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.)
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)?
Brittle materials fail without deformation ( $\delta l\approx0$ ) .So the value of strain is very low. Strain is lowest in the Fig D.
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______
$\sigma=200\;MPa\;\;,\;\varepsilon=0.001\;\;,\;\mu=0.3\;,\;G=?$
E=G/$\varepsilon$
=200/0.001=200 x $10^3$ MPa = 200 GPa
Modules of rigidity (G) = $\frac E{2(1+\mu)}$
=$\frac E{2(1+0.3)}=76.92\;GPa\;.$
For the given fluctuating fatigue load, the value of stress amplitude and stress ratio are respectively.
Stress amplitude=$\frac{6max-6min}2=\frac{250-50}2=100\;Mpa$
Stress ratio = $\frac{6min}{6max}=\frac{50}{250}=0.2$ .
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 L_{0} is subjected to a drawing process. The length of the rod at any instant is given by the expression, L(t)=L_{0}(1+t^{2}), 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 E_{1} to E_{2} 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
A rod of Length L and diameter D is subjected to a tensile load P. Which of the following is sufficient to calculate the resulting change in diameter?
A 200 × 100 × 50 mm steel block is subjected to a hydrostatic pressure of 15 MPa. The Young’s modulus and Poisson’s ratio of the material are 200 GPa and 0.3 respectively. The change in the volume of the block in mm^{3} is