Column uniaxial axial loaded column design

Column uniaxial axial loaded column design

1. Column

2. SHORT AND SLENDER COLUMNS Columns may fail due to one of three mechanisms: 1. compression failure of the concrete/steel reinforcement 2. buckling 3. combination of buckling and compression failure.

3. SHORT BRACED COLUMN DESIGN 1. columns resisting axial loads only; 2. columns supporting an approximately symmetrical arrangement of beams; 3. columns resisting axial loads and uniaxial or biaxial bending.

4. BS 8110 classifies a column as being short if

5. a) Condition 1. The end of the column is connected monolithically to beams on either side which are atleast as deep as the overall dimension of the column in the plane considered. Where the column is connected to a foundation structure, this should be of a form specifically designed to carry moment. b) Condition 2. The end of the column is connected monolithically to beams or slabs on either side which are shallower than the overall dimension of the column in the plane considered. c) Condition 3. The end of the column is connected to members which, while not specifically designed to provide restraint to rotation of the column will, nevertheless, provide some nominal restraint.

6. Determine if the column shown in Fig. is short. Or not For bending in the y direction: end condition at top of column = 1, end condition at bottom of column = 1. Hence from Table, βx = 0.75. For bending in the x direction: end condition at top of column = 2, end condition at bottom of column = 2. Hence from Table , βy = 0.85 Since both ɭex /h and ɭey /b are both less than 15, the column is short.

7. Axially loaded columns - clause 3.8.4.3, BS 8110 N = 0.4fcuAc + 0.8Ascfy

8. Sizing a concrete column A short-braced column in which f cu = 30 N/mm 2 and f y = 500 N/mm 2 is required to support an ultimate axial load of 2000 kN. Determine a suitable section for the column assuming that the area of longitudinal steel, A sc , is of the order of 3 per cent of the gross cross-sectional area of column, A col .

9. REINFORCEMENT DETAILS Longitudinal reinforcement Size and minimum number of bars (clause 3.12.5.4, BS 8110) . Columns with rectangular cross-sections should be reinforced with a minimum of four longitudinal bars; columns with circular cross-sections should be reinforced with a minimum of six longitudinal bars. Each of the bars should not be less than 12 mm in diameter. Reinforcement areas (clause 3.12.5, BS 8110). The code recommends that for columns with a gross cross-sectional area Acol , the area of longitudinal reinforcement ( Asc ) should lie within the following limits:

10. Links Size and spacing of links. Links should be at least one-quarter of the size of the largest longitudinal bar or 6 mm, whichever is the greater. However, in practice 6 mm bars may not be freely available and a minimum bar size of 8 mm is preferable.Links should be provided at a maximum spacing of 12 times the size of the smallest longitudinal bar or the smallest cross-sectional dimension of the column.

11. Axially loaded column Design the longitudinal steel and links for a 350 mm square, short-braced column which supports the following axial loads: G k = 1000 kN Q k = 1000 kN ,Assume f cu = 40 N/mm 2 and f y & f yv = 500 N/mm 2 . N = 0.4 f cu A c + 0.75 f y A sc Total ultimate load ( N ) = 1.4 G k + 1.6 Q k = 1.4 × 1000 + 1.6 × 1000 = 3000 kN Substituting this into the above equation for N gives 3000 × 10 3 = 0.4 × 40 × (350 2 - A sc) + 0.75 x 500 A sc A sc = 2897 mm 2 Hence from Table 3.10 , provide 4H32 ( A sc = 3220 mm2) LINKS The diameter of the links is one-quarter times the diameter of the largest longitudinal bar, that is, 1 / 4 × 32 = 8 mm, but not less than 8mm diameter. The spacing of the links is the lesser of 12 times the diameter of the smallest longitudinal bar, that is, 12 x 32 = 384 mm, or T he smallest cross-sectional dimension of the column ( = 350 mm). Hence, provide H8 links at 350 mm centres .

12. Columns supporting an approximately symmetrical arrangement of beams Load carrying capacity of the column: N = 0.35 f cu A c + 0.67 f y A sc

13. Column supporting an approximately symmetrical arrangement of beams An internal column in a braced two- storey building supporting an approximately symmetrical arrangement of beams (350 mm wide × 600 mm deep) results in characteristic dead and imposed loads each of 1100 kN being applied to the column. The column is 350 mm square and has a clear height of 4.5 m as shown in Fig. . Design the longitudinal reinforcement and links assuming f cu = 40 N/mm 2 and f y & f yv = 500 N/mm 2

14. CHECK IF COLUMN IS SHORT Effective height Depth of beams (600 mm) > depth of column (350 mm), therefore end condition at top of column = 1. Assuming that the pad footing is not designed to resist any moment, end condition at bottom of column = 3. Therefore, from Table ,  = 0.9. LONGITUDINAL STEEL Since column supports an approximately symmetrical arrangement of beams N = 0.35 f cu A c + 0.67 f y A sc Total axial load, N , is N = 1.4 G k + 1.6 Q k = 1.4 × 1100 + 1.6 × 1100 = 3300 kN

15. Substituting this into the above equation for N 3300 × 10 3 = 0.35 × 40(350 2 − Asc ) + 0.67 × 500Asc ⇒ Asc = 4938 mm2 Hence from Table, provide 4H32 and 4H25 ( Asc = 3220 + 1960 = 5180 mm 2 ) LINKS The diameter of the links is one-quarter times the diameter of the largest longitudinal bar, that is 1 / 4 × 32 = 8 mm, but not less than 8mm diameter. The spacing of the links is the lesser of (a) 12 times the diameter of the smallest longitudinal bar, that is, 12 × 25 = 300 mm, or (b) the smallest cross-sectional dimension of the column ( = 350 mm). Provide H8 links at 300 mm centres

16. Columns resisting an axial load and bending Design the longitudinal and shear reinforcement for a 275 mm square, short-braced column which supports either (a) an ultimate axial load of 1280 kN and a moment of 62.5 kNm about the x–x axis or (b) an ultimate axial load of 1280 kN and bending moments of 35 kNm about the x–x axis and 25 kNm about the y–y axis. Assume f cu = 30 N/mm 2 , f y = 500 30 N/mm 2 and cover to all reinforcement is 35 mm. LOAD CASE (A) Longitudinal steel

17. 100 A sc/ bh = 3, A sc = 3 x 275 × 275/100 = 2269 mm 2 Provide 8H20 ( A sc = 2510mm2, Table ) Links The diameter of the links is one-quarter times the diameter of the largest longitudinal bar, that is, 1 / 4 × 20 = 5 mm, but not less than 8 mm diameter. The spacing of the links is the lesser of (a) 12 times the diameter of the smallest longitudinal bar, that is, 12 × 20 = 240 mm, or (b) the smallest cross-sectional dimension of the column ( = 275 mm). Provide H8 links at 240 mm centres

18. LOAD CASE (B) Longitudinal steel