Test: Columns - Civil Engineering (CE) MCQ

As per IS 456: 2000, Clause 39.3
Short Axially Loaded Members in Compression:
The member shall be designed by considering the assumptions given in clause 39.1 and the minimum eccentricity. When the minimum eccentricity as per clause 25.4 does not exceed 0.05 times the lateral dimension, the member may be designed by the following equation:

Where P_u = Axial load on the member,
f_ck = Characteristic compressive strength of concrete,
A_c = Area of concrete,
f_y = Characteristic strength of the compression reinforcement,
A_sc = Area of longitudinal reinforcement for the column.

For both ends fixed,

And for both ends hinged

Slender column: Cross sections in which the elements buckle locally even before the attainment of yield stress are called slender sections.
The column is classified based on its slenderness ratio.

Considering the x-axis is as major axis because I_xx is greater and the y-axis as the minor axis
a > b ⇒ I_xx > I_yy
Slenderness ratio 

So,

Least radius of gyration will be along the major axis


Slenderness ratio =1000/2.887=3.46

Given data:
Width of square column (b) = 500 mm
Service load (P) = 2000 kN
Ultimate load (P_u) =?
The minimum area of longitudinal reinforcement (Ast_min) = ?
As per IS 456:2000 for the short axially loaded columns -
The minimum area of longitudinal reinforcement or steel (Ast_min)
= 0.8% of the gross area of the column
The minimum area of longitudinal reinforcement or steel (Ast_min)
= (0.8/100)x500²
The minimum area of longitudinal reinforcement or steel (Ast_min)
= 2000 mm²
Ultimateload(P_u) = FOS×Serviceload(P)
Where FOS = Factor of safety = 1.5
Ultimate load (P_u) = 1.5 × 2000 = 3000 kN
Ultimate load (P_u) = 3000 kN

According to Clause 26.5.3.1 of IS 456: 2000, the minimum longitudinal steel reinforcement for the column is 0.8 % of the gross column area and maximum longitudinal steel reinforcement is 6 % of the gross area.
Limit on the minimum reinforcement is specified due to the following reasons:

• Need to ensure minimum flexural resistance due to unexpected eccentricities that may occur in the column.
• To account for creep under sustained loading which is predominant in columns.

Important Points
For very large columns, the minimum longitudinal steel reinforcement for the column is 0.8 % of the actual column area.
Other specifications for the column:

Minimum Eccentricity for columns: 

As per IS 456: 2000, clause 25.4,
Minimum Eccentricity
All columns shall be designed for minimum eccentricity, equal to the addition of the unsupported length of column divided by 500 and lateral dimensions divided by 30, subject to a minimum of 20 mm.
Where biaxial bending is considered, it is sufficient to ensure that eccentricity exceeds the minimum about one axis at a time.
Calculation:
Unsupported length = 5000 mm
Size of the column = 400 mm
Minimum eccentricity 

But, in no case, the minimum eccentricity should be less than 20 mm.

Longitudinal Reinforcement:
(i) CI. 26.5.3 of IS 456:2000, specifies that the total area of longitudinal bars in a column section must NOT be less than 0.8% of the gross column area. This limit on minimum reinforcement is imposed because of the following reasons:

• In order to ensure that a minimum flexural resistance of the column exists due to unexpected eccentricities in the column loading.
• In compression members, creep under sustained loading is very predominant, especially at low percentages of steel. Thus, the resulting creep stress (due to creep strain) tries to yield the bars. 

(ii) Maximum Reinforcement: The maximum area of cross-section of longitudinal bars must NOT exceed 6% of gross column area. However, in practice, a maximum of 4% is recommended.
Additional Information
Diameter and Number of bar:
(i) The diameter of longitudinal bars in column NOT be less than 12 mm. These bars must NOT be spaced more than 300 mm apart on the column perimeter.
(ii) For rectangular columns. a minimum of 4 bars is provided.
(iii) For Circular columns, a minimum of 6 bars be provided.
Cover = 40 mm or bar diameter

As per IS 456:2000, clause 26.5.3.2 (c), 
Pitch:
The pitch of transverse reinforcement shall be not more than the least of the following distances:

• the least lateral dimension of the compression members
• 16 times the smallest diameter of the longitudinal reinforcement bar to be tied (i.e. 16 φ_min)
• 300 mm

The diameter of the Lateral Ties: The diameter of the lateral ties shall be not less than one-fourth of the diameter of the largest longitudinal bar and in no case less than 6 mm.
Calculations: The pitch of transverse reinforcement shall be

• The lest lateral dimension = 400 mm
• 16 × 20 mm = 320 mm
• 300 mm

whichever is smaller
Hence, the pitch of lateral ties shall be kept as 300 mm.