The shear strength of a sheet metal is $$300MPa.$$ The blanking force required to produce a blank of $$100$$ $$mm$$ diameter from a $$1.54$$ $$mm$$ thick sheet is close to

A hole is dimension $$\phi {9^{\matrix{ { + 0.015} \cr { + 0\,\,\,\,\,\,\,\,\,\,} \cr } }}\,mm.$$ The corresponding shaft is of dimension $$\phi {9^{\matrix{ { + 0.010} \cr { + 0.001} \cr } }}\,mm.$$ The resulting assembly has

A simply supported beam $$PQ$$ is loaded by a moment of $$1$$ $$kN-m$$ at the mid-span of the beam as shown in the figure. The reaction forces $${R_P}$$ and $${R_Q}$$ at supports $$P$$ and $$Q$$ respectively are

A torque $$T$$ is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is $$G.$$ The expressions for diameter to produce an angular twist $$\theta $$ at the free end is