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)

The percentage air voids in the mix is ____________. (round off to the nearest integer)

2 | |

4 | |

8 | |

16 |

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}

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

14.16 MPa | |

7.08 MPa | |

28.32 MPa | |

42.48 MPa |

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

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?

\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?

(i) - (P), (ii) - (Q) and (T), (iii) - (R) and (S) | |

(i) - (Q) and (T), (ii) - (P) and (S), (iii) - (R) | |

(i) - (P), (ii) - (Q) and (R), (iii) - (T) | |

(i) - (T), (ii) - (S), (iii) - (P) and (Q) |

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

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?

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?

I (True), II (True), III (False), IV (False) | |

I (True), II (True), III (False), IV (True) | |

I (False), II (False), III (True), IV (False) | |

I (False), II (True), III (True), IV (False) |

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.

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)

127 | |

101 | |

254 | |

331 |

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}

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?

Ca(OH)_2 + Reactive Superplasticiser + H_2O \rightarrow C-S-H | |

Ca(OH)_2 + Reactive Silicon dioxide + H_2O \rightarrow C-S-H | |

Ca(OH)_2 + Reactive Sulphates + H_2O \rightarrow C-S-H | |

Ca(OH)_2 + Reactive Sulphur + H_2O \rightarrow C-S-H |

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

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

Young's modulus of elasticity of reinforcement material to Young?s modulus of elasticity of concrete. | |

Youngs modulus of elasticity of concrete to Young?s modulus of elasticity of reinforcement material. | |

shear modulus of reinforcement material to the shear modulus of concrete. | |

Young's modulus of elasticity of reinforcement material to the shear modulus of concrete. |

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}}

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 ____________

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 ____________

129.4 | |

178.6 | |

145.6 | |

98.2 |

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 _____

If the stress beneath the footing is uniform, the length of the combined footing L (in m,round off to two decimal places) is _____

4.52 | |

2.78 | |

5.83 | |

2.45 |

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}

\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 _________

If the concentrated load, P=5 kN, the resultant stress (in Mpa,in integer) experienced at point 'Q' will be _________

3 | |

0 | |

5 | |

6 |

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.

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.