COLUMNS. Classification of columns:

Transcription

1 COLUMNS are vertical compression members in structures, the effective length of which exceeds three times its lateral dimension. Which are provided for bear the load of Beam, Slab, etc. since columns support beams and slabs, so the failure of column results in the collapse of structure. Classification of columns: A. Classification on the basis of its shape: I. Square column, II. Rectangle column, III. Circular column, IV. Desired polygon. B. Classification on the basis of its slenderness ratio: I. Short column & II. Long column. C. Classification on the basis of the manner of loading: I. Axially loaded column, II. Column subjected to axially load and uni-axial bending, III. Column subjected to axially load and bi-axial bending. D. Classification on the basis of the type of lateral reinforcement provided: I. Tied columns in which separate or individual ties are provided surrounding the longitudinal reinforcement. II. Spirally reinforced columns in which helical bars are provided surrounding the longitudinal reinforcement.

2 Pedestal: Effective length 3 x least lateral dim n. Short Column: Effective length 1 x least lateral dim n. Long Column: Effective length 1 x least lateral dim n. I.S. Recommendation regarding longitudinal reinforcements: (See IS 456: 000, page no 48) 1) Minimum % of Longitudinal reinforcement = 0.8% of gross c/s area (Max =6.0% ). ) Minimum numbers of longitudinal bars = 4 in rectangular and 6 in circular columns. 3) Minimum diameter of longitudinal bars = 1 mm. 4) Distance between longitudinal bars 300 mm. 5) Minimum % of Longitudinal bars in pedestal = 0.15% of gross c/s area. I.S. Recommendation regarding Transverse reinforcements: (See IS 456: 000, page no 49) 1) Diameter of Transverse reinforcements will be max m of, a) 5 mm, b) Diameter of longitudinal bar. ) Spacing of Transverse tie centre to centre is min m of, a) The least lateral dimension of the column, b) 16 diameter of longitudinal bar. c) 48 diameters of transverse ties. 3) The min m cover will be greater of, a) 40 mm or b) Diameter of bar. Department of civil engineering (surajjj445@gmail.com) Page of 16

3 Effective length of a column: (See IS 456: 000, page no 94) Effective length is the distance between two points of contra-flexure. L eff Notations used in Column: Permissible load on a short column: There are two methods for analysed a short column: 1. Simple elastic theory.. I.S. code method (working stress method). Simple Elastic theory : Where, Safe load on the column, W = Department of civil engineering (surajjj445@gmail.com) Page 3 of 16

4 I.S. code method (working stress method) : Where, Example 1: A reinforced concrete beam short column has to carry an axial compressive load of 150 KN. Design the column. Use M 0 concrete and Fe 415 steel. Sol n : Given data, Size of column = 400 mm x 400 mm Let, Now, Using working stress method; Let us provide 0 mm Ø bars, No. of bars required Department of civil engineering (surajjj445@gmail.com) Page 4 of 16

5 Calculation for Transverse reinforcements or Tie; Diameter of Transverse reinforcements will be max m of, A) 5 mm, B) Diameter of longitudinal bar. so provide 5 mm dia bar as tie. Spacing of Transverse tie centre to centre is min m of, a) The least lateral dimension of the column, b) 16 diameter of longitudinal bar, c) 48 diameters of transverse ties, Hence provide 5 mm 40mm c/c. Example : A short column of square section is to be designed to carry an axial load of 103 KN. Design the column as per I.S. code. Permissible stress in concrete and steel are 5 N/mm and 130 N/mm. Sol n : given data, From I.S. code longitudinal reinforcement in column must lie between 0.8 % to 6.0 % of C/S area. Let us provide.0% steel area of total C/S area... I.S. code method (working stress method) : Hence provide Department of civil engineering (surajjj445@gmail.com) Page 5 of 16

