Q 7. Explain Finite Elements Solution of Bean on Elastic Foundation.
Q 7. Explain Finite Elements Solution of Bean on Elastic Foundation.
Homework Answers
Answer-
Both beam and elastic foundations are separate structural elements, the problem of beam on elastic foundation is of greater significance, as this problem can help us solve problems like to study the behavior of floating body on water.
Various assumptions are followed from the elementary beam theory in order to do analysis of the beam on the elastic foundation like:
1) before and after the deformation of the beam, the plane section remain plane.
2) slopes of the beam are considered as small.
3) beams material is homogeneous, isotropic and continuous.
generally the analysis of beam for property like bending is based upon the assumption that the reaction forces on elastic foundation are proportional to the deflection at various points of the beam. the displacement finite element method can be used for analyzing the beam on elastic foundation.
The resultant finite element solution will help in finding accurate values of displacements, bending, shear of beam on elastic foundation.
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Q 7. Explain Finite Elements Solution of Bean on Elastic Foundation.
Let F be a finite field with q elements. a) S -1 for every a*0 in F. how that a-1 either f* 0 or ...
Let F be a finite field with q elements. a) S -1 for every a*0 in F. how that a-1 either f* 0 or deg(f*)<q, and f* induces the same function on F as f does. function on F, then f=g. b) Let j(X)E F[X]. Show that there exists a polynomial /*(X)EF[X] such that c) Show that if two polynomials f and g, each of degree <g, induce the same
Let F be a finite field with q elements. a)...
QUESTION 2 21 Finite elements can appear in many forms such as two-dimensional and three- dimensional domains Give two...
QUESTION 2 21 Finite elements can appear in many forms such as two-dimensional and three- dimensional domains Give two examples and a sketch for each domain. (4) 22 Explain the following terms as used in Finite element equations a Plain stress b Plain strain 23 Use the Finite element method to develop the stiffness matrix for element 2 of the steel cantilever beam structure shown in Figure 2 The elastic modulus IS 200 kN/mm2 with a thickness of 1 unit...
7. Let A, , An be non-empty subsets of a finite set Ω. If 1 k n and Ek is the set of elements in ...
7. Let A, , An be non-empty subsets of a finite set Ω. If 1 k n and Ek is the set of elements in Ω which belong to at least k of the Ai's show that Pal i-1
7. Let A, , An be non-empty subsets of a finite set Ω. If 1 k n and Ek is the set of elements in Ω which belong to at least k of the Ai's show that Pal i-1
A=4 B=7 1) For the foundation sitting on top of the 5m thick soil calculate dimension....
A=4 B=7
1) For the foundation sitting on top of the 5m thick soil calculate dimension. (Factor of Safety:3 (30p) (AX100) KN (B x3) kNm SPT-N (A+2B) 5 m b XD Uniform sand JIKUM) ya 15 kN/m a. Determine the q (angle of internal friction angle) of sand by using the given formula. b. Find the dimension b based on bearing capacity c. Find settlement by using 2:1 rule (DO NOT CHANGE DIMENSION AFTER SETTLEMENT Calculation) 9. = 1.3cN+y D,N,...
Define Jordan Measure and prove If is a finite set consisting of precisely n elements, show...
Define Jordan Measure and prove If
is a finite set consisting of precisely n elements, show that S
has zero Jordan measure.
Explain in Detail
{urg} = S
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...
A plane truss element is shown in Figure 4, All elements have cross-sectional area of A = 8 in, a...
A plane truss element is shown in Figure 4, All elements have cross-sectional area of A = 8 in, and elastic modulus of E-2 x 10° psi. Use long-hand solution 6. 6.(a). Solve for the unknown displacements. 6.(b). Solve for strains and stresses in al 3 elements. Show your work and follow the finite element method matrix formulation we have covered in lectures. 4 5 kip 10 240 ft 30 ft30 ft Figure 4.
A plane truss element is shown...
A plane truss element is shown in Figure 4. All elements have cross-sectional area of A = 8 in, a...
