The total strain energy for a unit cube subjected to three principal stresses is given by? a) U= [(σέ) 1 + (σέ) 2+ (σέ) 3]/3 b) U= [(σ12+σ22+σ32)/2E] – (σ1σ2+σ2σ3+σ3σ1)2μ c) U= [(σέ) 1 + (σέ) 2+ (σέ) 3]/4 d) None of the mentioned

The total strain energy for a unit cube subjected to three principal stresses is given by?

a) U= [(σέ) 1 + (σέ) 2+ (σέ) 3]/3

b) U= [(σ12+σ22+σ32)/2E] – (σ1σ2+σ2σ3+σ3σ1)2μ

c) U= [(σέ) 1 + (σέ) 2+ (σέ) 3]/4

d) None of the mentioned
by

1 Answer

Answer :

b) U= [(σ12+σ22+σ32)/2E] – (σ1σ2+σ2σ3+σ3σ1)2μ
by

Related questions

In distortion energy theorem, if a unit cube is subjected to biaxial stress, then S(yt) is given by which of the following? a) √ (σ12- σ1σ2 +σ22) b) σ12- σ1σ2 +σ22 c) √ (σ12+ σ1σ2 +σ22) d) σ12+ σ1σ2 +σ22

Description : In distortion energy theorem, if a unit cube is subjected to biaxial stress, then S(yt) is given by which of the following? a) √ (σ12- σ1σ2 +σ22) b) σ12- σ1σ2 +σ22 c) √ (σ12+ σ1σ2 +σ22) d) σ12+ σ1σ2 +σ22

Last Answer : a) √ (σ12- σ1σ2 +σ22)

In distortion energy theorem, if a unit cube is subjected to biaxial stress, then S(yt) is given by which of the following? a) √ (σ12- σ1σ2 +σ22) b) σ12- σ1σ2 +σ22 c) √ (σ12+ σ1σ2 +σ22) d) σ12+ σ1σ2 +σ22

Description : In distortion energy theorem, if a unit cube is subjected to biaxial stress, then S(yt) is given by which of the following? a) √ (σ12- σ1σ2 +σ22) b) σ12- σ1σ2 +σ22 c) √ (σ12+ σ1σ2 +σ22) d) σ12+ σ1σ2 +σ22

Last Answer : a) √ (σ12- σ1σ2 +σ22)

Resilience under principal tensile stresses σ1 and σ2 is (a) (1/2E)( σ1 2 + σ2 2 –μ σ1 σ2) (b) (1/2E)( σ1 2 + σ2 2 –4μ σ1 σ2) (c) (1/2E)( σ1 2 + σ2 2 –2μ σ1 σ2) (d) None

Description : Resilience under principal tensile stresses σ1 and σ2 is (a) (1/2E)( σ1 2 + σ2 2 –μ σ1 σ2) (b) (1/2E)( σ1 2 + σ2 2 –4μ σ1 σ2) (c) (1/2E)( σ1 2 + σ2 2 –2μ σ1 σ2) (d) None

Last Answer : (c) (1/2E)( σ1 2 + σ2 2 –2μ σ1 σ2)

Maximum total strain energy is equal to (a) (σ1 2 +σ2 2 )/2E (b) ( σ1 2 +σ2 2 + 2μ σ1 σ2)/2E (c) ( σ1 2 +σ2 2 — 2μ σ1 σ2)/2E (d) None

Description : Maximum total strain energy is equal to (a) (σ1 2 +σ2 2 )/2E (b) ( σ1 2 +σ2 2 + 2μ σ1 σ2)/2E (c) ( σ1 2 +σ2 2 — 2μ σ1 σ2)/2E (d) None

Last Answer : (c) ( σ1 2 +σ2 2 — 2μ σ1 σ2)/2E

Resilience under principal tensile stresses σ1 and σ2 is (a) (1/2E)( σ1 2 + σ2 2 –3μ σ1 σ2) (b) (1/2E)( σ1 2 + σ2 2 –4μ σ1 σ2) (c) (1/2E)( σ1 2 + σ2 2 –5μ σ1 σ2) (d) None

Description : Resilience under principal tensile stresses σ1 and σ2 is (a) (1/2E)( σ1 2 + σ2 2 –3μ σ1 σ2) (b) (1/2E)( σ1 2 + σ2 2 –4μ σ1 σ2) (c) (1/2E)( σ1 2 + σ2 2 –5μ σ1 σ2) (d) None

