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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
Answer & Solution
Correct Answer:
Option
A
Given: Diameter of R.C.C. column D = 30 cm; 6 bars of 12 mm (1.2 cm) diameter; Axial load P = 40,000 kg
Gross 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.
Gross 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.
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LoginAc= 3.14 d2/4 =706.5
Ast= 6x 3.14xd2/4 =7.065
modular ratio m=13
Putting Values Stress= 40000/706.5+ 13x7.065 = 50 apx =49.9