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Figure 116.1 is a sketch of the stress-strain diagram (tension and compression) for gray cast iron. Modulus of elasticity, E = 12.5 x 106. Determine for tension and compression:
(a) The proportional limit.
(b) The modulus of resilience.
(c) percent elongation.
S7P3A32 (Force - Push).
Pj Problem of Interest is of type force (push and pull). However in this case, compression is more pronounced. Hence the choice of force-push.
Formulas of interest:
Modulus of resilience ur, is strain energy absorbed per unit volume.
ur = (σpl)1/2/(2E)---------(1)
Proportional limit is the maximum stress a material can sustain without deviating from the law of stress-strain proportionality.
σpl is stress at proportional limit
E is modulus of elasticity.
For tension, from diagram:
σpl = 12,500 psi.
So, Modulus of resilience ur = (12,500 x 12,500)/(2 x 12.5 x 106)
So, Modulus of resilience ur = 6.25 lb-in/in3.
Percent elongation (used for ductility comparison) is strain at rupture x 100.
So from diagram, % elongation = 0.7(0.005) x 100 = 0.35
For compression, from diagram:
σpl =25,000 psi.
So, Modulus of resilience ur = (25,000 x 25,000)/(2 x 12.5 x 106)
So, Modulus of resilience ur = 25 lb-in/in3.
from diagram, % elongation = 0.065 x 100 = 6.5
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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