Structures and static indeterminacy
A Structure (in civil engineering terms) refers to a system of connected parts, which is used to support a load. Structures and static indeterminacy and all its types will be discussed in this post.
When any elastic body is subjected to a system of loads and deformation takes place and the resistance is set up against the deformation, then the elastic body is known as a structure.
The simply supported beam shown below is a stable structure.
If there is no resistance which has been set up in the body against the deformation then the structure is known as an unstable structure or mechanism.
The simply supported beam shown below with an internal hinge is an unstable structure.
CLASSIFICATION OF STRUCTURES
Structures are classified as follows
- Skeletal Structure:- The structure which can be idealized to series of straight or curved lines are called as skeletal Structure. Examples:- Roof trusses, Building frame.
- Surface structures:- These are the structures which can be idealized to a planar or curved surfaces. Examples:- Slabs and Shells
- Solid structures:- These are the structures which can neither be idealized to a skeleton or to a plane or curved surfaces. Examples:- massive Foundation.
Classification of Skeletal structures:-
Skeletal structures are further classified based on two types based on type of joint & based on dimensions. Both of the above classification of skeletal structures are described below.
Based on type of joint:-
- Pin jointed frames:- These are the type of skeletal structures, in which the members are connected by means of pin joints. These frames support the loads by developing only axial forces, if the external loads act at the joints and members are straight.
- Rigid jointed frames:- There are certain assumptions in this type of classification. Assumption that the joints of rigid jointed frames are rigid so that the angles between the members meeting at joint remain unchanged. These frames resist external forces by developing bending moment, shear forces, axial forces and twisting moment in the members of the frames.
Based on dimensions:-
- Plane frames:- All members of plane frames as well as the external load for resume to be in one plane. Plane frames are classified further as, pin jointed plane frame the members which carry only axial forces, and rigid jointed plane frames the members subjected to axial as well as shear forces and bending moments as well.
- Space frame:- All members do not lie in one plane. Very often it is also a combination of series of frame. Here also further classification of space frame is possible like pin jointed space frames and rigid jointed space frames. The former caring only axial forces and the latter carrying axial as well as well as shear forces, and bending and twisting moment.
Equations of static equilibrium:
For a plane frame subjected to in plane external force in X-Y plane:
∑Fx = ∑Fy = ∑M = 0
or which can also be expressed as:-
∑H = ∑V = ∑M = 0
- ∑H = Algebraic sum of components of all external forces including reacting forces in horizontal direction.
- ∑V = Algebraic sum of components of all external forces including reacting forces in vertical direction.
- ∑M = Algebraic sum of moments of all forces about any point in the Plane of the structure.
For a space frame:-
∑Fx = ∑Fy = ∑Fz = ∑Mx =∑My =∑Mz = 0
STATICALLY DETERMINATE STRUCTURE:
The structures that can be analysed with the help of equations of static equilibrium alone are called as statically determinate structures.
It can undergo finite deformation before the condition of equilibrium are satisfied.
Examples of statically determinate structures are:
- A cantilever beam
- A simply supported beam
- A suspension cable
STATICALLY INDETERMINATE STRUCTURE:
Any structure whose reaction components or internal stresses cannot be established by using the equations of static equilibrium alone are called as statically indeterminate structures.
- When the number of unknown forces is greater than the number of equilibrium equations then any structure will be known as statically indeterminate structure.
- For complete analysis of statically indeterminate structure, additional equations based on conditions of compatibility or consistent displacement shall be used.
Difference between statically determinate and indeterminate structure:
|Determinate Structures||Indeterminate Structures|
|Equations of equilibrium of sufficient to analyse.||Equations of equilibrium is insufficient to analyse.|
|Bending moment at a section or forcing any member is independent of material.||Bending moment at a section or forcing any member is dependent of material.|
|Stresses are not caused due to temperature changes.||Stresses are caused due to temperature changes.|
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