MCQs on compound stress

1. Principal planes are planes of/ eq[; lery----ds ry gksrs gSA
Maximum shearing stress/ vf/kdre vi:i.k izfrcy
Zero shearing stress/ 'kwU; vi:i.k izfrcy
Shearing stress having a magnitude of 50% of principal stress/ vi:i.k izfrcy tks
eq[; izfrcy dk 50 izfr’k= ifjek.k gksa
Will be maximum/ vf/kdre vi:i.k cy
1

2. Principal planes are planes of/ eq[; lery----ds ry gksrs gSA
Maximum shearing stress/ vf/kdre vi:i.k izfrcy
Zero shearing stress/ 'kwU; vi:i.k izfrcy
Shearing stress having a magnitude of 50% of principal stress/ vi:i.k izfrcy tks
eq[; izfrcy dk 50 izfr’k= ifjek.k gksa
Will be maximum/ vf/kdre vi:i.k cy
2

3. If a ductile material is subjected to a unidirectional tensile force, then to avoid
shear failure, the material should have its shear strength at least equal to/ ;fn ,d
rU; inkFkZ ,d&fn’kh; ruu cy ds izHkko esa gS] rks vi:i.k ls cpus ds fy,]
inkFkZ dks viuk vi:i.k lkeF;Z de ls de--------ds leku gksuk pkfg,A
Its tensile strength/ viuk ruu lkeF;Z
Half the tensile strength/ ruu lkeF;Z dk vk/kk
Its compressive strength/ viuk laihMu lkeF;Z
Twice the tensile strength/ ruu lkeF;Z dk nksxquk
3

4. If a ductile material is subjected to a unidirectional tensile force, then to avoid
shear failure, the material should have its shear strength at least equal to/ ;fn ,d
rU; inkFkZ ,d&fn’kh; ruu cy ds izHkko esa gS] rks vi:i.k ls cpus ds fy,]
inkFkZ dks viuk vi:i.k lkeF;Z de ls de--------ds leku gksuk pkfg,A
Its tensile strength/ viuk ruu lkeF;Z
Half the tensile strength/ ruu lkeF;Z dk vk/kk
Its compressive strength/ viuk laihMu lkeF;Z
Twice the tensile strength/ ruu lkeF;Z dk nksxquk
4

5. What is the angle between planes carrying maximum shear stress and planes
carrying maximum direct stress/ vf/kdre vi:i.k izfrcy okys leryksa vkSj
vf/kdre izR;{k izfrcy okys leryksa ds chp dks.k fdruk gSA
30º
45º
0º
90º
5

6. What is the angle between planes carrying maximum shear stress and planes
carrying maximum direct stress/ vf/kdre vi:i.k izfrcy okys leryksa vkSj
vf/kdre izR;{k izfrcy okys leryksa ds chp dks.k fdruk gSA
30º
45º
0º
90º
6

7. Consider the following statements/
1. On a principal plane, only normal stress acts
2. On a principal plane, both normal and shear stresses acts
3. On a principal plane, only shear stress acts/
4. Isotropic state of stress is independent of frame of reference/
Which of the above statement is/are correct/ fuEu dFkuksa ij fopkj djsA
1 ,d eq[; lery ij] dsoy lkekU; izfrcy dk;Z djrk gS
2 ,d eq[; lery ij] lkekU; vkSj vi:i.k izfrcy nksuks dke djrs gSA
3 ,d eq[; lery ij dsoy vi:i.k izfrcy dke djrk gS
4 izfrcy dh lenSf"kd fLFkfr] funsZ’k ra= ls fujis{k gksrh gS
mi;qZDr dFkuks es ls dkSu &lk dkSu ls lgh gSA
1 and 4 rFkk
2 only dsoy
2 and 4 only dsoy 2 rFkk 4
2 and 3 rFkk
7

