Page 184 - Marks Calculation for Machine Design

P1: Shibu
January 4, 2005
Brown˙C04
Brown.cls
166
U.S. Customary 14:25 STRENGTH OF MACHINES SI/Metric
Step 2. Calculate the axial stress (σ axial ) using Step 2. Calculate the axial stress (σ axial ) using
Eq. (4.1) as Eq. (4.1) as
σ axial = Eε axial σ axial = Eε axial
2
2
9
6
= (30 × 10 lb/in )(0.00087) = (207 × 10 N/m )(0.0008)
2
2
= 26,100 lb/in = 26.1 kpsi = 165,600,000 N/m = 165.6MPa
Step 3. Calculate the thermal stress (σ thermal ) Step 3. Calculate the thermal stress (σ thermal )
from Eq. (4.2) as from Eq. (4.2) as
σ thermal = Eε T = Eα( T ) σ thermal = Eε T = Eα( T )
2
6
2
9
= (30 × 10 lb/in ) = (207 × 10 N/m )
×(6.5 × 10 −06 in/in · F) ×(12 × 10 −6 cm/cm · C)
◦
◦
◦
◦
×(80 F) ×(45 C)
= 15,600 lb/in 2 = 111,800, 000 N/m 2
= 15.6 kpsi = 111.8MPa
Step 4. Combine the axial stress (σ axial ) from Step 4. Combine the axial stress (σ axial ) from
step 2 and the thermal stress (σ thermal ) from step 2 and the thermal stress (σ thermal ) from
step 3 using Eq. (4.3) to give the maximum step 3 using Eq. (4.3) to give the maximum
stress (σ xx ) as stress (σ xx ) as
σ xx = σ axial + σ thermal σ xx = σ axial + σ thermal
= (26.1 kpsi) + (15.6 kpsi) = (165.6MPa) + (111.8MPa)
= 41.7 kpsi = 277.4MPa
Step 5. Display the answer for the maximum Step 5. Display the answer for the maximum
stress (σ xx ) found in step 4, in kpsi, on a plane stress (σ xx ) found in step 4, in MPa, on a plane
stress element. stress element.
0 0
0 0
41.7 41.7 277.4 277.4

0 0

0 0
The above diagram will be a starting point The above diagram will be a starting point
for the discussions in Chap. 5. for the discussions in Chap. 5.