PRINCIPAL STRAINS MULTIPLE CHOICE QUESTIONS (MCQ) WITH ANSWERS
PRINCIPAL STRAINS
MULTIPLE CHOICE QUESTIONS
(MCQ) WITH ANSWERS
MCQ are helpful in understanding Principal
Strains. It also increases the level of clarity.
Stresses are not measurable. Strains are
measured with mechanical and electrical
strain gauges. Principal stresses are found
from strains. Planes of principal strains are
same as the planes of principal stresses.
These planes are at right angles to each
other. These planes carry zero shear strain.
Mohr’ s strain circle is drawn from
complex strains and from principal strains
respectively.

Principal strain is

€_{x}

€_{y}

γ

None
ANS: (d)

Symbols for principal strains are

€_{1}, €_{2} and €_{3}

€_{x}, €_{y} and €_{z}

Both (a) & (b)

None
ANS: (a)

Units of principal strains are

mm

m

Both (a) & (b)

None
ANS: (d)

Units of principal strains are

Radians

Degrees

No units

None
ANS: (c)

Principal strains causes

Deformation

Distortion

Both (a) & (b)

None
ANS: (a)

Principal strains can be found from

Principal stresses

Complex stresses

Both (a) &(b)

None
ANS: (c)

Principal strains are

Tensile strain

Compressive strain

Both (a) & (b)

None
ANS: (c)

Strains are measured with

Pressure gauge

Temperature gauge

Both (a) & (b)

None
ANS: (d)

Strains can be measured with

Mechanical strain gauges

Electrical strain gauges

Both (a) & (b)

None
ANS: (c)

Principal strains are found from

Mohr’s strain circle

Principal stresses

Both (a) & (b)

None
ANS: (c)

Principal strains are

Maximum normal strain

Minimum normal strain

Both (a) & (b)

None
ANS: (c)

The directions of principal strains are in the direction of

Principal stresses

Maximum shear stresses

Both (a) & (b)

None
ANS: (a)

Shear strain in the direction of principal strain is

Maximum

Minimum

Zero

None
ANS: (c)

The angles among the three principal strains are

30^{0}

60^{0}

75^{0}

None
ANS: (d)

The angles among the principal strains are

90^{0}

120^{0}

180^{0}

None
ANS: (a)

Principal strains from the three tensile principal stresses are

Firstly €_{1} = σ_{1}/E µσ_{2} /E – µσ_{3} /E, €_{2} = σ_{1}/E µσ_{2} /E – µσ_{3} /E, €_{3} = σ_{3}/E µσ_{1} /E – µσ_{2} /E

Secondly €_{1} = σ_{1}/E µσ_{2} /E – µσ_{3} /E, €_{2} = σ_{2 }/E µσ_{3} /E – µσ_{1} /E and €_{3} = σ_{3}/E µσ_{1} /E – µσ_{2} /E

Thirdly €_{1} = σ_{1}/E µσ_{2} /E – µσ_{3} /E, €_{2} = σ_{2}/E µσ_{3} /E – µσ_{1} /E and €_{3} = σ_{3}/E µσ_{1} /E – µσ_{3} /E

None
ANS: (b)

Principal strains from a 2dimensional strained element under complex strains €_{x}, €_{y} and γ are

Firstly +[(€_{x}–€_{y})^{2} +(γ)^{2}]^{5} and –[(€_{x}–€_{y})^{2} +(γ)^{2}]^{0.5}

Secondly +[(€_{x}–€_{y})^{2} +(γ)^{2}]^{5} and –[(€_{x}–€_{y})^{2} +(γ/2)^{2}]^{0.5}

Thirdly +(1/2)[(€_{x}–€_{y})^{2} +(γ)^{2}]^{5} and –(1/2)[(€_{x}–€_{y})^{2} +(γ/2)^{2}]^{0.5}

None
ANS: (c)

As per maximum principal strain theory for a brittle material, say €_{1} being the largest with σ1, σ2 and σ3 tensile and
σ1> σ2 > σ3

