Question 1 |

The number of boundary conditions required to solve the differential equation \frac{\partial^2 \phi }{\partial x^2}+\frac{\partial^2 \phi }{\partial y^2}=0 is

2 | |

0 | |

1 | |

4 |

Question 2 |

Value of the integral I=\int_{0}^{\pi /4}cos^{2}xdx is

\frac{\pi }{8}+\frac{1}{4} | |

\frac{\pi }{8}-\frac{1}{4} | |

-\frac{\pi }{8}-\frac{1}{4} | |

-\frac{\pi }{8}+\frac{1}{4} |

Question 2 Explanation:

\begin{aligned} I&=\int_{0}^{\pi /4}\cos ^{2}xdx \\ &=\int_{0}^{\pi /4}\frac{1+\cos 2x}{2}dx \\ &=\int_{0}^{\pi /4}\frac{dX}{2}+\int_{0}^{\pi /4}\frac{\cos 2x}{2}dx \\ &=\frac{1}{2}\left [ x \right ]_{0}^{\pi /4}+\frac{1}{2}\left [ \frac{\sin 2x}{2} \right ]_{0}^{\pi /4} \\ &=\frac{\pi }{8}+\frac{1}{4}\left [ \sin \frac{\pi }{2}-\sin x \right ] \\ &=\frac{\pi }{8}+\frac{1}{4}\times 1 =\frac{\pi }{8}+\frac{1}{4} \end{aligned}

Question 3 |

Limit of the following series as x approaches \frac{\pi }{2} is f(x)=x-\frac{x^{3}}{3!}+\frac{x^{5}}{5!}-\frac{x^{7}}{7!}

\frac{2\pi }{3} | |

\frac{\pi }{2} | |

\frac{\pi }{3} | |

1 |

Question 3 Explanation:

\lim_{x\rightarrow \frac{\pi }{2}}f\left ( x \right )=\lim_{x\rightarrow \frac{\pi }{2}}\sin x=1

Question 4 |

The degree of static indeterminacy, N_s, and the degree of kinematic indeterminacy, N_k , for the plane frame shown below, assuming axial deformations to be negligible, are given by

N_s = 6 and N_k = 11 | |

N_s = 6 and N_k = 6 | |

N_s = 4 and N_k = 6 | |

N_s = 4 and N_k = 4 |

Question 4 Explanation:

Degree of static indeterminacy,

\begin{aligned} N_{s} &=3 m+r_{e}-3 j-r_{r} \\ &=3 \times 5+(3+2+2)-3 \times 6-0 \\ &=4 \end{aligned}

Degree of kinematic indeterminacy,

\begin{aligned} N_{k} &=3 j-r_{e}-m \\ &=3 \times 6-(3+2+2)-5=6 \\ N_{s} &=4 \text { and } N_{k}=6 \end{aligned}

\begin{aligned} N_{s} &=3 m+r_{e}-3 j-r_{r} \\ &=3 \times 5+(3+2+2)-3 \times 6-0 \\ &=4 \end{aligned}

Degree of kinematic indeterminacy,

\begin{aligned} N_{k} &=3 j-r_{e}-m \\ &=3 \times 6-(3+2+2)-5=6 \\ N_{s} &=4 \text { and } N_{k}=6 \end{aligned}

Question 5 |

The bending moment (in kNm units) at the mid span location X in the beam
with overhangs shown below is equal to

0 | |

-10 | |

-15 | |

-20 |

Question 5 Explanation:

\begin{aligned} \mathrm{R}+\mathrm{V}&=30 &\ldots(i)\\ \text { Now, } \mathrm{V} &\times 2-20 \times 3+10 \times 1=0 \\ \mathrm{V}&=\frac{60-10}{2}=25 \mathrm{kN}\\ \therefore \quad \mathrm{R}&=5 \mathrm{kN}\\ \mathrm{BM} \text { at }\quad X&=25 \times 1-20 \times 2=-15 \mathrm{kNm} \end{aligned}

Question 6 |

Identify the FALSE statement from the following, pertaining to the effects due to a temperature rise \Delta T in the bar BD alone in the plane truss shown below:

No reactions develop at supports A and D | |

The bar BD will be subject to a tensile force | |

The bar AC will be subject to a compressive force | |

The bar BC will be subject to a tensile force |

Question 6 Explanation:

As temperature increases the bar AD will tend to
elongate but joint B and D will offer resistance.

Hence bar BD will be in compression.

Hence bar BD will be in compression.

Question 7 |

Identify the correct deflection diagram corresponding to the loading in the plane frame shown below:

A | |

B | |

C | |

D |

Question 7 Explanation:

Since, there is no bending moment in vertical leg so there will be no bending in member AB. And to maintain angle between AB and BC at joint 8, frame will sway as given below

Question 8 |

Identify the FALSE statement from the following, pertaining to the methods of structural analysis

Influence lines for stress resultants in beams can be drawn using Muller
Breslau's Principle | |

The Moment Distribution Method is a force method of analysis, not a
displacement method | |

The Principle of Virtual Displacements can be used to establish a condition
of equilibrium | |

The Substitute Frame Method is not applicable to frames subject to
significant sideway |

Question 9 |

Identify the FALSE statement from the following, pertaining to the design of concrete structures

The assumption of a linear strain profile in flexure is made use of in
working stress design, but not in ultimate limit state design. | |

Torsional reinforcement is not required to be provided at the corners of
simply supported rectangular slabs, if the corners are free to lift up. | |

A rectangular slab, whose length exceeds twice its width, always behaves as
a two way slab, regardless of the support conditions. | |

The 'load balancing' concept can be applied to select the appropriate
tendon profile in a prestressed concrete beam subject to a given pattern of loads. |

Question 10 |

Identify the most efficient but joint (with double cover plates) for a plate in tension from the patterns (plan views) shown below, each comprising 6 identical bolts with the same pitch and gauge.

A | |

B | |

C | |

D |

Question 10 Explanation:

The most common type of rivet patterns are chain riveting and diamond riveting. Staggered pattern in option (A) yields more net area of the section and because of this reaon this pattern is most suitable for tension members. Staggered and diamond pattern are better as compared to the chain pattern.

There are 10 questions to complete.