Mechanics of Solids 2011 Part 7

Tham khảo tài liệu 'mechanics of solids 2011 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1-84 Section 1 FIGURE Shear stress distributions in a shaft. where J the polar moment of inertia of the cross-sectional area for a solid circle J Kr4H for a tube J n 2 r04 - r . Power Transmission The power P transmitted by a shaft under torque T and rotating at angular velocity ữ is P Ta where O 2k f f frequency of rotation or number of revolutions per second. Angle of Twist For a homogeneous shaft of constant area and G over a length L under a torque T the angular displacement of one end relative to the other is TL JG For a shaft consisting of segments with various material and or geometric properties under several different torques in each the net angular displacement is calculated from the vector sum of the individual twists V TL -S Ji The right-hand rule is used for a sign convention for torques and angles both T and f are positive with the thumb pointing outward from a shaft and the fingers curling in the direction of torque and or rotation as in Figure . Note that regardless of the number of torques applied to a shaft at various places along its length there is only one torque at a given cross section and this torque is a constant in that segment of the shaft until another external torque is encountered requiring a different free-body diagram . FIGURE Right-hand rule for positive torque and angle. Inelastic Torsion A shaft may plastically deform under an increasing torque yielding first in its outer layers and ultimately throughout the cross section. Such a shaft is analyzed by assuming that the shear strains are still .