Consider a 50 mm × 50 mm × 50 mm element of graphite-reinforced material that is heated 50°C above some reference state and is restrained in the 2 direction. (a) What are the changes in dimensions of the heated element in the 1 and 3 directions? (b) What stress 02 is required to restrain the element against deformation in the 2 direction? Assume the material properties are independent of temperature. (c) How do the changes in dimensions of the heated element for this partially restrained case compare numerically with the changes in dimensions of the heated element for the case of free thermal strain, equation (2.101)? Why are they different? (d) What are the mechanical strains for this case? Numerically compare the mechanical strains with the fully constrained case, that is, equation (2.119). Hint: To solve the problem use either equation (2.107) or (2.108), assume &₁# 0 and 83 ‡ 0, and solve for 81, 83, and 02.

Consider a 50 mm × 50 mm × 50 mm element of graphite-reinforced material that is heated 50°C above some reference state and is restrained in the 2 direction. (a) What are the changes in dimensions of the heated element in the 1 and 3 directions? (b) What stress 02 is required to restrain the element against deformation in the 2 direction? Assume the material properties are independent of temperature. (c) How do the changes in dimensions of the heated element for this partially restrained case compare numerically with the changes in dimensions of the heated element for the case of free thermal strain, equation (2.101)? Why are they different? (d) What are the mechanical strains for this case? Numerically compare the mechanical strains with the fully constrained case, that is, equation (2.119). Hint: To solve the problem use either equation (2.107) or (2.108), assume &₁# 0 and 83 ‡ 0, and solve for 81, 83, and 02.

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

Related questions

Q: P2. Design a cylindrical thin-wall composite fuselage for storing compressed natural gas at a…

Q: Explain how the properties and structure of different given engineering materials affect their…

A: Given questions are related to material science and manufacturing.

Q: Steady-state creep rate data are given here for some alloy taken at 200°C (473 K): i Es (h-¹) 2.2 x…

Q: A cube of aluminum has a mass of 200 grams and its temperature rises from 15.0 °C to 28.5 °C when…

A: Given details: m=200 gramsCAl=0.921 J/g°CT1=15°CT2=28.5°C

Q: The assembly is the same as in problem 2. It consists D of two rods AC and BD attached to the 100-lb…

Q: (6) For an aluminum alloy under constant load, the creep rate increased by a factor of 2 when the…

Q: For safe and reliable operation, a certain polypropylene pipe must withstand an internal pressure of…

Q: 3.6. The temperature decreases at a constant rate from 1000 to 500 hPa. At Madison, the 500 hPa…

Q: Computational analysis has determined that a particular design of glass ceramic component has a…

Q: A piston, 9 cm in diameter, is used to increase the internal pressure in a cylinder from 0 to 50…

A: The diameter of the piston is .The yield strength of the cylinder is .The fracture toughness of the…

Q: A material is subjected to a general state of planestress. Express the strain energy density in…

A: E is the modulus of elasticity, G is the modulus of rigidity, and ν is the Poisson’s ratio these are…

Q: A hypothetical metal alloy has a grain diameter of 2.4 x 10-² mm. After a heat treatment at 575°C…

A: given data initial diameter di = 2.4 *10-2 mm heat treatment at temp = 575°c time taken = 500…

Q: 2. A brass ring of diameter 10.00 cm at 20.0°C is heated and slipped over an aluminum rod of…

A: Solution:

Q: A tensile force of 200 KN is applied on a 0.02-m diameter and.2-m long rod. After applying the load,…

Q: A copper wire is stretched elastically with a stress of 70 MPa at 20°C. If the length is held…

Q: The more severe the change in geometry, the larger the stress concentration. Is it true or false?…

A: Stress concentration is a location in a member under load where the magnitude of stress is…

Q: A 12-cm x 1-cm x 1-cm rectangular segment of a plasticizer-modified polycarbonate (CAS# 25037-45-0)…

A: Given: Length of the segment→L=12 Cm=0.12 m Cross sectional area of the segment:…

Q: onsider the tensile stress-strain diagram in the figure below labeled 1 and 2. These diagrams are…

