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# MCQs on Deflection of Cantilever

The ratio of maximum deflection of a beam to its ___________ is called stiffness of the beam.

a) Load

b) Slope

c) Span

d) Reaction at the support

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Answer: c

Explanation: The stiffness of a beam is a measure of it’s resistance against deflection. The ratio of the maximum deflection of a beam to its span can be termed as stiffness of the beam.

Stiffness of the beam is inversely proportional to the _____ of the beam.

a) Slope

b) Support reaction

c) Deflection

d) Load

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Answer: c

Explanation: Stiffness of a beam is inversely proportional to the deflection. Smaller the deflection in a beam due to given external load, greater is its stiffness.

The maximum ____ should not exceed the permissible limit to the span of the beam.

a) Slope

b) Deflection

c) Load

dl Bending moment

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Answer: b

Explanation: The maximum deflection of a loaded beam should not exceed the permissible limit in relation to the span of a beam. While designing the beam the designer should be keep in mind that both strength and stiffness criteria.

In cantilever beam the deflection occurs at ______

a) Free end

b) Point of loading

c) Through out

d) Fixed end

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Answer: a

Explanation: Deflection can be defined as the perpendicular displacement of a point on straight access to the curved axis. In cantilever beams, the maximum deflection occurs at free end.

The maximum deflection in cantilever beam of span “l”m and loading at free end is “W” kN.

a) Wl^{3}/2EI

b) Wl^{3}/3EI

c) Wl^{3}/4EI

d) Wl^{2}/2EI

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Answer: b

Explanation: Maximum deflection occurs at free end distance between centre of gravity of bending moment diagram and free end is x = 2l/3.

As deflection is equal to the slope × “x”. The slope = Wl2/2EI radians

Maximum deflection (y) = Ax/EI = Wl^{3}/3EI.

In an ideal fluid, the ____________ stresses are pretend to be absent.

a) Bending

b) Shearing

c) Tensile

d) Compressive

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Answer: b

Explanation: An ideal fluid is a fluid where there is no resistance to the deformation. Ideal Fluids are those Fluids which have no viscosity surface tension. The shear stress is also absent. This fluid is also called as perfect fluid.

Air and water are the examples of ___________

a) Non Newtonian fluids

b) Vortex fluids

c) Real fluids

d) Ideal fluids

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Answer: d

Explanation: The ideal Fluids are imaginary fluids in nature, they are incompressible. These fluids possess low viscosity. Air and water are considered as ideal fluids.

_______ fluids are practical fluids

a) Ideal

b) Real

c) Vortex

d) Newtonian

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Answer: b

Explanation: These fluids possess properties such as viscosity, surface tension. They are compressible in nature. The certain amount of resistance is always offered by the fluids, they also possess shear stress. They are also known as practical fluids.

Specific weight of water at 4°C is ____________ N/m^{3}.

a) 9810

b) 9760

c) 9950

d) 9865

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Answer: a

Explanation: The specific weight (weight density) of a fluid is weight per unit volume. It is represented by symbol w & it is expressed in Newton per metre cube (N/m^{3}). The specific weight of water at 4 degree centigrade is 9810 N/m3or 9.81 kN/m^{3}.

The inverse of specific weight of a fluid is __________

a) Specific gravity

b) Specific Volume

c) Compressibility

d) Viscosity

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Answer: b

Explanation: Specific volume is the volume of the fluid by Unit Weight it is the reciprocal of specific weight is denoted by “v”. SI units are m^{3}/N.

v= 1/specific weight.

Calculate the specific gravity of mercury.

a) 12.5

b) 14.7

c) 13.6

d) 11.8

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Answer: c

Explanation: The specific gravity of any fluid is the ratio of the specific weight of fluid by specific weight of water. For mercury, the specific weight is 133416 N/m^{3}. For water, w = 9810 N/m^{3}.

S = 133416/9810

S= 13.6.

Specific gravity of water is __________

a) 0.8

b) 1

c) 1.2

d) 1.5

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Answer: b

Explanation: The specific gravity is also called as relative density. It is dimensionless quantity and it has no units. The specific gravity of water is the ratio of specific weight of fluid to specific weight of water, as both the numerator and denominator are same. The value is 1.

Compute the maximum deflection at free end of a cantilever beam subjected to udl for entire span of l metres.

a) wl^{4}/8EI

b) wl^{4}/4EI

c) wl^{3}/8EI

d) wl^{2}/6EI

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Answer: a

Explanation: The slope at free end = A/EI = wl^{3}/6EI

Maximum deflection at free end is Ax/EI; [x= ¾ l] y= wl^{3}/6EI × ¾ l = wl^{4}/8EI.

Calculate the maximum deflection of a cantilever beam with udl on entire span of 3m the intensity of you udl be 25 kN/m. Take EI as 4000 kN/m^{2}.

a) 0.052m

b) 0.063m

c) 0.076m

d) 0.09m

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Answer: b

Explanation: For cantilever beams with udl on entire span, the maximum deflection = wl^{4}/8EI

y = wl^{4}/8EI = 25 × 3^{4}/ 8 × 4000 = 0.063m.

Which of the following is not an example of Malleability?

a) Wrought Iron

b) Ornamental silver

c) Torsteel

d) Ornamental gold

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Answer: c

Explanation: Torsteel is an example of mechanical property ductility. The ductility is a property of a material by which material can be fractured into thin wires after undergoing a considerable deformation without any rupture.