GATE 2021 CE (CE2) – Question 51
An uncracked RC section is 200 mm wide and 350 mm deep, reinforced with three 16 mm bars whose centres are 35 mm above the bottom. Ec=2×10⁴ MPa and Es=2.1×10⁵ MPa. Find distance x from steel centreline to transformed-section centroid in mm to one decimal.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 129 to 130
Explanation
Modular ratio is m=Es/Ec=10.5 and steel area is $A_s=3\pi16^2/4=603.186$ mm². Gross concrete area includes the steel locations, so add only (m−1)As=9.5As to the transformed area. The gross centroid is 140 mm above the steel line, giving $x=70000(140)/(70000+9.5A_s)=\mathbf{129.4}$ mm.