8. Consider the following statements/
1. On a principal plane, only normal stress acts
2. On a principal plane, both normal and shear stresses acts
3. On a principal plane, only shear stress acts/
4. Isotropic state of stress is independent of frame of reference/
Which of the above statement is/are correct/ fuEu dFkuksa ij fopkj djsA
1 ,d eq[; lery ij] dsoy lkekU; izfrcy dk;Z djrk gS
2 ,d eq[; lery ij] lkekU; vkSj vi:i.k izfrcy nksuks dke djrs gSA
3 ,d eq[; lery ij dsoy vi:i.k izfrcy dke djrk gS
4 izfrcy dh lenSf"kd fLFkfr] funsZ’k ra= ls fujis{k gksrh gS
mi;qZDr dFkuks es ls dkSu &lk dkSu ls lgh gSA
1 and 4 rFkk
2 only dsoy
2 and 4 only dsoy 2 rFkk 4
2 and 3 rFkk
8

9. If normal stresses due to longitudinal and transverse loads on a bar are 𝝈𝟏 and
𝝈𝟐 respectively, the normal component of the stress on an inclined plane θº to
the longitudinal load is/
;fn ,d ckj ij vuqnS/;Z vkSj vuqizLFk Hkkj ds dkj.k lekU; izfrcy dze’k% 𝝈𝟏
vkSj 𝝈𝟐 gks rks vuqnS/;Z Hkkj dh vkSj θº >qds ry ij izfrcy dk lkekU; ?kVd
gSA
𝛔𝟏𝐬𝐢𝐧 𝛉 × 𝛔𝟐𝐜𝐨𝐬𝛉
𝛔𝟏𝐬𝐢𝐧𝟐𝛉 + 𝛔𝟐𝐜𝐨𝐬𝟐𝛉
𝛔𝟏−𝛔𝟐 𝐬𝐢𝐧𝟐𝛉
𝟐
𝛔𝟏+𝛔𝟐 𝐬𝐢𝐧𝟐𝛉
9

10. If normal stresses due to longitudinal and transverse loads on a bar are 𝝈𝟏 and
𝝈𝟐 respectively, the normal component of the stress on an inclined plane θº to
the longitudinal load is/
;fn ,d ckj ij vuqnS/;Z vkSj vuqizLFk Hkkj ds dkj.k lekU; izfrcy dze’k% 𝝈𝟏
vkSj 𝝈𝟐 gks rks vuqnS/;Z Hkkj dh vkSj θº >qds ry ij izfrcy dk lkekU; ?kVd
gSA
𝛔𝟏𝐬𝐢𝐧 𝛉 × 𝛔𝟐𝐜𝐨𝐬𝛉
𝛔𝟏𝐬𝐢𝐧𝟐𝛉 + 𝛔𝟐𝐜𝐨𝐬𝟐𝛉
𝛔𝟏−𝛔𝟐 𝐬𝐢𝐧𝟐𝛉
𝟐
𝛔𝟏+𝛔𝟐 𝐬𝐢𝐧𝟐𝛉
10

11. The angle between the principle plane and the plane of maximum shear is/ eq[;
lery vkSj vf/kdre vi:i.k ds lery ds chp dk dks.k gksrk gS
90º
135º
60º
None of these/ bues ls dksbZ ugh
11

12. The angle between the principle plane and the plane of maximum shear is/ eq[;
lery vkSj vf/kdre vi:i.k ds lery ds chp dk dks.k gksrk gS
90º
135º
60º
None of these/ bues ls dksbZ ugh
12

13. Which of the following statements is true/
fuEufyf[kr es ls dkSu ls dFku lgh gSA
The sum of normal stresses is constant/ lkekU;r izfrcyksa dk ;ksx fu;r jgrk
gS
The sum of normal stresses is variable/ lkekU; izfrcyksa dk ;ksx pj gksrk gS
The sum of normal stresses is depends on the plane/ lkekU; izfrcyksa dk ;ksx
lery ij fuHkZj djrk gS
None of these/ buesa ls dksbZ ugh
13