6 Now, Let us provide 18 mm Ø bars, No. of bars required So provide 8 bars of 18 mm dia. Calculation for Transverse reinforcements or Tie; Diameter of Transverse reinforcements will be max m of, A) 5 mm, B) Diameter of longitudinal bar. so provide 5 mm dia bar as tie. Spacing of Transverse tie centre to centre is min m of, a) The least lateral dimension of the column, b) 16 diameter of longitudinal bar, c) 48 diameters of transverse ties, Hence provide 5 mm 40mm c/c. Department of civil engineering (surajjj445@gmail.com) Page 6 of 16

7 Permissible load on a long column: I.S. code method (working stress method) : Where, Determination of value of Reduction coefficient, ( ) For more accurate value, Where, Department of civil engineering (surajjj445@gmail.com) Page 7 of 16

8 Combined Bending and Direct stresses: When a column is subjected to an eccentric load, there occurs Direct stress as well as Bending stress too. a) If a column subjected to an axial load at junction of X-X and Y-Y axis, it produces Direct stress. b) If load acts on X-X and Y-Y axis, it produces Uni-axial moment along with axial load. c) If load doesn t acts on X-X and Y-Y axis, it produces Bi-axial moment along with axial load. Direct Stress in a column: Department of civil engineering (surajjj445@gmail.com) Page 8 of 16

9 Bending Stress in a column: There are three cases arises with values of Direct stress and Bending stress. Case 1: Value of Direct Stress > Bending stress. Case : Value of Direct Stress = Bending stress. Case 3: Value of Direct Stress < Bending stress. Case 3 should be avoided as far as possible. Department of civil engineering (surajjj445@gmail.com) Page 9 of 16

10 Stress Diagram for all 3 cases: Design of column subjected to combined axial load and uni-axial moment. There are two cases: 1. Uncracked section.. Cracked section. 1. Uncracked section: If the concrete in tension zone is considered, the section is uncracked.. Cracked section: If the concrete in tension zone is ignored, the section is assumed as cracked section. Department of civil engineering (surajjj445@gmail.com) Page 10 of 16

11 Design of R.C.C. column as Uncracked section: The direct stress in column: The bending stress in the column: We have; For safe design Interaction condition should be satisfied which is, Department of civil engineering Page 11 of 16

12 Example 1. Design a rectangular column section subjected to an axial load of 750 KN and uniaxial moment of 75 KN-m. Consider concrete of grade M 5 and steel Fe 415. [BNMU 010] Sol n : Allowable stresses of steel and concrete are;. It is clear that 100 mm is the small value of eccentricity, so we can design the column as an uncracked section. The size of the column let us provide 1% steel, so, For safe design it must be satisfy the interaction formula: Department of civil engineering (surajjj445@gmail.com) Page 1 of 16

13 Putting the value, So size of column = b D = Provide 6 bars of mm Ø Provided Calculation for Transverse reinforcements or Tie; Diameter of Transverse reinforcements will be max m of, A) 5 mm, B) Diameter of longitudinal bar. so provide 8 mm dia bar as tie. Spacing of Transverse tie centre to centre is min m of, a) The least lateral dimension of the column, b) 16 diameter of longitudinal bar, c) 48 diameters of transverse ties, Hence provide 8 mm Ø 300 mm c/c. Check: 1. Department of civil engineering (surajjj445@gmail.com) Page 13 of 16

14 . 3. Example : A rectangular column section 450mm x 600mm is acted upon by an axial load of 500 KN. M x and M y = 5KNm each. The steel provided is 8-0mmØ bars with an effective cover of 40 mm. check the safety of the section. [BNMU 009] Sol n : Axial load, P = 500 KN= 500 x 10 3 N M x = P x e y & M y = P x e x.. e x & e y both are equal, So, Mam m eccentricity to avoid tensile stress; It is clear that no tension develops anywhere in the column. So we can analyse the column as an uncracked section. Department of civil engineering (surajjj445@gmail.com) Page 14 of 16

15 Check: 1. Department of civil engineering Page 15 of 16

16 . 3. Department of civil engineering Page 16 of 16