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Complex Stresses · Strength of Materials · GATE ME

Marks 1
17
Marks 2
13
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Marks 1

1

The yield stress of a metal in uniaxial tension is 200 MPa . According to von Mises yield criterion, the yield stress (in MPa) of the metal in pure shear is closest to

GATE ME 2025
2

A metallic square plate is subjected to a uniform hydrostatic pressure $(P)$. Choose the correct Mohr's circle representing the state of stress at any point in the plate from the options given below.

For the Mohr's circle, normal stress is positive towards right and shear stress is positive in the upward direction.

GATE ME 2025
3

The phases present in pearlite are

GATE ME 2024
4
The principal stresses at a point P in a solid are 70 MPa, −70 MPa and 0. The yield stress of the material is 100 MPa. Which prediction(s) about material failure at P is/are CORRECT? 
GATE ME 2023
5

Which of the plot(s) shown is/are valid Mohr’s circle representations of a plane stress state in a material? (The center of each circle is indicated by O.)

GATE ME 2023 Strength of Materials - Complex Stresses Question 4 English
GATE ME 2023
6
A structural member under loading has a uniform state of plane stress which in usual notations is given by σx = 3P, σy = -2P and τxy = √2 P, where P > 0. The yield strength of the material is 350 MPa. If the member is designed using the maximum distortion energy theory, then the value of P at which yielding starts (according to the maximum distortion energy theory) is
GATE ME 2022 Set 2
7
Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE?
GATE ME 2022 Set 1
8
The state of stress at a point is $${\sigma _x} = {\sigma _y} = {\sigma _z} = {\tau _{xz}} = {\tau _{zx}} = {\tau _{yz}} = {\tau _{zy}} = 0$$ and $${\tau _{xy}} = {\tau _{yx}} = 50$$MPa. The maximum normal stress (in MPa) at the point is _________.
GATE ME 2017 Set 2
9
The state of stress at a point on an element is shown in figure (a). The same state of stress is shownin another coordinate system in figure (b). GATE ME 2016 Set 3 Strength of Materials - Complex Stresses Question 23 English

The components $$\left( {{\tau _{xx,}}{\tau _{yy,}}{\tau _{xy}}} \right)$$ are given by

GATE ME 2016 Set 3
10
A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is
GATE ME 2016 Set 2
11
A thin plate of uniform thickness is subject to pressure as shown in the figure below GATE ME 2014 Set 2 Strength of Materials - Complex Stresses Question 24 English

Under the assumption of plane stress, which one of the following is correct?

GATE ME 2014 Set 2
12
The state of plane-stress at a point is given by $${\sigma _x}\,\, = 200$$ MPa, $${\sigma _x}\,\, = 100$$ MPa and $${\tau _{xy}} = 100$$ MPa. The maximum shear stress (in MPa) is
GATE ME 2010
13
If the principal stresses in a plane stress problem are $${\sigma _1}$$ $$= 100$$ MPa, $${\sigma _2}$$ $$= 40$$ MPa, the magnitude of the maximum shear stress (in MPa) wil be
GATE ME 2009
14
The figure shows the state of stress at a certain point in a stressed body. The magnitudes of normal stresses in the $$x$$ and $$y$$ directions are $$100$$ MPa and $$20$$ MPa respectively. The radius of Mohr's stress circle representing this state of stress is GATE ME 2004 Strength of Materials - Complex Stresses Question 27 English
GATE ME 2004
15
If the two principal strains at a point are 1000 $$ \times $$ 10-6 and -600 $$ \times $$ 10-6, then the maximum shear strain is
GATE ME 1996
16
An elastic body is subjected to a tensile stress $$X$$ in a particular direction and a compressive stress $$Y$$ in its perpendicular direction. $$X$$ and $$Y$$ are unequal in magnitude. On the plane of maximum shear stress in the body there will be:
GATE ME 1989
17
A cylindrical elastic body subjected to pure torsion about its axis develops:
GATE ME 1989

Marks 2

1

The state of stress at a point is shown in the figure given below. Under plane stress assumption, the normal strain along the thickness direction $\left(\varepsilon_{z z}\right)$ is _________ (rounded off to 2 decimal places).

Use the Young's Modulus $E=200 \mathrm{GPa}$ and Poisson's ratio $v=0.27$.

GATE ME 2025 Strength of Materials - Complex Stresses Question 2 English
GATE ME 2025
2

A linear elastic structure under plane stress conditions is subjected to two sets of loading, I and II. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stress σxx is ________

GATE ME 2022 Set 2 Strength of Materials - Complex Stresses Question 6 English
GATE ME 2022 Set 2
3
A rectangular region in a solid is in a state of plane strain. The $$(x,y)$$ coordinates of the corners of the undeformed rectangle are given by $$P(0,0), Q(4,0), R(4,3), S(0,3).$$ The rectangle is subjected to uniform strains, $${\varepsilon _{xx}} = 0.001,\,\,{\varepsilon _{yy}} = 0.002,\,\,{\gamma _{xy}} = 0.003.$$ The deformed length of the elongated diagonal, upto three decimal places, is ______________ units.
GATE ME 2017 Set 1
4
In a plane stress condition, the components of stress at a point are $${\sigma _x} = 20$$ MPa, $${\sigma _y} = 80$$ MPa and $${\tau _{xy}} = 40$$ MPa, The maximum shear stress (in MPa) at the point is
GATE ME 2015 Set 2
5
The state of stress at a point under plane stress condition is
$${\sigma _{xx}} = 40\,$$ MPa, $${\sigma _{yy}} = 100\,$$ MPa & $${\tau _{xy}} = 40$$ MPa.
The radius of the Mohr's circle representing the given state of stress in MPa is
GATE ME 2012
6
A two dimensional fluid element rotates like a rigid body. At a point within the element, the pressure is $$1$$ unit. Radius of the Mohr's circle, characterizing the state at that point, is
GATE ME 2008
7
A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It further subjected to a torque of 10 KN-m. The maximum principal stress experienced on the shaft is closest to
GATE ME 2008
8
The Mohr's circle of plane stress for a point in a body is shown. The design is to be done on the basis of the maximum shear stress theory for yielding. Then, yielding will just begin if the designer chooses a ductile material whose yield strength is GATE ME 2004 Strength of Materials - Complex Stresses Question 15 English
GATE ME 2004
9
The state of stress at a point P in a two dimensional loading is such that the Mohr's circle is a point located at 175 MPa on the positive normal stress axis.

The distance of maximum and minimum principal stresses at the point ''P'' from the Mohr's circle are

GATE ME 2003
10
The state of stress at a point P in a two dimensional loading is such that the Mohr's circle is a point located at 175 MPa on the positive normal stress axis.

The maximum and minimum principal stresses respectively from the Mohr's circle are

GATE ME 2003
11
A shaft subjected to torsion experiences a pure shear stress $$\tau $$ on the surface. The maximum principal stress on the surface which is at $$45$$0 to the axis will have a value
GATE ME 2003
12
At a point in a stressed body the state of stress on two planes $$45$$0 apart is as shown below. Determine the two principal stresses GATE ME 1993 Strength of Materials - Complex Stresses Question 19 English
GATE ME 1993
13
The three - dimensional state of stress at a point is given by: $$$\left[ \sigma \right] = \left[ {\matrix{ {30} & {10} & { - 10} \cr {10} & 0 & {20} \cr { - 10} & {20} & 0 \cr } } \right]MN/{m^2}$$$

The shear stress in the $$x-y$$ plane at the same point is then equal to

GATE ME 1990
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