### Thermal Expansion Gap Problem: Polymer Bars#### Problem Statement:At a temperature of 11°C, a 2-mm gap exists between two polymer bars and a rigid support, as shown in the figure. Bars (1) and (2) have coefficients of thermal expansion of α₁ = 122 x 10⁻⁶ /°C and α₂ = 80 x 10⁻⁶ /°C, respectively. The supports at A and C are rigid. Determine the lowest temperature at which the 2-mm gap is closed. Assume L₁ = 580 mm and L₂ = 320 mm.#### Data:- Initial temperature (T₀): 11°C- Initial gap (g): 2 mm- Coefficient of thermal expansion for bar (1) (α₁): 122 x 10⁻⁶ /°C- Coefficient of thermal expansion for bar (2) (α₂): 80 x 10⁻⁶ /°C- Length of bar (1) (L₁): 580 mm- Length of bar (2) (L₂): 320 mm- Supports at points A and C are rigid#### Diagram Description:The diagram shows two polymer bars placed end-to-end between two rigid supports labeled A and C. - Bar (1) is on the left, with a length of L₁. It has a coefficient of thermal expansion α₁.- Bar (2) is on the right, with a length of L₂. It has a coefficient of thermal expansion α₂.- There is a gap (g) of 2 mm between the two bars.#### Calculation:Determine the lowest temperature (T) at which the 2-mm gap is closed.---#### Interactive Component:**Answer: T =** [________] °C---**Attempts: 0 of 5 used**---**Submit Answer**#### Resources:- eTextbook and MediaNote: Ensure to review all related textbook materials and example problems for further guidance on solving thermal expansion problems.

Answered: Image /qna-images/answer/1f04d3f3-cb7a-4bc7-aeeb-d17fbc35bd32.jpg

Answered: At a temperature of 11°C, a 2-mm gap…

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

Consider the bar in Figure 2, which has cross-sectional area A = 1·10−3 m2, modulus of elasticityE = 1·1011 N/m2, and length 1 m. The bar is fixed to a wall on its left hand side. Along the left halfof the bar, x=[0 m, 0.5 m], there is a constant distributed force of l(x) = 10 kN/m. Along the righthalf of the bar, x=[0.5 m, 1 m], there is a constant distributed force of l(x) = 20 kN/m. a) Given the finite element mesh in Figure 3, consisting of two elements of equal size L = 0.5 m,sketch the associated basis functions of the mesh, and write the approximation of the displacementfunction u(x) as an expansion of these basis functions. Use u1, u2 and u3 to denote the expansioncoefficients for each node. b) The general form of the element stiffness matrix system, with nodes indexed by i and j, is givenas shown in the image of eqaution 2, where F0 and f(1) denote boundary forces at positions x = 0 and x = 1, respectively. Form the two basis functions for element 2, and evaluate the right…
I need help with part e, thanks
A circular bar of length 400 mm and tapering uniformly from 50 mm to 25 mm diameter is held between rigid supports at the ends. Calculate the maximum and minimum stress developed in the bar when the temperature is raised by 30°C. Take E = 2 × 105 N/mm² and a = 1.2 x 10-5. per °c
Parvinbhai
a 20mm diameter bronze bar 3.4m long is place between two rigid walls. at a temperature of -31°C, the gap ∆= 4.7mm. Find the temperature (at degree Celsius) at which the compressive stress in the bar will be 39MPa . Use alpha = 19.59x10^-6 m/(m.°C) and E= 87GPa.
Problem 3: (M4) Your boss at a construction company asked you to verify the thickness of a 3 m long hollow-square steel column (E=200 GPA) that can withstand an axial compressive load of 50 MN, the outer dimension a is 400 mm. The column's cross section is shown in Figure.4. Assume the column is a fixed-free type. Figure.4: Cross-section of a hollow-square steel column
By the equipment as shown in the figure, temperature can be measured. The bar AB and CD are made from aluminum and titanium. The coefficients of thermal expansion are 23.6x106 1/K and 8.2x10-6 1/k. Obtain the relationship between the temperature and the vertical displacement at the point E. 6 mm 72 mm 36 mm D
A steel rod bolt 8mm diameter inside fits loosely on an aluminium tube and 16mm outside diameter. A nut is fitted into the bolt and tighten against the tube, until the stress in the bolt is 40N/mm². Calculate the stress in the tube. If the temperature of the assembly is now increased by 100°C. What will be the new stress in each component?
3. Three bars each made from different materials are placed between walls when the temperature is 14°C. Determine the support reaction when the temperature becomes 19°C. The material properties are given in the figure. Answer: R = 3502.30 N Steel Brass Copper Ebr 100 GPa Ecu = 120 GPa Est=200 GPa ast = 12(10-6)/°C abr = 21(106)/C acu = 17(10-6)/°C Acu = 515 mm² |Ast = 200 mm² Abr= 450 mm² -300 mm- 200 mm- 100 mm 4. The rigid slab is supported by two identical copper rods as shown. The copper rod has an area of 500 mm² with a = 16.8 μm/ (m°C) and E = 120 GPa. There is a gap of 0.18 mm between the slab and the aluminum rod. The aluminum rod has an area of 400 mm² with a = 23.1 μm/ ( mºC) and E = 70 GPa. Compute the stress developed in each rod when the temperature is raised to 85°C. Assume that the weight of the slab is negligible. Answer: OAI = 16.80 MPa 85 →TA Δ Copper Aluminum Copper 750 mm-
A 5-m rod having a uniform cross-sectional area of 1000 sq. mm. is secured between two walls5 meters apart. The load on the rod is zero at 27 °C. E = 200 GPa, α = 11.25x10-6 m/m-°C. Whenthe temperature rises to 57°C: What is the stress in the rod assuming that the walls are rigid and stress (in the rod) if the walls spring together with a total distance of 0.5 mm? pls box final answer
The depicted in the figure below has a length of 0.635m and a diameter of 50mm. The bar is made of a copper alloy with an elastic modulus E = 110 GPa and a linear thermal expansion coefficient a = 17.5 × 10-6/°C. The bar is initially positioned at room temperature with a gap of 0.2mm between end A and the rigid wall. The bar's right end at B is supported by an elastic spring of negligible thermal expansion coef- ficient and a spring constant of k = 210 × 10°N/m. A small gap maintained between the copper bar and the smooth surrounding sleeve facilitates frictionless motion as the bar thermally expands. Questions: (a) Compute the temperature increase ATer required to close the 0.2 mm gap. (b) Compute the axial force R developed in the copper bar due to a temperature increase of AT = 27°C. State the compatibility condition and solve it for R. (c) Compute the compressive (engineering) stress o developed within the copper bar due to the axial force R. Express your answer in MPa. (d) Compute…
Kindly show a step-by-step solution. Thank you A 6m rod with a 4mm gap between one of its ends and the surface of the wall next to it is secured solidly between two walls at 25°C. Calculate the highest temperature that the rod can withstand in degrees celsius while taking into account the maximum limiting stress of 67 MPa, where a = 19.5 m/mC°, and E = 130 GPa.

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:

9781118170519

Author:

Norman S. Nise

Publisher:

WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:

9781118807330

Author:

James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:

WILEY

SEE MORE TEXTBOOKS