Q145
An R.C.C. column of 30 cm diameter is reinforced with 6 bars 12 mm φ placed symmetrically along the circumference. If it carries a load of 40,000 kg axially, the stress is
A.
49.9 kg/cm2
AnswerB.
100 kg/cm2
C.
250 kg/cm2
D.
175 kg/cm2
Answer: Option A
Solution
Answer: Option A
Solution:
Given: Diameter of R.C.C. column D = 30 cm; 6 bars of 12 mm (1.2 cm) diameter; Axial load P = 40,000 kgGross area of column (Ag): (π/4)D2 = (π/4)(30)2 = 706.86 cm2
Area of one bar: (π/4)d2 = (π/4)(1.2)2 = 1.131 cm2 (approx.)
Total steel area (As): 6 × 1.131 = 6.786 cm2
Net concrete area (Ac): Ag − As = 706.86 − 6.786 = 700.07 cm2
Assume modular ratio (m): 15 (typical for RCC working stress method)
Transformed area carrying load: Ac + mAs = 700.07 + 15×6.786 = 801.86 cm2
Concrete stress (working): σc = P / (Ac + mAs) = 40,000 / 801.86 = 49.9 kg/cm2
Therefore, the stress is 49.9 kg/cm2 ⇒ Option A.