14. Which of the following statements is true/
fuEufyf[kr es ls dkSu ls dFku lgh gSA
The sum of normal stresses is constant/ lkekU;r izfrcyksa dk ;ksx fu;r jgrk gS
The sum of normal stresses is variable/ lkekU; izfrcyksa dk ;ksx pj gksrk gS
The sum of normal stresses is depends on the plane/ lkekU; izfrcyksa dk ;ksx
lery ij fuHkZj djrk gS
None of these/ buesa ls dksbZ ugh
14

15. The tangential component of stress on an plane inclined θº to the direction of
the force, may be obtained by multiplying the normal stress by/ θº ij >qds gq,
lery ij izfrcy vkSj cy dh fn’kk dk Li’khZ; vo;o] lkekU; izfrcy dks--------ls
xq.kk djds izkIr fd;k tk ldrk gSA
A. sinθ B. cos θ
C. tan θ D. sin2θ
A only dsoy
C only dsoy
B only dsoy
D only dsoy
15

16. The tangential component of stress on an plane inclined θº to the direction of
the force, may be obtained by multiplying the normal stress by/ θº ij >qds gq,
lery ij izfrcy vkSj cy dh fn’kk dk Li’khZ; vo;o] lkekU; izfrcy dks--------ls
xq.kk djds izkIr fd;k tk ldrk gSA
A. sinθ B. cos θ
C. tan θ D. sin2θ
A only dsoy
C only dsoy
B only dsoy
D only dsoy
16

17. The ratio of tangential and normal components of a stress on an inclined plane
through θº to the direction of the force is…….. θº ij >qds izfrcy ds cy dh
fn’kk esa Li’kZT;k vkSj v/kksyEc ?kVd ds e/; vuqikr-------gksxkA
sin θ
cos θ
tan θ
cosec θ
17

18. The ratio of tangential and normal components of a stress on an inclined plane
through θº to the direction of the force is…….. θº ij >qds izfrcy ds cy dh
fn’kk esa Li’kZT;k vkSj v/kksyEc ?kVd ds e/; vuqikr-------gksxkA
sin θ
cos θ
tan θ
cosec θ
18

19. In a plane stress problem/ ,d lery izfrcy leL;k gS
1 Normal stress in the third direction is zero rhljh fn’kk es vfHkyac izfrcy
'kwU: gksrk gSA
2. Strain in the third direction is zero rhljs fn’kk esa fod`fr 'kwU; gksrh gSA
3. Strain in all direction is present/ fod`fr mifLFkr gksrh gS
4. Normal stresses in all directions are present lHkh fn’kkvksa esa lkekU;
izfrcy mifLFkr gksrs gSA
The correct answer is/lgh mRrj gS
1 and vkSj 4
2 and vkSj 4
1 and vkSj 3
19

20. In a plane stress problem/ ,d lery izfrcy leL;k gS
1 Normal stress in the third direction is zero rhljh fn’kk es vfHkyac izfrcy
'kwU: gksrk gSA
2. Strain in the third direction is zero rhljs fn’kk esa fod`fr 'kwU; gksrh gSA
3. Strain in all direction is present/ fod`fr mifLFkr gksrh gS
4. Normal stresses in all directions are present lHkh fn’kkvksa esa lkekU;
izfrcy mifLFkr gksrs gSA
The correct answer is/lgh mRrj gS
1 and vkSj 4
2 and vkSj 4
1 and vkSj 3
20

21. In an element the complimentary shear stresses are always/ ,d vo;o esa iwjd
drZu izfrcy lnSo gSA
Equal in sign/ fpUg esa leku
Equal in both magnitude and sign/ ifjek.k vkSj fpUg nksuks esa leku
Equal in magnitude but opposite in sign/ ifjek.k esa leku ysfdu fpUg es
foijhr
None of these/ mijksDr es ls dksbZ ugh
21

22. In an element the complimentary shear stresses are always/ ,d vo;o esa iwjd
drZu izfrcy lnSo gSA
Equal in sign/ fpUg esa leku
Equal in both magnitude and sign/ ifjek.k vkSj fpUg nksuks esa leku
Equal in magnitude but opposite in sign/ ifjek.k esa leku ysfdu fpUg es foijhr
None of these/ mijksDr es ls dksbZ ugh
22

