Page 277 - Marks Calculation for Machine Design

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Brown.cls
Brown˙C06
STATIC DESIGN AND COLUMN BUCKLING
where (K ts ) is a stress-concentration factor in shear, and (τ o ) is the shear stress at a change
in the geometry of the machine element. 259
For many common changes in geometry, stress-concentration factors, both (K t ) and
(K ts ), have been developed (see Marks or Peterson, 1974). Stress-concentration factors are
dependent on the geometry of the machine element, not on the material used. However, some
materials are more sensitive to stress concentrations, or notches, so the stress-concentration
factors will be modified according to their notch sensitivity.
U.S. Customary SI/Metric
Example 1. For the rectangular bar with a Example 1. For the rectangular bar with a
transverse hole in Fig. 6.18 loaded in tension, transverse hole in Fig. 6.18 loaded in tension,
calculate the axial stress (σ axial ), the stress at calculate the axial stress (σ axial ), the stress at
the hole (σ o ), and the design normal stress (σ xx ) the hole (σ o ), and the design normal stress (σ xx )
using Eqs. (6.19), (6.20), and (6.21), where using Eqs. (6.19), (6.20), and (6.21), where

P = 1,200 lb P = 5,400 N
w = 3in w = 7.5 cm = 0.075 m
t = 0.25 in t = 0.6 cm = 0.006 m
d = 1in d = 2.5 = 0.025 m
K t = 2.35 K t = 2.35
solution solution
Step 1. Using Eq. (6.19) calculate the axial Step 1. Using Eq. (6.19) calculate the axial
stress (σ axial ) as stress (σ axial ) as
P P 1,200 lb P P 5,400 N
σ axial = = = σ axial = = =
A wt (3in)(0.25 in) A wt (0.075 m)(0.006 m)
1,200 lb 2 5,400 N 2
= = 1,600 lb/in = = 12,000,000 N/m
0.75 in 2 0.00045 m 2
= 1.6 kpsi = 12.0MPa
Step 2. Using Eq. (6.20) calculate the stress at Step 2. Using Eq. (6.20) calculate the stress at
the hole (σ o ) as the hole (σ o ) as
P P P P
σ o = = σ axial = =
A o (w − d)( t) A o (w − d)( t)
1,200 lb 5,400 N
= =
([3 − 1] in)(0.25 in) (0.05 m)(0.006 m)
1,200 lb 5,400 N
= = 2,400 lb/in 2 = = 18,000,000 N/m 2
0.5in 2 0.0003 m 2
= 2.4 kpsi = 18.0MPa
Step 3. Using Eq. (6.21) calculate the design Step 3. Using Eq. (6.21) calculate the design
normal stress (σ xx ) as normal stress (σ xx ) as

σ xx = K t σ o = (2.35)(2.4 kpsi) σ xx = K t σ o = (2.35)(18.0MPa)
= 5.6 kpsi = 42.3MPa