Strength of Materials & Elasticity

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The Fourier series representation of a square wave is shown in the figure below. The fluctuations seen near x = ±1 are named after which one of the following scientists?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Consider a unit square body as shown in the figure below. The body is subjected to the deformation field u = -ay and v = ax, where 'a' is a constant. Due to the application of this deformation field, the body undergoes _______ in the x-y plane.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The deformation of an open-section bar subjected to pure torsion can be solved by choosing an appropriate Prandtl stress function. Which of the following statements is/are true about the Prandtl stress function?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

WA and WB are the respective maximum take-off weights of an aircraft for two ambient air conditions given below. Condition A: p = 1 bar, T = 50 oC; Condition B: p = 0.66 bar, T = -30 oC If all other parameters relevant for take-off are kept the same in these two conditions, the ratio WB/WA is ________ (rounded off to 3 decimal places).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A stepped cantilever beam, made of a material having Young's modulus E = 200 GPa, is shown in the figure below. The length and the moment of inertia of the beam from point A to B are L1 = 100 mm and I1 = 100 mm4, respectively. The length and the moment of inertia of the beam from point B to C are L^2 = 100 mm and I^2 = 700 mm4, respectively. A shear force P = 30 N is applied at point A of the beam. The magnitude of the deflection of the beam at point A is ________ mm (rounded off to 1 decimal place).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A simply supported horizontal beam is subjected to a distributed transverse load varying linearly from q0 at A to zero at B, as shown in the figure. Which one of the following options is correct?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A stress field is given by $\sigma_{xx} = \sigma_{zz} = C_1y$; $\sigma_{yy} = C_2y$; $\tau_{xy} = \tau_{yz} = \tau_{zx} = 0$, where $C_1$ and $C_2$ are non-zero constants. If the stress field satisfies equilibrium, which one of the following options is correct?

Subtopic: Euler Buckling of Columns & Energy Methods

A uniform symmetric cross-section cantilever beam of length $L$ is subjected to a transverse force $P$ at the free end, as shown in the figure. The Young's modulus of the material is $E$ and the moment of inertia is $I$. Ignoring the contributions due to transverse shear, the strain energy stored in the beam is:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90o. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain $\gamma$xy is equal to ____.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A 1 m long rod is to be designed to support an axial tensile load P (P >> weight of the rod). The material for the rod is to be chosen from one of the four provided in the table. Using strength-based failure criterion for design, which material results in the lowest weight of the rod? Properties Material  Material  Material  Material  Density (kg/m^3) 2700 4500 7800 9000 Young's modulus (GPa) 70 115 200 130 Yield Strength (MPa) 270 900 520 540

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A 1 m long rod of 1 cm × 1 cm cross section is subjected to an axial tensile force of 35 kN. The Young's modulus of the material is 70 GPa. The cross-section of the deformed rod is 0.998 cm × 0.998 cm. The Poisson's ratio of the material is ________ (rounded off to one decimal place).

Subtopic: Airframe Structural Analysis & Trusses

For a three-bar truss loaded as shown in the figure, the magnitude of the force in the horizontal member AB is ___N (answer in integer).

Subtopic: Euler Buckling of Columns & Energy Methods

A prismatic vertical column of cross-section a × 0.5a and length l is rigidly fixed at the bottom and free at the top. A compressive force P is applied along the centroidal axis at the top surface. The Young's modulus of the material is 200 GPa and the uniaxial yield stress is 400 MPa. If the critical value of P for yielding and for buckling of the column are equal, the value of ( l a) is _____(rounded off to one decimal place).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A thin flat plate is subjected to the following stresses: $\sigma$xx = 160 MPa; $\sigma$yy = 40 MPa; $\tau$xy = 80 MPa. Factor of safety is defined as the ratio of the yield stress to the applied stress. The yield stress of the material under uniaxial tensile load is 250 MPa. The factor of safety for the plate assuming that material failure is governed by the von Mises criterion is _____ (rounded off to two decimal places).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A material has Poisson's ratio $\nu$ = 0.5 and Young's modulus E=2500 MPa. The percentage change in its volume when subjected to a hydrostatic stress of magnitude 10 MPa is ______ (answer in integer).

