For the four-bar linkage in the posture shown, the torque acting on link 2 at crankshaft O2 is T12 = −6 700kˆ ft · lb. There is also a torque, T14, acting on link 4 at crankshaft O4 to hold the linkage in static equilibrium. The length of coupler link 3 is AB = 6 in, and the cross section is rectangular with width 3t and thickness 4t (into the plane). The coupler link is a steel alloy with compressive yield strength Syc = 60 kpsi and a modulus of elasticity E = 30 Mpsi. If the critical load for the coupler link is Pcr = 150 000 lb, and the effects of gravity are ignored, then determine:

(a) the factor of safety guarding against buckling;

(b) the slenderness ratio at the point of tangency between the Euler column formula and the Johnson parabolic equation; and

(c) the numeric value of the parameter t.

(d) If the rectangular cross section is replaced by a circular cross section of the same material and diameter d = 0.200 in, then determine the factor of safety guarding against buckling of the coupler link.

Figure P11.48 Four-bar linkage.