1. A uniformly tapered tube AB of circular cross-section and length Lis shown in thefigure. The average diameters at the ends are dA and dB = 2dA. Assume E isconstant. Find the elongation o of the tube when it is subjected to loads Pactingat the ends.Use the following numerical data: dA = 40 mm, L = 400 mm, E = 200 Gpa, P = 40kN. Consider the following case:A hole of variable diameter d(x) is drilled from B toward A to form a hollow sectionof length x = L/2 and constant thickness t= dA/20.ВAPd(x)I constantdB

Answered: Image /qna-images/answer/0288211d-b0d6-4bd5-b1b6-0162a3cabf62.jpg

Answered: A uniformly tapered tube AB of circular…

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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A torsional moment T = 7,005 Nm and a load P = 92,107 N are applied at the same time to a circular hollow shaft of unknown length L, as shown in Figure Q6. The load P is offset from the centre of the circular cross-section by a distance e = 6 mm. The shaft has an inner diameter d = 46 mm and an outer diameter D = 86 mm. Point A in Figure Q6 is on the outer surface of the shaft. Figure 6 Calculate the shear stress τxy at point A. Assume the sign of τxy to be positive. Use π = 3.14159 if needed. Calculate your answer in the unit: mega-Pascal (MPa). Report you answer to 3 decimal places.
A steel wire (E = 200 GPa) of diameter d = 1.0 mm is bent around a pulley of radius R0 = 400 mm (see figure below).a. What is the maximum stress in the wire?b. Does the stress increase or decrease if the radius of the pulley is increased?
A train is parked on a steel bridge as shown in the figure below. The steel bridge is simply supported by a pin support at point A and a roller support at point B. The bridge has a modulus of E0=200 GPa, 2nd moment of area Iz=1.5 m^4 and length L=200m. The train has a weight of W=2000000N and the same length as the bridge. Use the SI Unit for calculation. a) Determine the intensity of the uniformly distributed load: f= b) Write the mathematical expression for the two quantities below, in terms of parameters ?, ??, ?0, ? and ?. Determine the elastic curve formula for the deflection of the bridge. v= determine the slope formula for the bridge under the applied loading dv/dx=
Consider a one-element triangular mesh shown in Figure 2. The edge AC is fixed. The edge BC is subject to lin- early varying traction normal to the edge as shown in Figure 2. Assume plane-stress conditions with thickness 1 = 1 cm and Young's modulus E = 70 GPa and Poisson's ratio v = 0.3. 150 kN/m 50 kN/m C (0,0.3) B (0.4,0.3) a) Specify the boundary condi- tions. b) Construct the stiffness matrix. A (0,0) c) Calculate the global force ma- Figure 2: Triangular element. All coordinates are in meters. trix. d) Solve for the unknown displace- ments and compute the stress at (0.1, 0.2).
The figure below shows a section of a column subjected to load P, which is applied 50 mm from the midline of the section's web. The column is made from material, which has an allowable normal stress of 180 MPa (both in tension and compression). The area of the section is 10050 mm?; the principal moments of inertia Imar = 146.554x106 mm and Imin 20.076x10° mm*. !! Determine the maximum allowable load P. 15 mm 150 mm 15 mm 150 mm 50 mm 15 mm 100 mm 100 mm 1194.6 kN 363.6 kN 1809.0 kN O 516.4 kN O 189.5 kN
A vertical load P is applied at the center B of the upper section of a homogeneous frustum of a circular cone of length L, minimum radius rB, and maximum radius rA, as shown in the figure below. It is made of a material with a modulus of elasticity E. Neglect the effect of its weight. Use the following values: rA = 2 in, rB = 0.5 in, L = 3 ft, E = 30 (103 ) ksi, and P = 1800 lbf. Discretize the original geometry into three equal-length finite elements and (a) Compute all the nodal displacements. (b) Compute all the element axial stresses. (c) Plot the displacement field from the finite element method solution. (d) Plot the axial stress field from the finite element method solution.
A torsional moment T = 5,382 Nm and a load P = 55,253 N are applied at the same time to a circular hollow shaft of unknown length L, as shown in Figure Q5. The load P is offset from the centre of the circular cross-section by a distance e = 6 mm. The shaft has an inner diameter d = 43 mm and an outer diameter D = 97 mm. Point A in Figure Q5 is on the outer surface of the shaft. Figure 5 Calculate the direct (or normal) stress in the x-direction σx at point A (the 'x-direction' is along the longitudinal axis of the shaft, along its length L). Use π = 3.14159 if needed. Calculate your answer in the unit: mega-Pascal (MPa). Report you answer to 3 decimal places.

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