Subtopic: Mohr's Circle for Plane Stress

The state of stress at a point is caused by two separate loading cases. One of them produces a pure uniaxial tension along the x′ direction, and other one produces a pure uniaxial compression along the y′ direction, as shown in the figure. The sum of maximum and minimum principal stresses for the resultant state of stress caused by both loads acting simultaneously is ___________ N/mm 2 (rounded off to 1 decimal place).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Consider the plane strain field given by 𝜀xx = 10 xy2, 𝜀yy = -5 x2y and $\gamma$xy = A xy (2x - y) where, A is a constant and $\gamma$xy is the engineering shear strain . The value of the constant A for the strain field to be compatible is _____________ (rounded off to 1 decimal place).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Consider the four basic symmetrical flight loading conditions corresponding to the corners of a typical V-n diagram. For one of these flight loading conditions, it is observed that (i) the compressive bending stresses have a maximum value in the bottom aft region (see figure) of the wing cross-section; and (ii) the tensile bending stresses are maximum in the upper forward region (see figure) of the wing cross-section. For the preceding observations, select the corresponding flight loading condition from the options given.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Which one of the following figures represents the qualitative variation of absolute deceleration dV dt with altitude h (measured from the mean sea level) for a space vehicle undergoing a ballistic entry into the Earth's atmosphere?

Subtopic: Mohr's Circle for Plane Stress

Which of the following statement(s) is/are true about the state of stress in a plane?

Subtopic: Euler Buckling of Columns & Energy Methods

Which of the following statement(s) is/are true about the ribs of an airplane wing with semi-monocoque construction?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The system of equations 20 2 4 0 0 x y z x y z x y z - + = + - = - + = has a non-trivial solution for  = ______. (Answer in integer)

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Consider a general aviation airplane with weight 10 kN and a wing planform area of 15 m^2. The drag coefficient of the airplane is given as 0 2 D D LC C KC=+ with 0 0.025DC = and 0.05K = . For level flight at an altitude where the density is 0.60 kg/m3 and thrust 1 kN, the maximum cruise speed is (rounded off to the nearest integer)

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Consider the equation sindy ay xdx += , where a and $\omega$ are constants. Given 1 at 0yx== , select all correct statement(s) from the following as x → .

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Given the vectors ˆˆˆ9 5 2 ˆˆˆ11 4 ˆˆˆ7 14 3 A i j k B i j k C i j k = - + = + + = - + - which of the following statement(s) is/are TRUE?

Subtopic: Euler Buckling of Columns & Energy Methods

Which of the following statement(s) about the elastic flexural buckling load of columns is/are correct?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The thickness of a uniform hollow circular shaft is equal to the difference between the outer radius and the inner radius. The ratio of the inner diameter to outer diameter of the shaft is 0.5 . For the shaft reacting to an applied torque, the ratio of the maximum shear stress  to the maximum shear stress thin wall - obtained using the thin-wall approximation is . (round off to one decimal place)

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A rigid bar AB is subjected to a uniformly distributed load of 100 N/m as shown in the figure. The bar is supported by rod CD, with A, C, and D as pin joints. The rod CD has axial stiffness of 40 N/mm. The vertical deflection at point D is __________ mm. (round off to nearest integer)

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A cantilever beam of length 2a is loaded at the tip with force F as shown in the figure. The beam is supported in the middle by a roller with a pin. The magnitude of moment reaction at the built -in end of the beam is  Fa, where  is ______ . (round off to one decimal place)

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Consider steady, two-dimensional, incompressible flow over a non-porous flat plate as shown in the figure. For the control volume $PQRS$, the speed, $u_\infty$, at section $PQ$ is uniform and the speed at section $RS$ is given by $u(y) = A_0 \left(\frac{y}{h}\right)^n$, where $n$ is a positive integer. The value of $A_0$ for which the flow through section $PS$ will vanish is:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Regarding the horizontal tail of a conventional airplane, which one of the following statements is true?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A beam with a symmetrical T-shaped cross-section, as shown in the figure, is subjected to pure bending. The maximum magnitude of the normal stress is realised:

Subtopic: Airframe Structural Analysis & Trusses

A three-member truss is simply supported at $Q$ and $R$, and loaded at $P$ by a horizontal force $F$ as shown. The force in $QR$ is:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

If $\hat{a}, \hat{b}, \hat{c}$ are three mutually perpendicular unit vectors, then $\hat{a} \cdot (\hat{b} \times \hat{c})$ can take the value(s):

Subtopic: Mohr's Circle for Plane Stress

Let $\sigma$ and $\tau$ represent the normal stress and shear stress on a plane, respectively. The Mohr circle(s) that may possibly represent the state of stress at points in a beam of rectangular cross-section under pure bending is/are:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

An isotropic linear elastic material point under plane strain condition in the $x$-$y$ plane always obeys:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The arc length of the parametric curve: x = cos $\theta$ , y = sin $\theta$ , z = $\theta$ from $\theta$ = 0 to $\theta$ = 2$\pi$ is equal to ________ (round off to one decimal place).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The two-dimensional plane-stress state at a point is: $\sigma_{xx} = 110\text{ MPa}; \sigma_{yy} = 30\text{ MPa}; \tau_{xy} = 40\text{ MPa}$. The normal stress, $\sigma_n$, on a plane inclined $45^\circ$ as shown in the figure is ______ $\text{MPa}$ (round off to the nearest integer).

Subtopic: Airframe Structural Analysis & Trusses

A horizontal load $F$ is applied at point $R$ on a two-member truss, as shown in the figure. Both the members are prismatic with cross-sectional area, $A_0$, and made of the same material with Young's modulus $E$. The horizontal displacement of point $R$ is:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Which of the following is NOT always true for a combustion process taking place in a closed system?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The real function $y = \sin^2(|x|)$ is:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

For a conventional airplane in straight, level, constant velocity flight condition, which of the following condition(s) is/are possible on Euler angles $(\phi, \theta, \psi)$, angle of attack $(\alpha)$ and the sideslip angle $(\beta)$?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A rotational velocity field in an air flow is given as ˆ ˆV ayi bxj   , with a = 10 s-1, b = 20 s-1. The air density is 1.0 kg/m3 and the pressure at (x, y) = (0 m, 0 m) is 100 kPa. Neglecting gravity, the pressure at (x, y) = (6 m, 8 m) is _____ kPa (rounded off to nearest integer).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Consider a solid cylinder housed inside another cylinder as shown in the figure. Radius of the inner cylinder is 1 m and its height is 2 m. The gap between the cylinders is 5 mm and is filled with a fluid of viscosity 10-4 Pa-s. The inner cylinder is rotating at a constant angular speed of 5 rad/s while the outer cylinder is stationary. Friction at the bottom surfaces can be ignored. Velocity profile in the vertical gap between the cylinders can be assumed to be linear. The driving moment required for the rotating motion of the inner cylinder is ____________ Nm (rounded off to two decimal places).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Given: The tip deflection and tip slope for a tip loaded cantilever of length $L$ are $\frac{NL^3}{3EI}$ and $\frac{NL^2}{2EI}$, respectively, where $N$ is the tip force and $EI$ is the flexural rigidity. A cantilever $PQ$ of rectangular cross-section is subjected to transverse load, $F$, at its mid-point. Two cases are considered as shown in the figure. In Case I, the end $Q$ is free and in Case II, $Q$ is simply supported. The ratio of the magnitude of the maximum bending stress at $P$ in Case I to that in Case II is ______ (rounded off to one decimal place).

