PRINCIPAL STRESSES

MULTIPLE CHOICE QUESTIONS

(MCQ) WITH ANSWERS

MCQ help increase of knowledge and

clarity about principal stresses. Principal

stresses are simple stresses. These are

either tensile or compressive stresses.

Failure in a material takes place due to

principal stresses, strains and energy. Thus

MCQ help to apply fundamentals in real

life applications.

1. A principal plane is a plane of

(a) Zero tensile stress
(b) Zero compressive stress
(c) Zero shear stress
(d) None
(Ans: c)

2. A principal plane is a plane of

(a) Only normal stress
(b) Only shear stress
(c) Only bending stress
(d) None
(Ans: a)

3. There are in all

(a) Two principal planes
(b) Three principal planes
(c) Four principal planes
(d) None
(Ans: b)

4. There are in all

(a) Two principal stresses
(b) Three principal stresses
(c) Four principal stresses
(d) None
(Ans: b)

5. There are in all

(a) Two principal strains
(b) Three principal strains
(c) Four principal strains
(d) None
(Ans: b)

6. Identify the principal stress

(a) Shear stress
(b) Bending stress
(c) Compressive stress
(d) None
(Ans: c)

7. On the planes of maximum shear, there are

(a) Normal stresses
(b) Bending stresses
(c) Bucking stresses
(d) None
(Ans: a)

8. 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
(Ans: b)

9. The magnitude of principal stresses due to complex stresses is

(a) (1/2)[ (σ_x + σ_y) ± ((σ_x –σ_y)² + 4 τ²))^0.5]
(b) (1/2)[ (σx + σy) ± (1/2)((σx –σy)² + 4 τ²))^0.5]
(c) (1/2)[ (σx + σy) ± ((1/2)(σx –σy)² + 4 τ²))^0.5]
(d) None
(Ans: a)

10. 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

(Ans: a)

11. The magnitude of maximum shear stress is

(a) ± (1/2)[ ((σx –σy)² + 4 τ²))^0.5]
(b) ± (1/2)[ (1/2)((σx –σy)² + 4 τ²))^0.5]
(c) ± (1/2)[ ((1/2)(σx –σy)² + 4 τ²))^0.5]
(d) None
(Ans: a)

12. A complementary shear stress is equal in magnitude and opposite in rotational tendency of an applied

(a) Tensile stress
(b) Compressive stress
(c) Shear stress
(d) None
(Ans: c)

13. All the principal stresses are at an angle of

(a) 45⁰
(b) 60⁰
(c) 75⁰
(d) None
(Ans: d)

14. All the principal stresses are at an angle of

(a)90⁰

(b) 45⁰   

(c) 135⁰

(d) None

Ans: (a)

15. All the principal strains are at an angle of

(a) 45⁰
(b) 60⁰
(c) 75⁰
(d) None
(Ans: d)

16. All the principal strains are at an angle of

 (a) 45⁰
(b) 90⁰
(c) 135⁰
(d) None
(Ans: b)

17. Total number of maximum shear stresses is

(a) One
(b) Three
(c) Five
(d) None
(Ans: b)

18. All the maximum shear stresses are at an angle of 

(a)45⁰
(b) 90⁰
(c) 135⁰
(d) None
(Ans: b)

19. Does a plane of maximum shear stress contain a?

(a) Normal stress
(b) Bending stress
(c) Torsional shear stress
(d) None
(Ans: a)

20. The order of magnitude of the principal stresses is

1. Firstly    σ₁>σ₂ >σ₃

2. Secondly   σ₂>σ₃ >σ₁

3. Thirdly    σ₁>σ₃ >σ₂

4. None

ANS: (a)

    21. Nature of the three principal stresses is

1. Firstly All tensile

2. Secondly All compressive

3. Thirdly All shear

4. None

ANS: (a)

    22. A principal stress is a

1. Shear stress with zero normal stress

2. Normal stress with zero shear stress

3. Both (a) & (b)

4. None

ANS: (b)

    23. Principal stresses are

1. Firstly  Maximum and minimum shear stresses

2. Secondly  Maximum and minimum normal stresses

3. Both (a) & (b)

4. None

ANS: (b)

     24. How many angles of obliquity are there for a cuboidal body under complex stresses?

1. 6

2. 8

3. 4

4. None

ANS: (a)

    25. How many maximum shear stresses are there with three principal stresses?

1. 1

2. 2

3. 3

4. None

ANS: ©

   26. In a body under pure shear, the magnitude and nature of the two principal stresses are

1. Firstly   Equals shear stress, opposite nature

2. Secondly   Equals shear stress, same nature

3. Both (a) & (b)

4. None

ANS: (a)

    27. Complementary shear stress is

1. > applied shear stress

2. < applied shear stress

3. = applied shear stress

4. None

ANS: (c )

