The pin-jointed right-isosceles truss shown has a 10 cm base. Each member has E=200 GPa and second moment of area 0.1 cm⁴. Determine the largest vertical load P in kN before a compressed member undergoes Euler buckling (nearest integer).
Each diagonal is $0.1/\sqrt2$ m long and carries compression P/√2. Convert I=0.1 cm⁴=10⁻⁹ m⁴. For pin-ended members, $N_{cr}=\pi^2EI/L^2=394784$ N. Hence $P_{cr}=\sqrt2N_{cr}=558.3$ kN, or 558 kN. The bottom member is in tension and is not the Euler-buckling constraint.
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