298 Mechanics of Materials (b)Under axial torque T sin2a cos2a Wind-up angle 0 2mnRT sec a GJ where a is the helix angle of the spring. 1 Axial deflection 8=2nnTR2 sina GJ EI Springs in series Stiffness S= SS2 (S1+S2) Springs in parallel Stiffness S=S+S2 Leaf or carriage springs (a)Semi-elliptic Under a central load W: 3WL maximum bending stress 2nbt2 3WL3 deflectionδ= 8Enbt3 where L is the length of spring,b is the breadth of each plate,t is the thickness of each plate, and n is the number of plates. 8Enbt3 Proof load W,33 where 6 is the initial central "deflection". 4tE Proof or limiting stress (b)Quarter-elliptic 6WL Maximum bending stress nbt2 6WL3 Deflection 6 Enbt3298 Mechanics of Materials (b) Under axial torque T sin’a cos2a Wind-up angle 8 = 2mRT sec a where a is the helix angle of the spring. Axial deflection 6 = 2nnTR’ sina - -- [;.l Ell] Springs in series Springs in parallel Stiffness S = SI + S, Leaf or carriage springs (a) Semi-elliptic Under a central load W 3 WL maximum bending stress = - 2nbtz 3 WL3 deflection 6 = - 8Enbt3 where L is the length of spring, b is the breadth of each plate, t is the thickness of each plate, and n is the number of plates. 8Enbt3 Proof load Wp = ~ 3L3 where 6, is the initial central “deflection”. 4tE Proof or limiting stress 0, = Lz6p (b) Quarter-elliptic 6WL Maximum bending stress = - nbt’ 6 WL3 Deflection 6 = - Enbt3