Chapter-12
Spring 16T 16 ( PD / 2 ) 8PD The torsional shear stress in the bar, τ 1 = = = πd3 πd3 πd3 The direct shear stress in the bar, τ 2 =
P
⎛ πd ⎞ ⎜ ⎟ ⎝ 4 ⎠
Therefore the total shear stress, τ = τ 1 + τ 2 =
τ = Ks Where K s = 1 +
=
2
4P
πd2
=
S K Mondal’s
8PD ⎛ 0.5d ⎞ π d 3 ⎜⎝ D ⎟⎠
8PD ⎛ 0.5d ⎞ 8PD 1+ = Ks ⎟ 3 ⎜ D ⎠ πd ⎝ πd3
8PD πd3
0.5d is correction factor for direct shear stress. D
3. Wahl’s stress correction factor τ =K
8PD πd3
⎛ 4C − 1 0.615 ⎞ + is known as Wahl’s stress correction factor C ⎟⎠ ⎝ 4C − 4
Where K = ⎜
Here K = KsKc; Where K s is correction factor for direct shear stress and Kc is correction factor for stress concentration due to curvature.
Note: When the spring is subjected to a static force, the effect of stress concentration is neglected due to localized yielding. So we will use, τ = K s
8PD πd3
4. Equivalent stiffness (keq) Spring in series (δ e = δ1 + δ 2 )
1 1 1 = + K eq K1 K 2
or K eq =
K1 K 2 K1 + K 2
Shaft in series ( θ = θ1 + θ 2 )
Spring in Parallel (δ e = δ1 = δ 2 )
K eq = K1 + K 2
Shaft in Parallel ( θ eq = θ1 = θ 2 )
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