Subtopic: Euler Buckling of Columns & Energy Methods

A simply supported Aluminium column of length 1 m and rectangular cross- section w × t with t ≤ w, is subjected to axial compressive loading. Young's modulus is 70 GPa. Yield stress under uniaxial compression is 120 MPa. The value of t at which the failure load for yielding and buckling coincide is _______mm.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A $10\text{ kN}$ axial load is applied eccentrically on a rod of square cross-section ($1\text{ cm} \times 1\text{ cm}$) as shown in the figure. The strains measured by the two strain gages attached to the top and bottom surfaces at a distance of $0.5\text{ m}$ from the tip are $\epsilon_1 = 0.0016$ and $\epsilon_2 = 0.0004$, respectively. The eccentricity in loading, $e$, is ______ $\text{mm}$.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Q.31 - Q.36 Multiple Select Question (MSQ), carry TWO mark each (no negative marks). Q.31 (A) (B)

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Q.49 A rigid horizontal bar ABC, with roller support at A, is pinned to the columns BD and CE at points B and C, respectively as shown in figure. The other end of the column BD is fixed at D, whereas the column CE is pinned at E. A vertical load P is applied on the bar at a distance 'a' from

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Q.50 A two-cell wing box is shown in the figure. The cell walls are 1.5 mm thick and the shear modulus G = 27 GPa. If the structure is subjected to a torque of 12 kNm, then the wall AD will experience a shear stress of magnitude

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Q.52 A 3 m x 1 m signboard is supported by a vertical hollow pole that is fixed to the ground. The pole has a square cross section with outer dimension 250 mm. The yield strength of the pole material is 240 MiPa. To sustain a wind pressure of 7.5 kPa, the dimension d of the pole is _

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Given access to the complete body geometry, surface static pressure distribution, and wall shear stress distribution over a body placed in a uniform flow, one can compute:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The streamlines of a steady 2D flow through a channel are plotted with upper bounding streamline $\psi = 0.5\text{ m}^2/\text{s}$ and lower bounding streamline $\psi = -0.5\text{ m}^2/\text{s}$. The volumetric flow rate per unit depth through the channel is:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

For the state of stress shown in the figure, which one of the following represents the correct free body diagram showing the maximum shear stress and the associated normal stresses? 12 MPa • 4 MPa 18 MPa

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The two masses of the two degree of freedom system shown in the figure are given initial displacements of 2 cm (xz) and 1.24 cm (x^2). The system starts to vibrate in the first mode. The first mode shape of this system is d = [1 a]', where a = . (round off to two decimal places). 1x, (t) 1x3(t)

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

As shown in the figure, a beam of length 1 m is rigidly clamped at one end ($x = 0$) and simply supported at the other ($x = 1$ m). Under the action of a uniformly distributed downward load of $w = 10$ N/m, the magnitude of the vertical reaction force (in N) at the simply supported end is _________ (round off to two decimal places).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The number of independent elastic constants for a homogeneous isotropic linear elastic material is _________.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A thin plate with Young's modulus 210 GPa and Poisson's ratio 0.3 is loaded under plane stress with $\sigma_x = 100$ MPa and $\sigma_y = -40$ MPa. The absolute value of the normal strain in the z-direction ($|\epsilon_z| \times 10^4$) is _________ (round off to 1 decimal place).

Subtopic: Mohr's Circle for Plane Stress

For the state of stress shown in the figure, the normal stress, $\sigma_n$, on a plane inclined at 45 degrees to the principal planes with $\sigma_1 = 300$ MPa and $\sigma_2 = 200$ MPa is _________ MPa (round off to the nearest integer).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

For a 1 m long simply supported beam with a concentrated vertical load of 200 N and a concentrated bending moment of 100 N-m applied at mid-span, the vertical reaction at the left support is _________ N.

Subtopic: Euler Buckling of Columns & Energy Methods

All the bars in the given truss are elastic with Young's modulus 200 GPa, and have identical cross-sections with moment of inertia $I = 0.1$ cm$^4$. The lowest value of the load $P$ (in kN) at which the truss fails due to buckling of member BC (length $L = 10$ cm) is _________ kN (round off to the nearest integer).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A solid circular shaft is designed to transmit a torque $T$ with a factor of safety of 2. It is proposed to replace the solid shaft by a hollow shaft of the same material and identical outer radius. If the inner radius is half the outer radius, the factor of safety for the hollow shaft is _________ (round off to 1 decimal place).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

