Some Important Definition

Framed structures: A frame structures is defined as which is basically resists applied load by virtue of its geometrical shape and configuration.

Body Mass Structures: A body mass structures explained as those which can resists load by virtue of their weight. The basic three elements of framed structures are,

  • Reinforcement
  • Beam
  • Column
  • Slab

What is Reiforcement?

It is specifically subject  to applied load on body structures along the axis.Functionally it is tensile for a tie , and compressive for a column or a strut.In case of reinforcement deformation under load is a simply change in length.

What is Beams?

It is basically supported at one or multiple point in lengthwise and carry loads normal to the member axis. It also act as a bending deformation on a plane surface of curvature. A shaft basically carries torsional load and moments and also giving rise to twist without deformation of the axis of member.

What is slab?

Slab carries two types of loadings. One type of load is produced by a load normal to the slab, and geometrically deforms like a beam structures, but shape os deformation follows two way curvature and the other load is edge load in the plane of slab.

Plane Frame

A plane frame structures exists with all its members in one plane is termed as plane frame.

Space Frame

A space frame structure having all it members in three dimensions is known as space frame.

Statically Determinate Structures

It can be simply defined as the structures which can be analyzed by basic three equilibrium equation.

Basic examples of statically determinate structures are as follows,

Simply supported beams, cantilevers beams , double overhanging beams, three hinged arches etc.

Statically Indeterminate Structures

             A statically inderminate structures is defined as if it cannot be analysed from the principles of statics alone.

Externally Indeterminate Structures

Some externally indeterminate structures are continuous beams and frames. A structures externally redundant if the reactions at support cannot be determined by using three equations of equilibrium . Statically indeterminate beams and frames can be analysed by strain energy method. Three moments equations, slope deflection method of moment distribution method.

Internally Inderminate Structues

A truss is statically determinate internally, if the total number of members , m= 2j-3 where j is the number of joints.

The internally inderminate trusses can be analysed by strain energy method.

Degree of Redundancy

In order to determinate the number of redundants, it is necessary to cut sufficient supports and structural members so that all loads are carried by simple beam and cantilever action. The number of redundants is then equal to the numbers of forces and moments required to restore continuity.

Important required formulae for statically Indeterminacy

2D Truss                         n=m+r-2j

3D Truss                           n=m+r-3J

2D Beams and Frames    n=3(m-j)+r-t

3D Beams and Frames    n=6(m-j)+r-t

Where,

n =  degree of statically indeterminacy

m =  number of members

j = number of joints including supports

r = number of reactions

t = number of releases like hinges, mr-1

mr = number of element meeting at the hinge

What is Kinematic Indeterminacy?

  • Static Indeterminacy: It may be defined as the number of redundant forces which are acting that are to be released to transform a structure into a stable and and statically indeterminate structure.
  • Kinematic Indeterminacy: Kinematic Indeterminacy explained as number of independent components or portions of various joint displacements with respect to a specified set of axes. These displacements at nodal points completely describes the response of the structure of any loading conditions. Any structure reformed as kinematically determinate if all joint displacement are restrained.
  • Any joint in space will have six independents components defined as degree of freedom three translations and three rotations.
  • A joint in a plane frame will have three degrees of freedom two translations and one rotations.

Degree of Kinematic Indeterminacy:  It can be defined as the number of unrestrained components of  joint displacements.

Kinematic Indeterminacy is given by ,

Ik=NJ-C

N=Number of degree of freedom

J= Number of joints

C= Number of restraints against displacement giving rise to reaction components