# RCC Structures

 Question 1
A rectangular cross-section of a reinforced concrete beam is shown in the figure. The diameter of each reinforcing bar is 16 mm. The values of modulus of elasticity of concrete and steel are $2.0 \times 10^{4} \mathrm{MPa} \text { and } 2.1 \times 10^{5} \mathrm{MPa}$, respectively. The distance of the centroidal axis from the centerline of the reinforcement (x) for the uncracked section (in mm,round off to one decimal place) is ____________
 A 129.4 B 178.6 C 145.6 D 98.2
GATE CE 2021 SET-2      Footing, Columns, Beams and Slabs
Question 1 Explanation: \begin{aligned} m&=\frac{E_{s}}{E_{C}}=\frac{2.1 \times 10^{5}}{2 \times 10^{4}}=10.5 \\ A_{s t}&=3 \times \frac{\pi}{4}(16)^{2}=603.20 \mathrm{~mm}^{2} \\ \bar{y}&=\frac{\left(B \cdot D \cdot \frac{D}{2}+(m-1) \times A_{s t} \times d\right)}{B \cdot D+(m-1) \cdot A_{s t}} \\ &=\frac{\left(200 \times \frac{350^{2}}{2}+(10.5-1) \times 603.2 \times 315\right)}{200 \times 350+(10.5-1) \times 603.2}=185.59 \mathrm{~mm}\\ & \text{Distance of N-A from reinforcement}\\ y_{2} &=d-\bar{y} \\ &=315-185.59=129.41 \mathrm{~mm} \end{aligned}
 Question 2
A combined trapezoidal footing of length L supports two identical square columns ($P_{1}$ and $P_{2}$) of size 0.5m x 0.5m, as shown in the figure. The columns $P_{1}$ and $P_{2}$ carry loads of 2000 kN and 1500 kN, respectively. If the stress beneath the footing is uniform, the length of the combined footing L (in m,round off to two decimal places) is _____
 A 4.52 B 2.78 C 5.83 D 2.45
GATE CE 2021 SET-1      Footing, Columns, Beams and Slabs
Question 2 Explanation:
C.G. of load from $P_{1}$ \begin{aligned} P_{R} \bar{x} &=P_{1} \times 0+P_{2} \times 5 \\ \bar{x} &=\frac{1500 \times 5}{3500}=2.143 \mathrm{~m} \end{aligned}
Distance of C.G. of footing from face of $P_{1}$
$\bar{y}=\bar{x}+0.25=2.393 \mathrm{~m}$ C.G of footing \begin{aligned} \bar{y} &=\left(\frac{B_{1}+2 B_{2}}{B_{1}+B_{2}}\right) \times \frac{L}{3} \\ 2.393 &=\left(\frac{5+2 \times 1.5}{5+1.5}\right) \times \frac{L}{3} \\ L &=5.833 \mathrm{~m} \text { say } 5.83 \mathrm{~m} \end{aligned}
 Question 3
A prismatic cantilever prestressed concrete beam of span length, L=1.5 m has one straight tendon placed in the cross-section as shown in the following figure (not to scale). The total prestressing force of 50 kN in the tendon is applied at $d_{c}=50 \mathrm{~mm}$ from the top in the cross-section of width, b=200 mm and depth, d=300 mm. If the concentrated load, P=5 kN, the resultant stress (in Mpa,in integer) experienced at point 'Q' will be _________
 A 3 B 0 C 5 D 6
GATE CE 2021 SET-1      Prestressed Concrete Beams
Question 3 Explanation: \begin{aligned} \mathrm{e} &=\frac{D}{2}-50=\frac{300}{2}-50=100 \mathrm{~mm} \\ \mathrm{DL} &=0.2 \times 0.3 \times 1.0 \times 25=1.50 \mathrm{kN} / \mathrm{m} \\ P &=50 \mathrm{kN}=50000 \mathrm{~N} \\ W &=5 \mathrm{kN} \\ \text { Maximum BM } &=\frac{w^{2}}{2}+\mathrm{W} \\ &=\frac{1.5 \times 1.5^{2}}{2}+5 \times 1.50=9.1875 \mathrm{kNm} \end{aligned} \begin{aligned} \frac{P}{A}&=\frac{50000}{200 \times 300}=0.833 \mathrm{~N} / \mathrm{mm}^{2} \\ \frac{P e}{Z}&=\frac{50000 \times 100}{200 \times \frac{300^{2}}{6}}=1.67 \mathrm{~N} / \mathrm{mm}^{2} \\ \frac{M}{Z}&=\frac{9.1875 \times 10^{6}}{200 \times \frac{300^{2}}{6}}=3.0625 \mathrm{~N} / \mathrm{mm}^{2}\\ \text{Stress at Q,}\qquad \qquad\\ \text { Stress at } Q &=\frac{P}{A}+\frac{P e}{Z}-\frac{M}{Z} \\ &=0.833+1.67-3.0625 \\ &=-0.56 \mathrm{~N} / \mathrm{mm}^{2} \text { (Tensile) } \end{aligned}
 Question 4
The cross-section of the reinforced concrete beam having an effective depth of 500 mm is shown in the figure (not drawn to the scale). The grades of concrete and steel used are M35 and Fe550, respectively. The area of tension reinforcement is 400 $mm^2$. It is given that corresponding to 0.2% proof stress, the material safety factor is 1.15 and the yield strain of Fe550 steel is 0.0044. As per IS 456:2000, the limiting depth (in mm, round off to the nearest integer) of the neutral axis measured from the extreme compression fiber, is ________.
 A 125.14 B 235.21 C 365.47 D 221.52
GATE CE 2020 SET-2      Footing, Columns, Beams and Slabs
Question 4 Explanation: For a RCC T-Beam
(For limiting depth of neutral axis)
Considering d=500mm
