### Tensile Load Experiment on a Rectangular Alloy Bar#### Problem DescriptionA 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 DescriptionThe 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}

Here I have used the simple definitions of Poisson ratio and the stress and strain relationship.

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

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

We're measuring axial load in a rectangular bar with two strain gauges: one on the top in the axial direction and the other on the bottom in the transverse direction). An axial load, P, is applied and the ambient temperature is varying with time. P # Strain gages > Р (a) If one strain gauge is connected to leg 1 of the Wheatstone bridge, which leg (2, 3, or 4) would you connect the other strain gauge in order to achieve temperature compensation? Please explain your choice by writing out the equation. (b) Calculate the bridge constant of this arrangement, your (c) If some bending moment were inadvertently applied (in addition to the axial load), would choice in part (a) provide compensation for bending loading? Justify your answer by writing out the equation.
material with a rectangular cross-section of 4 mm by 25 mm is loaded in tension with a force of 32 kN. A strain gauge bonded to the material measures a strain of 400 microstrain when the sample is loaded. culate Young's modulus of the material, measured to the nearest GPa (GN/m2) and enter your answer in the box below. ung's modulus: [ GPa
A 45° degree strain gauge rosette positioned on the surface of a structure under stress recorded the following values of normal strain: Gauge A: Gauge B: (oriented at 45° anti-clockwise to gauge A) Gauge C: -275×10 (oriented at 90° anti-clockwise to gauge A) What is the value of normal strain and shear strain on a plane inclined at 29° clockwise from gauge B? -6 - 195 × 10 (oriented in the postive x direction) 145 x 10-6 a) The normal strain and shear strain on a plane inclined at 29° clockwise from gauge B are 0.3 microstrain and 602.1 microstrain, respectively. b) The normal strain and shear strain on a plane inclined at 29° clockwise from gauge B are 0.3 microstrain and 301.1 microstrain, respectively. c) The normal strain and shear strain on a plane inclined at 29° clockwise from gauge B are 108.5 microstrain and 334.9 microstrain, respectively. d) The normal strain and shear strain on a plane inclined at 29° clockwise from gauge B are 108.5 microstrain and 167.4 microstrain,…
Q1 The 45° strain rosette is mounted on a steel robotic am as shown in Figure Ql. The robotic arm is made from steel with Esel = 200 GRA and poison ratio, v= 0.3. The following readings are obtained for each gauge: E=[Y+Z](10“) E = -250(10-) E= -200(10) Here the value of Y and Z depends on the 5th digit and 6th digit of your matric number as shown in Table 1. For example, if your matrix number is DD 070112 gives the value of Y=300 and Z-60: Table 1 5 digit of matric 6* digit of matric number number 250 300 350 30 2 60 3 400 3 90 4 450 120 5 500 150 6. 550 180 7 600 7 210 650 700 240 270 (a) Prove that &= E, and E, = E. Determine the shear strain, yand the normal strain, E, and &. (b) Estimate the in-plane principal strains and the angle associated with the principal strains, and (c) Calculate the principal stress associated with the prihcipal strains in (c). (d)
A polypropylene has the following tensile creep compliance measured at 40 °C: D(t) = 1.2 x t0.1 GPa-1 where t is expressed in seconds. It is subjected to the following tensile stress sequence at 40 °C. Find the tensile strain at 3200 sec. Stress (MPa) 1.5 1.0 0.5 1000 2000 3000 Time (s)
6. State your answers to the following questions.Strain Gauge represents the deformation of a material through a change in resistance. If so, explain how temperature will affect the strain gauge in the experimental environment.①:In this experiment, the Strain Gauge measures the strain in micro units. Explain one possible error factor when applying a load by hanging a weight on the material with the strain gauge attached. (Hint: It is easy to shake by hanging the weight using a thread)①:
A 45° degree strain gauge rosette positioned on the surface of a structure under stress recorded the following values of normal strain: Gauge A: -195×10 (oriented in the postive x direction) Gauge B: 145 x 10- (oriented at 45° anti-clockwise to gauge A) Gauge C: -275×10-8 (oriented at 90° anti-clockwise to gauge A) What is the value of normal strain and shear strain on a plane inclined at 29° clockwise from gauge B? a) The normal strain and shear strain on a plane inclined at 29° clockwise from gauge B are 0.3 microstrain and 602.1 microstrain, respectively. b) The normal strain and shear strain on a plane inclined at 29° clockwise from gauge B are 0.3 microstrain and 301.1 microstrain, respectively. c) The normal strain and shear strain on a plane inclined at 29° clockwise from gauge B are 108.5 microstrain and 334.9 microstrain, respectively. d) The normal strain and shear strain on a plane inclined at 29° clockwise from gauge B are 108.5 microstrain and 167.4 microstrain,…
Problem 2: A specimen of steel having an initial diameter of 0.503 in was tested in tension using a gauge length of 2 inches. The following data were obtained for the tension. Plot the stress strain data and determine the modulus of elasticity, and the yield strength of the material. Elastic State Load P Ibf Elongation in 1 000 0.0004 2 000 0.0006 3 000 0.0010 4 000 0.0013 7 000 0.0023 8 400 0.0028 8 800 0.0036 9 200 0.0089
5. Please calculate the strain and stress in the following two prompts a. A 1 cm long section of tendon stretches to 1.011 cm when it is subjected to a tensile force of 40,000 N. What is the strain in this segment of tendon? @? 17 b. The section of the patellar ligament in the previous question is 0.02 m² in the cross section. What is the stress in this section of ligament as a result of 50,000 N tensile force? E = Δι 19 0 = A 1.011 cm 50000 0,02 Scoco 40000 1.25 = T % 2500000 strain N/m² on trito flox your wrist, you may notice that your
Help me please
4. A cylindrical specimen of stainless steel having a diameter of 12.8 mm and a gauge length of 50.800 mm is pulled in tension. The load- elongation characteristics are tabulated below as follows: Load (N) Length (mm) 0 12,700 25,400 38,100 50,800 76,200 89,100 92,700 102,500 107,800 119,400 128,300 149,700 159,000 160,400 159,500 151,500 124,700 Fracture 50.800 50.825 50.851 50.876 50.902 50.952 51.003 51.054 51.181 51.308 51.562 51.816 52.832 53.848 54.356 54.864 55.880 56.642 (a) Plot the data as engineering stress versus engineering strain. (b) Compute the modulus of elasticity. (c) Determine the yield strength at a strain offset of 0.002. (d) Determine the tensile strength of this alloy.
You need the shear modulus for a particular material in order to calculate shear strain for a known applied shear shear stress. You can't find shear modulus for the material, but you can find elastic modulus (200 GPa) and Poisson's ratio (0.3). Which of the following could you use as the shear modulus for your calculations? 200 GPa O 60 GPa O 77 GPa O 154 GPa