It is required to design the screw of a screw-jack by buckling consideration. One end of the screw is fixed in the nut and the other end supports a load of 20 kN. The length of the screw between the fixed and free ends is 500 mm, when the load is completely raised. The screw is made of steel 40C8 $\left(S_{y t}=380 N / mm ^{2} \text { and } E=207000 N / mm ^{2}\right)$ .
Assuming a factor of safety of 2.5, determine the core diameter of the screw.

Question

It is required to design the screw of a screw-jack by buckling consideration. One end of the screw is fixed in the nut and the other end supports a load of 20 kN. The length of the screw between the fixed and free ends is 500 mm, when the load is completely raised. The screw is made of steel 40C8 [latex] \left(S_{y t}=380 N / mm ^{2} ext { and } E=207000 N / mm ^{2} ight) [/latex].
Assuming a factor of safety of 2.5, determine the core diameter of the screw.

Accepted Answer

[latex] ext { Given } S_{y t}=380 N / mm ^{2} \quad E=207000 N / mm ^{2} [/latex].

l = 500 mm P = 20 kN (fs) = 2.5
Step I Diameter of screw using Euler’s equation
The end fixity coefficient is 0.25 when one end is fixed and the other free. As a fi rst trial, using Euler’s equation,

[latex] P_{c r}=\frac{n \pi^{2} E A}{(l / k)^{2}} [/latex].

[latex] (20000)(2.5)=\frac{(0.25) \pi^{2}(207000)\left(\pi d^{2} / 4 ight)}{\left[\frac{500}{(d / 4)} ight]^{2}} [/latex].

or d = 26.57 mm

Step II Check for design

k = d/4 = 6.64 mm

[latex] \left(\frac{l}{k} ight)=\frac{500}{6.64}=75.3 [/latex]. (i)
The border line between Euler’s and Johnson’s equations is given by

[latex] \frac{S_{y t}}{2}=\frac{n \pi^{2} E}{(l / k)^{2}} \quad ext { or } \quad \frac{380}{2}=\frac{(0.25) \pi^{2}(207000)}{(l / k)^{2}} [/latex].

[latex] herefore \quad\left(\frac{l}{k} ight)=51.85 [/latex] (ii).

From (i) and (ii), it is concluded that the screw is a long column and Euler’s equation considered in the first trial is justified. Therefore,
d = 26.57 mm or 28 mm.

Question 23.8: It is required to design the screw of a screw-jack by buckli...

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