05 Strain Gages Concept Overview
STRAIN GAGES | CONCEPT OVERVIEW
The topic of STRAIN GAGES can be referenced on page 125 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
CONCEPT INTRO: A STRAIN GAGE is a device that experiences a change in electrical resistance proportional to the amount of strain exerted on the device. Strain gages are attached to a member or system elements and measure the strain that component experiences during a defined time period. A strain gage operates on the principle that if a strip of conductive metal is placed under compressive force, it will broaden and shorten resulting in the resistance to decrease (-). If the same strip of conductive metal is instead stretched in tension, it will become skinnier and longer, resulting in the resistance to increase (+). Both forces acting on the strain gage will results in an increase of electrical resistance end-to-end.
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The formula for the GAGE FACTOR can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 124 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. A GAGE FACTOR (GF) is the ratio of fractional change in electrical resistance to the fractional change in length (strain). The gage factor represents the ratio of the change in gage resistance to the change in length or strain of the gage.
GF =
ΔR/R ΔR/R = ΔL/L ε
Where: • 𝑅 is the nominal resistance of the strain gage at nominal length 𝐿 • 𝛥𝑅 is the change in resistance due to the change in length 𝛥𝐿 • 𝜀 is the normal strain sensed by the gage The value for the GAGE FACTOR OF METALLIC STRAIN GAGES can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 125 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. In applications of strain gages, a high degree of sensitivity is desired to acquire the most accurate data possible. A high gage factor indicates a relatively large resistance change for a given strain, where such a change is more easily measured than any small changes in the resistance. The gage factor for the metallic strain gages is typically around 2.
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The table for the GAGE SETUP FOR DIFFERENT TYPE OF STRAIN can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 125 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. For the purposes of the FE Exam, the applications of strain gages will be limited to axial strain, bending strain, and torsional and shear strain. Based on the type of strain being analyzed, there are various setup and configurations for the strain gages as shown in the table below. For each set up, there is an associated sensitivity and bridge type classification to analyze a particular strain.
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WHEATSTONE BRIDGE: The topic of WHEATSTONE BRIDGE can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 126 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. A WHEATSTONE BRIDGE is an electrical circuit used to measure strain of a member or object by utilizing a particular arrangement of strain gages and resistors to measure changes in resistance as dictated by the strain experienced by the strain gages.
The Wheatstone bridge circuit consists of four resistors arranged in a symmetrical configuration as shown above. An input DC voltage, or excitation voltage is applied between the left and right of the square section of resistors, and the output voltage is measured across the middle.
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Another common configuration for the Wheatstone bridge is the diamond configuration shown below. The top and bottom of the diamond, and the output voltage is measured across the middle.
When the current flowing through all four resistors is identical, the bridge is said to be BALANCED as the current is the same on the left and right legs of the bridge. As the current is balanced on both sides of the bridge, the output voltage is 𝑉. = 0. The formula for a BALANCED WHEATSTONE BRIDGE can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 126 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. In the case that the resistance in each resistor is not identical, the equivalent resistance on the left leg and right leg is equivalent, the bridge is said to still be balanced. This is due to the current division being equally divided for each leg as shown by the formula:
𝐼𝑓
𝑅4 𝑅6 = 𝑡ℎ𝑒𝑛 𝑉. = 0 𝑉 𝑅5 𝑅7
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The formula for an UNBALANCED WHEATSTONE BRIDGE can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 126 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. As the resistance of one of the legs changes due a perceived strain in the strain gage, the resistance will change accordingly, and the previously balanced bridge will become UNBALANCED. If one of the resistances of the resistors starts to vary with the measured variable such as temperature or pressure, then the output voltage V. will also vary with the measured variable. Therefore, the bridge output can be used to indicate the measure variable. 𝐼𝑓 𝑅4 = 𝑅5 = 𝑅6 = 𝑅 𝑎𝑛𝑑 𝑅 = 𝑅 + 𝛥𝑅, 𝑤ℎ𝑒𝑟𝑒 𝛥𝑅 ≪ 𝑅 𝑡ℎ𝑒𝑛: The formula for an ¼ QUARTER WHEATSTONE BRIDGE can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 126 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. A ¼ quarter arm Wheatstone bridge circuit is used for individual strain gages where the resistance 𝑅4 is the strain gage and the other three resistances are precision resistors equal to the nominal resistance of equivalent resistance. If the strain gage experiences a strain, the strain gage resistance changes, causing the bridge to become unbalanced. The resulting output voltage is given by: 𝑉. ≈
