A cylindrical aluminum rod with a diameter of 10 mm is subjected to an axial tensile load of 5 kN. A foil strain gauge with the following properties is bonded axially along the surface of the rod:

Gauge factor (GF): 2.1

Unstrained resistance: 120.0 Ω

Measured change in resistance (ΔR): 0.189 Ω

Assume the strain gauge perfectly follows the deformation of the rod.

3. Is the strain value within the elastic range of aluminum (assume yield strain ≈ 0.0025). True or False?

Question

A cylindrical aluminum rod with a diameter of 10 mm is subjected to an axial tensile load of 5 kN. A foil strain gauge with the following properties is bonded axially along the surface of the rod:

Gauge factor (GF): 2.1

Unstrained resistance: 120.0 Ω

Measured change in resistance (ΔR): 0.189 Ω

Assume the strain gauge perfectly follows the deformation of the rod.

3. Is the strain value within the elastic range of aluminum (assume yield strain ≈ 0.0025). True or False?

BlackTom AI · Accepted Answer

The question asks whether the strain value is within the elastic range of aluminum given the rod under axial tension and the foil strain gauge reading.
First, examine the mechanical loading and material properties: the rod has a diameter of 10 mm, so its cross‑sectional area is A = π(0.005 m)^2 ≈ 7.85×10^-5 m^2. The applied axial load is F = 5 kN = 5000 N.
Next, compute the axial stress: σ = F / A ≈ 5000 / 7.85×10^-5 ≈ 6.37×10^7 Pa = 63.7 MPa.
To assess elastic range, we compare the stress to a typical aluminum yield stress. Given a yield strain ε_y ≈ 0.0025 and using a common Young’s modulus for aluminum E ≈ 70 GPa, the yield stress σ_y ≈ E·ε_y ≈ 70×10^9 × 0.0025 ≈ 175 MPa. Since 63.7 MPa < 175 MPa, the loading is within the elastic range, from a purely mechanical standpoint.
Now, determine the strain from the gauge reading: the foil gauge has GF = 2.1, initial resistance R0 = 120 Ω, and measured ΔR = 0.189 Ω.
Using the gauge factor definition, ε = ΔR / (GF · R0) = 0.189 / (2.1 × 120) = 0.189 / 252 ≈ 0.00075 (7.5×10^-4).
This strain value (7.5×10^-4) is well below the assumed yield strain (0.0025), and thus lies in the elastic regime for aluminum.
As a cross-check, one can also estimate strain from the mechanical stress: ε_mech ≈ σ / E ≈ 63.7 MPa / 70 GPa ≈ 0.00091 (9.1×10^-4), which is on the same order of magnitude as 0.00075 and also below ε_y. Given both independent approaches indicate elastic behavior, the statement that the strain value is within the elastic range is consistent.
In summary, the calculated strain from the gauge reading is small enough to be considered elastic for aluminum under these conditions, and the comparison with yield strain supports this conclusion.

类似问题

What was the world's first widely adopted biodiversity policy?

The aim of the Paris Agreement is to ensure that the earth’s preindustrial temperature is not exceeded by more than º Celsius.

The IPCC's mission is to Blank ______.

Why have most international agreements for environmental protection been based on the honor system?

As was exhibited with the Montreal Protocol and the encouragement of reduced CFC production, trade can be an effective tool to compel compliance with international treaties.

The Stockholm Declaration and UNEP were the result of the Blank ______ first conference on the Human Environment in 1972.

In addition to the direct mission of the Convention on International Trade in Endangered Species (CITES), why was CITES so important?

President Trump hiring a corporate leader from the oil and gas industry to head the Department of Energy is an example of regulatory ; one intention behind this was to change environmental policy.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单