Test Coupon
Consider a 10 cm diameter steel coupon used for a tensile strength test is subjected to a 500 N compressive force for 5 minutes. After completing the test, the specimen measured a length decrease of 0.5 cm and a new diameter of 10.01 cm. If the Poisson’s ratio is 0.3, what was the coupon’s original length in cm?
Expand Hint
Poisson’s ratio measures a material’s deformation in directions perpendicular to the loading/pressure direction:
$$$\upsilon=-\frac{\varepsilon_{lateral}}{\varepsilon_{longitudinal}}$$$
where
$$\varepsilon_{lateral}$$
is the lateral strain, and
$$\varepsilon_{longitudinal}$$
is the longitudinal strain.
Hint 2
Strain is the change in length per unit length.
$$$\varepsilon=\frac{\Delta L}{L_o} $$$
where
$$\varepsilon$$
is the engineering strain,
$$\Delta L$$
is the change in length, and
$$L_o$$
is the original length.
Poisson’s ratio measures a material’s deformation in directions perpendicular to the loading/pressure direction:
$$$\upsilon=-\frac{\varepsilon_{lateral}}{\varepsilon_{longitudinal}}$$$
where
$$\varepsilon_{lateral}$$
is the lateral strain, and
$$\varepsilon_{longitudinal}$$
is the longitudinal strain.
Strain is the change in length per unit length.
$$$\varepsilon=\frac{\Delta L}{L_o} $$$
where
$$\varepsilon$$
is the engineering strain,
$$\Delta L$$
is the change in length, and
$$L_o$$
is the original length.
First, let’s analyze the strain in the lateral direction:
$$$\varepsilon_{lateral}=\frac{\Delta D}{D_o}=\frac{(10.01cm-10cm)}{10cm}=\frac{0.01cm}{10cm}=0.001$$$
Because the Poisson’s ratio is known, let’s solve for the strain in the longitudinal direction next:
$$$0.3=\frac{0.001}{\varepsilon_{longitudinal}}\Rightarrow \varepsilon_{longitudinal}=\frac{0.001}{0.3}=0.0033$$$
Thus, the original length is:
$$$0.0033=\frac{0.5cm}{L_o}\Rightarrow L_o=\frac{0.5cm}{0.0033}=150\:cm$$$
150 cm
Time Analysis
See how quickly you looked at the hint, solution, and answer. This is important for making sure you will finish the FE Exam in time.- Hint: Not clicked
- Solution: Not clicked
- Answer: Not clicked
Similar Problems from FE Sub Section: Shear Stress-Strain
004. Stress and Strain
350. Poisson’s Ratio
374. Test Specimen
453. Shear Stress & Strain
460. Shear Modulus
467. Bulk vs Shear Modulus
Similar Problems from FE Sub Section: Engineering Strain
004. Stress and Strain
231. Subway Hand Rail
275. Unpressurized Vessel
309. Strain
317. Utility Pole
350. Poisson’s Ratio
374. Test Specimen
403. Train Tracks
573. Hooke’s Law
648. Elongating
Similar Problems from FE Section: Definitions
002. Piston Basics
004. Stress and Strain
007. Aluminum Alloy Graphs
032. Viscosity Variations
074. Dynamic Viscosity
084. Specific Gravity
174. Elongation
202. Uniaxial Loading
214. Steam Engine Piston
231. Subway Hand Rail
235. Kinematic Viscosity
275. Unpressurized Vessel
309. Strain
317. Utility Pole
332. Bulk Modulus of Elasticity
349. Compressibility Modulus
350. Poisson’s Ratio
374. Test Specimen
403. Train Tracks
446. Viscous Density
451. Poisson
453. Shear Stress & Strain
460. Shear Modulus
463. Newtonian Fluid
467. Bulk vs Shear Modulus
469. Flow Characterization
479. Piston Loading
527. S.G.
530. Spec Weight
534. SW
573. Hooke’s Law
580. Modulus of Elasticity
648. Elongating