EGB373-TUT 10-Week 11 - Shear Strength of Soils -2 (Triaxial Tests)-Answers

650 600 550 500 450 400 350 300 250 200 150 100 50 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Strain mm/mm The graph above shows the stress-strain relationship of a steel bar under tension test. The steel bar diameter = 8 mm and the bar gauge length = 100 mm. Determine the following: If the specimen is loaded to 550 MPa and then unloaded. What would be the modulus of resilience of the sample after reloading? Stress (MPa)

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Q1) A solid steel shaft subjected to a moment M. The shaft diameter is 60 mm. A Wheatstone Bridge has been used to measure the strain generated due to the moment M. The Wheatstone Bridge has three resistances of 1202, and the fourth one is a strain gauge with 120, and 2 gauge factor. The excitation voltage is 10V. The Wheatstone Bridge output voltage is 153.26 μV when the moment M is applied on the shaft. Compute the value of the moment M. (Steel's modulus of elasticity is E = 200 GPa and Poisson's ratio is v=0.3)

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.

A metallic strain gauge produces an electrical resistance change when subjected to mechanical strain. However, engineers don't measure this voltage drop directly using a voltmeter. Why don't we directly measure the voltage drop across the strain gauge, and instead, use a Wheatstone Bridge? Damgraph >

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,…

2) The stress-strain diagram for an alloy specimen having an original diameter of 0.5 in. and a gage length of 2 in. is shown in the figure below. TENSILE STRESS (MPA) 450 400 350 300 250 200 150 100 50 Part A 0 0 STRESS VS. STRAIN 0.002 0.004 STRAIN 0.006 Determine the modulus of resilience. Show units. Part B Determine the modulus of elasticity of the material. Part C Estimate the Yield Strength of the material. 0.008 0.01

1. A tension test on an aluminum plate resulted in the following engineering stress-engineering strain data as reported in the first and second column of the table below (reduction of area, RA=17%): S (psi) e (in/in) σ (psi) ε (in/in) 10500 0.001 10510.5 0.000995 21000 0.002 31200 0.003 41300 0.004 51200 0.005 61200 0.006 70600 0.007 74700 0.0075 76800 0.008 77600 0.0085 78000 0.009 78400 0.0095 78700 0.01 81200 0.02 83000 0.03 84200 0.04 85400 0.05 86200 0.06 86800 0.07 *87200 0.08 **86200 0.1 Note: * maximum load, ** load at fracture a) Calculate the corresponding true stress and true strain and give your results in a table along with the engineering stress, engineering strain shown in the of table above (column 3 and 4). b) Plot the true stress-true strain curve on a rectangular coordinate. c) Plot the true stress-true strain curve on a log-log graph and determine the plastic flow curve parameters K and n, the yield strength, Y, and the elastic modulus, E of the material.

The purpose of this problem is to show the relationship between material constants typically used in engineering practice. This is useful because you may often have access to measurements of or tabulated values of some constants (e.g., Young's modulus and Poisson's ratio) but need another constant (e.g., shear modulus) for a calculation. Use the expression Cijkl = µ(dildjk + dikdjl) + Ad¿jdkl to derive the following: (a) Young's modulus, E = µ(3X+2µ)/(X+μ), from the definition 11 = Ee11 in a unconfined (022 = 0,033 = 0) uniaxial tension test. (b) Poisson's ratio, v = \/(2(X + μ)), from the definition v = €22/11 in the same test as in (a). (c) Shear modulus, μ = G = 012/(2€12) = E/(2(1 + v)). Use the results to show that C can also be written Cijkl Ev/((1+v)(1 − 2v))dij§kl. = E/(2(1 + v))(duðjk + dikdjl) +