PRINCIPAL STRESSES MULTIPLE CHOICE QUESTIONS (MCQ) WITH ANSWERS
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.

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 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}]
(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 τ^{2}))^{0.5}]
(b) ± (1/2)[ (1/2)((σx –σy)^{2} + 4 τ^{2}))^{0.5}]
(c) ± (1/2)[ ((1/2)(σx –σy)^{2} + 4 τ^{2}))^{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) 45^{0}
(b) 60^{0}
(c) 75^{0}
(d) None
(Ans: d)
14. All the principal stresses are at an angle of
(a)90^{0}
(b) 45^{0 }
(c) 135^{0}
(d) None
Ans: (a)
15. All the principal strains are at an angle of
(a) 45^{0}
(b) 60^{0}
(c) 75^{0}
(d) None
(Ans: d)
16. All the principal strains are at an angle of
(a) 45^{0}
(b) 90^{0}
(c) 135^{0}
(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)45^{0}
(b) 90^{0}
(c) 135^{0}
(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

Firstly σ_{1}>σ_{2} >σ_{3}

Secondly σ_{2}>σ_{3} >σ_{1}

Thirdly σ_{1}>σ_{3} >σ_{2}

None
ANS: (a)
21. Nature of the three principal stresses is

Firstly All tensile

Secondly All compressive

Thirdly All shear

None
ANS: (a)
22. A principal stress is a

Shear stress with zero normal stress

Normal stress with zero shear stress

Both (a) & (b)

None
ANS: (b)
23. Principal stresses are

Firstly Maximum and minimum shear stresses

Secondly Maximum and minimum normal stresses

Both (a) & (b)

None
ANS: (b)
24. How many angles of obliquity are there for a cuboidal body under complex stresses?

6

8

4

None
ANS: (a)
25. How many maximum shear stresses are there with three principal stresses?

1

2

3

None
ANS: ©
26. In a body under pure shear, the magnitude and nature of the two principal stresses are

Firstly Equals shear stress, opposite nature

Secondly Equals shear stress, same nature

Both (a) & (b)

None
ANS: (a)
27. Complementary shear stress is

> applied shear stress

< applied shear stress

= applied shear stress

None
ANS: (c )
28. Complementary shear stress is

Parallel to applied stress

Perpendicular to the applied shear stress

Inclined to the applied shear stress

None
ANS: (b)
29. The angle between a principal plane and a plane of maximum shear is

30^{0}

60^{0}

90^{0}

None
ANS: (d)
30. The angle between a principal plane and a plane of maximum shear is

15^{0}

45^{0}

75^{0}

None
ANS: (b)
31. Which is the maximum principal stress?

Firstly σ_{2}

Secondly σ _{3}

Thirdly σ_{1}

None
ANS: (c )
32. In the analysis, all the principal stresses are assumed as

Shear stresses

Compressive stresses

Tensile stresses

None
ANS: (c )
33. The magnitude of maximum principal stress is

Firstly (σ_{x}+σ_{y})/2+ (1/2)( σ_{x}+σ_{y}) +4τ^{2})^{5}

Secondly (σ_{x}+σ_{y})/2+ (1/2)( σ_{x}σ_{y})^{2} +4τ^{2})^{5}

Thirdly (σ_{x}+σ_{y})/2+ (1/2)( σ_{x}+σ_{y})^{2} +4τ^{2})^{5}

None
ANS: (b)
34. Maximum shear stress in terms of principal stresses is

Firstly (σ_{1} +σ_{2})/2

Secondly (σ_{1}/σ_{2})

Thirdly (σ_{1} –σ_{2})/2

None
ANS: (c )
35. Principal stresses are found by

Analytical method

Graphical method

Analytical & graphical methods

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

Tensile or shear stress

Compressive or shear stress

Tensile or compressive stress

None
ANS: (c )
39. Is principal a?

Simple stress

Complex stress

Bending stress

None
ANS: (a)
40. The principal stress ha a

Variable

Constant

Constant & variable

None
ANS: (b)
41. 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
(Ans: d)
42. 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
(Ans: d)
43. 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
( ANS: c)
44. 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
(Ans: b)
45. Why do we determine principal stresses?

Failure is due to simple stress or strain

Failure is due to complex stress or strain

Both (a) & (b)

None
ANS: (a)
46. The maximum number of principal stresses is

2

4

6

None
ANS: (d)
47. The maximum number of principal stresses is

1

3

5

None
ANS: (b)
48. Symbols for principal stresses are

Firstly σ, τ & γ

Secondly σ_{1}, σ_{2} & σ_{3}

Thirdly τ_{1}, τ_{2} &τ_{3}

None
ANS: (b)
49. The angle of obliquity is the angle between the

Firstly Resultant and the shear stress

Secondly Resultant & the normal stress

Both (a) & (b)

None
ANS: (b)
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