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Strength of Materials Or Solid Mechanics
Centroid and Moment of InertiaTorsionPure BendingShear Stress In BeamsStrain Energy MethodColumns and StrutsComplex StressDeflection of BeamsThin CylinderSimple StressesShear Force and Bending MomentPropped Cantilever Beam
Complex Stress
Practice Questions
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 7 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 17 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 16 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

Let the state of stress at a point in a body be the difference of two plane states of stress shown in the figure. Consider all the possible planes perpendicular to the $x-y$ plane and passing through that point. The magnitude of the maximum compressive stress on any such plane is $k \sigma_0$, where $k$ is equal to _________ (round off to one decimal place).

GATE CE 2025 Set 2 Strength of Materials Or Solid Mechanics - Complex Stress Question 1 English
GATE CE 2025 Set 2
2

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 5 English
GATE CE 2024 Set 1
3

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 3 English
GATE CE 2023 Set 2
4
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
5

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 4 English
GATE CE 2023 Set 1
6
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 10 English

The shear stress $$\tau $$ is

GATE CE 2016 Set 2
7
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 11 English
GATE CE 2014 Set 2
8
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
9
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 8 English

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

GATE CE 2004
10
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
11
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
12
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
13
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