Page 24 - Marks Calculation for Machine Design

P1: Shibu
January 4, 2005
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Brown.cls
Brown˙C01
6
STRENGTH OF MACHINES
P
Prismatic bar P
FIGURE 1.6 Axial loading.
Strain is a dimensionless quantity and does not have a unit if the change in length ε and
the length (L) are in the same units. However, if the change in length (δ) is in inches or
millimeters, and the length (L) is in feet or meters, then the strain (ε) will have a unit.
U.S. Customary SI/Metric
Example 3. Calculate the strain (ε) for a Example 3. Calculate the strain (ε) for a
change in length (δ) and a length (L), where change in length (δ) and a length (L), where
δ = 0.015 in δ = 0.038 cm
L = 5ft L = 1.9 m
solution solution
Step 1. Calculate the strain (ε) from Eq. (1.2). Step 1. Calculate the strain (ε) from Eq. (1.2).
δ 0.015 in δ 0.038 cm
ε = = ε = =
L 5ft L 1.9m
= 0.003 in /ft × 1 ft /12 in = 0.02 cm /m × 1 m /100 cm
= 0.00025 in /in = 0.00025 = 0.0002 m /m = 0.0002

Stress-Strain Diagrams. If the stress (σ) is plotted against the strain (ε) for an axially
loaded bar, the stress-strain diagram for a ductile material in Fig. 1.7 results, where A is
proportional limit, B elastic limit, C yield point, D ultimate strength, and F fracture point.

s D

F
B, C
A

E

e
FIGURE 1.7 Stress-strain diagram (ductile material).

The stress-strain diagram is linear up to the proportional limit, and has a slope (E) called
the modulus of elasticity. In this region the equation of the straight line up to the proportional
limit is called Hooke’s law, and is given by Eq. (1.3).
σ = E ε (1.3)
The numerical value for the modulus of elasticity (E) is very large, so the stress-strain
diagram is almost vertical to point A, the proportional limit. However, for clarity the hori-
zontal placement of point A has been exaggerated on both Figs. 1.7 and 1.8.