1) The triangular plane stress problem connected to a spring, is subjected to a uniformly distributed loadand two point forces. Calculate the nodal displacements and the spring force using two triangular finiteelements.k = 3x105 kN/m (spring constant)h = 0.20 m (thickness)E = 3x107 kN/m² (modulus of elasticity)v = 0.20 (Poisson's ratio)1.5 m40 kN30 kN/m50 kN2 m2 m

Here's a detailed Python script that you can run on your local machine to perform the calculations:…

Answered: 1) The triangular plane stress problem…

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 the loaded shaft illustrated in Figure Q4 (i). The shaft is simply supported at A and D. The shoulder fillet radius is 0.3 cm at B and C. If the shaft is subjected to a force of F-800 N, determine the following: (a) The reaction forces at the two ends of the shaft A and D. (b) The bending moments at shoulder fillets B andC. (c) The nominal stresses at shoulder fillets B and C. (d) The stress concentration factor at shoulder fillet B. (e) The maximum stress in the shaft taking into account stress concentrations. 800 N T-0.3 can A d, - 3 cm d, = 5 cm d, - 3 cm 5 cm 8 cm 8 cm 12 cm Figure Q4 (i) The reference parameters are shown in Figure Q4 (ii) in the page that follows. For 0.002 srlds 0.3 and 1.01 s Dlds 6.0, the stress concentration factor for bar bending is given as: kn -4.4 = 0.632 + 0.377 -0.14 – 0.363(P/a)" + 0.503(P/a) 1- 2.39(P/a) + 3.368(2la)* -0.5 The nominal stress is: 32M %3D nd3
A close-coil helical spring is to have a stiffness of 1,000 N/m in compression, with a maximum load of 50 N and a maximum shearing stress of 125 N/mm². The solid length of the spring is 50 mm. Find the wire diameter, mean coil radius, and a number of coils. G= 54,000 N/mm². (Assume shear stress is produced only due to the torque produced in the wire due to axial loading).
A hollow circular shaft of inner radius 20 mm, outer radius 40 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, Calculate the torsional stiffness of the shaft (in kN-m/rad) is
In the figure, copper AB copper with a diameter of 24 mm and BC steel bars with a diameter of 20 mm are rigidly connected to each other at point B. A force of 6 kN was applied to the rod at the B point and 12 kN at the C point. Since the modulus of elasticity of copper is 100 GPa and the modulus of elasticity of steel is 200 GPa, find the displacement of the C point.
Define the terms load , stress and strain. Discuss the various types of stresses and strain p 4:19 /
A 50-mm diameter cylinder is made of a brass for which the stress-strain diagram is as shown. The angle of twist is 5° in a length L = 725 mm. The three points on the nonlinear stress-strain diagram used are (0, 0), (0.0015, 55 MPa), and (0.003, 80 MPa). By fitting the polynomial T = A + By + Cy² through these points, the following approximate relation has been obtained. T= 46.7 × 10%y-6.67 × 1012/2 Determine the magnitude Tof torque applied to the shaft using this relation and the two equations given below. Y Ty - ρφ T (MPa) 2π ζ ρ?τὰρ 100 80 60 40 20 0 0.001 0.002 0.003 Y d = 50 mm L The magnitude T of torque applied to the shaft is kN.m.
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).
Q1/ The stress array for the torsion problem of a circular cross section bar of radius a and with longitudi- nal axis coincident with the z axis of rectangular Cartesian axes (x, y, z) is T = X 0 -Gyß 0 Gxß -Gyß Gxß 0 0 where G and ß are constants (a) Determine the principal stresses at a point x = y on the lateral surface of the bar. (b) Determine the principal stress axes for a point on the lateral surface of the bar. 0¹. 40
The figure illustrates a torsion-bar spring OA having a diameter d = 12 mm. The actuating cantilever AB also has d = 12 mm. Both parts are of carbon steel. Use Castigliano’s theorem and find the spring rake k corresponding to a force F acting at B.
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