# The figure shows a simple model of the loading of a square thread of a power screw

## Question:

From the figure, dm = dr + p/2, where dr is the root diameter of the thread and p is the pitch of the thread.

(a) Considering the thread to be a cantilever beam as shown in the cutaway view, show that the bending stress at the root of the thread can be approximated by

Ïƒb = ± 6F/ Ï€dr nt p

(b) Show that the axial and maximum torsional shear stresses in the body of the shaft can be approximated by

Ïƒa = ˆ’ 4F/Ï€d2r and Ï„t = 16T/Ï€d3r

(c) For the stresses of parts (a) and (b) show a three-dimensional representation of the state of stress on an element located at the intersection of the lower thread root base and the thread body. Using the given coordinate system label the stresses using the notation given in Fig. 3€“8a.

(d) A square-thread power screw has an outside diameter d = 1.5 in, pitch p = 0.25 in, and transmits a load F = 1 500 lbf through the application of a torque T = 235 lbf ãƒ»in. If nt = 2, determine the key stresses and the corresponding principal stresses (normal andshear).

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**Related Book For**

## Shigleys Mechanical Engineering Design

**ISBN:** 978-1121345317

9th edition

**Authors:** Richard G. Budynas, J. Keith Nisbett