In the structure shown in the figure, bars AB and BC are made of identical material and have circular cross-sections of 10 mm radii. The yield stress of the material under uniaxial tension is 280 MPa. Using the von Mises yield criterion, the maximum load (in N) along the z-direction (perpendicular to the plane of paper) that can be applied at C, such that AB does not yield is _________ N (round off to the nearest integer). (Take $AB = 0.55$ m, $BC = 0.50$ m)

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Determine the correctness or otherwise of the following statements, [a] and [r]: [a] A closed-section box beam configuration is used in aircraft wings. [r] Closed-section box beam configuration is capable of resisting torsional loads.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Which of the following statement(s) is/are true about the state of a body in plane strain condition? P: All the points in the body undergo displacements in one plane only, for example the x -y plane, leading to 𝜀zz = $\gamma$xz = $\gamma$yz = 0. Q: All the components of stress perpendicular to the plane of deformation, for example the x-y plane, of the body are equal to zero, i.e. $\sigma$zz = $\tau$xz = $\tau$yz = 0. R: Except the normal component, all the other components of stress perpendicular to the plane of deformation of the body, for example the x -y plane, are equal to zero, i.e. $\sigma$zz ≠ 0, $\tau$xz = $\tau$yz = 0.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A 1 m long massless cantilever beam oscillates at 2Hz, while a 60 kg mass is attached at the tip of it. The flexural rigidity of the beam (in kN-m^2) is _________________ (accurate to two decimal places).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The components of stress in a bo dy under plane stress condition, in the absence of body forces, is given by: $\sigma$xx = Ax2; $\sigma$yy = 12x2 - 6y2 and $\sigma$xy = 12xy. The coefficient, A, such that the body is under equilibrium is _____ (accurate to one decimal place).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A 1 m long massless cantilever beam oscillates at 2 Hz, while a 60 kg mass is attached at the tip of it. The flexural rigidity of the beam (in kN-m$^2$) is _________________ (accurate to two decimal places).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The components of stress in a body under plane stress condition, in the absence of body forces, is given by: $\sigma_{xx} = Ax^2; \sigma_{yy} = 12x^2 - 6y^2$ and $\sigma_{xy} = 12xy$. The coefficient, $A$, such that the body is in static equilibrium is _________.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Which of the following statements about the neutral axis of a beam with unsymmetrical cross section is true:

Subtopic: Euler Buckling of Columns & Energy Methods

Assuming that the aircraft is flying straight, the top spar cap / flange of a wing is most likely to fail 1n: Top spar cap / flange

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Which of the following statements about the compatibility equations are true: P. Strain compatibility equations must be satisfied in the solution of three-dimensional problems in elasticity. Q. Six strains are defined in terms of three displacement functions and can have arbitrary values. R. Compatibility equations are an expression of the continuity of displacements.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Correct: 2 Wrong: -0.66 "If you are looking for a history of India, or for an account of the rise and fall of the British Raj. or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections. and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters." Which of the following statements best reflects the author's opinion?

Subtopic: Airframe Structural Analysis & Trusses

Each of P. Q. R, S, W. X. Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further. Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A batch of aluminium alloy yields in uniaxial tension at the stress $\sigma_y = 330$ MPa. Using the von Mises yield criterion, the yield stress in pure shear (in MPa) is _________ (round off to 1 decimal place).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

An aircraft wing is idealized as a cantilever beam of constant width and length $L = 5$ m, carrying a uniformly distributed aerodynamic lift load of $w = 2$ kN/m. If the flexural rigidity of the wing box is $EI = 10^7$ N-m$^2$, the tip deflection (in mm) of the wing is _________ (round off to the nearest integer).

Subtopic: Mohr's Circle for Plane Stress

For the state of plane stress shown in the figure with $\sigma_x = 80$ MPa, $\sigma_y = -20$ MPa, and $\tau_{xy} = 40$ MPa, the minimum principal stress (in MPa) is _________ (round off to the nearest integer).