A plane truss element is shown in Figure 4. All elements have cross-sectional area of A = 8 in, and elastic modulus of E 2 x 10 psi. Use long-hand solution. 6. 6.(a). Solve for the unknown displacements 6.(b). Solve for strains and stresses in all 3 elements. Show your work and follow the finite element method matrix formulation we have covered in lectures 4 3 20 ft 5 kip 10 kip 240 ft ft 30 ft- Figure 4
A...
Consider the finite automaton M = (Q,{a, b},8,90,F) defined by the following illustration. -0.00 7 92...
Consider the finite automaton M = (Q,{a, b},8,90,F) defined by the following illustration. -0.00 7 92 Part (a) (8 MARKS] For all i e {0,1,2,3}, write a regular expression Ri such that L(R;) = {we {a,b}* | ** (90, w) = qi}. Briefly justify your answers for R2 and R3.
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...
Let F be a finite field with q elements. a) S -1 for every a*0 in F. how that a-1 either f* 0 or deg(f*)<q, and f* induces the same function on F as f does. function on F, then f=g. b) Let j(X)E F[X]. Show that there exists a polynomial /*(X)EF[X] such that c) Show that if two polynomials f and g, each of degree <g, induce the same
Let F be a finite field with q elements. a)...
QUESTION 2 21 Finite elements can appear in many forms such as two-dimensional and three- dimensional domains Give two examples and a sketch for each domain. (4) 22 Explain the following terms as used in Finite element equations a Plain stress b Plain strain 23 Use the Finite element method to develop the stiffness matrix for element 2 of the steel cantilever beam structure shown in Figure 2 The elastic modulus IS 200 kN/mm2 with a thickness of 1 unit...
7. Let A, , An be non-empty subsets of a finite set Ω. If 1 k n and Ek is the set of elements in Ω which belong to at least k of the Ai's show that Pal i-1
7. Let A, , An be non-empty subsets of a finite set Ω. If 1 k n and Ek is the set of elements in Ω which belong to at least k of the Ai's show that Pal i-1
A=4 B=7
1) For the foundation sitting on top of the 5m thick soil calculate dimension. (Factor of Safety:3 (30p) (AX100) KN (B x3) kNm SPT-N (A+2B) 5 m b XD Uniform sand JIKUM) ya 15 kN/m a. Determine the q (angle of internal friction angle) of sand by using the given formula. b. Find the dimension b based on bearing capacity c. Find settlement by using 2:1 rule (DO NOT CHANGE DIMENSION AFTER SETTLEMENT Calculation) 9. = 1.3cN+y D,N,...
Define Jordan Measure and prove If
is a finite set consisting of precisely n elements, show that S
has zero Jordan measure.
Explain in Detail
{urg} = S
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...
A plane truss element is shown in Figure 4, All elements have cross-sectional area of A = 8 in, and elastic modulus of E-2 x 10° psi. Use long-hand solution 6. 6.(a). Solve for the unknown displacements. 6.(b). Solve for strains and stresses in al 3 elements. Show your work and follow the finite element method matrix formulation we have covered in lectures. 4 5 kip 10 240 ft 30 ft30 ft Figure 4.
A plane truss element is shown...
A plane truss element is shown in Figure 4. All elements have cross-sectional area of A = 8 in, and elastic modulus of E 2 x 10 psi. Use long-hand solution. 6. 6.(a). Solve for the unknown displacements 6.(b). Solve for strains and stresses in all 3 elements. Show your work and follow the finite element method matrix formulation we have covered in lectures 4 3 20 ft 5 kip 10 kip 240 ft ft 30 ft- Figure 4
A...
Consider the finite automaton M = (Q,{a, b},8,90,F) defined by the following illustration. -0.00 7 92 Part (a) (8 MARKS] For all i e {0,1,2,3}, write a regular expression Ri such that L(R;) = {we {a,b}* | ** (90, w) = qi}. Briefly justify your answers for R2 and R3.
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...
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