Engineering strain of a mild steel sample is recorded as $0.100\%$. The true strain is

0.010%
0.055%
0.099%
0.101%

Correct answer: 0.099%

Solution

Engineering strain is $0.100\%=0.001$. True strain is $\ln(1+0.001)\approx 0.0009995$, which is $0.09995\%$, closest to $0.099\%$.

Related GATE Technical questions

The three-dimensional state of stress at a point is given by $\sigma = \begin{bmatrix}10 & 0 & 0\\0 & 40 & 0\\0 & 0 & 0\end{bmatrix}$ MPa. The maximum shear stress at the point is
Find the correct match between the plane stress states and the Mohr’s circles. (P) horizontal tensile stresses of 10 on the left and right faces; (Q) shear stresses of 10 acting clockwise on all four faces; (R) vertical compressive stress of 10 on the top face and vertical tensile stress of 10 on the bottom face; (S) normal stresses of 10 acting inward on all four faces.
A structural member subjected to compression has both translation and rotation restrained at one end, while only translation is restrained at the other end. As per IS 456: 2000, the effective length factor recommended for design is
For a linear elastic and isotropic material, the correct relationship among Young’s modulus of elasticity ($E$), Poisson’s ratio ($\nu$), and shear modulus ($G$) is
A circular solid shaft of span $L = 5\,\text{m}$ is fixed at one end and free at the other end. A torque $T = 100\,\text{kN}\cdot\text{m}$ is applied at the free end. The shear modulus and polar moment of inertia of the section are denoted by $G$ and $J$, respectively. The torsional rigidity $GJ$ is $50{,}000\,\text{kN}\cdot\text{m}^2/\text{rad}$. The following are reported for this shaft: Statement i) The rotation at the free end is 0.01 rad Statement ii) The torsional strain energy is 1.0 kN\cdotm With reference to the above statements, which of the following is true?
When a simply supported elastic beam of span $L$ and flexural rigidity $EI$ (where $E$ is the modulus of elasticity and $I$ is the moment of inertia of the section) is loaded with a uniformly distributed load $w$ per unit length, the deflection at the mid-span is $\Delta_0 = \frac{5wL^4}{384EI}$. If the load on one half of the span is now removed, the mid-span deflection ________.

⚔️ Practice GATE Technical free + battle 1v1 →