# RCC Structures

 Question 1
It is given that an aggregate mix has 260 grams of coarse aggregates and 240 grams of fine aggregates. The specific gravities of the coarse and fine aggregates are 2.6 and 2.4, respectively. The bulk specific gravity of the mix is 2.3.
The percentage air voids in the mix is ____________. (round off to the nearest integer)
 A 2 B 4 C 8 D 16
GATE CE 2022 SET-2      Concrete Technology
Question 1 Explanation:
Given that,
Coarse aggregate = 260 gms
Fine aggregate = 240 gms
$G_{CA}=2.6$
$G_{FA}=2.4$
Bulk specific gravity $G_m=2.3$
Percentage air voids in the mix = ?
$G_t$ (Theoretical specific gravity)

\begin{aligned} &=\frac{\Sigma W}{\Sigma \frac{W}{G}}\\ &=\frac{260+240}{\frac{260}{2.6}+\frac{240}{2.4}}\\ &=2.5 \end{aligned}
\begin{aligned} % \text{ air voids} (V_V)&=\frac{G_t-G_m}{G_t} \times 100\\ &=\frac{2.5-2.3}{2.3}\times 100\\ V_V&=8% \end{aligned}
 Question 2
A post-tensioned concrete member of span 15 m and cross-section of 450 mm x 450 mm is prestressed with three steel tendons, each of cross-sectional area 200 $mm^2$. The tendons are tensioned one after another to a stress of 1500 MPa. All the tendons are straight and located at 125 mm from the bottom of the member. Assume the prestress to be the same in all tendons and the modular ratio to be 6. The average loss of prestress, due to elastic deformation of concrete, considering all three tendons is
 A 14.16 MPa B 7.08 MPa C 28.32 MPa D 42.48 MPa
GATE CE 2022 SET-2      Prestressed Concrete Beams
Question 2 Explanation:
This is a question of calculation of elastic shortening loss in post tensioned member.
Given data,
length = 15 m
b x D = 450 mm x 450 mm
Numberof tendons = 3
Cross-section area of each tendon $(A_s)=200 mm^2$.
Prestress = 1500 MPa
Modular ratio (m) = 6 From the given data, eccentricity (e) = 450/2-125 = 100 mm
Force in each cable $(P) = 1500 \times 200 \times 10^{-3} = 300 kN$
The tendons are tensioned one after another, and hence when tendon (1) is pulled no loss in tenson (1)
When tendon (2) is pulled, loss in tendon (1) but no loss in tendon (2).
When tendon (3) is pulled, loss in tendon (1) and (2), but no loss in tendon (3).
Hence, there will be 2 times losses in tendon (1), time loss in tendon (1) and no loss in tendon (3).
While calculating elastic shortening loss, self weight of the structure is neglected to be on the conservative side.
Consider tensioning of tendon-1
No loss in tendon (1)
Consider tensioning of tendon-2 Stress in concrete at the level of prestressing tendon
\begin{aligned} f_c&= \frac{P}{A}+\frac{Pe}{I}\\ e&=\frac{300 \times 10^3}{450 \times 450}+\frac{300 \times 10^3 \times 100 \times 100}{\frac{450 \times 450^3}{12}} \\ &= 2.36MPa \end{aligned} I = moment of inertial of the section about the centroidal axis.
As the tendons are horizontal and at the same level $f_{c,avg} = f_c$.
Loss due to elastic deformation $= mfc = 6 \times 2.36 = 14.16 MPa.$
Considering tensioning of tendon 3
Loss due to elastic deformation in (1) $= mfc = 6 \times 2.36 = 14.16 MPa.$
Loss due to elastic deformation in (2) $= mfc = 6 \times 2.36 = 14.16 MPa.$
Total loss in tendon (1) = 2 x 14.16 = 28.32 MPa
Total loss in tendon (1) = 2 x 14.16 = 28.32 MPa
In tendon (2) = 14.16 MPa
In tendon (3) = 0
Average loss of pre-stress, considering all three tendons is $=\frac{28.32+14.16+0}{3}=14.16MPa$
 Question 3
Match all the possible combinations between Column X (Cement compounds) and Column Y (Cement properties):
$\begin{array}{|c|l|}\hline \text{Column X}&\text{Column Y} \\ \hline (i) C_3S & \text{(P) Early age strength} \\ \hline (ii) C_2S & \text{(Q) Later age strength}\\ \hline (iii) C_3A& \text{(R) Flash setting}\\ \hline & \text{(S) Highest heat of hydration}\\ \hline & \text{(T) Lowest heat of hydration}\\ \hline \end{array}$
Which one of the following combinations is correct?
 A (i) - (P), (ii) - (Q) and (T), (iii) - (R) and (S) B (i) - (Q) and (T), (ii) - (P) and (S), (iii) - (R) C (i) - (P), (ii) - (Q) and (R), (iii) - (T) D (i) - (T), (ii) - (S), (iii) - (P) and (Q)
GATE CE 2022 SET-2      Concreate Technology
Question 3 Explanation:
$C_3S-$ Responsible for early age strength
$C_2S -$ Responsible for later age strength and lowest heat of hydration
$C_3A-$ Flash setting and highest heat of hydration
 Question 4
Read the following statements relating to flexure of reinforced concrete beams:

I. In over-reinforced sections, the failure strain in concrete reaches earlier than the yield strain in steel.
II. In under-reinforced sections, steel reaches yielding at a load lower than the load at which the concrete reaches failure strain.
III. Over-reinforced beams are recommended in practice as compared to the under-reinforced beams.
IV. In balanced sections, the concrete reaches failure strain earlier than the yield strain in tensile steel.