    28. Complementary shear stress is

1. Parallel to applied stress

2. Perpendicular to the applied shear stress

3. Inclined to the applied shear stress

4. None

ANS: (b)

    29. The angle between a principal plane and a plane of maximum shear is

1. 30⁰

2. 60⁰

3. 90⁰

4. None

ANS: (d)

30. The angle between a principal plane and a plane of maximum shear is

1. 15⁰

2. 45⁰

3. 75⁰

4. None

ANS: (b)

    31. Which is the maximum principal stress?

1. Firstly         σ₂

2. Secondly    σ ₃

3. Thirdly        σ₁

4. None

ANS: (c ) 

    32. In the analysis, all the  principal stresses are assumed as

1. Shear stresses

2. Compressive stresses

3. Tensile stresses

4. None

ANS: (c )

    33. The magnitude of maximum principal stress is

1. Firstly          (σ_x+σ_y)/2+ (1/2)( σ_x+σ_y) +4τ²)⁵

2. Secondly     (σ_x+σ_y)/2+ (1/2)( σ_x-σ_y)² +4τ²)⁵

3. Thirdly         (σ_x+σ_y)/2+ (1/2)( σ_x+σ_y)² +4τ²)⁵

4. None

ANS: (b)

    34. Maximum shear stress in terms of principal stresses is

1. Firstly           (σ₁ +σ₂)/2

2. Secondly       (σ₁/σ₂)

3. Thirdly          (σ₁ –σ₂)/2

4. None

ANS: (c )

    35. Principal stresses are found by

1. Analytical method

2. Graphical method

3. Analytical & graphical methods

4. None

ANS: (c )

     36. The principal strain due to σ1(tensile) and σ2 (Compressive ) stress is

(a) Firstly               (1/E)( σ1 + σ2)
(b)Secondly           (1/E)( σ1 +µ σ2)
(c)Thirdly              (1/E)( σ1 -µ σ2)
(d) None
(Ans: b)

     37. The principal strain due to σ1 (compressive) and σ2 (tensile) stress is

(a) Firstly                  (1/E)( -σ1 + σ2)
(b) Secondly             (1/E)( -σ1 +µ σ2)
(c)Thirdly                 (1/E)(- σ1 -µ σ2)
(d) None

(Ans: c)

    38. A principal stress is

1. Tensile or shear stress

2. Compressive or shear stress

3. Tensile or compressive stress

4. None

ANS: (c )

    39. Is principal a?

1. Simple stress

2. Complex stress

3. Bending stress

4. None

ANS: (a)

    40. The principal stress ha a

1. Variable

2. Constant

3. Constant & variable

4. None

ANS: (b)

41. Resilience under principal tensile stresses σ1 and σ2 is

(a) (1/2E)( σ1² + σ2² –3µ σ1 σ2)
(b) (1/2E)( σ1² + σ2² –4µ σ1 σ2)
(c) (1/2E)( σ1² + σ2² –5µ σ1 σ2)
(d) None
(Ans: d)

42. Resilience under principal tensile stresses σ1 and σ2 is

(a) (1/2E)( σ1² + σ2² –3µ σ1 σ2)
(b) (1/2E)( σ1² + σ2² –4µ σ1 σ2)
(c) (1/2E)( σ1² + σ2² –5µ σ1 σ2)
(d) None
(Ans: d)

43. Resilience under principal tensile stresses σ1 and σ2 is

(a) (1/2E)( σ1² + σ2² –µ σ1 σ2)
(b) (1/2E)( σ1² + σ2² –4µ σ1 σ2)
(c) (1/2E)( σ1² + σ2² –2µ σ1 σ2)
(d) None
( ANS: c)

44. Shear strain energy under principal tensile stresses σ1 and σ2 is

(a) (1/12E) (σ1 — σ2)² + σ2²— σ1² )
(b) (1/12G) (σ1 — σ2)² + σ2²+ σ1² )
(c) (1/12K) (σ1 — σ2)² + σ2²+ σ1² )
(d) None
(Ans: b)

    45. Why do we determine principal stresses?

1. Failure is due to simple stress or strain

2. Failure is due to complex stress or strain

3. Both (a) & (b)

4. None

ANS: (a)

    46. The maximum number of principal stresses is

1. 2

2. 4

3. 6

4. None

ANS: (d)

    47. The maximum number of principal stresses is

1. 1

2. 3

3. 5

4. None

ANS: (b)

   

    48. Symbols for principal stresses are

1. Firstly      σ, τ & γ

2. Secondly   σ₁, σ₂ & σ₃

3. Thirdly       τ₁, τ₂ &τ₃

4. None

ANS: (b)

49. The angle of obliquity is the angle between the

1. Firstly    Resultant and the shear stress

2. Secondly    Resultant & the normal stress

3. Both (a) & (b)

4. None

ANS: (b)

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