Last Answer : (d) None

Resilience under principal tensile stresses σ1 and σ2 is (a) (1/2E)( σ1 2 + σ2 2 –3μ σ1 σ2) (b) (1/2E)( σ1 2 + σ2 2 –4μ σ1 σ2) (c) (1/2E)( σ1 2 + σ2 2 –5μ σ1 σ2) (d) None

Description : Resilience under principal tensile stresses σ1 and σ2 is (a) (1/2E)( σ1 2 + σ2 2 –3μ σ1 σ2) (b) (1/2E)( σ1 2 + σ2 2 –4μ σ1 σ2) (c) (1/2E)( σ1 2 + σ2 2 –5μ σ1 σ2) (d) None

Last Answer : (d) None

Shear strain energy under principal tensile stresses σ1 and σ2 is (a) (1/12E) (σ1 — σ2) 2 + σ2 2 — σ1 2 ) (b) (1/12G) (σ1 — σ2) 2 + σ2 2 + σ1 2 ) (c) (1/12K) (σ1 — σ2) 2 + σ2 2 + σ1 2 ) (d) None

Description : Shear strain energy under principal tensile stresses σ1 and σ2 is (a) (1/12E) (σ1 — σ2) 2 + σ2 2 — σ1 2 ) (b) (1/12G) (σ1 — σ2) 2 + σ2 2 + σ1 2 ) (c) (1/12K) (σ1 — σ2) 2 + σ2 2 + σ1 2 ) (d) None

Last Answer : (b) (1/12G) (σ1 — σ2) 2 + σ2 2 + σ1 2 )

Why do we determine principal stresses? a. Failure is due to simple stress or strain b. Failure is due to complex stress or strain c. Both (a) & (b) d. None

Description : Why do we determine principal stresses? a. Failure is due to simple stress or strain b. Failure is due to complex stress or strain c. Both (a) & (b) d. None

Last Answer : a. Failure is due to simple stress or strain

Cotter joint is used when the members are subjected to which type of stresses? a) Axial tensile b) Axial compressive c) Axial tensile or compressive d) None of the mentioned

Description : Cotter joint is used when the members are subjected to which type of stresses? a) Axial tensile b) Axial compressive c) Axial tensile or compressive d) None of the mentioned

Last Answer : c) Axial tensile or compressive

How many maximum shear stresses are there with three principal stresses? a. 1 b. 2 c. 3 d. None

Description : How many maximum shear stresses are there with three principal stresses? a. 1 b. 2 c. 3 d. None

Last Answer : c. 3

Nature of the three principal stresses is a. Firstly All tensile b. Secondly All compressive c. Thirdly All shear d. None

Description : Nature of the three principal stresses is a. Firstly All tensile b. Secondly All compressive c. Thirdly All shear d. None

Last Answer : a. Firstly All tensile

There are in all (a) Two principal stresses (b) Three principal stresses (c) Four principal stresses (d) None

Description : There are in all (a) Two principal stresses (b) Three principal stresses (c) Four principal stresses (d) None

Last Answer : (b) Three principal stresses

Modulus of resilience is defined as a) Strain energy per unit volume b) Strain energy per unit area c) Independent of strain energy d) None of the mentioned

Description : Modulus of resilience is defined as a) Strain energy per unit volume b) Strain energy per unit area c) Independent of strain energy d) None of the mentioned

Last Answer : a) Strain energy per unit volume

For a homogeneous & isotropic body under hydrostatic pressure, which theory of elastic failure fails (a) Firstly Maximum Principal Theory (b) Secondly Maximum Principal strain Theory (c) Thirdly Maximum Principal Energy Theory (d) None

Description : For a homogeneous & isotropic body under hydrostatic pressure, which theory of elastic failure fails (a) Firstly Maximum Principal Theory (b) Secondly Maximum Principal strain Theory (c) Thirdly Maximum Principal Energy Theory (d) None

Last Answer : (c) Thirdly Maximum Principal Energy Theory

Under complex loading, if elastic limit reaches in tension, then failure occurs due to (a) Firstly Maximum principal strain theory (b) Secondly Maximum principal theory of strain energy (c) Thirdly Maximum Principal stress theory (d) None

Description : Under complex loading, if elastic limit reaches in tension, then failure occurs due to (a) Firstly Maximum principal strain theory (b) Secondly Maximum principal theory of strain energy (c) Thirdly Maximum Principal stress theory (d) None