Each of the above statements is either True or False.
Which one of the following combinations is correct?
 A I (True), II (True), III (False), IV (False) B I (True), II (True), III (False), IV (True) C I (False), II (False), III (True), IV (False) D I (False), II (True), III (True), IV (False)
GATE CE 2022 SET-2      Footing, Columns, Beams and Slabs
Question 4 Explanation:
The question is based on LSM design principle as it is describing different conditions related to strain
Depending on amount of reinforcement in a cross- section, here ca be three types of sections viz. balanced, under reinforced and over reinforced.
Balanced section is a section that is expected to result in a balanced failure. It means at the ultimate limit state in flexure, the concrete will attain a limiting compressive strain of 0.0035 and steel will attain minimum specified tensile strain of $0.002+\frac{0.87f_y}{E_s}$
Under reinforced section is a section in which steel yield before collapse. Over reinforced section is a section in which crushing of concrete in compression i.e. attainment of compressive strain of 0.0035 occurs prior to yielding of steel.
In case of over reinforced section the deflection, crack width remain relatively low and failure occurs without any sign of warning and hence over reinforced flexural members are not recommended by IS code.
Based on the above information:
Statement I is true.
Statement II is true.
Statement III is false.
Statement IV is false.
 Question 5
A reinforced concrete beam with rectangular cross section (width = 300 mm, effective depth = 580 mm) is made of $M30$ grade concrete. It has 1% longitudinal tension reinforcement of $Fe 415$ grade steel. The design shear strength for this beam is 0.66 $N/mm^2$. The beam has to resist a factored shear force of 440 kN. The spacing of two-legged, 10 mm diameter vertical stirrups of $Fe 415$ grade steel is ______mm. (round off to the nearest integer)
 A 127 B 101 C 254 D 331
GATE CE 2022 SET-1      Shear, Torsion, Bond, Anchorage and Development Length
Question 5 Explanation:
$b=300mm$
$d=580 mm$
$V_u=440 kN$
Concrete used is M30
Raft steel is Fe415
$V_{cu}=\tau _c Bd=0.66 \times 300 \times \frac{580}{1000}=114.84 kN$
$V_{su}=V_u-V_{cu}=440-114.84=325.16 kN$
Spacing of 2-legged shear reinforcement
\begin{aligned} s_V&=\frac{A_{SV} \times 0.87 f_y \times d}{V_{su}}\\ &=\frac{2 \times \frac{\pi}{2} \times (10)^2 \times 0.87 \times 415 \times 580}{325.16 \times 1000}\\ &=101.16 mm \end{aligned}
 Question 6
Which of the following equations is correct for the Pozzolanic reaction?
 A $Ca(OH)_2$ + Reactive Superplasticiser + $H_2O \rightarrow C-S-H$ B $Ca(OH)_2$ + Reactive Silicon dioxide + $H_2O \rightarrow C-S-H$ C $Ca(OH)_2$ + Reactive Sulphates + $H_2O \rightarrow C-S-H$ D $Ca(OH)_2$ + Reactive Sulphur + $H_2O \rightarrow C-S-H$
GATE CE 2022 SET-1      Concrete Technology
Question 6 Explanation:
Pozzolanic materials have no cementing properties itself but have the property of combining with lime to produce stable compound.
Pozzolana is considered as siliceous and aluminous materials and when added in cement it have $SiO_2$ and $Al_2O_3$ form.
So, pozzolanic reaction :
$H_2O$ + Reactive slilica-di-oxide + $H_2O \rightarrow C-S-H$ gel or tobermonite gel
 Question 7
In the context of elastic theory of reinforced concrete, the modular ratio is defined as the ratio of
 A Young's modulus of elasticity of reinforcement material to Young?s modulus of elasticity of concrete. B Youngs modulus of elasticity of concrete to Young?s modulus of elasticity of reinforcement material. C shear modulus of reinforcement material to the shear modulus of concrete. D Young's modulus of elasticity of reinforcement material to the shear modulus of concrete.
GATE CE 2022 SET-1      Working Stress and Limit State Method
Question 7 Explanation:
This is a question of working stress method i.e. elastic theory.
Modular ratio
$=\frac{E_s}{E_c}=\frac{\text{Young's modulus of steel}}{\text{Young's modulus of concrete}}$
 Question 8
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 8 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 9
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 9 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 10
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 10 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}

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.