23. A shear stress in a given plane will be automatically accompanied by a
balancing shear stress of equal magnitude in a------plane for equilibrium/ ,d fn,
x, lery es ,d vi:i.k izfrcy Lopkfyr :i ls leku ifj.kke ds ,d larqfyr vi:i.k izfrcy
}kjk ,d-----lery ij lkE;koLFkk esa vk tkrk gSA
Parallel/ lekukarj
Perpendicular/ yEco~r
45 degrees inclined/ 45 fMxzh >qdk gqvk
60 degrees inclined/ 60 fMxzh >qdk gqvk
23

24. A shear stress in a given plane will be automatically accompanied by a
balancing shear stress of equal magnitude in a------plane for equilibrium/ ,d fn,
x, lery es ,d vi:i.k izfrcy Lopkfyr :i ls leku ifj.kke ds ,d larqfyr vi:i.k izfrcy
}kjk ,d-----lery ij lkE;koLFkk esa vk tkrk gSA
Parallel/ lekukarj
Perpendicular/ yEco~r
45 degrees inclined/ 45 fMxzh >qdk gqvk
60 degrees inclined/ 60 fMxzh >qdk gqvk
24

25. If Mohr’s circle for two dimensional stress system has zero radius, both
principal stresses are/ ;fn f}&vk;keh izfrcy iz.kkyh ds fy, eksgj o`r dh f=T;k
'kwU; gS rks nksuksa eq[; izfrcy gksxsA
Of equal magnitude and of same sign/ leku ifjek.k vkSj leku fpUg ds
Of equal magnitude and of opposite sign/ leku ifjek.k vkSj foijhr fpUg ds
Equal to zero and shear stress is non zero/ 'kwU; ds cjkcj vkSj drZu izfrcy
v’kwU; gS
Equal to zero and shear stress is also equal to zero/ 'kwU; ds cjkcj vkSj drZu
izfrcy Hkh 'kwU; ds cjkcj gSA
25

26. If Mohr’s circle for two dimensional stress system has zero radius, both
principal stresses are/ ;fn f}&vk;keh izfrcy iz.kkyh ds fy, eksgj o`r dh f=T;k
'kwU; gS rks nksuksa eq[; izfrcy gksxsA
Of equal magnitude and of same sign/ leku ifjek.k vkSj leku fpUg ds
Of equal magnitude and of opposite sign/ leku ifjek.k vkSj foijhr fpUg ds
Equal to zero and shear stress is non zero/ 'kwU; ds cjkcj vkSj drZu izfrcy
v’kwU; gS
Equal to zero and shear stress is also equal to zero/ 'kwU; ds cjkcj vkSj drZu
izfrcy Hkh 'kwU; ds cjkcj gSA
26

27. The radius of Mohr’s circle, when a particle is subjected to pure shear stress 𝝉
is/ eksgj o`r dh f=T;k] tc ,d Hkkx (Particle) 'kq) drZu izfrcy 𝝉 ds v/khu
gksrk gSA
𝝉/2
𝝉
2 𝝉
0
27

28. The radius of Mohr’s circle, when a particle is subjected to pure shear stress 𝝉
is/ eksgj o`r dh f=T;k] tc ,d Hkkx (Particle) 'kq) drZu izfrcy 𝝉 ds v/khu
gksrk gSA
𝝉/2
𝝉
2 𝝉
0
28

29. The radius of Mohr’s circle for two equal unlike principal stresses of
magnitude p is/ p ifjek.k ds nks leku foijhr izd`fr ds eq[; izfrcyksa ds fy,
eksgj o`r dh f=T;k gksrh gS
p
p/2
0
None of these/ bues ls dksbZ ugh
29

30. The radius of Mohr’s circle for two equal unlike principal stresses of
magnitude p is/ p ifjek.k ds nks leku foijhr izd`fr ds eq[; izfrcyksa ds fy,
eksgj o`r dh f=T;k gksrh gS
p
p/2
0
None of these/ bues ls dksbZ ugh
30

