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Complex Stress Β· Strength of Materials Or Solid Mechanics Β· GATE CE

Marks 1
12
Marks 2
12
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Marks 1

1

The three-dimensional state of stress at a point is given by

$$\sigma = \begin{pmatrix} 10 & 0 & 0 \\ 0 & 40 & 0 \\ 0 & 0 & 0 \end{pmatrix} \text{ MPa.}$$

The maximum shear stress at the point is

GATE CE 2024 Set 1
2

Stresses acting on an infinitesimal soil element are shown in the figure (with $$\sigma$$z > $$\sigma$$x). The major and minor principal stresses are $$\sigma$$1 and $$\sigma$$3, respectively. Considering the compressive stresses as positive, which one of the following expressions correctly represents the angle between the major principal stress plane and the horizontal plane?

GATE CE 2022 Set 2 Strength of Materials Or Solid Mechanics - Complex Stress Question 6 English

GATE CE 2022 Set 2
3
Two triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface, $${\sigma _n}$$ is _____$$MPa.$$ GATE CE 2015 Set 1 Strength of Materials Or Solid Mechanics - Complex Stress Question 16 English
GATE CE 2015 Set 1
4
For the plane stress situation shown in the figure, the maximum shear stress and the plane on which it acts are: GATE CE 2015 Set 2 Strength of Materials Or Solid Mechanics - Complex Stress Question 15 English
GATE CE 2015 Set 2
5
If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cube is $$p,$$ then the maximum shear stress developed inside the cube is
GATE CE 2012
6
The major and minor principal stresses at a point are $$3MPa$$ and $$-3MPa$$ respectively. The maximum shear stress at the point is
GATE CE 2010
7
Consider the following statements:
$$1.$$ On a principal plane, only normal stress acts
$$2.$$ On a principal plane, both normal and shear stresses act
$$3.$$ On a principal plane, only shear stress acts
$$4.$$ Isotropic state of stress is independent of frame of reference.

Which of the above statements is/are correct ?

GATE CE 2009
8
An axially loaded bar is subjected to a normal stress of $$173$$ $$MPa.$$ The maximum shear stress in the bar is
GATE CE 2007
9
Mohr's cicle for the state of stress defined by $$\left[ {\matrix{ {30} & 0 \cr 0 & {30} \cr } } \right]$$ $$MPa$$ is a circle with
GATE CE 2006
10
The components of strain tensor at a point in the plane strain case can be obtained by measuring longitudinal strain in following directions.
GATE CE 2005
11
The symmetry of stress tensor at a point in the body under equilibrium is obtained from
GATE CE 2005
12
A small element at the critical section of component is in a state of stress with the two principal stresses being $$360$$ $$MPa$$ and $$140$$ $$MPa$$ . The maximum shear stress is
GATE CE 1997

Marks 2

1

Find the correct match between the plane stress states and the Mohr’s circles.

GATE CE 2024 Set 1 Strength of Materials Or Solid Mechanics - Complex Stress Question 4 English
GATE CE 2024 Set 1
2

In a two-dimensional stress analysis, the state of stress at a point is shown in the figure. The values of length of PQ, QR, and RP are 4, 3, and 5 units, respectively. The principal stresses are ________. (round off to one decimal place)

GATE CE 2023 Set 2 Strength of Materials Or Solid Mechanics - Complex Stress Question 2 English
GATE CE 2023 Set 2
3
A 2D thin plate with modulus of elasticity, 𝐸 = 1.0 N/m2, and Poisson’s ratio, πœ‡ = 0.5, is in plane stress condition. The displacement field in the plate is given by 𝑒 = 𝐢π‘₯2𝑦 and 𝑣 = 0, where 𝑒 and 𝑣 are displacements (in m) along the 𝑋 and π‘Œ directions, respectively, and 𝐢 is a constant (in mβˆ’2). The distances x and y along X and Y, respectively, are in m. The stress in the 𝑋 direction is πœŽπ‘‹π‘‹ = 40π‘₯𝑦 N/m2, and the shear stress is πœπ‘‹π‘Œ = 𝛼π‘₯2 N/m2. What is the value of 𝛼 (in N/m4, in integer)? ________
GATE CE 2023 Set 2
4

The infinitesimal element shown in the figure (not to scale) represents the state of stress at a point in a body. What is the magnitude of the maximum principal stress (in N/mm2, in integer) at the point? ________

GATE CE 2023 Set 1 Strength of Materials Or Solid Mechanics - Complex Stress Question 3 English
GATE CE 2023 Set 1
5
For the stress state (in MPa) shown in the figure, the major principal stress is 10 MPa. GATE CE 2016 Set 2 Strength of Materials Or Solid Mechanics - Complex Stress Question 9 English

The shear stress $$\tau $$ is

GATE CE 2016 Set 2
6
For the state of plane stress (in $$MPa$$) shown in the figure below, the maximum shear stress (in $$MPa$$) is ___________ GATE CE 2014 Set 2 Strength of Materials Or Solid Mechanics - Complex Stress Question 10 English
GATE CE 2014 Set 2
7
The state of $$2D$$-stress at a point is given by the following matrix of stresses: $$$\left[ {\matrix{ {{\sigma _{xx}}} & {{\sigma _{xy}}} \cr {{\sigma _{xy}}} & {{\sigma _{yy}}} \cr } } \right] = \left[ {\matrix{ {100} & {30} \cr {30} & {20} \cr } } \right]MPa$$$

What is the magnitude of maximum shear stress in $$MPa$$ ?

GATE CE 2013
8
In a two dimensional analysis, the state of stress at a point is shown below. GATE CE 2004 Strength of Materials Or Solid Mechanics - Complex Stress Question 7 English

If $$\sigma = 120\,\,MPa$$ and $${\tau _{xy}} = 70\,\,MPa,\,\,{\sigma _x}$$ and $${\sigma _y},$$ are respectively

GATE CE 2004
9
If principle stresses in two-dimensional case are $$\left( - \right)\,\,10\,MPa$$ and $$20$$ $$MPa$$ respectively, then maximum shear stress at the point is
GATE CE 2004
10
The state of two dimensional stresses acting on a concrete lamina consists of a direct tensile stress, $${\sigma _x} = 1.5\,\,N/m{m^2},$$ and shear stress, $$\tau = 1.20\,N/m{m^2},$$ which cause cracking of concrete. Then the tensile strength of the concrete in $$N/m{m^2}$$ is
GATE CE 1994
11
Which of the following Mohr's circles shown below qualitatively and correctly represents the state of plane stress at a point in a beam above the neutral axis, where it is subjected to combined shear and bending compressive stresses
GATE CE 1993
12
The magnitude of the only shear stresses acting at a point in plane stress situation is $$7.5\,N/n{m^2}.$$ The magnitudes of the principle stresses will be:
GATE CE 1990
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