# GATE Mechanical 2014 Set 2 | Question: 6

A steel cube, with all faces free to deform, has Young’s modulus, $E$, Poisson’s ratio, $ν$, and coefficient of thermal expansion, $\alpha$. The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, $\Delta T$, is given by

1. $0 \\$
2. $\dfrac{\alpha (\Delta T)E}{1-2V} \\$
3. $-\dfrac{\alpha (\Delta T)E}{1-2V} \\$
4. $\dfrac{\alpha (\Delta T)E}{3(1-2V)}$

recategorized

## Related questions

A rectangular hole of size $100$ $mm \times 50$ $mm$ is to be made on a $5$ $mm$ thick sheet of steel having ultimate tensile strength and shear strength of $500$ $MPa$ and $300$ $MPa$, respectively. The hole is made by punching process. Neglecting the effect of clearance, the punching force (in $kN$) is $300$ $450$ $600$ $750$
A cantilever beam of length, $L$, with uniform cross-section and flexural rigidity, $EI$, is loaded uniformly by a vertical load, $w$ per unit length. The maximum vertical deflection of the beam is given by $\dfrac{wL^4}{8EI} \\$ $\dfrac{wL^4}{16EI} \\$ $\dfrac{wL^4}{4EI} \\$ $\dfrac{wL^4}{24EI}$
The flexural rigidity $(EI)$ of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load $P$ and bending moment $PL/2$ are applied at the free end of the beam then the value of the slope at the free end is $\dfrac{1}{2}\dfrac{PL^2}{EI} \\$ $\dfrac{PL^2}{EI} \\$ $\dfrac{3}{2}\dfrac{PL^2}{EI} \\$ $\dfrac{5}{2}\dfrac{PL^2}{EI}$
The relationship between true strain ($\epsilon _T$) and engineering strain ($\epsilon _E$) in a uniaxial tension test is given as $\epsilon _E=ln(1+\epsilon _T)$ $\epsilon _E=ln(1-\epsilon _T)$ $\epsilon _T=ln(1+\epsilon _E)$ $\epsilon _T=ln(1-\epsilon _E)$
In a structure subjected to fatigue loading, the minimum and maximum stresses developed in a cycle are $200$ $MPa$ and $400$ $MPa$ respectively. The value of stress amplitude (in $MPa$) is _______