31. For such element only under normal stresses, the radius of Mohr circle is/ ,sls
rRo tks dsoy lkekU; izfrcyksa ds v/khu gS] ds fy, eksgj o`r dh f=T;k gksrh
gS
𝝈
𝝈/2
2𝝈
0.6 𝝈
31

32. For such element only under normal stresses, the radius of Mohr circle is/ ,sls
rRo tks dsoy lkekU; izfrcyksa ds v/khu gS] ds fy, eksgj o`r dh f=T;k gksrh
gS
𝝈
𝝈/2
2𝝈
0.6 𝝈
32

33. Mohr’s circle for the state of stress defined by
𝟑𝟎 𝟎
𝟎 𝟑𝟎
MPa is circle with/ ,d
o`r ------ds lkFk izfrcy dh voLFkk dks
𝟑𝟎 𝟎
𝟎 𝟑𝟎
MPa ds :i esa ifjHkkf"kr
fd;k tkrk gSA
Center at (0,0) and radius 30 MPa/(0,0) ij dsUnz vkSj 30 MPa f=T;k
Center at (0,0) and radius 60 MPa/(0,0) ij dsUnz vkSj 60 MPa f=T;k
Center at (30,0) and radius 30 MPa/(30,0) ij dsUnz vkSj 30 MPa f=T;k
Center at (30,0) and zero radius (30,0) ij dsUnz vkSj 'kwU; f=T;k
33

34. Mohr’s circle for the state of stress defined by
𝟑𝟎 𝟎
𝟎 𝟑𝟎
MPa is circle with/ ,d
o`r ------ds lkFk izfrcy dh voLFkk dks
𝟑𝟎 𝟎
𝟎 𝟑𝟎
MPa ds :i esa ifjHkkf"kr
fd;k tkrk gSA
Center at (0,0) and radius 30 MPa/(0,0) ij dsUnz vkSj 30 MPa f=T;k
Center at (0,0) and radius 60 MPa/(0,0) ij dsUnz vkSj 60 MPa f=T;k
Center at (30,0) and radius 30 MPa/(30,0) ij dsUnz vkSj 30 MPa f=T;k
Center at (30,0) and zero radius (30,0) ij dsUnz vkSj 'kwU; f=T;k
34

35. In a plane strain problem in xy plane, the shear strain = 15×10-6 and the
normal strain in x and y direction is zero. For the strain, what is the diameter
of the Mohr’s circle of strain/ ,d xy Iysu esa lery fod`fr leL;k] drZu fod`fr =
15× 10-6 vkSj yEco~r fod`fr x vkSj y fn’kk esa ml fod`fr ds fy, 0 gSA ml
fod`fr ds fy, eksgj o`r dk O;kl D;k gksxkA
5×10-6
7.5×10-6
15×10-6
30×10-6
35

36. In a plane strain problem in xy plane, the shear strain = 15×10-6 and the
normal strain in x and y direction is zero. For the strain, what is the diameter
of the Mohr’s circle of strain/ ,d xy Iysu esa lery fod`fr leL;k] drZu fod`fr =
15× 10-6 vkSj yEco~r fod`fr x vkSj y fn’kk esa ml fod`fr ds fy, 0 gSA ml
fod`fr ds fy, eksgj o`r dk O;kl D;k gksxkA
5×10-6
7.5×10-6
15×10-6
30×10-6
36

37. A soil element is subjected to minor and major principal stress of 30 kPa and 50
kPa respectively. The maximum shear stress is/ ,d e`nk rRo dze’k% 30 kPa
vkSj 50 kPa ds U;wure vkSj vf/kdre eq[; izfrcy ds v/khu gSA vf/kdre vi:i.k
izfrcy-------gksxkA
10 kPa
40 kPa
80 kPa
20 kPa
37

