The aircraft brake discussed in class is mounted on a landin

The aircraft brake discussed in class is mounted on a landing gear assembly using a grade 5 titanium flanged tube. E = 113.8 GPa, G = 44 GPa The tube side is fixed to the landing gear (assume rigid) and has an ID of 120 mm and an OD of 150 mm. The bolts are made of A36 steel with a minor diameter of 18 mm. The flange is 20 mm thick. The tube extends out a distance of 150 mm from the fixed point on the landing gear to the inside edge of the flange. The torque from the brake during a landing is T = 9575.84 N. m. Calculate the shear strain tau_max at the tube. Determine the angle of twist delta of the tube. Will the tube yield or go beyond its proportional limit? Will the bolts shear off?

Solution

Cross section area of one bolt = 3.14/4 ( 18x18) = 254.34 sq.mm = 254.34/ 1000x1000 sq meter

tthe shear load on bolt , the bolts are assumed to be on a pcd of 200mm

load = 9575.8 Nm/ 6 x0.1 = 15,959.6 N

shear stress = 15,959.6/254.34x 10^-6    = 6.27 x 10 ^{6 ,}

the allowable shear stress for A36 steel is 120 kg/mm²

   = 12x 10^{6 N hrnce the bolt is safe}

T/J = G x (theta)/L = 9575.8/( 3.14 ( .15⁴-.12⁴)/32) = (44x 10⁹x theta)/ .15 = 0.000859 radian = 0.49 degree

Shear strain = tan( theta) = 0.008