\begin{aligned} \frac{0.0035}{x_{u,lim}}&=\frac{0.0044}{d-x_{u,lim}}\\ d-x_{u,lim}&=\frac{0.0044}{0.0035} \times x_{u,lim}\\ 35 \times 500&=35x_{u,lim}+44x_{u,lim}\\ &=79x_{u,lim}\\ x_{u,lim}&=\frac{35 \times 500}{79}\\ &=221.52 mm \end{aligned}
Limiting depth of neutral axis
$x_{0,lim}=221.52mm$
 Question 5
A concrete beam of span 15 m, 150 mm wide and 350 mm deep is prestressed with a parabolic cable as shown in the figure (not drawn to the scale). Coefficient of friction for the cable is 0.35, and coefficient of wave effect is 0.0015 per metre. If the cable is tensioned from one end only, the percentage loss (round off to one decimal place) in the cable force due to friction, is ________.
 A 4.49 B 2.45 C 8.56 D 9.47
GATE CE 2020 SET-2      Prestressed Concrete Beams
Question 5 Explanation: Jacking from one end
x = L = 15 m
Wobble correction factor, K = 0.0015
Coefficient of friction = 0.35 = $\mu$
P = Not given
$p_0$ = Unknown
Change of gradient, $\alpha = \tan \alpha =\frac{8h}{L}=\frac{8 \times 120}{15000}=0.064$
% loss of stress in steel due to friction
\begin{aligned} &=\frac{p_0(Kx+\mu \alpha )}{p_0} \times 100\\ &=(0.0015 \times 15+0.35 \times 0.064)\times 100 \\ &= 4.49\% \end{aligned}
 Question 6
The maximum applied load on a cylindrical concrete specimen of diameter 150 mm and length 300 mm tested as per the split tensile strength test guidelines of IS 5816 : 1999 is 157 kN. The split tensile strength (in MPa, round off to one decimal place) of the specimen is _______.
 A 1.4 B 2.2 C 4.2 D 6.4
GATE CE 2020 SET-2      Working Stress and Limit State Method
Question 6 Explanation: P = 157 kN
D = 150 mm
L = 300 mm
In split tensile strength test, split tensile
strength of concrete
\begin{aligned} f_{et}&=\frac{2P}{\pi DL}=\frac{2 \times 157000}{\pi \times 150 \times 300}\\ &=2.22 N/mm^2 \end{aligned}
 Question 7
As per IS 456:2000, the pH value of water for concrete mix shall NOT be less than
 A 4.5 B 5 C 5.5 D 6
GATE CE 2020 SET-2      Working Stress and Limit State Method
Question 7 Explanation:
1. Minimum pH value of water for concrete = 6.0
As per IS code provision no. 5.4.2, the pH value of water shall not less than 6.0.
 Question 8
A simply supported prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.
 A 25 B 40 C 80 D 120
GATE CE 2020 SET-1      Prestressed Concrete Beams
Question 8 Explanation: P = 600 kN
Simply supported span = L = 8 m
To support a point load applied at mid span (W) = 12 kN
\begin{aligned} \text{Balancing load} &= \text{Point load}\\ 2P \sin \theta &=Q\\ 2P\left ( \frac{e}{L/2} \right )&=2\\ \frac{2Pe \times 2}{L}&=W\\ \frac{4Pe}{L}&=W\\ e&=\frac{WL}{4P}\\ &=\frac{12000 N \times 8000mm}{4 \times 600 \times 1000N}\\ &=40mm \end{aligned}
 Question 9
The singly reinforced concrete beam section shown in the figure (not drawn to the scale) is made of M25 grade concrete and Fe500 grade reinforcing steel. The total crosssectional area of the tension steel is 942 $mm^2$. As per Limit State Design of IS 456 : 2000, the design moment capacity (in kNm round off to two decimal places) of the beam section, is __________
 A 151.77 B 252.36 C 121.12 D 158.28
GATE CE 2020 SET-1      Footing, Columns, Beams and Slabs
Question 9 Explanation:
\begin{aligned} B&=300mm\\ d&=450mm\\ A_{st}&=942 mm^2\\ M_u&=?\\ (i)\; x_{ulim}&=0.46 \times d\\ &=0.46 \times 450=207mm\\ (ii)\;\; x_u&=\frac{0.87f_yA_{st}}{0.36 f_{ck}B}\\ &=\frac{0.87 \times 500 \times 942}{0.36 \times 25 \times 300}\\ &=151.77mm\\ (iii)\;\; x_y &\lt x_{ulim}\; \text{It is under reinforcement section}\\ (iv)\;\; M_u&=0.36f_{ck}B x_u(d-0.42x_u)\\ &=0.36 \times 25 \times 300 \times 151.77 \\ &\times (450-0.42 \times 151.77)/10^6\\ &=158.28kN-m \end{aligned}
 Question 10
During the process of hydration of cement, due to increase in Dicalcium Silicate ($C_2S$) content in cement clinker, the heat of hydration
 A increases B decreases C initially decreases and then increases D does not change
GATE CE 2020 SET-1      Working Stress and Limit State Method
Question 10 Explanation:
Due to increase in $C_2S$ heat of hydration decreases.

There are 10 questions to complete.

### 1 thought on “RCC Structures”

1. The answer of q.9 shall be 122 kN-m as it is under reinforced section the evaluation of moment of the resistance will be based on tension not the compression. 