Question 1 |

For the integral

\mathrm{I}=\int_{-1}^{1} \frac{1}{\mathrm{x}^{2}} \mathrm{dx}

which of the following statements is TRUE?

\mathrm{I}=\int_{-1}^{1} \frac{1}{\mathrm{x}^{2}} \mathrm{dx}

which of the following statements is TRUE?

\quad \mathrm{I}=0 | |

\quad \mathrm{I}=2 | |

\quad \mathrm{I}=-2 | |

The integral does not converge |

Question 1 Explanation:

\begin{aligned}
I & =\int_{-1}^{1} \frac{1}{x^{2}} d x \\
& =2 \int_{0}^{1} \frac{1}{x^{2}} d x \quad(\because \quad f(-x)=f(x)) \\
& =2 \lim _{t \rightarrow 0^{+}} \int_{t}^{1} \frac{d x}{x^{2}} \\
& =2 \lim _{t \rightarrow 0^{+}}\left(\frac{-1}{x}\right)_{t}^{1} \\
& =-2 \lim _{t \rightarrow 0^{+}}\left(1-\frac{1}{t}\right) \\
& =2 \lim _{t \rightarrow 0^{+}}\left(\frac{1}{t}-1\right) \\
& =2 \lim _{h \rightarrow 0^{+}}\left(\frac{1}{0+h}-1\right)\\
& =2(\infty-1) \\
& =\infty \;\;\; (Divergent)
\end{aligned}

Question 2 |

A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the figure. Ignore the self-weight of the hanger. What is the maximum tensile stress in \mathrm{N} / \mathrm{mm}^{2} anywhere in the hanger without considering stress concentration effects?

15 | |

25 | |

35 | |

45 |

Question 2 Explanation:

\sigma_{A B}=\frac{P_{A B}}{A_{A B}}=\frac{250 \times 10^{3}}{100 \times 100}=25 \mathrm{~N} / \mathrm{mm}^{2}

\sigma_{B C}=\frac{P_{B C}}{A_{B C}}=\frac{50 \times 10^3}{50 \times 50}=20 \mathrm{N} / \mathrm{mm}^{2}

\sigma_{\max }=\sigma_{\mathrm{AB}}=25 \mathrm{~N} / \mathrm{mm}^{2}

Question 3 |

Creep of concrete under compression is defined as the

increase in the magnitude of strain under
constant stress | |

increase in the magnitude of stress under
constant strain | |

decrease in the magnitude of strain under
constant stress | |

decrease in the magnitude of stress under
constant strain |

Question 3 Explanation:

Under sustained compressive loading, deformation in concrete increases with time even through the applied stress level is not changed. The time dependent component of strain is called creep.

Hence, correct answer is (A).

Hence, correct answer is (A).

Question 4 |

A singly reinforced concrete beam of balanced section is made of M20 grade concrete and \mathrm{Fe} 415 grade steel bars. The magnitudes of the maximum compressive strain in concrete and the tensile strain in the bars at ultimate state under flexure, as per IS 456: 2000 are _______ respectively. (round off to four decimal places)

0.0035 and 0.0038 | |

0.0020 and 0.0018 | |

0.0035 and 0.0041 | |

0.0020 and 0.0031 |

Question 4 Explanation:

Given data,

Grade of concrete M-20

Grade of steel Fe-415

Balanced section, singly reinforced beam.

As per Clause No. 38.1, IS 456: 2000,

Maximum strain in concrete at the outermost compression fibre =0.0035

and strain in the tension reinforcement for balanced section at ultimate state under flexure

\begin{aligned} & =0.002+\frac{f_{y}}{1.15 E_{s}} \\ & =0.002+\frac{415}{1.15 \times 2 \times 10^{5}}=0.0038 \end{aligned}

Hence, correct answer is (A).

Grade of concrete M-20

Grade of steel Fe-415

Balanced section, singly reinforced beam.

As per Clause No. 38.1, IS 456: 2000,

Maximum strain in concrete at the outermost compression fibre =0.0035

and strain in the tension reinforcement for balanced section at ultimate state under flexure

\begin{aligned} & =0.002+\frac{f_{y}}{1.15 E_{s}} \\ & =0.002+\frac{415}{1.15 \times 2 \times 10^{5}}=0.0038 \end{aligned}

Hence, correct answer is (A).

Question 5 |

In cement concrete mix design, with the increase in water-cement ratio, which one of the following statements is TRUE?

Compressive strength decreases but workability
increase | |

Compressive strength increases but workability
decreases | |

Both compressive strength and workability
decrease | |

Both compressive strength and workability
increase |

Question 5 Explanation:

As the water-cement ratio increases, the porosity in the hardened concrete increases and hence the strength decreases.

Also, as water-cement ratio increases, ducts higher water availability, the workability increases.

Hence, correct answer is (A).

Also, as water-cement ratio increases, ducts higher water availability, the workability increases.

Hence, correct answer is (A).

There are 5 questions to complete.