𝛥𝑅 ∙𝑉 4𝑅 HI
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CONCEPT EXAMPLE: A football team is looking to measure the strain on an aluminum bench during a big game. The strain gage being used has a gage factor of 2, a resistance of 350 𝛺, and a length of 3 mm. After a touchdown, the resistance is found to have changed to 420 𝛺. What is the increase of the length of the strain gage closest too? A. 0.3 B. 1.3 C. 3.0 D. 3.3
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SOLUTION: In this problem we are given all of the information we need to calculate the change in length as indicated by the change in resistance: • Gage Factor: 𝐺𝐹 = 2 • 𝑅4 = 350 𝛺 • 𝐿4 = 3 𝑚𝑚 • 𝑅5 = 420 𝛺
The formula for the GAGE FACTOR can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 125 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
A GAGE FACTOR (GF) is the ratio of fractional change in electrical resistance to the fractional change in length (strain). The gage factor represents the ratio of the change in gage resistance to the change in length or strain of the gage.
GF =
ΔR/R ΔR/R = ΔL/L ε
Where: • R is the nominal resistance of the strain gage at nominal length L • ΔR is the change in resistance due to the change in length ΔL • ε is the normal strain sensed by the gage
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Plugging the given values into the expression for the gage factor, we begin to isolate the term representing the final length, given as 𝐿5 :
2=
(420 − 350)/350 (L5 − 3)/3
Solving for the length, we get: 𝐿5 = 3.3 Now that we have the initial start and final end location of the strain gage, we can calculate the increase of length as: 𝛥𝐿 = 𝐿5 − 𝐿4 Plugging in the values for the initial and final lengths, we calculate the change in length as: 𝛥 = 3.3 − 3.0 = 0.3
Therefore, the correct answer choice is A. 𝟎. 𝟑
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The topic of STRAIN GAGES can be referenced on page 125 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
CONCEPT INTRO: A STRAIN GAGE is a device that experiences a change in electrical resistance proportional to the amount of strain exerted on the device. Strain gages are attached to a member or system elements and measure the strain that component experiences during a defined time period. A strain gage operates on the principle that if a strip of conductive metal is placed under compressive force, it will broaden and shorten resulting in the resistance to decrease (-). If the same strip of conductive metal is instead stretched in tension, it will become skinnier and longer, resulting in the resistance to increase (+). Both forces acting on the strain gage will results in an increase of electrical resistance end-to-end.
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The formula for the GAGE FACTOR can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 124 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. A GAGE FACTOR (GF) is the ratio of fractional change in electrical resistance to the fractional change in length (strain). The gage factor represents the ratio of the change in gage resistance to the change in length or strain of the gage.
GF =
ΔR/R ΔR/R = ΔL/L ε
Where: • 𝑅 is the nominal resistance of the strain gage at nominal length 𝐿 • 𝛥𝑅 is the change in resistance due to the change in length 𝛥𝐿 • 𝜀 is the normal strain sensed by the gage The value for the GAGE FACTOR OF METALLIC STRAIN GAGES can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 125 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. In applications of strain gages, a high degree of sensitivity is desired to acquire the most accurate data possible. A high gage factor indicates a relatively large resistance change for a given strain, where such a change is more easily measured than any small changes in the resistance. The gage factor for the metallic strain gages is typically around 2.
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The table for the GAGE SETUP FOR DIFFERENT TYPE OF STRAIN can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 125 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. For the purposes of the FE Exam, the applications of strain gages will be limited to axial strain, bending strain, and torsional and shear strain. Based on the type of strain being analyzed, there are various setup and configurations for the strain gages as shown in the table below. For each set up, there is an associated sensitivity and bridge type classification to analyze a particular strain.
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WHEATSTONE BRIDGE: The topic of WHEATSTONE BRIDGE can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 126 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. A WHEATSTONE BRIDGE is an electrical circuit used to measure strain of a member or object by utilizing a particular arrangement of strain gages and resistors to measure changes in resistance as dictated by the strain experienced by the strain gages.
