A rectangular element as shown in the figure is used to represent a purebending problem. Due to the bending moment M, the element is deformed asshown in the figure with displacement {d} = {u1, v1, U2, V2, U3, V3, U4, V4} = {−1, 0,1, 0, -1, 0, 1, 037.(a) Derive expressions of strain component Exx, Ɛyy, and xy, as functions of xand y based on the shape functions.(b) Does the element satisfy pure bending condition? Explain your answer.yM| AUAИз4 (0,2)3 (3,2)1 (0,0)2 (3,0)xB12UI

Answered: Image /qna-images/answer/467d534e-54d4-449f-bc77-2f1dcb12b6a2.jpg

Answered: A rectangular element as shown in the…

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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Consider a two-component rod fixed at the left end. The first component (on the left, positioned from z=0 to z=L/2) is a solid rod with a shear modulus of G and radius c1. The second component (on the right, positioned from z=L/2 to z=L) is a hollow pipe fixed to component 1 at z=L/2 with the same shear modulus and outer radius c1, but with an inner radius of c2. A torque of 6To is applied at z=L/2, and a torque of -2To is applied at z=L. What value of c2 is required to make the maximum shear stress equivalent in each component? What is the angle of twist at the free end at z=L?
5. Determine the value of the distributed load w and the concentrated loads x, y and z in the load diagram. [x=5.75kN, y=15kN, w= 5kN/m, z=34.25kN] 80 kN-m 5.75 X V (kN) 50N A 5m V (N) M (Nm) B 5 -9.25 6. Determine the value of A, B in the shear force diagram and C in the bending moment diagram. [A =50N; B = -50N; C = 125Nm] 10N/m 10m -5m- C W Z -.x(m) -34.25 50N -x (m) B -x (m)
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The bending moment in a horizontally placed beam at distance x from one of the ends is given by the expression M = 13x - 3x - 12 . The shear force in the beam is zero at, O a. x = 7.12 O b.x = 3 and x = 1.33 O C. X = 2.16 O d. Need more data and a figure to solve the problem.
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Figure attached.
Analyse the statically determinate bar illustrated below by expressing the loading as a single function using Macaulay brackets and the Dirac delta, integrating to find th axial force and integrating again to find the displacements, applying the boundary conditions appropriately. Find the axial force in the bar at point A and the displaceme at point B. The cross section of the bar is constant with EA = 18000 kN. a = 4 m, b = 2 m, c = 2 m and d = 4 m. w1 = 12 kN/m, w2 = 17 kN/m,, P1 = 12 kN and P2 = 19kN. a W1 L/2 W2 Multiple Choice Answers Multiple Choice Answer: Axial force at point A (kN, tension positive): a. 3.31 b. 31.97 c. 37.33 d. 31 Multiple Choice Answer: Displacement at point B (mm, positive to right): a. 0.0061 b. 0.0395 c. 0.0193 d. 0.0261 Axial force at point A (kN, tension positive): Displacement at point B (mm, positive to right): L/2 P1 P2 (type in your multiple choice answer, e.g. a, b, c or d) (type in your multiple choice answer, e.g. a, b, c or d)
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