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Columns and STruts s
- 1. COLUMNS AND STRUTS Subject: StructuralMechanics (S.M.) Semester: 4th Course: Diploma Trade: Civil Engineering
- 2. COLUMN………………It’s Definition A baror member of a structure which carries an axial compressive load is known as ‘Strut’. A strut inclined at 90˚ to the horizontal (i.e. vertical strut) is known as ‘Column’.
- 3. COLUMN………………It’s Classification Classification of Columns: 1.Based on Shape of Column 2. Based on Material used 3. Based on Length of Column 4. Based on Line of action of load
- 4. Classification Based on ShapeOf Column… (a) Square Column (b) Rectangular Column (c) Circular Column (d) Hexagonal Column
- 5. Classification Based on MaterialOf Column… RCC Column (COLUMN) Steel Column (STANCHION)
- 6. Classification Based on MaterialOf Column… Brick Column (PILLAR) Wooden Column (POST)
- 7. Classification Based on LengthOf Column… (a) Short Column: The column whose slenderness ratio is less than 32 is known as ‘Short Column’. (b) Intermediate Column: The column whose slenderness ratio is between 32 and 120 is known as ‘Intermediate Column’. (c) Long Column: The column whose slenderness ratio is more than 120 is known as ‘Long Column’.
- 8. Classification Based online of action of load… Axial Column: The column in which load is applied at centroid of column is known as ‘Axial Column’. Eccentric Column: The column in which load is applied at a distance from centroid of column is known as ‘Eccentric Column’.
- 9. Failure of ShortColumns Short column fails by Crushing.
- 10. Failure of IntermediateColumns Intermediate Column fails by Crushing and buckling both.
- 11. Failure of LongColumns Intermediate Column fails by buckling alone.
- 12. Buckling Load The maximumaxial compressive load which a column can take without failure by buckling is known as Buckling Load. It is also called CRIPPLING LOAD or CRITICAL LOAD.
- 13.
- 14. Safe Load The ratioof Buckling Load to a suitable factor of safety is known as Safe Load. It is also known as Service load (or) working load. Mathematically, Safe Load = 𝐵𝑢𝑐𝑘𝑙𝑖𝑛𝑔 𝐿𝑜𝑎𝑑 𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦
- 15. Factor of safety Theratio of Buckling Load to Safe load is known as Factor of safety. It is also known as Factor of Ignorance. For (a) Timber – FOS is 6 (b) Cast iron – FOS is 5 (c) Wrought iron, Mild steel – FOS is 3
- 16. Slenderness Ratio The ratioof Effective length of column to minimum radius of gyration is known as Slenderness Ratio. It has no units. Mathematically, Slenderness ratio = 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑐𝑜𝑙𝑢𝑚𝑛 (𝐿𝑒) 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑔𝑦𝑟𝑎𝑡𝑖𝑜𝑛 (𝑘)
- 17. Effective Length ofColumn Effective length of a column is the distance between two adjacent points of inflexion. The length of the column which is affected by load coming over column is called ‘Effective Length’.
- 18. Effective Length ofColumn
- 19. Effective Length ofColumn
- 20. Euler’s formula forCrippling Load P = π2 E I Le 2 where, P = Crippling Load/ Crushing Load/ Critical Load/ Buckling Load E = Young’s modulus of elasticity I = Moment of Inertia Le = Effective Length of column
- 21. Assumptions in Euler’sTheory 1. The column is initially straight and load is applied axially. 2. The cross-section is uniform throughout the length. 3. Material is homogenous and isotropic. 4. The length of the column is very large as compared to cross- sectional dimensions. 5. Direct stress is very small compared to bending stress. 6. Column fails by buckling alone. 7. Self weight of the column is neglected.
- 22. Limitations of Euler’sFormula 1. Euler’s formula is valid only if assumptions made by Euler’s are fulfilled. 2. This formula is valid only for long columns.
- 23. NUMERICAL PROBLEM A 2m long cast iron column has a circular cross section of diameter 60 mm. One end of the column is fixed and other is free. Taking factor of safety as 5, Find the safe load using Euler’s formula. Consider E = 1.3 × 105 N/𝑚𝑚2 .