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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A close-coiled helical spring is made of a wire of diameter 20 mm. The mean radius of the coils is 100 mm. Find the number of turns required and the maximum axial load permissible if the shear stress is not to exceed 100 MPa and the maximum elongation is limited to 40 mm. G = 83 GPa.
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Solid Mechanics In the figure, solid copper rod with expansion coefficient αB = 165.10-7 1 / 0C It is 20 mm in diameter. Inner diameter is 2mm larger than this bar and expansion into a steel pipe of 30 mm outer diameter with coefficient αÇ = 125.10-7 1 / 0C so that they move together. It is combined with a rigid plate. System with temperature difference Δt = 80 0C Find the stresses that will occur in steel and copper when heated. (Eç= 200 GPa, Eb= 100 GPa)
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A cylindrical bar made of brittle material has been subjected to pure torsion by a torque M and tension from the force F (Figure Q6.c). The torque gives rise to the shear stresses T = T = 32 MPa and the force F gives rise to the tensile stress ху yx 0, = 65 MPa. The stress along the y-axis is zero (o, = 0). Determine whether there will be a failure due to the maximum tensile stress if the tensile strength of the material is 90 MPa. F X Figure Q6.c
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The bar shown in the figure is made of cold-drawn steel, having an yield strength of 280 MPa. Loads applied are F = 1 kN, P = 5 kN, and torque T = 20 kN. For each element shown in the figure (element A and element B, separately, • Determine the principal stresses at A and B (eigenvalues) • Using DET, determine whether the bar will yield. What is the factor of safety for the loading situation shown, based on DET? 15-mm D. -100 mm
2. A composite spring has two closed coiled springs connected in series, each spring has 12 coils at a mean diameter of 25mm. Find the wire diameter for one if the other is of 2.5mm diameter and the stiffness of the composite spring is 700N/m. Estimate the greatest load that can be carried by the composite spring, and the corresponding extension, for a maximum shear stress of 180MPa. Take G=80GPa.
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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
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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).

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