38. A soil element is subjected to minor and major principal stress of 30 kPa and 50
kPa respectively. The maximum shear stress is/ ,d e`nk rRo dze’k% 30 kPa
vkSj 50 kPa ds U;wure vkSj vf/kdre eq[; izfrcy ds v/khu gSA vf/kdre vi:i.k
izfrcy-------gksxkA
10 kPa
40 kPa
80 kPa
20 kPa
38

39. Mohr’s circle is drawn for/ eksgj dk o`r fuEu ds fy, [khpk tkrk gSA
(1) A point/ ,d fcUnqa
(2) A square block/ ,d oxkZdkj CykWd
(3) A rectangular block/,d vk;rkdkj CykWd
(4) Isotropic material/ lenSf’kd inkFkZ
The correct answer is/ lgh mRrj gSA
1,2 and 3
2 and 4
1 and 4
2, 3 and 4
39

41. Mohr’s circle is drawn for/ eksgj dk o`r fuEu ds fy, [khpk tkrk gSA
(1) A point/ ,d fcUnqa
(2) A square block/ ,d oxkZdkj CykWd
(3) A rectangular block/,d vk;rkdkj CykWd
(4) Isotropic material/ lenSf’kd inkFkZ
The correct answer is/ lgh mRrj gSA
1,2 and 3
2 and 4
1 and 4
2, 3 and 4
41

42. Max shear stress theory of failure was postulated by/ vf/kdre drZu izfrcy
fl)kUr dk foQyrk fdlds }kjk izfrikfnr fd;k x;k gS
St. Venant/ lsaV osusaV
Rankine/ jSfdu
Castigliano/ dSfLVfXyvkuksa
Tresca/ VSªLdks
42

45. Max shear stress theory of failure was postulated by/ vf/kdre drZu izfrcy
fl)kUr dk foQyrk fdlds }kjk izfrikfnr fd;k x;k gS
St. Venant/ lsaV osusaV
Rankine/ jSfdu
Castigliano/ dSfLVfXyvkuksa
Tresca/ VSªLdks
45

46. A graphical Representation of the elastic failure theory is shown in the below
figure. The theory is called/ izR;kLFk foQyrk fl)kUr dk T;kferh; izn’kZu uhps
fp= esa fn[kk;k x;k gSA bl fl)kUr dks dgrs gSA
Maximum principal stress theory/ vf/kdre eq[; izfrcy fl)kar
Maximum shear stress theory/ vf/kdre drZu izfrcy fl)kar
Maximum shear strain energy theory/ vf/kdre drZu fod`fr ÅtkZ fl)kar
Maximum principal strain theory/ vf/kdre eq[; fod`fr fl)kr
46

48. A graphical Representation of the elastic failure theory is shown in the below
figure. The theory is called/ izR;kLFk foQyrk fl)kUr dk T;kferh; izn’kZu uhps
fp= esa fn[kk;k x;k gSA bl fl)kUr dks dgrs gSA
Diagram
Maximum principal stress theory/ vf/kdre eq[; izfrcy fl)kar
Maximum shear stress theory/ vf/kdre drZu izfrcy fl)kar
Maximum shear strain energy theory/ vf/kdre drZu fod`fr ÅtkZ fl)kar
Maximum principal strain theory/ vf/kdre eq[; fod`fr fl)kr
48

49. The locus of the end point of the resultant of the normal and tangential
components of the stress on an inclined plane is/ >qds ry ij izfrcy dk vfHkyEc
vkSj Li’khZ; ?kVdksa ds ifjek.k ds vUr fcUnqvks dk fcUnqiFk yksdl--------
gksrk gSA
Circle/ o`r
Parabola/ ijoy;
Ellipse/ nh/kZo`r
Straight line/lh/kh js[kk
49

50. The locus of the end point of the resultant of the normal and tangential
components of the stress on an inclined plane is/ >qds ry ij izfrcy dk vfHkyEc
vkSj Li’khZ; ?kVdksa ds ifjek.k ds vUr fcUnqvks dk fcUnqiFk yksdl--------
gksrk gSA
Circle/ o`r
Parabola/ ijoy;
Ellipse/ nh/kZo`r
Straight line/lh/kh js[kk
50

