STRUCTURAL ANALYSIS
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Introduction to structures
A system subjected to external loads will undergo deformation. If the internal resistance is developed and the body is able to come back to its original state is is called structure.
Deflected profile of a structure is non linear hence it is also called elastic line.
Mechanism – Unstable systems are called mechanisms. It will have a linear deformation like rigid body.
Classification of structures :
1. Skeletal structures : A structure which had linear and non linear members as elements. ex portal frames.
2D and 3D skeletal structures are also possible.
In skeletal structures only 1 dimension is predominant, say length.
2. Surface structures : 2 dimension are considerable i.e length and breadth.
3. Solid structures : All the three dimensions are considered. Skeletal structures can be analysed using the traditional methods such as force methods and displacement methods.
Analysis of 2 way slabs (surface structures) is done using Johonsons yield line theory.
Based on type of joints :
1. Pin jointed structures (trusses)
Plane trusses and Space trusses. Load applied at a joint is transferred to other members in axial directions. Therefore axial forces are the design forces only. They cannot resist Bending moments and shear forces.
2. Rigid jointed structures :
2D frame and 3D frame.
Design forces are axial forces, shear forces are Bending Moments because of rigidity for in plane loading.
If the centroidal plane of the structural members and plane of the loading coincide, then it is called in plane loading.
If a rigid jointed structural member is subjected to out plane loading, possible design forces are axial forces, shear force and Bending moment and torsional moment.
Difference between Bending moment and Torsional moment : The moments which are within the plane of cross section. Torsional moment or twisting moment or torque us the moment about longitudinal axis of the member.
Reaction is the resistance against deformation. For free end, due to vertical load, tip of the free end has the deformation as no resistance against the deformation, no reaction.
Roller support shown is free to move horizontally,free to rotate. Hence neither horizontal reaction nor moment reaction at roller support. However it cannot move in the vertical direction. Hence it has only one reaction that is vertical reaction.
Hinged support is free to rotate. Hence no moment reaction.
A hinge is a device which makes some force zero. Moment hinge releases moment. Shear hinge releases shear force. Reaction at a support is nothing but the shear force at the support. In the support, horizontal reaction, rollers are in the horizontal place is zero which implies that horizontal shear force is zero. Hence it is called horizontal shear hinge support. Reaction at a roller support is normal to the plane of rolling.
Compatibility equations : Compatibility equations deal with displacements. These equations are related to balancing of deformation. Elastic props can compress. Ex springs. Rigid props cannot deform. Number of compatibility equations at a support shall be equal to number of reaction components.
Static indeterminacy : If equilibrium equations are sufficient to analyse a structure completely for unknown forces, it is called statically determinate structure. If all the unknown forces at fixed support are calculated using the equilibrium equations alone, it is called Statically Indeterminate Structures.
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