A power source at C actuates valves at A arid B through a long round steel contr

Question

A power source at C actuates valves at A arid B through a long round steel control rod. A torque of 8.5 kN-m is required to actuate each valve. If the allowable shear stress in the control rod is 80 MPa, (a) what diameters are required for each section of the rod? (b) What is the angle of twist in the rod between the power source at C and the valve at A? Prob. 12.20 at A through a shaft AB and a set of gears the shaft CD. The shear stress in shaft AB is . If the shear stress in CD is also 55 MPa, is the diameter of shaft CD? (b) What is angle of twist between the motor at A at D? (Hint: From the shaft at B to at C through the set of gears, the torques are proportional to the pitch diameters DB/DC), and the angles of rotation are proportional to the pitch diameters DC/DB). The torques and angles of ro opposite directions.) Prob. 12.21 A solid steel shaft delivers 5 hp at 30 revolutions per second. If the allowable shearing stress is limited to 95 MPa, find the required diameter of the shaft. The allowable stress in a steel shaft with an outside diameter of 1.5 in. and an inside diameter of 1.1 in. is 12,000 psi. What hp can the shaft deliver at 1750 rpm? A steel shaft with a diameter of 40 mm and length of 1.1 m transmits 60 hp from an electric motor to a compressor. If the allowable shear stress is 50 MPa and the allowable angle of twist is 1.5degree, what is the minimum allowable speed of rotation? A steel shaft is used to transmit 9 hp while rotating at 1200 rpm. If the allowable shear stress is 8000 psi, (a) what is the smallest permissible diameter for the shaft? (b) What is the angle of twist in degrees per foot of shaft? A steel shaft is used to transmit 50 hp. The shaft has a diameter of 1-3/8 in. and a length of 5 ft. If the allowable shear stress is 8000 psi and the allowable angle of twist is 2.5degree, find the lowest permissible speed of rotation. A motor through a set of gears delivers power to a hollow steel shaft with an outside diameter of 40 mm and an inside diameter of 30 mm. The shaft is rotating at 900 rpm. Twenty-five percent of the power supplied by the motor is transmitted to A, and 75 percent of the power supplied is transmitted to C. If the allowable shear stress in the shaft is 105 MPa. what is the maximum power that the motor can deliver to the shaft? Prob. 12.27

Explanation / Answer

Do =40mm=>ro = 20mm Di=30mm=>ri = 15mm J =(ro4-ri4)/2 J = (0.024-0.0154)/2 J = 1.718*10-7 m4 maximum power = 0.75P = 2N/60 = 2*900/60 = 94.248 rad/sec So.T = 0.75P/ T = 0.75P/94.248 T = 7.958 *10-3 P but, = T*r/J 105*106 = 7.958*10-3P*0.02/1.718*10-7 So, P = 113.338 kWatt So, P = 113.338 kWatt

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