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ISRO Mechanical Strength of Materials Questions, Answers and Explanation

Strength of Materials

Simple Stresses and Strains


2017.2.9. Which of the following is true for ductile materials?
a) Engineering stress – strain curve cannot have negative slope
b) Most applicable failure theory is maximum principal stress theory
c) Ultimate strain is the strain at ultimate stress
d) Strain hardening is represented by a negative slope in engineering stress strain curve



Answer

c) Ultimate strain is the strain at ultimate stress



Explanation 

Principal stress theory is applicable for brittle materials.

Elastic Constants

2017.2. 2. For isotropic materials, the modulus of Elasticity in tension and shear (E and G) are related to the Poisson's ratio (&nu) as follows
a) E = G/(2(1+ν))
b) G = E/(2(1+ν))
c) G = E/(2(1-ν))
d) E = G/(2(1-ν))

Answer
b) G = E/(2(1+ν))

Explanation
Derivation of relation between Modulus of elasticity in tension and shear

Torsion

2017.2.76. A 3m long steel shaft has to transmit 7.5kW at 3600rpm. Required shaft diameter is given by(Take allowable shear stress = 100N/mm2, π2 = 10)?
a) 10mm
b) 7.5mm
c) 25mm
d) 12.5mm

Answer
a) 10mm

Explanation [Strength of Materials]
From the torsion theory 
T/Ip = τ/r
and 
P = 2πNT/60
where
T - Torque
Ip - polar moment of inertia = π d4/32
τ - shear stress
r - radius where shear stress is measured
P - power transmitted
N - revolutions per minute
Maximum shear stress occurs at r = d/2

Combining the 2 equations
P = 2πN/60 *2 Ipτ/d
P = πNπ d4τ/(15*32d)
d3 = 15*32*P/(π2Nτ)
   = 15*32*7500/(10*3600*100*106)
   = 0.000001
d = 0.01m = 10mm

Testing of Materials

2018.7. The impact strength of a material is an index of its
a) fatigue strength
b) tensile strength
c) hardness
d) toughness

Answer
d) toughness

Explanation 
Yield strength is the lowest stress that produces a permanent deformation in a material. In some materials, like aluminium alloys, the point of yielding is difficult to identify, thus it is usually defined as the stress required to cause 0.2% plastic strain.
Compressive strength is a limit state of compressive stress that leads to failure in a material in the manner of ductile failure (infinite theoretical yield) or brittle failure (rupture as the result of crack propagation, or sliding along a weak plane — see shear strength).
Tensile strength or ultimate tensile strength is a limit state of tensile stress that leads to tensile failure in the manner of ductile failure (yield as the first stage of that failure, some hardening in the second stage and breakage after a possible "neck" formation) or brittle failure (sudden breaking in two or more pieces at a low stress state). 
Fatigue strength is a measure of the strength of a material or a component under cyclic loading. Fatigue strength is quoted as stress amplitude or stress range , usually at zero mean stress, along with the number of cycles to failure under that condition of stress.
Impact strength is the capability of the material to withstand a suddenly applied load and is expressed in terms of energy. In order for a material or object to have a high impact strength the stresses must be distributed evenly throughout the object. It also must have a large volume with a low modulus of elasticity and a high material yield strength. In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing. One definition of material toughness is the amount of energy per unit volume that a material can absorb before rupturing. It is also defined as a material's resistance to fracture when stressed. The toughness of a material can be measured using a small specimen of that material. A typical testing machine uses a pendulum to strike a notched specimen of defined cross-section and deform it. The height from which the pendulum fell, minus the height to which it rose after deforming the specimen, multiplied by the weight of the pendulum is a measure of the energy absorbed by the specimen as it was deformed during the impact with the pendulum.

Failure Theories

2015.11. Which of the following is applied to brittle materials?
a) maximum principal stress theory
b) maximum principal strain theory
c) maximum strain energy theory
d) maximum shear stress theory

Answer
a) maximum principal stress theory

Explanation
Ductile Materials - Planes of maximum shear exist in the material at 45o and the material begins to slide along these planes. Maximum shear stress theory/ Total strain energy theory can be used.
Brittle Materials - When the normal stress in the material reaches the ultimate stress the material fails suddenly by fracture. Maximum principal stress theory can be used.

2017.2.77. For thin cylindrical shell structures loaded in compression, the design is based on
a) Yield strength of material
b) Ultimate strength of material
c) Buckling strength of the structure
d) Shear strength of the structure

Answer
c) Buckling stress of the structure.

Explanation
Yield strength is the point where the material tends to deform. For the structures that should not deform on usage, the design is based on yield strength of material.
Brittle materials generally fails at the ultimate strength of material.
Buckling under axial compression is normally the controlling design consideration for thin cylindrical structures. Thin and long cylindrical structures fail before the yield strength of the member is reached. 
Shear strength of a component is important for designing the dimensions and materials to be used for the manufacture or construction of the component e.g. beams, plates, or bolts

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