A long circular shaft of length L with variable cross-section is fixed onto rigid walls as shown inFigure 1.1. The polar moment of inertia of the L/3-long segment (J1) with a larger cross sectionis three times larger than that of a 2L/3-long segment (J2) on the right. Assume the shear modulusis constant and equal to G for the entire shaft and that strains are small and linear elastic.L/3L/3L/3Figure 1.1. Shaft with variable cross-section and external torque T.(a) If the shaft is subjected to an external torque T at point b, find the angle of twist of point bwith respect to point a.(b) If the shaft is subjected to an external torque T at point a, as shown in Figure 1.2, find theangle of twist of point a with respect to point b.L/3-L/3bJ2L/3Figure 1.2. Shaft with variable cross-section and external torque T.

The objective of the question is to find the angle of twist at different points of a long circular…

Answered: A long circular shaft of length L with…

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 rectangular plate ABCD with base L = 283 mm and height H = 376 mm experiences the deformation illustrated below, resulting in the deformed plate shown by dotted lines. Determine the average shear strain y at the corner C when a = 3 mm, b = 4 mm, c = 4 mm, d = 4 mm, e = 3 mm and f = 3 mm. Assume small deformations. %Matlab input: L = 283; H = 376; a = 3; b = 4; C = 4; d = 4; e = 3; f = 3: y d B C H b A a L
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You may need to apply hooke's law . Simple one
A heavy spool rests on the ground at point A and against the wall at point B. Find force F required to pull the cable off the spool in the direction shown, given:Mspool = 100 kg, rI = 200 mm, rO = 460 mm, μ = 0.2 for all surfaces.
An idealized model of a thin-walled convertible car body cross-section is shown in figure Q16. The effect of doors and windows has been ignored. The car has vertical side walls of thickness t1 and length 1 m and a horizontal base of thickness t2 and length 1.9 m. It is constructed from aluminium with a shear modulus of 24 GPa. t₁ = 15 mm t2 = 15 mm a. For this open section determine the torsional stiffness? Give your answer to 3 significant figures in Pa m4 and non-scientific notation e.g. 10000 rather than 10e05. Do not include units in your answer Note that for an open section, the total area moment JT is the sum over all plates i as given by equation (1) below. Ir = = = Ei bit? Torsional stiffness = GJT t₂ 1.9 m 1m Figure Q16 - idealised model of a thin-walled convertible car body
See the attached image1) A long rod in the shape of a circular cone is rotating with constant angular velocity c about an axis located at the left end of the rod as shown in the figure below. The bar has length L, major and minor diameters D and d, respectively, and its material has linear elastic behavior with modulus of elasticity E. The values of the problem parameters must be defined by the student a) From the balance of a differential member of the bar, derive the differential equation of balance for the bar. Solve the equation analytically to obtain the bar displacement field, U(X). Give the expression for the displacement at the free end of the member. b) Implement a computational code in MATLAB (or any other software) to solve this problem with "n" two-node bar finite elements. c) Run different simulations by increasing the number of finite elements in each simulation. At each simulation, obtain the displacement of the free end of the member. Graphically compare your results…
Given the stress tensor: Find: 3 36 27 0 σ = 27-36 00 0 18 (a) The components of the traction (force per unit area) acting on a plane with unit normal n= 2 21 3 3'3 T (b) The component of the traction in the direction of the normal (c) The angle between the traction and the normal vector (d) The magnitude of the traction vector (e) The net force acting on a cube with corners at (x,y,z)=(±1,±1,±1)
Thank you. Please help me.
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A steel ring at a room temperature has a radius of R, of 1.00 mm x 1.00 mm. One like to insert a bar of radius R, = 2.002 cm into the ring. The following data is known for steel: 2.00 cm and a cross section area • Young Modulus E = 2.00 × 1011 Pa. • Coefficient of length contraction a = 1.20 x 10-5 C-1 • Specific heat capacity c = 511 J.kg-1.C-1 • Mass density p= 8050 kg.m -3 (a) What is the amount of heat needed for heating the ring so that the rod can fitted into it. (b) Assume the rod is rigid, calculate the pressure on the surface of the rod as the steel cool down to the room temperature.
L1 PB 2 E2 L2 D2 Dimensions: L2 L1 D2 D1 17 mm 18 cm 23 cm 15 mm Problem Statement: The rod shown is subjected to loads of PR = 112 kN and Pe = 18 kN. Segments AB and BC have elastic moduli of E, = 206 GPa and E = 73 GPa. The rod has circular cross-sections, and the dimensions of the rod are given above. Find the overall change in length of the rod under this load. Assume: • The collar at B is rigid • Stress concentration effects may be neglected 2014 Michael Swanbom

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