Flight vehicle structures - Structures - Aerospace Engineering Previous Year Questions

1

2007 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2007

A circular shaft is made-up of two materials A and B. The inner core is made-up of material A with diameter \(d_A\), torsion constant \(J_A\), and shear modulus \(G_A\). The outer sleeve is made-up of material B with diameter \(d_B\), torsion constant \(J_B\), and shear modulus \(G_B\). The composite shaft is of length \(L\) and is subjected to pure torsion moment \(T\). The torsional stiffness, \(\frac{T}{\phi}\), where \(\phi\) is the angle of twist, of this composite shaft is then

A

\(\frac{\left(\frac{G_A J_A}{L} + \frac{G_B J_B}{L}\right)}{\left(\frac{G_A J_A}{L} \cdot \frac{G_B J_B}{L}\right)}\)

B

\(\frac{G_A J_A}{L} + \frac{G_B J_B}{L}\)

C

\(\frac{(G_A + G_B)(J_A + J_B)}{L}\)

D

\(\frac{G_A J_B}{L} + \frac{G_B J_A}{L}\)

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2

2007 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2007

The von Mises yield criterion or the maximum distortion energy criterion for a plane stress problem with \(\sigma_1\) and \(\sigma_2\) as the principal stresses in the plane, and \(\sigma_Y\) as the yield stress, requires

A

\(\sigma_1^2 - \sigma_1\sigma_2 + \sigma_2^2 \leq \sigma_Y^2\)

B

\(|\sigma_1 - \sigma_2| \leq \sigma_Y\)

C

\(|\sigma_1| \leq \sigma_Y\)

D

\(|\sigma_2| \leq \sigma_Y\)

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3

2007 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2007

An Euler-Bernoulli beam having a rectangular cross-section, as shown in the figure, is subjected to a non-uniform bending moment along its length. \( V_z = \frac{dM_y}{dx} \). The shear stress distribution \( \tau_{zx} \) across its cross-section is given by

A

\(\tau_{zx} = \frac{V_z}{2I_y} \frac{z}{(h/2)} \)

B

\(\tau_{zx} = \frac{V_z (h/2)^2}{2I_y} \left( 1 - \frac{z^2}{(h/2)^2} \right) \)

C

\(\tau_{zx} = \frac{V_z}{2I_y} \left( \frac{z}{(h/2)} \right)^2 \)

D

\(\tau_{zx} = \frac{V_z (h/2)^2}{2I_y} \)

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4

2007 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2007

The torsion constant \( J \) of a thin-walled closed tube of thickness \( t \) and mean radius \( r \) is given by

A

\(J = 2 \pi r t^3 \)

B

\(J = 2 \pi r^3 t \)

C

\(J = 2 \pi r^2 t^3 \)

D

\(J = 2 \pi r^4 \)

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5

2007 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2007

The boundary conditions needed for a rod fixed at the root (\( x = 0 \)) and free at the tip (\( x = l \)) are

A

\(u(x=0)=0, \frac{\partial u}{\partial x}(x=l)=0 \)

B

\(u(x=l)=0, \frac{\partial u}{\partial x}(x=l)=0 \)

C

\(u(x=0)=0, u(x=l)=0 \)

D

\(\frac{\partial u}{\partial x}(x=0)=0, \frac{\partial u}{\partial x}(x=l)=0 \)

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6

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

The compatibility conditions in theory of elasticity ensure that

A

there is compatibility between various direct and shear stresses

B

relationships between stresses and strains are consistent with constitutive relations

C

displacements are single-valued and continuous

D

stresses satisfy bi-harmonic equation

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7

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

A parallelogram shaped plate of dimensions 'a' and 'b' as shown in the figure, is subjected to a uniform loading of normal stresses \(\sigma_1\) and \(\sigma_2\). The plate is in equilibrium for

A

any value of \(\sigma_1\) and \(\sigma_2\)

B

\(\sigma_2 = \sigma_1 \cos \theta\)

C

\(\sigma_1 = \sigma_2 \cos \theta\)

D

\(\sigma_2 = \sigma_1\)

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8

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

A column of solid circular cross-section and length L can have various end conditions. Choose the correct set that matches the end conditions (listed in Group I) with the corresponding effective length for buckling (listed in Group II).

