A 4 mm thick aluminum sheet of width w = 100 mm is rolled in a two-roll mill of roll diameter 200 mm each. The workpiece is lubricated with a mineral oil, which gives a coefficient of friction, μ = 0.1. The flow stress (σ) of the material in MPa is σ = 207 + 414 𝜀, where 𝜀 is the true strain. Assuming rolling to be a plane strain deformation process, the roll separation force (F) for maximum permissible draft (thickness reduction) is _________ kN (round off to the nearest integer).
Use:
$F = 1.15 \barσ \left( 1 + \frac{\mu L}{2 \bar h} \right)$ wL, where $\bar \sigma$ is average flow stress, L is roll-workpiece contact length, and $\bar h$ is the average sheet thickness
Two mild steel plates of similar thickness, in butt-joint configuration, are welded by gas tungsten arc welding process using the following welding parameters.
$$ \begin{array}{|l|l|} \hline \text { Welding voltage } & 20 \mathrm{~V} \\ \hline \text { Welding current } & 150 \mathrm{~A} \\ \hline \text { Welding speed } & 5 \mathrm{~mm} / \mathrm{s} \\ \hline \end{array} $$A filler wire of the same mild steel material having 3 mm diameter is used in this welding process. The filler wire feed rate is selected such that the final weld bead is composed of 60% volume of filler and 40% volume of plate material. The heat required to melt the mild steel material is 10 J/mm3. The heat transfer factor is 0.7 and melting factor is 0.6. The feed rate of the filler wire is __________ mm/s (round off to one decimal place).
A uniform light slender beam AB of section modulus EI is pinned by a frictionless joint A to the ground and supported by a light inextensible cable CB to hang a weight W as shown. If the maximum value of W to avoid buckling of the beam AB is obtained as βπ2EI, where π is the ratio of circumference to diameter of a circle, then the value of β is
