Stiffness Matrix

RAM Frame assembles the building (global) stiffness matrix considering all lateral members in a 3-D fashion. As a result of this, there is full compatibility of displacements and equilibrium of forces at all nodal points in the building structure. The stiffness matrix assembled is a sparse, symmetric system.

By default, the assembled stiffness matrix is in memory (random access memory, RAM). The in-core solvers directly solve system in memory. For large structures, out-of-core solvers are recommended, which directly work with files on hard disk. See Finite Element Analysis Library provides further information.

Mass Matrix

For building structures, the masses are assumed to be lumped at the centers of mass of the diaphragms for rigid diaphragms or it is distributed among frames if it is a pseudo-flexible diaphragm or it is spatially distributed over diaphragms if it is a Semirigid diaphragm. It should be noted that computed mass matrix is always a diagonal matrix.

Referring to rigid diaphragm, RAM Frame provides an option whereby users can specify that the masses of stories such as penthouses, mechanical levels and stair landings be combined to the mass of another diaphragm as desired. However, for eigenvalue analysis, it is necessary that each lateral stiffness equation (i.e., associated with rigid diaphragms) have a corresponding non-zero mass coefficient. Therefore, whenever the user requests such combining of mass, RAM Frame combines the mass to the desired diaphragm, however, if the original diaphragm contains lateral members, then 5% of its original mass is assigned to its corresponding entry in the mass matrix. The combining of masses will affect not only the inertia response (periods and modes) but also the distribution of generated seismic loads. The seismic diaphragm loads will be generated based on the combined mass distribution as requested by the user.