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Determine the correctness or otherwise of the following statements, [a] and [r]: [a]: In a plane stress problem, the shear strains along the thickness direction of a body are zero but the normal strain along the thickness is not zero. [r]: In a plane stress problem, Poisson effect induces the normal strain along the thickness direction of the body.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Consider four thin -walled beams of different open cross-sections, as shown in the cases (i-iv). A shear force of magnitude 'F' acts vertically downward at the location 'P' in all the beams. In which of the following case, does the shear force induce bending and twisting? Case (i) Case (ii) Case (iii) Case (iv)

Subtopic: Mohr's Circle for Plane Stress

A structural member supports loads, which produce at a particular point, a state of pure shear stress of 50 N/mm 2. At what angles are the principal planes oriented with respect to the plane of pure shear?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A cantilever beam -spring system is shown in the figure. The beam is made with a material of Young's modulus 1105 N/mm 2 and geometry such that its moment of inertia is 100 mm 4 and length l = 100 mm. It is supported by a spring of stiffness K = 30 N/mm and subjected to a load of P = 100 N at the point 'B'. The deflection at the point 'B' due to the load P is ____mm.

Subtopic: Euler Buckling of Columns & Energy Methods

Determine the correctness or otherwise of the following statements, [a] and [r], [a]: Ribs, used in airplane wings, increase the column buckling strength of the longitudinal stiffeners. [r]: Ribs distribute concentrated loads into the structure and redistribute stresses around discontinuities.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The two dimensional state of stress in a body is described by the Airy's stress function: 12 yE6 xy72 y x36 y x 12 x5 432 23 4      . The Airy's stress function will satisfy the equilibrium and the compatibility requirements if and only if the value of the coefficient E is ____.

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Which one of the following objects with inclined face at 45oo , subjected to the given stresses, are in static equilibrium:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

For a steady, incompressible two-dimensional flow, represented in Cartesian co-ordinates (xx, yy), a student correctly writes the equation of pathline of any arbitrary particle as, ddxx dddd = aaxx and ddyy dddd = bbyy, wherea and bare constants having unit of (second)-1. If value of a is 5, the value of b is _____. AE 5/11 AE (GATE 2014) - AE

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A structural member of rectangular cross-section 10mm× 6mm and length 1m is made of steel (Young's modulus is 200GPa and coefficient of thermal expansion is 12 × 10-6 / CCoo ). It is rigidly fixed at both the ends and then subjected to a gradual increase in temperature. Ignoring the three dimensional effects, the structural member will buckle if the temperature is increased by ∆TT CCoo which is

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A cantilevered beam is subjected to a parabolic distribution of shear traction at the right edge while the top and bottom surfaces are traction free. To solve this problem, following Airy's stress function is proposed: $\phi \phi$ = CC1xxyy + CC2xxyy3 + CC3xx2yy2 + CC4xx3yy. This is an admissible Airy's function that would satisfy the bi-harmonic equation as well as the boundary conditions if and only if

Subtopic: Euler Buckling of Columns & Energy Methods

In the steel structure (Young's modulus = 200 GPa) shown in the figure, all members have a circular cross-section of radius 10 mm. Column BD is pinned at B and D. The support at A is hinged. The minimum value of load ܲat which the column BD may buckle in Newtons is approximately ____________

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The thin rectangular plate has dimensions L×b×t. It develops a stress field corresponding to an applied bending moment M as shown in the figure. A valid Airy's stress function is

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

A simply supported beam with overhang is loaded by uniformly distributed load of intensity q as shown in the figure. The bending moment at the mid-point of AB is

Subtopic: Euler Buckling of Columns & Energy Methods

Select the pair that best expresses a relationship similar to that expressed in the pair: water: pipe::

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

In a semi-monocoque construction of an aircraft wing, the skin and spar webs are the primary carriers of

Subtopic: Airframe Structural Analysis & Trusses

The volume of a solid generated by rotating the region between semi-circle 211y x=- - and straight line y = 1, about x axis, is

