A solid circular rod with a a circular groove (r = 1.5 mm) and diameter D = 18 mm, Q4 is subjected to an axial loadP, as shown in figure below. The rod is made of an aluminum alloy that has an elastic modulus E = 72 GPa and a Poisson's ratio v subjected to the axial load P, the diameter of the rod (d) decreases by 0.025 mm. For a factor of safety of 1.75, Determine the magnitude of the safe allowable load P. 0.32. When %3D 个 D P

A solid circular rod with a a circular groove (r = 1.5 mm) and diameter D = 18 mm, Q4 is subjected to an axial loadP, as shown in figure below. The rod is made of an aluminum alloy that has an elastic modulus E = 72 GPa and a Poisson's ratio v subjected to the axial load P, the diameter of the rod (d) decreases by 0.025 mm. For a factor of safety of 1.75, Determine the magnitude of the safe allowable load P. 0.32. When %3D 个 D P

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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The bar shown in the following figure has a diameter of 40 mm and is subjected to a force P = 3500 N and a force F = 1500 N. It is made from a material which has a yield strength of 60 MPa. Determine the factor of safety at points A and B using the Von-Mises Theory. Select one: a. NA = 1.414, NB = 0.628 b. NA = 1.649, NB = 0.718 c. NA = 1.238 , NB = 0.558 d. NA = 1.977 , NB = 0.837
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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).
Problem 3: (M4) Your boss at a construction company asked you to verify the thickness of a 3 m long hollow-square steel column (E=200 GPA) that can withstand an axial compressive load of 50 MN, the outer dimension a is 400 mm. The column's cross section is shown in Figure.4. Assume the column is a fixed-free type. b Figure.4: Cross-section of a hollow-square steel column
The stress-strain plot of the polyester resin material is given in the figure. The AC beam is supported by the AB rod and CD column made of this material and is subjected to a single load of P = 80 kN. As the diameter of AB rod is 40mm and diameter of CD column is 80mm(a) What is the modulus of elasticity? Calculate the elasticity coefficient of the material whose stress-strain graph is given.(b) Find the slope of the AC rod after loading.
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 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.
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The pin-connected structure shown in the figure consists of a rigid beam ABCD and two supporting bars. Bar (1) is a bronze alloy [E = 100 GPa] with a cross-sectional area of A1 = 270 mm2. Bar (2) is an aluminum alloy [E = 73 GPa] with a cross-sectional area of A2 = 630 mm2. All bars are unstressed before the load P is applied; however, there is a 4-mm clearance in the pin connection at A. Assume L1 = 1890 mm, a = 870 mm, b = 540 mm, c = 410 mm, and L2 = 1450 mm. If a load of P = 127 kN is applied at B, determine(a) the normal stresses in both bars (1) and (2).(b) the downward deflection of point A on the rigid bar.