A Structural Engineer's journey starts with 2D structural analysis. The current scenario of Structural consultancy is almost entirely governed by the use of Structural Analysis Software like STAAD Pro or ETABS for analysis and design of structures.
Why then do we need to go through the pain of manual calculations of 2D structures when in fact we almost never deal with 2-dimensional structures in real life nor do we almost ever use manual calculations for analysis and design?
This is similar to asking whether we need the knowledge of plus or minus operators or what it does in maths to truly use the calculator. And you must have guessed it, the basic knowledge is most definitely required.
As I keep repeating over and over again when it comes to the use of any Software "Garbage In, Garbage Out!". The software can only do what the user asks it to. It doesn't have any analytical brain of its own. That is where we humans come into the picture. We tell the software what we want of it and we let the software run calculations to fetch us desired results.
Like every field of learning, basics are the key to mastery. Tools are just that, tools. You are the brain of the operation. In structural analysis, the journey truly begins by understanding the determinacy of structures.
Statical determinacy or indeterminacy of any structure plays a crucial role in our ability to solve the structure easily. For a statically determinate structure, the entire structure can be effectively analyzed using just the equations of statical equilibrium.
Statically determinate and indeterminate structures are differentiated using these 03 criteria which are based upon:
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Whether a structure can be completely analyzed by just the equations of equilibrium
Determinate Structures - Structure that CAN be fully analyzed using just the equations of static equilibrium
Indeterminate Structures - Structure that CANNOT be fully analyzed using just the equations of static equilibrium
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Whether internal stresses can be developed without an external force such as due to temperature variation and lack of fit.
Determinate Structures - Structure that CANNOT develop internal stresses due to temperature variation or lack of fit
Indeterminate Structures - Structure that CAN develop internal stresses due to temperature variation or lack of fit
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Whether the Internal Forces (Shear Force, Bending Moment, etc.) depend on the material i.e. Type of Material or area of cross-section of the body
Determinate Structures - Structures whose internal forces are INDEPENDENT of Material properties
Indeterminate Structures - Structures whose internal forces are DEPENDENT on Material properties
The above 03 criteria will help you determine the determinacy of the structures. Structures however are divided into 03 categories again:
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Beams
- These are structures subjected to transverse loads only
- Based upon Coplanar Parallel Force System
- The structure is termed completely solved when Shear Force Diagram & Bending Moment Diagram is known
- Total equations of static equilibrium is 02 i.e. Sum of Fy and Mz is Zero
-
Frames
- These are structures subjected to lateral & transverse loads only
- Members connected by rigid joints
- Based upon Coplanar Force System
- The structure is termed completely solved when Shear Force Diagram, Axial Force Diagram & Bending Moment Diagram is known
- Total equations of static equilibrium is 03 i.e. Sum of Fx, Fy and Mz is Zero
-
Truss
- Members in such a structure are connected by Pinned Joints only
- Hence, members are subjected to Axial forces only
- No Shear forces or Bending is generated in the structural members
- The structure is termed completely solved when Axial Forces in each member are known
- Total equations of static equilibrium "for each joint" is 03 i.e. Sum of Fx, Fy and Mz is Zero
Knowledge of whether a structure is determinate or indeterminate is not enough. We need to further investigate the degree of indeterminacy which is calculated by using a simple equation:
Degree of Indeterminacy = Unknown Forces - Equations of Equilibrium
Degree of Indeterminacy is also known as Structural redundancy
Unknown Forces are Reactions
If, Degree of Indeterminacy = 0, the structure is Determinate
If, Degree of Indeterminacy > 0, the structure is Indeterminate
For different types of structures the equations can be modified as follows:
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Beams
Equations of Equilibrium = 2
Degree of Indeterminacy = Reactions - 2
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Frames
Equations of Equilibrium = 3
Degree of Indeterminacy = Reactions - 3
-
Truss
Equations of Equilibrium (each joint) = 2
Total Equations of Equilibrium = 2j
Unknowns = Reactions + Each Member Axial Force = R + m
Degree of Indeterminacy = Internal DOI + External DOI
Internal DOI = m - (2j - 3)
External DOI = R -3
Knowledge of the degree of Indeterminacy is very crucial in manual calculations of the structure since it provides the total redundancy of the structure. this tells us how many additional equations are necessary to fully analyze the structure.
For in-depth knowledge on the subject check out the YouTube Video: https://youtu.be/acx_55ZcpZg
Thanks,
Kushal
PS: Please share the video with your friend and colleagues to help us out!
harshit chauhan