Last Answer : (c) Thirdly Maximum Principal stress theory

Under complex loading, if elastic limit reaches in tension, then failure occurs due to (a) Firstly Maximum principal strain theory (b) Secondly Maximum principal theory of strain energy (c) Thirdly Maximum shear stress theory (d) None

Description : Under complex loading, if elastic limit reaches in tension, then failure occurs due to (a) Firstly Maximum principal strain theory (b) Secondly Maximum principal theory of strain energy (c) Thirdly Maximum shear stress theory (d) None

Last Answer : (d) None

A ductile material may not meet a failure if it has been tested for the theories of failure (a) Firstly Maximum Principal Theory (b) Secondly Maximum Principal Strain Theory (c) Thirdly Maximum principal strain energy theory (d) None

Description : A ductile material may not meet a failure if it has been tested for the theories of failure (a) Firstly Maximum Principal Theory (b) Secondly Maximum Principal Strain Theory (c) Thirdly Maximum principal strain energy theory (d) None

Last Answer : (d) None

A transmission shaft subjected to pure bending moment should be designed on the basis of (A) Maximum principal stress theory (B) Maximum shear stress theory (C) Distortion energy theory (D) Goodman or Soderberg diagrams

Description : A transmission shaft subjected to pure bending moment should be designed on the basis of (A) Maximum principal stress theory (B) Maximum shear stress theory (C) Distortion energy theory (D) Goodman or Soderberg diagrams

Last Answer : (A) Maximum principal stress theory

The helical spring ad wire of helical torsion spring, both are subjected to torsional shear stresses. a) True b) False

Description : The helical spring ad wire of helical torsion spring, both are subjected to torsional shear stresses. a) True b) False

Last Answer : b) False

Cotter joint is employed when the members are subjected to which sort of stresses? a) Axial tensile b) Axial compressive c) Axial tensile or compressive d) None of the above

Description : Cotter joint is employed when the members are subjected to which sort of stresses? a) Axial tensile b) Axial compressive c) Axial tensile or compressive d) None of the above

Last Answer : c) Axial tensile or compressive

Under complex loading, principal stresses exist as (a) Firstly σ 1 > σ 2 =σ 3 (b) Secondly σ 1 = σ 2 =σ 3 (c) Thirdly σ 1 > σ 2 < σ 3 (d) None

Description : Under complex loading, principal stresses exist as (a) Firstly σ 1 > σ 2 =σ 3 (b) Secondly σ 1 = σ 2 =σ 3 (c) Thirdly σ 1 > σ 2 < σ 3 (d) None

Last Answer : (d) None

Symbols for principal stresses are a. Firstly σ, τ & γ b. Secondly σ 1 , σ 2 & σ 3

Description : Symbols for principal stresses are a. Firstly σ, τ & γ b. Secondly σ 1 , σ 2 & σ 3

Last Answer : b. Secondly σ 1 , σ 2 & σ 3

The maximum number of principal stresses is a. 1 b. 3 c. 5 d. None

Description : The maximum number of principal stresses is a. 1 b. 3 c. 5 d. None

Last Answer : b. 3

The maximum number of principal stresses is a. 2 b. 4 c. 6 d. None

Description : The maximum number of principal stresses is a. 2 b. 4 c. 6 d. None

Last Answer : d. None

Principal stresses are found by a. Analytical method b. Graphical method c. Analytical & graphical methods d. None

Description : Principal stresses are found by a. Analytical method b. Graphical method c. Analytical & graphical methods d. None

Last Answer : c. Analytical & graphical methods

Maximum shear stress in terms of principal stresses is a. Firstly (σ 1 +σ 2 )/2 b. Secondly (σ 1 /σ 2 ) c. Thirdly (σ 1 –σ 2 )/2 d. None

Description : Maximum shear stress in terms of principal stresses is a. Firstly (σ 1 +σ 2 )/2 b. Secondly (σ 1 /σ 2 ) c. Thirdly (σ 1 –σ 2 )/2 d. None

Last Answer : c. Thirdly (σ 1 –σ 2 )/2

In the analysis, all the principal stresses are assumed as a. Shear stresses b. Compressive stresses c. Tensile stresses d. None

Description : In the analysis, all the principal stresses are assumed as a. Shear stresses b. Compressive stresses c. Tensile stresses d. None