The Wheatstone bridge circuit consists of four resistors arranged in a symmetrical configuration as shown above. An input DC voltage, or excitation voltage is applied between the left and right of the square section of resistors, and the output voltage is measured across the middle.
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Another common configuration for the Wheatstone bridge is the diamond configuration shown below. The top and bottom of the diamond, and the output voltage is measured across the middle.
When the current flowing through all four resistors is identical, the bridge is said to be BALANCED as the current is the same on the left and right legs of the bridge. As the current is balanced on both sides of the bridge, the output voltage is 𝑉. = 0. The formula for a BALANCED WHEATSTONE BRIDGE can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 126 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. In the case that the resistance in each resistor is not identical, the equivalent resistance on the left leg and right leg is equivalent, the bridge is said to still be balanced. This is due to the current division being equally divided for each leg as shown by the formula:
𝐼𝑓
𝑅4 𝑅6 = 𝑡ℎ𝑒𝑛 𝑉. = 0 𝑉 𝑅5 𝑅7
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The formula for an UNBALANCED WHEATSTONE BRIDGE can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 126 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. As the resistance of one of the legs changes due a perceived strain in the strain gage, the resistance will change accordingly, and the previously balanced bridge will become UNBALANCED. If one of the resistances of the resistors starts to vary with the measured variable such as temperature or pressure, then the output voltage V. will also vary with the measured variable. Therefore, the bridge output can be used to indicate the measure variable. 𝐼𝑓 𝑅4 = 𝑅5 = 𝑅6 = 𝑅 𝑎𝑛𝑑 𝑅 = 𝑅 + 𝛥𝑅, 𝑤ℎ𝑒𝑟𝑒 𝛥𝑅 ≪ 𝑅 𝑡ℎ𝑒𝑛: The formula for an ¼ QUARTER WHEATSTONE BRIDGE can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 126 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. A ¼ quarter arm Wheatstone bridge circuit is used for individual strain gages where the resistance 𝑅4 is the strain gage and the other three resistances are precision resistors equal to the nominal resistance of equivalent resistance. If the strain gage experiences a strain, the strain gage resistance changes, causing the bridge to become unbalanced. The resulting output voltage is given by: 𝑉. ≈
𝛥𝑅 ∙𝑉 4𝑅 HI
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CONCEPT EXAMPLE: A football team is looking to measure the strain on an aluminum bench during a big game. The strain gage being used has a gage factor of 2, a resistance of 350 𝛺, and a length of 3 mm. After a touchdown, the resistance is found to have changed to 420 𝛺. What is the increase of the length of the strain gage closest too? A. 0.3 B. 1.3 C. 3.0 D. 3.3
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SOLUTION: In this problem we are given all of the information we need to calculate the change in length as indicated by the change in resistance: • Gage Factor: 𝐺𝐹 = 2 • 𝑅4 = 350 𝛺 • 𝐿4 = 3 𝑚𝑚 • 𝑅5 = 420 𝛺
The formula for the GAGE FACTOR can be referenced under the topic of INSTRUMENTATION, MEASUREMENT, AND CONTROLS on page 125 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
A GAGE FACTOR (GF) is the ratio of fractional change in electrical resistance to the fractional change in length (strain). The gage factor represents the ratio of the change in gage resistance to the change in length or strain of the gage.
GF =
ΔR/R ΔR/R = ΔL/L ε
Where: • R is the nominal resistance of the strain gage at nominal length L • ΔR is the change in resistance due to the change in length ΔL • ε is the normal strain sensed by the gage
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Plugging the given values into the expression for the gage factor, we begin to isolate the term representing the final length, given as 𝐿5 :
2=
(420 − 350)/350 (L5 − 3)/3
Solving for the length, we get: 𝐿5 = 3.3 Now that we have the initial start and final end location of the strain gage, we can calculate the increase of length as: 𝛥𝐿 = 𝐿5 − 𝐿4 Plugging in the values for the initial and final lengths, we calculate the change in length as: 𝛥 = 3.3 − 3.0 = 0.3
Therefore, the correct answer choice is A. 𝟎. 𝟑
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