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MECH221 ASSIGNMENT #5 – CHAPTER 6 SOLUTIONS CONCORDIA UNIVERSITY
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MECH221 ASSIGNMENT #5 – CHAPTER 6 SOLUTIONS CONCORDIAUNIVERSITY
6.11 Figure 6.23 shows the tensile engineering stress–strain curve in the elastic region for a gray cast iron.
Determine (a) the tangent modulus at 25 MPa (3625 psi) and (b) the secant modulus taken to 35 MPa (5000 psi).
Solution
(a) This portion of the problem asks that the tangent modulus be determined for the gray cast iron, the
stress-strain behavior of which is shown in Figure 6.23. In the figure below is shown a tangent draw on the curve
at a stress of 25 MPa.
The slope of this line (i.e., ∆ /∆ ), the tangent modulus, is computed as follows:
57 MPa 5 MPa
= = 86,700 MPa = 86.7 GPa (12.6 106 psi)
0.0006 0
(b) The secant modulus taken from the origin is calculated by taking the slope of a secant drawn from the
origin through the stress-strain curve at 35 MPa (5,000 psi). This secant modulus is drawn on the curve shown
below:
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