Calculate the radius of plates, Mechanical Engineering

Calculate the radius of plates:

A laminated steel spring, simply supported at the ends & centrally loaded, along a span of 0.8 m; is needed to carry a proof load of 8 kN; and the central deflection is not to exceed 50 mm; the bending stress should not exceed 400 kN/mm2, plates are available in multiples of 1 mm for thickness and 4 mm for width. Calculate appropriate values of width, thickness and number of plates, & calculate the radius to which the plates should be made. Consider width = 12 × thickness.

E = 200 GPa.

Solution

Simply Supported Spring l = 0.8 m

W = 8 kN = 800 N

Δ = 50 mm

σb = 400 N/mm2

b = 12 t

E = 200 GPa = 200 × 103 N/mm2

Δ= 3W l 3 / 8 nb t 3 E

⇒         50 =3 × 8000 × 8003 / 8 × n (12 t ) t 3 (200 × 103 )

∴          nt 4  = 12,800                                               ---------- (1)

σ=  3Wl  /2 nb t 2

⇒         400 = 3 × 8000 × 800 / 2 n (12 t ) t 2

∴          nt 3  = 2, 000                                             ----------- (2)

From Eq. (1) to Eq. (2), we obtain

⇒         t = 6.4 mm = 7 mm

b = 12 t = 12 × 7 = 84 mm

nt 3  = 2, 000

⇒         n × 73  = 200

∴          n = 5.8 ;  6

Actual deflection under the proof load,

Δ0 =      (3 (8000) (800)3 )/ (8 × 6 × 84 × 73  × 200 × 10) = 44.4 mm

Initial radius of curvature,

R0  = l 2 / 8 Δ0 =(800)2/(8 × 44.4) = 1802 mm

Posted Date: 1/21/2013 1:58:43 AM | Location : United States







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