Page 443 - Shigley's Mechanical Engineering Design

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418 Mechanical Engineering Design
The axial stress σ in the body of the screw due to load F is

F 4F
σ = = (8–8)
A πd r 2
in the absence of column action. For a short column the J. B. Johnson buckling
formula is given by Eq. (4–43), which is

F S y l 1
2
= S y − (8–9)
A crit 2π k CE
Nominal thread stresses in power screws can be related to thread parameters as
follows. The bearing stress in Fig. 8–8, σ B , is

F 2F
σ B =− =− (8–10)
πd m n t p/2 πd m n t p
where n t is the number of engaged threads. The bending stress at the root of the thread
σ b is found from

I (πd r n t ) (p/2) 2 π Fp
Z = = = d r n t p 2 M =
c 6 24 4
so

M Fp 24 6F
σ b = = = (8–11)
Z 4 πd r n t p 2 πd r n t p
The transverse shear stress τ at the center of the root of the thread due to load F is
3V 3 F 3F
τ = = = (8–12)
2A 2 πd r n t p/2 πd r n t p
and at the top of the root it is zero. The von Mises stress σ at the top of the root “plane”

is found by first identifying the orthogonal normal stresses and the shear stresses. From

Figure 8–8 d m
F
Geometry of square thread
useful in finding bending and
transverse shear stresses at the
thread root.
y
F f
x
p/2

p/2

T
F