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A 5-mm-thick rectangular alloy bar is subjected to a tensile load P by pins at A and B, as shown in the figure. The width of the bar is w= 26 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: Ex = 840 με and Ey = -265 με. (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of P = 18 kN, what is the modulus of elasticity for this specimen?

A 5-mm-thick rectangular alloy bar is subjected to a tensile load P by pins at A and B, as shown in the figure. The width of the bar is w= 26 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: Ex = 840 με and Ey = -265 με. (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of P = 18 kN, what is the modulus of elasticity for this specimen?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Tensile Load Experiment on a Rectangular Alloy Bar #### Problem Description A 5-mm-thick rectangular alloy bar is subjected to a tensile load \( P \) by pins at points \( A \) and \( B \), as illustrated in the figure below. The width of the bar is \( w = 26 \) mm. Strain gauges bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: - \(\epsilon_x = 840 \, \mu\epsilon\) - \(\epsilon_y = -265 \, \mu\epsilon\). #### Questions (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of \( P = 18 \) kN, what is the modulus of elasticity for this specimen? #### Diagram Description The provided diagram shows a rectangular alloy bar, with thickness \( t \), subjected to a tensile load \( P \). The bar is pinned at points \( A \) and \( B \). The direction of the tensile load \( P \) is indicated by arrows pointing outward from the ends of the bar. Additionally, the diagram highlights the longitudinal direction \( x \) and the transverse direction \( y \). #### Solutions ##### (a) Poisson's Ratio (\(\nu\)): Given: - \(\epsilon_x = 840 \, \mu\epsilon\) - \(\epsilon_y = -265 \, \mu\epsilon\) \[ \nu = -\frac{\epsilon_y}{\epsilon_x} = -\frac{-265 \, \mu\epsilon}{840 \, \mu\epsilon} = 0.315 \] ##### (b) Modulus of Elasticity (E): \[ P = 18 \, \text{kN} = 18000 \, \text{N} \] Strain (\(\epsilon\)) and stress (\(\sigma\)) relationship: \[ \sigma_x = \frac{P}{A} = \frac{P}{w \times t} = \frac{18000 \, \text{N}}{26 \, \text{mm} \times 5 \, \text{mm}} = \frac{18000}{130} \, \text{N/mm}^2 = 138.462 \, \text{MPa}
Transcribed Image Text:### Tensile Load Experiment on a Rectangular Alloy Bar #### Problem Description A 5-mm-thick rectangular alloy bar is subjected to a tensile load \( P \) by pins at points \( A \) and \( B \), as illustrated in the figure below. The width of the bar is \( w = 26 \) mm. Strain gauges bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: - \(\epsilon_x = 840 \, \mu\epsilon\) - \(\epsilon_y = -265 \, \mu\epsilon\). #### Questions (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of \( P = 18 \) kN, what is the modulus of elasticity for this specimen? #### Diagram Description The provided diagram shows a rectangular alloy bar, with thickness \( t \), subjected to a tensile load \( P \). The bar is pinned at points \( A \) and \( B \). The direction of the tensile load \( P \) is indicated by arrows pointing outward from the ends of the bar. Additionally, the diagram highlights the longitudinal direction \( x \) and the transverse direction \( y \). #### Solutions ##### (a) Poisson's Ratio (\(\nu\)): Given: - \(\epsilon_x = 840 \, \mu\epsilon\) - \(\epsilon_y = -265 \, \mu\epsilon\) \[ \nu = -\frac{\epsilon_y}{\epsilon_x} = -\frac{-265 \, \mu\epsilon}{840 \, \mu\epsilon} = 0.315 \] ##### (b) Modulus of Elasticity (E): \[ P = 18 \, \text{kN} = 18000 \, \text{N} \] Strain (\(\epsilon\)) and stress (\(\sigma\)) relationship: \[ \sigma_x = \frac{P}{A} = \frac{P}{w \times t} = \frac{18000 \, \text{N}}{26 \, \text{mm} \times 5 \, \text{mm}} = \frac{18000}{130} \, \text{N/mm}^2 = 138.462 \, \text{MPa}
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