Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
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Chapter 11, Problem 11.26P
Show that four strain gauges mounted to a shaft such that the gauge pairs measure equal and opposite strain can be used to measure torsional twist (as suggested in Table 11.1). Show that this method compensates for axial and bending strains and for temperature.
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Besides using strain gauges, name and describe two
alternative ways of measuring strains or deformations. List two
benefits of using each strain measuring system, compared to
strain gauges.
1) A compressive force is applied to a structural member. Two separate strain gauges are attached
to the structural member; one is a nickel wire strain gauge having a gauge factor of -12.1 and the
other is nichrome wire strain gauge having a gauge factor of 2. Calculate the value of resistance of
the two gauges after they are strained, if the resistance of strain gauges before being strained is
120 2, and the compressive strain is 5 micro-strain. Assume positive value for tensile strain and
negative for compressive strain.
(Answer: For Nickel, R = 120.00726 Q. For Nichrome, R = 119.9988 Q)
What is self-heating in strain gauges? Why is it caused and what are its implications on end result?
Chapter 11 Solutions
Theory and Design for Mechanical Measurements
Ch. 11 - Prob. 11.1PCh. 11 - 11.2 Calculate the change in length of a steel rod...Ch. 11 - 11.1 Calculate the change in length of a steel rod...Ch. 11 - 11.2 Calculate the change in length of a steel rod...Ch. 11 - 11.5 An electrical coil is made by winding copper...Ch. 11 - Compare the resistance of a volume of k X IO-2* m3...Ch. 11 - A conductor made of nickel (p, = 6.8 x 10-8 Q m)...Ch. 11 - Consider a Wheatstone bridge circuit that has all...Ch. 11 - 11.9 Consider a Wheatstone bridge circuit that has...Ch. 11 - 11.10 A resistance strain gauge with R = 120 Q and...
Ch. 11 - 11.11 A strain gauge that has a nominal resistance...Ch. 11 - Prob. 11.12PCh. 11 - 11.13 A single strain gauge is mounted as shown in...Ch. 11 - 11.14 A single strain gauge is mounted on a...Ch. 11 - 11.15 Equation 11.15 provides an expression for...Ch. 11 - 11.17 A steel beam member (vp = 0.3) is subjected...Ch. 11 - An axial strain gauge and a transverse strain...Ch. 11 - A strain gauge is mounted on a steel cantilever...Ch. 11 - Two strain gauges are mounted so that they sense...Ch. 11 - A rectangular bar is instrumented with strain...Ch. 11 - 11.23 A round member having a cross-sectional area...Ch. 11 - 11.24 A square structural member having a cross...Ch. 11 - 11.25 Show that the use of a dummy gauge together...Ch. 11 - Show that four strain gauges mounted to a shaft...Ch. 11 - 11.27 For each bridge configuration described...Ch. 11 -
Figure 11.25 Bridge arrangement for Problems...Ch. 11 - Prob. 11.29PCh. 11 - Prob. 11.30P
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- 3. Compare the resistance change produced by a strain of 150 microstrain if a strain gauge of nominal resistance of 120 N is used (i) when made of wire resistance having a gauge factor of 2.13 and (ii) when made of a semiconducting material having a gauge factor of 151. 4. A metallic strain gauge has a resistance of 120 Q and a gauge factor of 2. It is installed on an aluminium structure which has a yield point stress of 0.2 GN/m² and young's modulus of 68.7 GN/m?, determine the change in resistance of the gauge that would be caused by loading the material to yield point.arrow_forwardA single-strain gauge is mounted on the surface of a thin-walled pressure vessel that has a diameter of 1 m. For a strain gauge oriented along the tangential stress direction, determine the ratio between transverse and axial strain. The lateral sensitivity is 0.03. Take help from Mechanics of Material, Thin pressure vessels hoop stresses and longitudinal stresses equation.arrow_forwardFour strain gauges are formed into bridge with only one active gauge. The nominal resistance of all of them is 120 W. The gauge factor is 2.1 and the supply voltage is 10 V. Calculate the strain when the output from the bridge is 20 mV.arrow_forward
- A tensile test was conducted on a mild steel bar. The diameter and the gauge length of the bar were 3cm and 20cm respectively. The extension was 0.21mm. What is the value of strain?arrow_forwardThe strains measured by a rosette strain gauge arearrow_forward6. 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:arrow_forward
- 1. A strain gauge is glued to a structure. It has a gauge factor of 2.1 and a resistance of 120.2 2. The structure is stressed and the resistance changes to 120.25 2. Calculate the strain and convert this into stress. Take E = 205 GPa.arrow_forwardA strain gauge is used to measure the tension force in a 1-in. diameter bar of steel (E = 30, 000, 000 lb/ in?). The strain gauge has a nominal resistance of 140 N and a gauge factor (GF) of 4. The strain gauge is connected to a bridge (which is supplied with 10 Vdc). The bridge was initially balanced. After the bar is put under tension, the bridge output voltage goes to 0.0008 Vdc. Draw a schematic of the setup and calculate the force.arrow_forwardIn a tensile test on a specimen of black mild steel of 12 mm diameter, the following results were obtained for a gauge length of 60 mm. Load W(kN) 5 10 15 20 25 30 35 40 Extension x (10 mm) 14 27.2 41 54 67.6 81.2 96 112 When tested to destruction. Maximum load = 65 kN; load at fracture = 50 kN, diameter at fracture = 7.5 mm, total extension on gauge length = 17 mm. Find young's modulus, specific modulus, ultimate tensile stressarrow_forward
- In a tensile test on a specimen of black mild steel of 12 mm diameter, the following results were obtained for a gauge length of 60 mm. Load W(kN) 5 10 15 20 25 30 35 40 Extension x (10-3 mm) 14 27.2 41 54 67.6 81.2 96 112 When tested to destruction. Maximum load = 65 kN; load at fracture = 50 kN, diameter at fracture = 7.5 mm, total extension on gauge length = 17 mm. Find young's modulus, specific modulus, ultimate tensile stress, breaking stress, true stress at fracture, limit of proportionality, percentage elongation, percentage reduction in area. The relative density of the steel is 7.8. Draw the straight line graph.arrow_forwardIn a tensile test on a specimen of black mild steel of 12 mm diameter, the following results were obtained for a gauge length of 60 mm. Load W(kN) 5 10 15 20 25 30 35 40 Extension x (10-3 mm) 14 27.2 41 54 67.6 81.2 96 112 When tested to destruction. Maximum load = 65 kN; load at fracture = 50 kN, diameter at fracture = 7.5 mm, total extension on gauge length = 17 mm. Find young's modulus, specific modulus, ultimate tensile stress, breaking stress, true stress at fracture, limit of proportionality, percentage elongation, percentage reduction in area. The relative density of the steel is 7.8. Draw the straight line graph. Answer: breaking stress,true stress at fracture and limit of proportionality.arrow_forward5. A semiconductor gauge having a resistance of 1000 2 and a gauge factor of (-133) is subjected to a compressive strain of 500 microstrains. Calculate the new value of resistance of the gauge. 6. A strain gauge having a gauge factor of 4 is used for testing a machine. If the gauge resistance is 100 2 and the strain is 20 x 10-6, how much will the resistance of strain gauge change?arrow_forward
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