Page 367 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
15:14
Brown.cls
Brown˙C08
MACHINE ASSEMBLY
and the shear stress (τ butt ) produced by the shear force (V ) is given by Eq. (8.69) as
V V 349
τ butt = = (8.69)
A butt HL
If both are acting simultaneously, then there is combined loading on the weld and the
methods of Chap. 5 are used to determine the principal stresses and the maximum and
minimum shear stresses, either mathematically or graphically from Mohr’s circle.
U.S. Customary SI/Metric
Example 1. A butt weld like that shown in Example 1. A butt weld like that shown in
Fig. 8.7 is subjected to both tensile force (P) Fig. 8.7 is subjected to both a tensile force (P)
and shear force (V ). Determine the principal and a shear force (V ). Determine the principal
stress (σ 1 ) and the maximum shear stress (τ max ) stress (σ 1 ) and the maximum shear stress (τ max )
using the mathematical formulas for combined using the mathematical formulas for combined
loading, where loading, where
P = 1,200 lb P = 5,400 N
V = 900 lb V = 4,050 N
L = 3in L = 8cm = 0.08 m
H = 0.25 in H = 0.6 cm = 0.006 m
solution solution
Step 1. Using Eq. (8.68), calculate the normal Step 1. Using Eq. (8.68), calculate the normal
stress in the butt weld (σ butt ) as stress in the butt weld (σ butt ) as
P P 1,200 lb P P 5,400 N
σ butt = = = σ butt = = =
A butt HL (0.25 in)(3in) A butt HL (0.006 m)(0.08 m)
2
2
= 1,600 lb/in = 1.6 kpsi = 11,250,000 N/m = 11.25 MPa
= σ xx = σ xx
σ yy = 0 σ yy = 0
Step 2. Using Eq. (8.69), calculate the shear Step 2. Using Eq. (8.69), calculate the shear
stress in the butt weld (τ butt ) as stress in the butt weld (τ butt ) as
V V 900 lb V V 4,050 N
τ butt = = = τ butt = = =
A butt HL (0.25 in)(3in) A butt HL (0.006 m)(0.08 m)
2
2
= 1,200 lb/in = 1.2 kpsi = 8,437,500 N/m = 8.44 MPa
= τ xy = τ xy
Step 3. Substitute the normal stresses (σ butt = Step 3. Substitute the normal stresses (σ butt =
σ xx ) and (σ yy = 0) from step 1 in Eq. (5.14) to σ xx ) and (σ yy = 0) from step 1 in Eq. (5.14) to
determine the average stress (σ avg ) as determine the average stress (σ avg ) as
σ xx + σ yy (1.6 kpsi) + (0) σ xx + σ yy (11.25 MPa) + (0)
σ avg = = σ avg = =
2 2 2 2
= 0.8 kpsi = 5.63 MPa
Step 4. Substitute the normal stresses (σ butt = Step 4. Substitute the normal stresses (σ butt =
σ xx ) and (σ yy = 0) from step 1 and the shear σ xx ) and (σ yy = 0) from step 1 and the shear
stress (τ butt = τ xy ) from step 2 in Eq. (5.14) to stress (τ butt = τ xy ) from step 2 in Eq. (5.14) to