A

P - 3
Q - 1
R - 4
S - 2

B

P - 4
Q - 1
R - 2
S - 3

C

P - 2
Q - 1
R - 3
S - 4

D

P - 3
Q - 1
R - 2
S - 4

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9

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

A concentrated bending moment M is acting at mid-span of a beam as shown. The shear force diagram for the beam is:

A

Image A

B

Image B

C

Image C

D

Image D

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10

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

An idealized thin-walled cross-section of a beam and the respective areas of the booms are as shown. A bending moment \(M_y\) is acting on the cross-section. The ratio of the magnitude of normal stress in the top booms to that of the bottom boom is

A

5/11

B

2/5

C

1

D

5/2

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11

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

A beam occupies a region \(0 \le x \le L; \; -c \le y \le c; \; -0.5 \le z \le 0.5\) as shown below. The beam can be considered to be in plane stress condition in x-y plane. Airy's stress function for the beam is given as:
\(\phi(x, y) = -\frac{Pxy^3}{4c^3} + \frac{3Pxy}{4c}\)
where \(P\) is a constant.
The above stress function pertains to a

A

simply supported beam carrying a point load \(P\) at mid span

B

simply supported beam carrying a uniform distributed load of intensity \(P\) per unit length

C

cantilever beam clamped at end \(x = L\) and carrying a shear load \(P\) at \(x = 0\)

D

cantilever beam clamped at end \(x = 0\) and carrying a shear load \(P\) at \(x = L\)

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12

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

The principal stresses are

A

\(\sigma_1 = 17c\) MPa, \(\sigma_2 = -9c\) MPa

B

\(\sigma_1 = 9c\) MPa, \(\sigma_2 = 17c\) MPa

C

\(\sigma_1 = -17c\) MPa, \(\sigma_2 = -9c\) MPa

D

\(\sigma_1 = -17c\) MPa, \(\sigma_2 = 9c\) MPa

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13

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

The maximum shear stress is

A

\(\tau_{max} = 7c\) MPa

B

\(\tau_{max} = 10c\) MPa

C

\(\tau_{max} = 13c\) MPa

D

\(\tau_{max} = 15c\) MPa

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14

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

The maximum value of \(c\) for safe loading of the structure, based on von-Mises failure criterion is

A

10.2

B

15.3

C

25.4

D

31.8

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15

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

The shear flows \(q_1\) and \(q_2\) are

A

\(q_1 = -2\) N/cm, \(q_2 = +22\) N/cm

B

\(q_1 = +2\) N/cm, \(q_2 = +22\) N/cm

C

\(q_1 = +2\) N/cm, \(q_2 = -22\) N/cm

D

\(q_1 = -2\) N/cm, \(q_2 = -22\) N/cm

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16

2008 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2008

The torque \(M\) is

A

3360 N·cm

B

5760 N·cm

C

6960 N·cm

D

8160 N·cm

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17

2009 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2009

In a thin walled rectangular tube subjected to equal and opposite forces \(P\) as shown in the figure, the shear stress along leg AB is

A

zero

B

constant non-zero

C

varies linearly

D

varies parabolically

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18

2009 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2009

Consider a simply supported beam of length 2L with an overhang of length L, loaded by an end moment M, as shown below.
The bending moment distribution for this beam is

A

[image]

B

[image]

C

[image]

D

[image]

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19

2009 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2009

The buckling load for a simply supported column of rectangular cross section of dimensions 1 cm×1.5 cm and length 0.5 m made of steel (E = 210×10⁹ N/m²) is approximately

A

10 kN

B

4 kN

C

23 kN

D

46 kN

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20

2009 · Aerospace Engineering · Structures · Flight vehicle structures

Aerospace Engineering (AE) 2009

A 2-celled tube with wall thickness 0.5 mm is subjected to a torque of 10 N-m. The resulting shear flows in the two cells are \(q_1\) and \(q_2\) as shown below.
The torque balance equation (Bredt-Batho formula) for this section leads to

A

\(q_1 - q_2 = 2000\) N/m

B

\(q_1 + 2q_2 = 2000\) N/m

C

\(q_1 + q_2 = 2000\) N/m

D

\(2q_1 + q_2 = 2000\) N/m

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