# GATE Questions & Answers of Stress and Strain, Elastic Constants, Poisson's Ratio

## What is the Weightage of Stress and Strain, Elastic Constants, Poisson's Ratio in GATE Exam?

Total 22 Questions have been asked from Stress and Strain, Elastic Constants, Poisson's Ratio topic of Mechanics of Materials subject in previous GATE papers. Average marks 1.41.

In a linearly hardening plastic material, the true stress beyond initial yielding

The true stress $\left(\sigma\right)$ - true strain $\left(\varepsilon\right)$ diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to stress of 500 MPa and strain of 0.5. Then from point A, there is unloading up to point B, i.e., to stress of 100 MPa. Given that the Young’s modulus E = 200 GPa, the natural strain at point B $\left(\varepsilon_B\right)$ is _________ (correct to three decimal places). A bar is compressed to half of its original length. The magnitude of true strain produced in the deformed bar is _________________ (correct to two decimal places).

A bimetallic cylindrical bar of cross sectional area 1 m2 is made by bonding Steel (Young’s modulus = 210 GPa) and Aluminium (Young’s modulus = 70 GPa) as shown in the figure. To maintain tensile axial strain of magnitude $10^{-6}$ in Steel bar and compressive axial strain of magnitude $10^{-6}$ in Aluminum bar, the magnitude of the required force $P$ (in kN) along the indicated direction is The true stress (in MPa) versus true strain relationship for a metal is given by

$\sigma=1020\varepsilon^{0.4}$ .

The cross-sectional area at the start of a test (when the stress and strain values are equal to zero) is 100 mm2 . The cross-sectional area at the time of necking (in mm2 ) is ________ (correct to two decimal places)

The Poisson's ratio for a perfectly incompressible linear elastic  material is

The value of true strain produced in compressing a cylinder to half its original length is

In the figure, the load P = 1 N, length L = 1 m, Young’s modulus E = 70 GPa, and the cross-section of the links is a square with dimension 10 mm × 10 mm. All joints are pin joints. The stress (in Pa) in the link AB is ___________

(Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

A square plate of dimension L × L is subjected to a uniform pressure load p = 250 MPa on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus E = 200 GPa. The deformed shape is a square of dimension $L-\;2\;\delta$. If $L=\;2\;\mathrm m$ and $\delta=0.001\;\mathrm m$, the poisson's ratio of the plate material is _________

Which of the following types of stress strain relationship best describes the behaviour of brittle materials, such as ceramics and thermosetting plastics, ($\sigma$ stress and $\epsilon$ = strain)?

A rod is subjected to a un-axial load within linear elastic limit. When the change in the stress is 200 MPa, the change in the strain is 0.001. If the Poisson’s ratio of the rod is 0.3, the modulus of rigidity ( in GPa) is______

For the given fluctuating fatigue load, the value of stress amplitude and stress ratio are respectively. A metallic  rod of 500 mm  length and 50mm diameter when subjected to a tensile force of 100KN at the ends,experinces an increse an its length by 0.5mm and a reduction in its diameter by 0.015mm.The poission's ratio of the road material is__________

A metal rod of initial length L0 is subjected to a drawing process. The length of the rod at any instant is given by the expression, L(t)=L0(1+t2), where t is the time in minutes. The true strain rate (in min−1) at the end of one minute is _______

A thin plate of uniform thickness is subject to pressure as shown in the figure below Under the assumption of plane stress, which one of the following is correct?

The relationship between true strain (${\epsilon }_{T}$) and engineering strain (${\epsilon }_{E}$) in a uniaxial tension test is given as

If the Poisson's ratio of an elastic material is 0.4, the ratio of modulus of rigidity to Young's modulus is _______

The number of independent elastic constants required to define the stress-strain relationship for an isotropic elastic solid is _______

A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young’s modulus of the material varies linearly from E1 to E2 along the length of the rod, the normal stress developed at the section-SS is The homogeneous state of stress for a metal part undergoing plastic deformation is

$T=\left(\begin{array}{ccc}10& 5& 0\\ 5& 20& 0\\ 0& 0& -10\end{array}\right)$,

where the stress component values are in MPa. Using von Mises yield criterion, the value of estimated shear yield stress, in MPa is