Q: How does strain hardening and grain size reduction affect elastic modulus

Q: The flow stress of a coarse-grained dilute copper alloy increased from 2 to 55 MPa when the…

A: according to the given detail:

Q: A stress of 1 kPa in a polymer deceased to 0.98 kPa after six weeks. This polymer is to hold a…

Q: Advanced hybrid materials technology has been used in automotive applications. A good example is…

A: Hybrid composite materials are employed in a variety of engineering applications due to their…

Q: Table: Properties for different ceramic materials Material/ Property Elastic modulus Thermal…

Q: How does the slenderness ratio affect the buckling behavior of columns in mechanical engineering?

A: The slenderness ratio is a key concept in the field of mechanical engineering, particularly in the…

Q: A hypothetical metal alloy has a grain diameter of 2.4 × 10-2 mm. After a heat treatment at 575°C…

Question

Consider a 50 mm × 50 mm × 50 mm element of graphite-reinforced material that
is heated 50°C above some reference state and is restrained in the 2 direction. (a)
What are the changes in dimensions of the heated element in the 1 and 3 directions?
(b) What stress 02 is required to restrain the element against deformation in the 2
direction? Assume the material properties are independent of temperature. (c) How
do the changes in dimensions of the heated element for this partially restrained case
compare numerically with the changes in dimensions of the heated element for the
case of free thermal strain, equation (2.101)? Why are they different? (d) What are
the mechanical strains for this case? Numerically compare the mechanical strains with
the fully constrained case, that is, equation (2.119). Hint: To solve the problem use
either equation (2.107) or (2.108), assume &₁# 0 and 83 ‡ 0, and solve for 81, 83,
and 02.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Help me please
Consider a 50 mm × 50 mm × 50 mm element of graphite-reinforced material with its ﬁbers oriented at 45◦ and constrained against deformation in the x direction. The element is heated 50◦C. What is the stress σx required to enforce this constraint and what are the strains εy, γxy, and εz?
What is a solid solution? In general, what is its implication on the mechanical behavior of metals (i.e., increase or decrease in strength)?
(b) (i) Describe the stages of cracking in brittle materials with reference to applied stress. staronoo to dionile lliw eresnigna adalé no Honove
Pravinbhai
A 3105 aluminum plate is reduced from 4.38 cm to 2.88 cm. Determine the final properties of the plate. See attached figure
A particular device needs to be made that will experience a change in temperature of 100 °C. Two materials are being considered: copper (α = 1.7*10-5 °C-1) and steel (α = 1.3*10-5 °C-1). If made of copper, the device would be 2 m in length. If made of steel, the device would be 2.615 m in length. Which device would experience more thermal expansion?
A 1.02den silk fiber has reached its maximum tenacity value. How many grams (force) would it take to rupture such fiber when dry? Provide your answer with two (2) decimal positions and no unit Answer:
Explain the method of representing the combination of normal and shear stresses acting on any plane through an incremental element on shear stress–normal stress coordinates.
The assembly shown below consists of a brass shell (1) fully bonded to a ceramic core (2). The brass shell [E = 115 GPa; α = 18.7 x 10-6 /°C] has an outside diameter of 50 mm and an inside diameter of 35 mm. The ceramic core [E = 290 GPa; α = 3.1 x 10-6 /°C] has a diameter of 35 mm. At a temperature of 15°C, the assembly is unstressed. Determine the largest temperature increase that is acceptable for the assembly if the normal stress in the longitudinal direction of the brass shell must not exceed 80 MPa.
It has been found that 'pyrex' cookware made of borosilicate glass does not shatter during baking or cooking around 300°F. However, shattering of cookware made of soda-lime-silicate glass was frequently reported during the years 2012-2013. Find and explain the possible reasons for cookware shattering. Show your calculation. Assume that the cookwares are free of pores, cracks, and scratches. Given: Material/properties Borosilicate Soda-lime-silicate glass glass Thermal expansion coefficient (x106/°C) Elastic modulus (GPa) Failure stress (MPa) 3 9. 62 68 30 30
This question was answered for me but the second answer is not clear how he/she got 0.55 and 0.45 for the rods.