*9-68. The bar has a cross-sectional area A, length L,modulus of elasticity E, and coefficient of thermal expansiona. The temperature of the bar changes uniformly along itslength from Ta at A to Ta at B so that at any point x alongthe bar T = TA + 1(Ta - TA)/L. Determine the force thebar exerts on the rigid walk Initially no axial force is in thebar and the bar has a temperature of TA-TA

The average temperature of the bar, The change in temperature,

Answered: *9-68. The bar has a cross-sectional…

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

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The rod has a circular cross section. If it is made of an elastic perfectly plastic material, determine the shape factor for the rod.
The metal strap has a thickness t and width w and is subjected to a temperature gradient T1 to T2 (T1 6 T2). This causes the modulus of elasticity for the material to vary linearly from E1 at the top to a smaller amount E2 at the bottom. As a result, for any vertical position y, measured from the top surface, E = [(E2 - E1)>w]y + E1. Determine the position d where the axial force P must be applied so that the bar stretches uniformly over its cross-section. w
The A-36 steel bar consists of two segments, one of a circular cross-section of radius r, and one of square cross-section. If the bar is subjected to the axial loading of P, determine the dimensions of the square segment so that the strain energy within the square segment is the same as in the circular segment.
The rigid beam is supported by three 25-mm diameter A-36 steel rods. If the beam supports the force of P=230 kN, determine the force developed in each rod. Consider the steel to be an elastic perfectly plastic material.
The rod has a circular cross section. If it is made of an elastic perfectly plastic material, determine the shape factor.
If the elongation of wire BC is 0.2 mm after the force P is applied, determine the magnitude of P. The wire is A-36 steel and has a diameter of 3 mm.
The spherical pressure vessel has an inner diameter of 2 m and a thickness of 10 mm. A strain gage having a length of 20 mm is attached to it, and it is observed to increase in length by 0.012 mm when the vessel is pressurized. Determine the pressure causing this deformation, and find the maximum in-plane shear stress, and the absolute maximum shear stress at a point on theouter surface of the vessel. The material is steel, for which Est = 200 GPa and nst = 0.3.
The rigid beam is supported by three 25-mm diameters A-36 steel rods. If the beam supports the force of P = 230 kN, determine the force developed in each rod. Consider the steel to be an elastic perfectly plastic material.
The cylinder CD of the assembly is heated from T1 = 30°C to T2 = 180°C using electrical resistance. Also, the two end rods AB and EF are heated from T1 = 30°C to T2 = 50°C. At the lower temperature T1 the gap between C and the rigid bar is 0.7 mm. Determine the force in rods AB and EF caused by the increase in temperature. Rods AB and EF are made of steel, and each has a cross-sectional area of 125 mm2. CD is made of aluminum and has a cross-sectional area of 375 mm2. Est = 200 GPa, Eal = 70 GPa, ast = 12(10-6)>°C, and aal = 23(10-6)>°C.
The collar has a weight of 50 lb and falls down the titanium bar. If the bar has a diameter of 0.5 in., determine the largest height h at which the weight can be released and not permanently damage the bar after striking the flange at A. Eti = 16(103) ksi, sY = 60 ksi.
The 10-mm-diameter bolt is made of an aluminum alloy. It fits through a magnesium sleeve that has an inner diameter of 15 mm and an outer diameter of 25 mm. The original lengths of the bolt and sleeve are 80 mm and 50 mm, respectively. If after the nut on the bolt is tightened the tension in the bolt is 10 kN, determine the change of volume of the bolt and the new length of the sleeve. Wherein both materials behave linearly elastic. Assume the material at A is rigid. E = 68.9 GPa, Emg = 44.6 GPa, Ga = 26 GPa, Gmg = 18 GPa.
The pipe is stuck in the ground so that when it is pulled upward the frictional force along its length varies linearly from zero at B to fmax (force/length) at C. Determine the initial force P required to pull the pipe out and the pipe’s elongation just before it starts to slip. The pipe has a length L, cross-sectional area A, and the material from which it is made has a modulus of elasticity E.

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