphragm at that level. As a result, story displacements and drifts of zero are printed for such a story level since its only displacements are the joint displacements of the disconnected nodes.