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An infinite plate with a through-thickness crack of length 2 mm is subjected to a tensile stress (as shown in the figure). Assuming the plate to be linear elastic, the fracture stress is ____________ MPa (round off to the nearest whole number) (Given: Fracture toughness, 𝐾𝐼𝐶=25 𝑀𝑃𝑎 √𝑚)0 AnswerL ength, width and thickness of a plate are 400 mm, 400 mm and 30 mm, respectively. For the material of the plate, Young’s modulus of elasticity is 70 GPa, yield stress is 80 MPa and Poisson’s ratio is 0.33. When the plate is subjected to a longitudinal tensile stress of 70 MPa, the increase in the volume (in mm3) of the plate is ______0 AnswerA metallic rod of diameter 0 d is subjected to the tensile test. The engineering stress and the true stress at fracture are 800 MPa and 900 MPa, respectively. The ratio of the rod diameter at fracture f d to the initial diameter 0 d is ______ (round off to 2 decimal places)0 AnswerA glass fibre of 5 micron diameter is subjected to a tensile stress of 20 MPa. The surface energy and elastic modulus of this material are 0.3 Jm2 and 70 GPa, respectively. Pick the correct answer based on the information provided above: Note: The glass fibre contains a population of flaws of different lengths.1 AnswerIn stress strain curve of mild steel Ultimate Tensile Stress is1 AnswerConsider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young’s modulus E = 200 MPa and Poisson’s ratio ν = 0.3 are given. The principal strains in the plane of the sheet are0 AnswerIn the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength (UTS) refers to1 AnswerA 0.2 m thick infinite black plate having a thermal conductivity of 3.96 W/m-K is exposed to two infinite black surfaces at 300 K and 400 K as shown in the figure. At steady state, the surface temperature of the plate facing the cold side is 350 K. The value of Stefan- Boltzmann constant, , is 5.67 × 10-8 W/m2 K4. Assuming 1-D heat conduction, the magnitude of heat flux through the plate (in W/m2) is ________ (correct to two decimal places).1 AnswerA thin-walled cylindrical can with rigid end caps has a mean radius 100R mm and a wall thickness of 5 t mm. The can is pressurized and an additional tensile stress of 50 MPa is imposed along the axial direction as shown in the figure. Assume that the state of stress in the wall is uniform along its length. If the magnitudes of axial and circumferential components of stress in the can are equal, the pressure (in MPa) inside the can is ___________ (correct to two decimal places).1 AnswerConsider a laminar flow in the x-direction between two infinite parallel plates (Couette flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/s in the x-direction. The distance between the plates is 5 mm and the dynamic viscosity of the fluid is 0.01 N-s/m2 .0 AnswerFor the state of stress shown in the figure, the normal stress, σn , on a plane inclined at 45 degrees to the x-axis is _________ MPa (round off to the nearest integer).0 AnswerConsider the singly reinforced beam shown in the figure below:At cross-section XX, which of the following statements is TRUE at the limit state? - gate civil 2017 1 AnswerT he viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length L isL. When the plate length is increased to twice its original length, the percentage change in laminar boundary layer thickness at the end of the plate (with respect to L) is ________ (correct to two decimal places). 1 AnswerA thin-walled tube, with the cross-section shown in the figure, is subjected to a torque of T = 1 kN-m. The walls have uniform thickness t = 1 mm and shear modulus G = 26 GPa. Assume that the curved portion is semi-circular. The shear stress in the wall is _____ MPa (round off to 1 decimal place).0 AnswerA reservoir model consisting of two porous matrices M and N, separated by a fracture, is shown in the figure. The matrices are strongly water-wet and are saturated with oil of specific gravity 0.8. Water is injected only in the fracture at injection well A. If the Reynolds number for the flow in the fracture conduit is assumed to be less than unity, which one of the following force will dominate oil recovery from the porous matrix M during the water-flood operation?1 AnswerA reservoir model consisting of two porous matrices M and N, separated by a fracture, is shown in the figure. The matrices are strongly water-wet and are saturated with oil of specific gravity 0.8. Water is injected only in the fracture at injection well A. If the Reynolds number for the flow in the fracture conduit is assumed to be less than unity, which one of the following force will dominate oil recovery from the porous matrix M during the water-flood operation?1 AnswerThe flexural rigidity (D) of the oceanic lithosphere (assuming no secondary thermal perturbations) _________.0 AnswerA thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatures of the plate and the surroundings, and the properties of the surrounding fluid, are constant. The relationship between the average Nusselt and Rayleigh numbers is given as 1 4 Nu K Ra , where K is a constant. The length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the plate is increased to 16L keeping all other factors constant.0 AnswerA thin plate with Young’s modulus 210 GPa and Poisson’s ratio 0.3 is loaded as shown in the figure. The change in length along the y-direction is __________ mm (round off to 1 decimal place).0 AnswerThe S-N curve for a steel is shown below. If the stress ratio, (σmin/σmax) = −0.8, the maximum stress (in MPa, rounded off to the nearest integer) that the steel can withstand for infinite fatigue life is ____________.0 Answer
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