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

An L-shaped elastic member ABC with slender arms AB and BC of uniform crosssection is clamped at end A and connected to a pin at end C. The pin remains in continuous contact with and is constrained to move in a smooth horizontal slot. The section modulus of the member is same in both the arms. The end C is subjected to a horizontal force P and all the deflections are in the plane of the figure. Given the length AB is 4a and length BC is 𝑎, the magnitude and direction of the normal force on the pin from the slot, respectively, are

A thin-walled cylindrical pressure vessel has mean wall thickness of t and nominal radius of r. The Poisson’s ratio of the wall material is 1/3. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased by 0.1% and the corresponding wall thickness became t̅. The corresponding change in the wall thickness of the cylindrical portion, i.e. 100 × (t̅ − t)/t, is ________% (round off to 3 decimal places).