calculate the stiffness matrix [K]
For the bar with three nodes, O is the original point, the displacement function is set as U=C1+C2*x+C3x2. If elastic modulus E and cross section A is constant, calculate the stiffness matrix [K]
Homework Answers
a. Compute the total stiffness matrix [K] of the assemblage shown in Figure 3-1 by superimposing...
a. Compute the total stiffness matrix [K] of the assemblage shown in Figure 3-1 by superimposing the stiffness matrices of the individual bars. Note that should be in terms of A. As, A, E, E E, L. and L. Here A, E, and are generic symbols used for cross-sectional area modulus of elasticity, and length, respectively Figure P3-1 Now let As - Ag-A-A.E E, E E and L-L L -L nodes 1 and 4 are fixed and a force Pacts...
as shown in Fig.2. The lengths of two 2. Three bars form an isosceles right triangle,...
as shown in Fig.2. The lengths of two 2. Three bars form an isosceles right triangle, right angle sides are L, which is 1000 mm. The cross section area of the three bars are 1000 mm2. Young's modulus of bars are E-21x10 N/ mnt Please find the global stiffness matrix of these bar element system. If the numbering of the bar nodes changes, does the global stiffness matrix change? (15 %) y 1 (3) (1) (2) 3 2 Fig.2 Bar...
Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected...
Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected to an increase in temperature of 60°C in an unnatural environment. The equation governing the displacement of the elastic column and the finite element stiffness matrix are respectively given as -O and ΑΕ) - where A is the cross sectional area of the beam, E is the Young's modulus of the beam material, u is the displacement and / is the finite element length....
13. Based on the stiffness method, determine the stiffness matrix K for the truss shown in...
13. Based on the stiffness method, determine the stiffness matrix K for the truss shown in figure. Use the stiffness matrix to calculate the unknown displacement (D1 and D2) at the node where the load 5 kN and 10 kN are applied, and then determine the reactions at the pinned supports (Q3, Q4, Q5 and 26). Note that the degrees of freedom (DOFs) of the truss are indicated in the figure. Take EA as constant. The supports are pinned. 4....
ME major: based on a motion equation (see below) discuss how an individual component (Mass, damping, and Stiffness...
ME major: based on a motion equation (see below) discuss how an individual component (Mass, damping, and Stiffness) of a vibration system contributes to motion and vibration of a vehicle and how an individual component can influence the accuracy of the vibration analysis. A Motion equation can be expressed as: a. where [M][C] and [K] represent the total mass matrix, the total damping matrix, and the total stiffness matrix of a vehicle; (ü), {ú), and (u) are acceleration, speed, and...
The figure below shows a uniform slender bar supported by cantilevers at A and C. At B a linear spring with stiffness K' is connected to an additional point mass 'm'. Note the physical pr...
The figure below shows a uniform slender bar supported by cantilevers at A and C. At B a linear spring with stiffness K' is connected to an additional point mass 'm'. Note the physical properties of the bar include cross sectional area A, Young's modulus E, second moment of area I, and, density ρ, and length AB-BC-L. 1. 2. Develop the matrix equation of motion for the FEM system in the model How many natural frequencies are in the system?...
need to solve the mathematical model to prove that we can get the equations i Q1...
need to solve the mathematical model to prove
that we can get the equations i Q1 a methematically
QI. A vertical pile is used to transfer the vertical load from the soft ground surface to the rock surface. It is assumed that the stiffness of the rock is sufficient to prevent any vertical displacement so that the lower edge of the rod may be considered as fixed. The soft ground acts on the pile along its length with a force...
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.
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Elem...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
Q.2: Taking A, B, C and D as the nodes for the grillage frame (AB and...
Q.2: Taking A, B, C and D as the nodes for the grillage frame (AB and BC are parallel to Y axis and BD is parallel to X axis) shown below, evaluate the nodal load vector {P) and the stiffness matrix [K] of the structure taking same elastic modulus (E = 100GPa) and Poisson's ratio (v = 0.25) for all members. The members are having same rectangular cross-section (a = 200mm, b = 250 mm). Solve the governing equation [K]{X}={P}...
a. Compute the total stiffness matrix [K] of the assemblage shown in Figure 3-1 by superimposing the stiffness matrices of the individual bars. Note that should be in terms of A. As, A, E, E E, L. and L. Here A, E, and are generic symbols used for cross-sectional area modulus of elasticity, and length, respectively Figure P3-1 Now let As - Ag-A-A.E E, E E and L-L L -L nodes 1 and 4 are fixed and a force Pacts...
as shown in Fig.2. The lengths of two 2. Three bars form an isosceles right triangle, right angle sides are L, which is 1000 mm. The cross section area of the three bars are 1000 mm2. Young's modulus of bars are E-21x10 N/ mnt Please find the global stiffness matrix of these bar element system. If the numbering of the bar nodes changes, does the global stiffness matrix change? (15 %) y 1 (3) (1) (2) 3 2 Fig.2 Bar...
Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected to an increase in temperature of 60°C in an unnatural environment. The equation governing the displacement of the elastic column and the finite element stiffness matrix are respectively given as -O and ΑΕ) - where A is the cross sectional area of the beam, E is the Young's modulus of the beam material, u is the displacement and / is the finite element length....
13. Based on the stiffness method, determine the stiffness matrix K for the truss shown in figure. Use the stiffness matrix to calculate the unknown displacement (D1 and D2) at the node where the load 5 kN and 10 kN are applied, and then determine the reactions at the pinned supports (Q3, Q4, Q5 and 26). Note that the degrees of freedom (DOFs) of the truss are indicated in the figure. Take EA as constant. The supports are pinned. 4....
ME major: based on a motion equation (see below) discuss how an individual component (Mass, damping, and Stiffness) of a vibration system contributes to motion and vibration of a vehicle and how an individual component can influence the accuracy of the vibration analysis. A Motion equation can be expressed as: a. where [M][C] and [K] represent the total mass matrix, the total damping matrix, and the total stiffness matrix of a vehicle; (ü), {ú), and (u) are acceleration, speed, and...
The figure below shows a uniform slender bar supported by cantilevers at A and C. At B a linear spring with stiffness K' is connected to an additional point mass 'm'. Note the physical properties of the bar include cross sectional area A, Young's modulus E, second moment of area I, and, density ρ, and length AB-BC-L. 1. 2. Develop the matrix equation of motion for the FEM system in the model How many natural frequencies are in the system?...
need to solve the mathematical model to prove
that we can get the equations i Q1 a methematically
QI. A vertical pile is used to transfer the vertical load from the soft ground surface to the rock surface. It is assumed that the stiffness of the rock is sufficient to prevent any vertical displacement so that the lower edge of the rod may be considered as fixed. The soft ground acts on the pile along its length with a force...
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.
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
Q.2: Taking A, B, C and D as the nodes for the grillage frame (AB and BC are parallel to Y axis and BD is parallel to X axis) shown below, evaluate the nodal load vector {P) and the stiffness matrix [K] of the structure taking same elastic modulus (E = 100GPa) and Poisson's ratio (v = 0.25) for all members. The members are having same rectangular cross-section (a = 200mm, b = 250 mm). Solve the governing equation [K]{X}={P}...
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