Last Answer : c. Tensile stresses

In a body under pure shear, the magnitude and nature of the two principal stresses are a. Firstly Equals shear stress, opposite nature b. Secondly Equals shear stress, same nature c. Both (a) & (b) d. None

Description : In a body under pure shear, the magnitude and nature of the two principal stresses are a. Firstly Equals shear stress, opposite nature b. Secondly Equals shear stress, same nature c. Both (a) & (b) d. None

Last Answer : a. Firstly Equals shear stress, opposite nature

Principal stresses are a. Firstly Maximum and minimum shear stresses b. Secondly Maximum and minimum normal stresses c. Both (a) & (b) d. None

Description : Principal stresses are a. Firstly Maximum and minimum shear stresses b. Secondly Maximum and minimum normal stresses c. Both (a) & (b) d. None

Last Answer : b. Secondly Maximum and minimum normal stresses

The order of magnitude of the principal stresses is a. Firstly σ 1 >σ 2 >σ 3 b. Secondly σ 2 >σ 3 >σ 1 c. Thirdly σ 1 >σ 3 >σ 2 d. None

Description : The order of magnitude of the principal stresses is a. Firstly σ 1 >σ 2 >σ 3 b. Secondly σ 2 >σ 3 >σ 1 c. Thirdly σ 1 >σ 3 >σ 2 d. None

Last Answer : a. Firstly σ 1 >σ 2 >σ 3

All the principal stresses are at an angle of (a)90 0 (b) 45 0 (c) 135 0 (d) None

Description : All the principal stresses are at an angle of (a)90 0 (b) 45 0 (c) 135 0 (d) None

Last Answer : (a)90 0

All the principal stresses are at an angle of (a) 45 0 (b) 60 0 (c) 75 0 (d) None

Description : All the principal stresses are at an angle of (a) 45 0 (b) 60 0 (c) 75 0 (d) None

Last Answer : (d) None

The equations for principal stresses are valid only when (a)σ x and σ y are both tensile (b) σ x is compressive and σ y is tensile (c) σ x is tensile and σ y is compressive (d) None

Description : The equations for principal stresses are valid only when (a)σ x and σ y are both tensile (b) σ x is compressive and σ y is tensile (c) σ x is tensile and σ y is compressive (d) None

Last Answer : (a)σ x and σ y are both tensile

The magnitude of principal stresses due to complex stresses is (a) (1/2)[ (σ x + σ y ) ± ((σ x –σ y ) 2 + 4 τ 2 )) 0.5 ] (b) (1/2)[ (σx + σy) ± (1/2)((σx –σy) 2 + 4 τ 2 )) 0.5 ] (c) (1/2)[ (σx + σy) ± ((1/2)(σx –σy) 2 + 4 τ 2 )) 0.5 ]

Description : The magnitude of principal stresses due to complex stresses is (a) (1/2)[ (σ x + σ y ) ± ((σ x –σ y ) 2 + 4 τ 2 )) 0.5 ] (b) (1/2)[ (σx + σy) ± (1/2)((σx –σy) 2 + 4 τ 2 )) 0.5 ] (c) (1/2)[ (σx + σy) ± ((1/2)(σx –σy) 2 + 4 τ 2 )) 0.5 ]

Last Answer : (a) (1/2)[ (σ x + σ y ) ± ((σ x –σ y ) 2 + 4 τ 2 )) 0.5 ]

Maximum shear stress is (a) Average sum of principal stresses (b) Average difference of principal stresses (c) Average sum as well as difference of principal stresses (d) None

Description : Maximum shear stress is (a) Average sum of principal stresses (b) Average difference of principal stresses (c) Average sum as well as difference of principal stresses (d) None

Last Answer : (b) Average difference of principal stresses

Which of the following stresses can be determined using Mohr's circle method? a. Torsional stress b. Bending stress c. Principal stress d. All of the above

Description : Which of the following stresses can be determined using Mohr's circle method? a. Torsional stress b. Bending stress c. Principal stress d. All of the above

Last Answer : c. Principal stress

Maximum principal strain is equal to when σ1 and σ2 are tensile (a) (σ1 –μσ2)/E (b) (σ1 + μσ2)/E (c) (–σ1 –μσ2)/E (d) None