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The Airy stress function, 22x xy y$\phi \alpha \beta \gamma$=++ for a thin square panel of size ll× automatically satisfies compatibility. If the panel is subjected to uniform tensile stress, o$\sigma$ on all four edges, the traction boundary conditions are satisfied by

Subtopic: Euler Buckling of Columns & Energy Methods

Buckling of the fuselage skin can be delayed by

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The internal pressure Yp at yield, based on the von Mises yield criterion, if the vessel is floating in space, is approximately

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

If the vessel is evacuated (internal pressure = 0) and subjected to external pressure, yielding according to the von Mises yield criterion (assuming elastic stability until yield)

Subtopic: Euler Buckling of Columns & Energy Methods

The arithmetic mean of five different natural numbers is 12. The largest possible value among the numbers is:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Consider a simply supported two-dimensional beam. If the beam is converted into a fixed-fixed beam, then the degree of static indeterminacy will:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

P L L/2 2011 AEROSPACE ENGINEERING - AE AE Consider a beam in bending with a solid circular cross-section of 1 mm2, which is subjected to a transverse shear force of 1 N. The shear stress at the center of the cross-section (in N/mm2) is

Subtopic: Euler Buckling of Columns & Energy Methods

A simp ly supported slender column of square cross section (width=depth= d) has to be designed such that it buckles at the same instant as it yields. Length of the column is given to be 1.57 m and it is made of a material whose Young's modulus is 200 GPa and yield stress is 240 MPa. The width, d, of the column (in cm) should be

Subtopic: Airframe Structural Analysis & Trusses

Consider a thin symmetric aerofoil at an angle of attack alpha. According to thin aerofoil theory, the lift coefficient C_l is:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Which of the following Airy's stress functions could satisfy the given boundary conditions, assuming constant values of xx = P, yy = Q and xy = R, along the boundary? (A) RxyyQxP   2 2 22  (B) RxyxQyP   2 2 22 

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Which of the above materials would you choose such that weight of the shaft subjected to torsion is minimum?

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

For a statically indeterminate beam, the number of compatibility equations required equals:

Subtopic: Euler Buckling of Columns & Energy Methods

A column of length / and flexural rigidity El. has one end fixed and the other end hinged. The critical buckling load for the column is

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Following stress state is proposed for a^2-D problem with no body forces: $\sigma$_xx = 3x^2 y + 4y^3, $\sigma$_yy = 5x^2 + 14y^2, $\tau$_xy = -3xy^2 - 7x^2. It satisfies:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Consider a l-D adiabatic, inviscid, compressible flow of air (R = 287 J/Kg-K, c, = 718 J/Kg-K) through a duct of constant cross-sectional area A=1m'. If the valumetric flow rate is = 680 m/s and stagnation temperature is T, = 580.05 K. then the air temperature inside the duct is

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Maximun value of shear stress is

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Il we manage to our natural resources, we would leave a better planet for our children.

Subtopic: Euler Buckling of Columns & Energy Methods

The buckling load for a simply supported column of rectangular cross section of dimensions 1 cmx1.5 cm and length 0.5 m made of steel (E = 210x10% N/m') is approximately

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

In the absence of body moments, the symmetry of the stress tensor is derived from

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

In a 3-D orthotropic material, the number of independent elastic constants in the linear stress-strain relationship is:

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

The compatibility conditions in theory of elasticity ensure that

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

In the definition of the aircraft Euler angles @ (roll), ® (pitch), and v (yaw), the correct sequence of rotations required to make the inertial frame coincide with the aircraft body frame is

Subtopic: Euler Buckling of Columns & Energy Methods

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). Group I (end conditions) (P) one end built-in and other end free Q) both ends pinned (R) both ends built-in (S) one end built-in and other end pinned

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Pxy® 4c* 3 Рху 4c where P is a constant. x L The above stress function pertains to a

Subtopic: Euler Buckling of Columns & Energy Methods

Mises yield criterion or the maximum distortion energy criterion for a plane stress problem with o, and o, as the principal stresses in the plane, and oy as the yield stress, requires

Subtopic: Euler Buckling of Columns & Energy Methods

The span efficiency factor of this wing is