51. If Rankine’s criteria is applied for failure of brittle material, then which of the
following will be a necessary condition/ ;fn jSUdkbu dk eki/kju Hkaxqj
lkexzh ds foQyrk ij ykxw fd;k tkrk gS rc fuEufyf[kr esa ls dkSu vko’;d
'krZ gksxkA
Maximum shear stress/ vf/kdre drZu izfrcy
Maximum principal stress/ vf/kdre eq[; izfrcy
Maximum shear strain energy/ vf/kdre drZu fod`fr ÅtkZ
Maximum strain energy/ vf/kdre fod`fr ÅtkZ
51

52. If Rankine’s criteria is applied for failure of brittle material, then which of the
following will be a necessary condition/ ;fn jSUdkbu dk eki/kju Hkaxqj
lkexzh ds foQyrk ij ykxw fd;k tkrk gS rc fuEufyf[kr esa ls dkSu vko’;d
'krZ gksxkA
Maximum shear stress/ vf/kdre drZu izfrcy
Maximum principal stress/ vf/kdre eq[; izfrcy
Maximum shear strain energy/ vf/kdre drZu fod`fr ÅtkZ
Maximum strain energy/ vf/kdre fod`fr ÅtkZ
52

53. Maximum Shear Stress Theory is also known as/ vf/kdre drZu izfrcy fl)kUr
dks fuEu :i esa Hkh tkuk tkrk gSA
Rankine’s Theory/ jSUdkbu dk fl)kUr
Coulomb’s Theory/ dwykEc dk fl)kUr
St. Venant’s Theory/ lsaV osukV dk fl)kUr
Beltrami and Haigh’s Theory/ csyVªkeh vkSj gsx dk fl)kUr
53

54. Maximum Shear Stress Theory is also known as/ vf/kdre drZu izfrcy fl)kUr
dks fuEu :i esa Hkh tkuk tkrk gSA
Rankine’s Theory/ jSUdkbu dk fl)kUr
Coulomb’s Theory/ dwykEc dk fl)kUr
St. Venant’s Theory/ lsaV osukV dk fl)kUr
Beltrami and Haigh’s Theory/ csyVªkeh vkSj gsx dk fl)kUr
54

55. Which theory of failure will you use for aluminium components under steady
loading/ fLFkj Hkkj ds v/khu ,Y;qfefu;e ?kVdksa dh [kjkch ds fy, bues ld
fdl fl)kar dk iz;ksx gksxkA
Principal stress theory/ eq[; izfrcy fl)kar
Principal strain theory/ eq[; fod`fr fl)kar
Strain energy theory/ fod`fr ÅtkZ fl)kar
Maximum shear stress theory/ vf/kdre vi:i.k izfrcy fl)kar
55

56. Which theory of failure will you use for aluminium components under steady
loading/ fLFkj Hkkj ds v/khu ,Y;qfefu;e ?kVdksa dh [kjkch ds fy, bues ld
fdl fl)kar dk iz;ksx gksxkA
Principal stress theory/ eq[; izfrcy fl)kar
Principal strain theory/ eq[; fod`fr fl)kar
Strain energy theory/ fod`fr ÅtkZ fl)kar
Maximum shear stress theory/ vf/kdre vi:i.k izfrcy fl)kar
56

57. In case of biaxial stress, the maximum value of shear stress is given by/ f}v{kh;
izfrcy dh fLFkfr es] vi:i.k izfrcy dk vf/kdre eku fdlds }kjk fn;k tkrk gS
Difference of the normal stresses/ lkekU; izfrcyksa esa vUrj
Sum of the normal stresses/ lkekU; izfrcyksa dk ;ksx
Half the sum of the normal stresses/ lkekU; izfrcyksa ds ;ksx dk vk/kk
None of these/ buesa ls dksbZ ugh
57

