Finite Element Method (FEM)

•      Finite Element Method (FEM)

     “A numerical procedure for solving (partial) differential equations associated with field problems, with an accuracy acceptable to engineers”

•       Non-linear Analysis

–      P-Delta Analysis

–      Buckling Analysis

–      Static Pushover Analysis

–      Fast Non-Linear Analysis (FNA)

–      Large Displacement Analysis

–     Dynamic Analysis

–      Free Vibration and Modal Analysis

–      Response Spectrum Analysis

–      Steady State Dynamic Analysis.

–   Static Excitation

–      When the Excitation (Load) does not vary rapidly with Time

–      When the Load can be assumed to be applied “Slowly”

–    Dynamic Excitation

–      When the Excitation varies rapidly with Time

–      When the “Inertial Force” becomes significant

–      Most Real Excitation are Dynamic but are considered
 “Quasi Static”

–      Most Dynamic Excitation can be converted to
 “Equivalent Static Loads”

–Elastic Material

–      Follows the same path during loading and unloading and returns to initial state of deformation, stress, strain etc. after removal of load/ excitation

–   Inelastic Material

–      Does not follow the same path during loading and unloading and may not returns to initial state of deformation, stress, strain etc. after removal of load/ excitation

–   Linearity

–      The response is directly proportional to excitation

–      (Deflection doubles if load is doubled)

–     Non-Linearity

–      The response is not directly proportional to excitation

–      (deflection may become 4 times if load is doubled)

–      Non-linear response may be produced by:

–      Geometric Effects  (Geometric non-linearity)

–      Material Effects (Material non-linearity)

–      Both

•        A continuum extends in all direction, has infinite particles, with continuous variation of material properties, deformation characteristics and stress state

•        A Structure is of finite size and is made up of an assemblage of substructures, components and  members

•        Dicretization process is used to convert Structure to Finite Element Models for determining response

•        All types of Static Loads can be represented as:

–      Point Loads

–      Line Loads

–      Area Loads

–      Volume Loads

•        The Load is transferred through a medium which may be:

–      A Point

–      A Line

–      An Area

–      A Volume

–      A system consisting of combination of several mediums

•        The supports may be represented as:

–      Point Supports

–      Line Supports

–      Area Supports

–      Volume Supports

•      Typical Characteristics of Residential Bldg

•        Known location of partitions and their load.

•        Column lines generally matches archit­ectural  layout.

•        Typical spans 15-22 ft.

•        Tall buildings economy in achieved using the thinnest slab.

•        One way pre-cast or flat slab – popular.

•        Lateral load resistance provided by frame or shear walls.

•        More or less fixed M/E system layouts.

Typical Characteristics of Office and Commercial  Bldg

•        Unknown location of partitions and their load.

•        Typical spans 20-35 ft.

•        Need for flexible M/E layouts.

•        Post-tension or ribbed and flat slab with drop panel – popular.

•        Ideal balance between vertical and lateral load resisting systems: sufficient shear walls to limit the resultant tension under gravity plus wind .

•        Lateral load resistance varies significantly.