Project ForgeA 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 (AB is horizontal, length 2.5 m, cable CB makes a 30° angle with AB at B). 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
- 0.0924 m⁻²
- B0.0713 m⁻²
- C0.1261 m⁻²
- D0.1417 m⁻²
Explanation
Since loads act only at A (pin) and B (where the cable and weight attach) with nothing along its length, beam AB is a two-force (pin-pin) member carrying pure axial compression. Joint equilibrium at B: the cable tension T (at 30° above the beam's axis) and weight W give T sin30°=W and the beam's axial compression P=T cos30°. So P=W·cos30°/sin30°=W√3. Euler buckling (pin-pin, L=2.5m): Pcr=π²EI/L²=π²EI/6.25. Setting P=Pcr at the limit: √3·W_max=π²EI/6.25, so W_max=π²EI/(6.25√3)≈0.0924π²EI — β=0.0924.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.