A two-layered material is made of two metal bars, each with square cross-sectional area t² and length L, fixed together in parallel along their lengths. The bars are made of different materials, with the linear coefficient of expansion of one bar being significantly larger than that of the other. When heated, the compound bar begins to bend. Show that the radius of curvature of the curved, compound bar is t/(AGAT), where t is the thickness, or smallest dimension, of a single bar, Aa is the difference between the linear expansion coefficients of the two materials and AT is the increase in temperature.

A two-layered material is made of two metal bars, each with square cross-sectional area t² and length L, fixed together in parallel along their lengths. The bars are made of different materials, with the linear coefficient of expansion of one bar being significantly larger than that of the other. When heated, the compound bar begins to bend. Show that the radius of curvature of the curved, compound bar is t/(AGAT), where t is the thickness, or smallest dimension, of a single bar, Aa is the difference between the linear expansion coefficients of the two materials and AT is the increase in temperature.

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

A rod with cross-sectional area of 100mm2 is stretched between two fixed points such that the initial tensile load is 10kN. The rod has a modulus of elasticity equal to 180 GPa and a coefficient of linear expansion of 0.00001m/m-C. The initial tension is designed such that the rod will have zero stress when there is a certain change n temperature of the rod environment. What is the temperature (in C, 2 decimal places)?
A steel rod with a diameter of 25 mm and 831 mm long is heated to 203 °C from an initial temperature of 25 °C. Steel has a modulus of elasticity and coefficient of thermal expansion of 200 GPa and 11.7 x 10-6 /°C respectively. Determine the change in length in millimeters.
A square bar subjected to a tensile load of 100KN having a gauge length of 200mm, extends to a length of 0.19mm. Given the tensile strength as 200 MPa, determine, () Side of the bar (express in mm) (ii) Final length (express in mm) (ii) Modulus of elasticity (express in GPa)
A metal has a flexural stress of 564 Pa. The W is measured to be 1 meter, while the load was 10 N. The thickness of the metal is twice its L. Using the formula on the three-point test of materials, compute for the thickness of the metal in centimeters.
Measure the outside diameter of a flagpole or a street-light pole by first wrapping a piece of string around the object to determine its circumference. Why do you think the flagpole or the streetlight pole is designed to be thicker at the bottom near the ground than at the top? Explain your answer.
How can we consider the radius of curvature?
Find the ox value for the plate as shown below, where b1=d2%=D16 mm, d1=70 mm,b2%=90mm. (ENTER ONLY THE VALUES IN THE BOXES BY REFERING THE UNITS GIVEN IN THE BRACKET) b1 b2 d2 d1
For many viscous materials, the viscosity n may be defined in terms of the expression deldt where o and dɛ/dt are, respectively, the tensile stress and the strain rate. A cylindrical specimen of a soda-lime glass of diameter 6 mm (0.24 in.) and length 250 mm (9.9 in.) is subjected to a tensile force of 9 N (2.02 Ib;) along its axis. If its deformation is to be less than 1.7 mm (0.067 in.) over a week's time, using Figure 13.14, determine the maximum temperature to which the specimen may be heated.
Young Modulus of a material has characteristics of : (Choose TRUE or FALSE for each statement) Can be obtained by the gradient of stress versus strain graph. OTRUE OFALSE As a measurement for a material due to its resistance, subjected to the exerted forces. O TRUE O FALSE The two-dimensional plane of the material depends on Young Modulus. O TRUE OFALSE
the ability of fluid to resist shear stresses is known as bulk modulus Select one: O True O False
The beam is supported by rods AB and CD that have different cross-sectional areas. The area of rod AB is AAB = 10 mm² .The area of rod CD is Acp = 8.25 mm². B F₁ Values for the figure are given in the following table. Note the figure may not be to scale. Variable Value F₁ d₁ d₂ NAB= 5050 N 3.25 mm 0.5 mm a. Determine the magnitude of the normal internal force in rod CD, NCD. b. Determine the magnitude of the normal internal force in rod AB, NAB. c. Determine the normal stress in rod CD, OCD. d. Determine the normal stress in rod AB, O AB. Round your final answers to 3 significant digits/figures. NCD = N N
1.The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35.0 °C. What will its height be on a day when the temperature falls to -10.0 ° C? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble's. 2.How much taller does the Eiffel Tower become at the end of a day when the temperature has increased by 15 ° C? Its original height is 321 m and you can assume it is made of steel. 3.What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from 37.0 ° C to 40.0 ° C, assuming the mercury is unconstrained? 4.How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature 35.0 ° C greater than when they were laid? Their original length is 10.0 m