If the permissible compressive and tensile stresses in a singly reinforced beam are 50 kg/cm2 and 1400 kg/cm2 respectively and the modular ratio is 18, the percentage area Ast of the steel required for an economic section, is
A. 0.496%
B. 0.596%
C. 0.696%
D. 0.796%
Answer: Option C
Solution (By Examveda Team)
Permissible compressive stress in concrete (σcbc) = 50 kg/cm2Permissible tensile stress in steel (σst) = 1400 kg/cm2
Modular ratio (m) = 18
To find the depth of the neutral axis (Xc):
Xc = (m × σcbc) / (m × σcbc + σst) × d
= (18 × 50) / (18 × 50 + 1400) × d
= 900 / (900 + 1400) × d
= 900 / 2300 × d
= 0.3913d ≈ 0.39d
From moment of resistance equation:
0.5 × b × n2 = m × Ast × (d - n)
Divide both sides by b × d2 to get percentage reinforcement:
Ast / (b × d) = 0.692%
Therefore, the required percentage area of steel Ast is:
0.692%
Correct Option: C) 0.696%
(Note: The small rounding difference from 0.692% to 0.696% is acceptable in multiple-choice exams.)
This Question Belongs to Civil Engineering >> RCC Structures Design
Join The Discussion
Comments (2)
Distribution of shear intensity over a rectangular section of a beam, follows:
A. A circular curve
B. A straight line
C. A parabolic curve
D. An elliptical curve
If the shear stress in a R.C.C. beam is
A. Equal or less than 5 kg/cm2, no shear reinforcement is provided
B. Greater than 4 kg/cm2, but less than 20 kg/cm2, shear reinforcement is provided
C. Greater than 20 kg/cm2, the size of the section is changed
D. All the above
In a pre-stressed member it is advisable to use
A. Low strength concrete only
B. High strength concrete only
C. Low strength concrete but high tensile steel
D. High strength concrete and high tensile steel
In a simply supported slab, alternate bars are curtailed at
A. $${\frac{1}{4}^{{\text{th}}}}$$ of the span
B. $${\frac{1}{5}^{{\text{th}}}}$$ of the span
C. $${\frac{1}{6}^{{\text{th}}}}$$ of the span
D. $${\frac{1}{7}^{{\text{th}}}}$$ of the span
Xc=(mc/mc+t) *d
=(18*50/18*50+1400)*d=0.39d
0.5*b*n^2=m*Ast*(d-n)
Ast/bd=0.692
How,,,?