Description : Maximum principal strain is equal to when σ1 and σ2 are tensile (a) (σ1 –μσ2)/E (b) (σ1 + μσ2)/E (c) (–σ1 –μσ2)/E (d) None

Last Answer : (a) (σ1 –μσ2)/E

Maximum principal strain theory is also called as (a) Guest’s theory (b) Haigh theory (c) St.Venant’s theory (d) None

Description : Maximum principal strain theory is also called as (a) Guest’s theory (b) Haigh theory (c) St.Venant’s theory (d) None

Last Answer : (c) St.Venant’s theory

Maximum principal strain theory is applicable to (a) Ductile materials (b) Brittle materials (c) Composite materials (d) None

Description : Maximum principal strain theory is applicable to (a) Ductile materials (b) Brittle materials (c) Composite materials (d) None

Last Answer : (b) Brittle materials

The principal strain due to σ1(tensile) and σ2 (Compressive ) stress is (a) Firstly (b)Secondly (c)Thirdly (d) None

Description : The principal strain due to σ1(tensile) and σ2 (Compressive ) stress is (a) Firstly (b)Secondly (c)Thirdly (d) None

Last Answer : (b)Secondly

A solid cube is subjected to equal normal forces on all its faces. The volumetric strain will be x- times the linear strain in any of the three axes when (A) x = 1 (B) x = 2 (C) x = 3 (D) x = 4

Description : A solid cube is subjected to equal normal forces on all its faces. The volumetric strain will be x- times the linear strain in any of the three axes when (A) x = 1 (B) x = 2 (C) x = 3 (D) x = 4

Last Answer : (C) x = 3

Total number of maximum shear stresses is (a) One (b) Three (c) Five (d) None

Description : Total number of maximum shear stresses is (a) One (b) Three (c) Five (d) None

Last Answer : (b) Three

The stress represented by sin (t) + 4 belongs to which category? a) Alternating Stresses b) None of the mentioned c) Repeated Stresses d) Reversed Stresses

Description : The stress represented by sin (t) + 4 belongs to which category? a) Alternating Stresses b) None of the mentioned c) Repeated Stresses d) Reversed Stresses

Last Answer : a) Alternating Stresses

The stress represented by sin (t) + 2 belongs to which category? a) Fluctuating Stresses b) None of the mentioned c) Repeated Stresses d) Reversed Stresses

Description : The stress represented by sin (t) + 2 belongs to which category? a) Fluctuating Stresses b) None of the mentioned c) Repeated Stresses d) Reversed Stresses

Last Answer : a) Fluctuating Stresses

The phenomenon of decreased resistance of the materials to fluctuating stresses is the main characteristic of _____ failure. a) Fracture b) Fatigue c) Yielding d) None of the mentioned

Description : The phenomenon of decreased resistance of the materials to fluctuating stresses is the main characteristic of _____ failure. a) Fracture b) Fatigue c) Yielding d) None of the mentioned

Last Answer : b) Fatigue

Principal planes are subjected to (A) Normal stresses only (B) Tangential stresses only (C) Normal stresses as well as tangential stresses (D) None of these

Description : Principal planes are subjected to  (A) Normal stresses only  (B) Tangential stresses only  (C) Normal stresses as well as tangential stresses  (D) None of these

Last Answer : (A) Normal stresses only

Maximum total strain energy theory is applicable to (a) Ductile materials (b) Brittle materials (c) Composite materials (d) None

Description : Maximum total strain energy theory is applicable to (a) Ductile materials (b) Brittle materials (c) Composite materials (d) None

Last Answer : (a) Ductile materials

Maximum total strain energy theory is applicable to (a) Ductile materials (b) Brittle materials (c) Composite materials (d) None

Description : Maximum total strain energy theory is applicable to (a) Ductile materials (b) Brittle materials (c) Composite materials (d) None

Last Answer : (b) Brittle materials

Maximum total strain energy theory is also known as (a) Huber theory (b) Rankine theory (c) St.Venant’s theory (d) None

Description : Maximum total strain energy theory is also known as (a) Huber theory (b) Rankine theory (c) St.Venant’s theory (d) None

Last Answer : (a) Huber theory

Maximum total strain energy theory is also known as (a) Guest’s theory (b) Haigh theory (c) St.Venant’s theory (d) None

Description : Maximum total strain energy theory is also known as (a) Guest’s theory (b) Haigh theory (c) St.Venant’s theory (d) None

Last Answer : (b) Haigh theory