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3. Consider a two-d.o.f bar element, as shown below, but let the cross-sectional area vary linearly...
Element 1 is a steel bar that has a circular cross-section with a radius of 30...
Element 1 is a steel bar that has a circular cross-section with a radius of 30 mm. Element 2 is an aluminum bar that has a circular cross-section with a radius of 50 mm. Element 3 is a steel bar that has a circular cross- section with a radius of 60 mm. Assume for steel, the moduļus, E, is 2.0E11 Pa, and the density, p, is 7800 kg/m3. Assume for aluminum, E-7.0E10 Pa, and p-2700 kg/m3. The rigid, massless rod...
finaite element 3. Consider the beam-bending problem shown below. Using one element and assuming that the...
finaite element
3. Consider the beam-bending problem shown below. Using one element and assuming that the beam length is , modulus of elasticity E, area A, and moment of inertial: a) Solve for unknown displacements. b) Find the displacement at x = 1/2 4. For problem 3 above assume that these is no truss axial effect or D.O.F Compute components of the element stiffness matrix using shape functions. K22 k23 k24 k33 k34 K44
Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the ele...
Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the element stiffness matrix in global axis system [KG] of the members and assembled them to generate the overall stiffness matrix [K of the truss. Modify the stiffness matrix [K] in order to incorporate boundary conditions following the elimination technique of rows and columns. Take E 200 GPa...
Problem 1 Consider the bar shown below with a cross-sectional area A, 1.2 m2, and Young's...
Problem 1 Consider the bar shown below with a cross-sectional area A, 1.2 m2, and Young's modulus E-200 X 109 Pa. Ifq,-0.02 m and q,-0.025 m determine the following (by hand calculation) (a) the displacement at point P., (b) the strain E and stress σ (e) the element stiffness matrix, and (d) the strain energy in the element 91 *p 20 m x,-15 m x,-23 m Problem 2. Consider a finite element with shape functions N1) and N2(Š) used to...
5) Consider a bar shown below. Cross-sectional area Ae = 1.2 in., and Young's modulus E...
5) Consider a bar shown below. Cross-sectional area Ae = 1.2 in., and Young's modulus E = 35 x 106 psi. If ui = 0.02 in, and u2 = 0.025 in., considering linear interpolation, determine the following: (a) the displacement at point P; (b) the strain & and stress o; and (c) the element stiffness matrix. u2 2 x = 20 in. x = 15 in. X = 23 in.
Element 1 is a steel bar that has a circular cross-section with a radius of 30 mm. Element 2 is an aluminum bar that has a circular cross-section with a radius of 50 mm. Element 3 is a steel bar that has a circular cross- section with a radius of 60 mm. Assume for steel, the moduļus, E, is 2.0E11 Pa, and the density, p, is 7800 kg/m3. Assume for aluminum, E-7.0E10 Pa, and p-2700 kg/m3. The rigid, massless rod...
finaite element
3. Consider the beam-bending problem shown below. Using one element and assuming that the beam length is , modulus of elasticity E, area A, and moment of inertial: a) Solve for unknown displacements. b) Find the displacement at x = 1/2 4. For problem 3 above assume that these is no truss axial effect or D.O.F Compute components of the element stiffness matrix using shape functions. K22 k23 k24 k33 k34 K44
Question 1: For the plane (2D) truss shown below, evaluate the transformation matrix [T] and the stiffness matrix in the local axis system [KL] of all elements. Use these matrices to evaluate the element stiffness matrix in global axis system [KG] of the members and assembled them to generate the overall stiffness matrix [K of the truss. Modify the stiffness matrix [K] in order to incorporate boundary conditions following the elimination technique of rows and columns. Take E 200 GPa...
Problem 1 Consider the bar shown below with a cross-sectional area A, 1.2 m2, and Young's modulus E-200 X 109 Pa. Ifq,-0.02 m and q,-0.025 m determine the following (by hand calculation) (a) the displacement at point P., (b) the strain E and stress σ (e) the element stiffness matrix, and (d) the strain energy in the element 91 *p 20 m x,-15 m x,-23 m Problem 2. Consider a finite element with shape functions N1) and N2(Š) used to...
5) Consider a bar shown below. Cross-sectional area Ae = 1.2 in., and Young's modulus E = 35 x 106 psi. If ui = 0.02 in, and u2 = 0.025 in., considering linear interpolation, determine the following: (a) the displacement at point P; (b) the strain & and stress o; and (c) the element stiffness matrix. u2 2 x = 20 in. x = 15 in. X = 23 in.
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