Question

Q.3 Three identical compression springs were used to support a platform ( weight| = 300 lbs) shown in figure below. Spring properties are: ASTM A 227 steel wire, hard drawn ( Fig 19-8), G=11.5*10°, E = 28.6*10°, total number of coils are 7, both ends are squared and ground, wire diameter = 0.15 in, outside diameter = 1.5 inches, free length = 4 inches. All ends of all springs are fixed. Find stability of this system. (7) %3D %3D %3D O'5

Answer 1

The maximum deflection is more than the deflection under given load.

given '(N) = 7 , N=7-2-5 active turn K = (1-5X106) - Weight of platform (W)=300lbs modulus of rigidity (G) = 11.5x106 modulus of elasticity (E)=20.68100 Number of turnin coil (N), - 7,N,=7 wire diometer (d)= 0.15 in N, &, are Outside diameter (D) = 1.5 inches active free length (L) = 4inches. Number of turn is inner spring loven) = 6,02= 6-2 o Siffress calculation of spring Kia la Gdy (Forouter - Crisxiob) (0.15) BD3a . spring) Esslin B (115)3(55) ke = 11:5X106) (0.15)" ze abslin (1.513 (4) Equivalent Stithress K - 2k, tkz = 2(3)+36 | | 0 -13 8 24 ① Deflection of springs s=W = 30 stasin - To = 2:17 in © Pitch (P2 = free longth = 4 =0.0.in Piter (P) = 3.5 = 0.875 in © Deflection of coil (8') = BP DAN AX 300 X (1-55x5 - 6-96 in 8 = C11.5x106) (0.151" 42 54 629 8x300X (1.53x4. 82= (15X105 0.15) Hence in buth outerar inner allowable deflection h in the range 6.96 in to 5.56 in. Since spring are stable under 300lbs load.