Firstly σ_{1}/E µσ_{2} /E – µσ_{3} /E =σ _{ult }/(FOS x E)

Secondly σ_{1}/E µσ_{2} /E – µσ_{3} /E =σ _{yp }/(FOS x E)

Thirdly σ_{1}/E µσ_{2} /E – µσ_{3} /E =σ _{elastic limit }/(FOS x E)

None
ANS: (a)

As per maximum principal strain theory for a ductile material, say €_{1} being the largest with σ1, σ2 and σ3 tensile and σ1> σ2 > σ3

Firstly σ_{1}/E µσ_{2} /E – µσ_{3} /E =σ _{ult }/(FOS x E)

Secondly σ_{1}/E µσ_{2} /E – µσ_{3} /E =σ _{yp }/(FOS x E)

Thirdly σ_{1}/E µσ_{2} /E – µσ_{3} /E =σ _{elastic limit }/(FOS x E)

None
ANS: (b)

As per maximum principal strain energy theory for a brittle material, say €_{1} being the largest with σ1, σ2 and σ3 tensile and σ_{1}> σ_{2} > σ_{3}

Firstly (1/2)(€_{1}σ_{1}+ €_{2}σ_{2}+ €_{3}σ_{3}) =σ^{2}_{ult }/2E

Secondly (1/2)(€_{1}σ_{1}+ €_{2}σ_{2}+ €_{3}σ_{3}) =σ^{2}_{yp }/2E

Thirdly (1/2)(€_{1}σ_{1}+ €_{2}σ_{2}+ €_{3}σ_{3}) =σ^{2}_{elastic limit }/2E

None
ANS: (a)

As per maximum principal strain energy theory for a ductile material, say €_{1} being the largest with σ1, σ2 and σ3 tensile and σ_{1}> σ_{2} > σ_{3}

Firstly (1/2)(€_{1}σ_{1}+ €_{2}σ_{2}+ €_{3}σ_{3}) =σ^{2}_{ult }/2E

Secondly (1/2)(€_{1}σ_{1}+ €_{2}σ_{2}+ €_{3}σ_{3}) =σ^{2}_{yp }/2E

Thirdly (1/2)(€_{1}σ_{1}+ €_{2}σ_{2}+ €_{3}σ_{3}) =σ^{2}_{elastic limit }/2E

None
ANS: (b)
22. For a 3 dimensional complex strained body, the number of Mohr’s strain circles is

3

6

9

None
ANS: (a)

For drawing the Mohr’s strain circle from complex strains, replace

Firstly σ_{x}=€_{x}, σ_{y} =€_{y} and τ =γ

Secondly σ_{x}=€_{x}, σ_{y} =€_{y} and τ =γ/2

Thirdly σ_{x}=€_{x}, σ_{y} =€_{y} and τ =2γ

None
ANS: (b)

For drawing the Mohr’s strain circle from principal strains, replace

Firstly σ_{1}=€_{1}, σ_{2} =€_{2} and τ=γ

Secondly σ_{1}=€_{1}, σ_{2} =€_{2} and τ=γ/2

Thirdly σ_{1}=€_{1}, σ_{2} =€_{2} and τ=0

None
ANS: (c)

Plane of maximum principal strain carries

Maximum shear strain

Zero shear strain

Can’t say

None
ANS: (b)

In a two dimensional strain system, the number of principal planes of strain is

1

2

3

None
ANS: (b)

When principal strain are like and equal, the maximum shear strain is

γ

2γ

γ/2

None
ANS: (d)

When principal strain are like and equal, the maximum shear strain is

Infinity

Zero

–infinity

None
ANS: (b)

When principal strains are like and equal, the Mohr’s strain circle is a point. Then Mohr’s point strain circle

Coincides with pole

Do not coincide with pole

Passes though the point of maximum shear strain

None
ANS: (b)
https://mesubjects.net/wpadmin/post.php?post=4223&action=edit MCQ PRINCIPAL STRESSES
https://mesubjects.net/wpadmin/post.php?post=13392&action=edit MCQ SIMPLE STRAINS