STEEL - Materials for Civil and Construction Engineers - page 132

In designing a typical structure made of this material, would you
expect the stress applied in (e) reasonable? Why?
3.20 During the tension test on a steel rod within the elastic region the
following data were measured:
Applied load
Original diameter
Current diameter
Original gauge length
Current gauge length
Calculate the Young's modulus and Poisson's ratio.

= 102 kN

= 25 mm

= 24.99325 mm

= 100 mm

= 100.1 mm

3.21 A grade 36 round steel bar with a diameter of 0.5 inches and a
gauge length of 2 inches was subjected to tension to rupture follow-
ing ASTM E-8 test procedure. The load and deformation data were
as shown in the following table:

Load (kips) Displacement (in.) Load (kips) Displacement (in.)

0 0 8.56 0.08301

2.75 0.00096 8.79 0.09557

4.07 0.00141 8.98 0.10878

7.12 0.00242 9.15 0.12207

7.14 0.01691 9.25 0.13372

7.34 0.04196 9.35 0.14741

7.53 0.04599 9.44 0.18199

7.91 0.05847 7.87 0.29814

8.28 0.07117

Using a spreadsheet program obtain the following:
a. A plot of the stress-strain relationship. Label the axes and show
units.
b. A plot of the linear portion of the stress-strain relationship. De-
termine modulus of elasticity using the best fit approach.
c. Proportional limit.
d. Yield stress.
e. Ultimate strength.
f. When the applied load was 4.07 kips, the diameter was measured
as 0.499905 inches. Determine Poisson's ratio.
g. After the rod was broken, the two parts were put together and the
diameter at the neck was measured as 0.416012 in. What is the
true stress value at fracture? Is the true stress at fracture larger or
smaller than the engineering stress at fracture? Why?
h. Do you expect the true strain at fracture to be larger or smaller
than the engineering strain at fracture? Why?