Page 29 - Marks Calculation for Machine Design

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12:26
January 4, 2005
Brown.cls
Brown˙C01
U.S. Customary FUNDAMENTAL LOADINGS SI/Metric 11
Example 7. Calculate the change in length of Example 7. Calculate the change in length of
◦
a steel bar that is heated to 250 F, where a steel bar that is heated to 125 C, where
◦
◦
◦
α = 6.5 × 10 −6 in/in · F (steel) α = 12 × 10 −6 cm/cm C (steel)
L = 9ft L = 3m
solution solution
Step 1. Calculate the change in length (δ T ) Step 1. Calculate the change in length (δ T )
owing to temperature increase using Eq. (1.10) owing to temperature increase using Eq. (1.10).
δ T = α(
T ) L δ T = α(
T ) L
◦
◦
= (6.5 × 10 −6 in/in · F)(260 F)(9ft) = (12 × 10 −6 m/m · C)(125 C)(3m)
◦
◦
= 0.015 ft = 0.18 in = 0.0045 m = 0.45 cm
Example 8. If the bar in Example 7 is con- Example 8. If the bar in Example 7 is con-
strained, then calculate the thermal stress (σ T ) strained, then calculate the thermal stress (σ T )
developed, where developed, where
2
6
9
2
E = 30 × 10 lb/in (steel) E = 207 × 10 N/m (steel)
solution solution
Step 1. Calculate the thermal strain (ε T ) using Step 1. Calculate the thermal strain (ε T ) using
Eq. (1.9). Eq. (1.9).
ε T = α(
T ) ε T = α(
T )
◦
◦
◦
◦
= (6.5 × 10 −6 in/in · F)(260 F) = (12 × 10 −6 m/m · C)(125 C)
= 0.00169 = 0.0015
Step 2. Substitute this thermal strain in Step 2. Substitute this thermal strain in
Eq. (1.11) to give the thermal stress. Eq. (1.11) to give the thermal stress.
9
6
2
2
σ T = Eε T = (30 × 10 lb/in )(0.00169) σ T = Eε T = (207 × 10 N/m )(0.0015)
2
2
= 50,700 lb/in = 50.7 ksi = 310,500,000 N/m = 310.5MPa
1.3 DIRECT SHEAR
The overlapping bars in Fig. 1.11 are held together by a single rivet as shown.
P
P
Riveted joint
FIGURE 1.11 Direct shear loading.
Stress. If the rivet is cut in half at the overlap to expose the cross-sectional area (A) of
the rivet, then Fig. 1.12 shows the resulting free-body-diagram.