58. The tensile stress at a point across two mutual perpendicular planes are 150
N/mm2 and 75 N/mm2. What is the normal stress on the plane inclined at 35º to
axis of the minor stress/ nks ijLij yaco~r ryks ij] ,d fcUnw ij ruu ncko 150
N/mm2 vkSj 75 N/mm2 gSA de ncko ds v{k dh vkSj 35º >qds ry ij lkekU;
ncko fdruk gksxkA
120.50 N/mm2
128.64 N/mm2
125.33 N/mm2
115 N/mm2
58

59. Two dimensional stress at a point is given by
(Notations have their usual meaning)
,d fcUnw ij f}vk;keh izfrcy fn;k x;k gSA
¼ladsrksa dk vFkZ ;gkW iz;ksx fd;k x;k gSA½
𝛔𝐱𝐱 𝛕𝐲𝐲
𝛕𝐲𝐱 𝛔𝐲𝐲
=
𝟏𝟎𝟎 𝟑𝟎
−𝟑𝟎 𝟐𝟎
𝐌𝐏𝐚
The maximum shear stress is given by /vf/kdre drZu izfrcy fn;k tk;sxkA
50 MPa
75 MPa
100MPa
110 MPa
59

60. Two dimensional stress at a point is given by
(Notations have their usual meaning)
,d fcUnw ij f}vk;keh izfrcy fn;k x;k gSA
¼ladsrksa dk vFkZ ;gkW iz;ksx fd;k x;k gSA½
𝛔𝐱𝐱 𝛕𝐲𝐲
𝛕𝐲𝐱 𝛔𝐲𝐲
=
𝟏𝟎𝟎 𝟑𝟎
−𝟑𝟎 𝟐𝟎
𝐌𝐏𝐚
The maximum shear stress is given by /vf/kdre drZu izfrcy fn;k tk;sxkA
50 MPa
75 MPa
100MPa
110 MPa
60

61. If the ratio of two principal stresses is ½, what is the ratio of minimum
principal stress to maximum shear stress/ ;fn nks eq[; izfrcyksa dk vuqikr
1@2 gS] rks U;wure eq[; izfrcy vkSj vf/kdre drZu izfrcy dk vuqikr gksxkA
1/2
1
2
4
61

62. If the ratio of two principal stresses is ½, what is the ratio of minimum
principal stress to maximum shear stress/ ;fn nks eq[; izfrcyksa dk vuqikr
1@2 gS] rks U;wure eq[; izfrcy vkSj vf/kdre drZu izfrcy dk vuqikr gksxkA
1/2
1
2
4
62

63. When a body is subjected to a direct tensile stress (p) in one plane accompanied
by a simple shear stress (q), the maximum normal stress is/;fn ,d fi.M ij ,d ry ij
(p) ruu izfrcy rFkk vi:i.k izfrcy (q) yxk gqvk gS] vf/kdre vfHkyEco`r izfrcy
gksxkA
𝑷
𝟐
+
𝟏
𝟐
𝒑𝟐 + 𝟒𝒒𝟐
𝑷
𝟐
−
𝟏
𝟐
𝒑𝟐 + 𝟒𝒒𝟐
𝑷
𝟐
+
𝟏
𝟐
𝒑𝟐 − 𝟒𝒒𝟐
𝑷
𝟐
−
𝟏
𝟐
𝒑𝟐 − 𝟒𝒒𝟐
63

64. When a body is subjected to a direct tensile stress (p) in one plane accompanied
by a simple shear stress (q), the maximum normal stress is/;fn ,d fi.M ij ,d ry ij
(p) ruu izfrcy rFkk vi:i.k izfrcy (q) yxk gqvk gS] vf/kdre vfHkyEco`r izfrcy
gksxkA
𝑷
𝟐
+
𝟏
𝟐
𝒑𝟐 + 𝟒𝒒𝟐
𝑷
𝟐
−
𝟏
𝟐
𝒑𝟐 + 𝟒𝒒𝟐
𝑷
𝟐
+
𝟏
𝟐
𝒑𝟐 − 𝟒𝒒𝟐
𝑷
𝟐
−
𝟏
𝟐
𝒑𝟐 − 𝟒𝒒𝟐
64