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1) A structural system is consisted of three 1D bar elements (A, B, C). Using the...
Model the bar with three finite elements and determine: a) The global stiffness matrix b)The global...
Model the bar with three finite elements and determine: a) The global stiffness matrix b)The global load vector c) The nodal displacement d) The stresses in each bar ろ-75 kN 400 ma 600 mm+ Aluminum 1200 mm2 70 GPa トー800 mm Bronze A=2400 mm2 E 83 GPa Steel 600 mm2 200 GPa
Using Finite Element with a minimum of 3 elements (Penalty Approach). For the beam and loading sh...
Using Finite Element with a minimum of 3 elements
(Penalty Approach). For the beam and loading shown,
determine (a) the slope at the end A, (b) the deflection at point
C. Use E= 200 GPa And I = 6.83 x 106 mm4
or the beam and loading shown, determine (a) the slope at end A, (6) the deflection at point C. Use E 200 GPa and I -6.83 x 10+6mm4 Use FEM with a minimum of 3 elements(Penalty Approach). 20...
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...
Chapter 3, Reserve Problem 122 The rigid bar AC is supported by two axial bars (1)...
Chapter 3, Reserve Problem 122 The rigid bar AC is supported by two axial bars (1) and (2). Both axial bars are made of bronze [E = 100 GPa; a = 18 × 10-mm/mm/°C]. The cross-sectional area of bar (1) is A1 = 236 mm2 and the cross- sectional area of bar (2) is Az = 389 mm2. After load P has been applied and the temperature of the entire assembly has increased by 26°C, the total strain in bar...
The rigid bar shown is supported by axial bar (1) and by a pin connection at C. Axial bar (1) has...
The rigid bar shown is supported by axial bar (1) and by a pin
connection at C. Axial bar (1) has a cross-sectional area
of A1 = 250 mm2, an elastic modulus
of E = 200 GPa, and a coefficient of thermal expansion of
α= 11.3 × 10-6/°C. The pin at C has a diameter
of 40 mm. After load P has been applied and the
temperature of the entire assembly has been increased by 10°C, the
total strain in...
A 3 m rigid bar AB is supported with a vertical translational spring at A and a pin at B The bar is subjected to a linearly varying distributed load with maximum intensity g Calculate the ver...
A 3 m rigid bar AB is supported with a vertical translational spring at A and a pin at B The bar is subjected to a linearly varying distributed load with maximum intensity g Calculate the vertical deformation of the spring if the spring constant is 700 kN/m. (ans: 21.43 mm) 2. A steel cable with a nominal diameter of 25 mm is used in a construction yard to lift a bridge section weighing 38 kN. The cable has an...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic elastic bar element can be written as follows: ū(x) = [N]{u} where, [N] = [N1 N2 N3] and {u} u2 13 1 and Ni L2 L2 [N] and {u} are known as interpolation function matrix and nodal displacement, respectively. (272 – 3L + L´), N= = (22- La), Ns = 12 (2=– LE) Derive the expression for element stiffness matrix, (Kelem) and element force...
Bar B of the pin connected system is made of aluminum alloy (E=105 GPa, A=1200 mm^2)...
Bar B of the pin connected system is made of aluminum alloy
(E=105 GPa, A=1200 mm^2) and bar A is made of a hardened carbon
steel (E=210 GPa, A=1200 mm^2). Bar CDE is rigid. When the system
is unloaded, Bars A and B are unstressed.
Determine:
a) The Normal Stress in bars A and B. (5pts)
b) The Shearing Stress in the 20-mm diameter pin E which is in
double shear. (5pts)
c) If the yield stress of the material...
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
please use only the weighted resedual and gerkins
methods to prove it
1. A metal bar of length, L = 100 mm, and a constant cross-sectional area of A = 10 mm? is shown in figure Q1. The bar material has an elastic modulus, E = 200,000 N/mm2 with an applied load P at one end. The governing equation for elastostatic problems...
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...
Model the bar with three finite elements and determine: a) The global stiffness matrix b)The global load vector c) The nodal displacement d) The stresses in each bar ろ-75 kN 400 ma 600 mm+ Aluminum 1200 mm2 70 GPa トー800 mm Bronze A=2400 mm2 E 83 GPa Steel 600 mm2 200 GPa
Using Finite Element with a minimum of 3 elements
(Penalty Approach). For the beam and loading shown,
determine (a) the slope at the end A, (b) the deflection at point
C. Use E= 200 GPa And I = 6.83 x 106 mm4
or the beam and loading shown, determine (a) the slope at end A, (6) the deflection at point C. Use E 200 GPa and I -6.83 x 10+6mm4 Use FEM with a minimum of 3 elements(Penalty Approach). 20...
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...
Chapter 3, Reserve Problem 122 The rigid bar AC is supported by two axial bars (1) and (2). Both axial bars are made of bronze [E = 100 GPa; a = 18 × 10-mm/mm/°C]. The cross-sectional area of bar (1) is A1 = 236 mm2 and the cross- sectional area of bar (2) is Az = 389 mm2. After load P has been applied and the temperature of the entire assembly has increased by 26°C, the total strain in bar...
The rigid bar shown is supported by axial bar (1) and by a pin
connection at C. Axial bar (1) has a cross-sectional area
of A1 = 250 mm2, an elastic modulus
of E = 200 GPa, and a coefficient of thermal expansion of
α= 11.3 × 10-6/°C. The pin at C has a diameter
of 40 mm. After load P has been applied and the
temperature of the entire assembly has been increased by 10°C, the
total strain in...
A 3 m rigid bar AB is supported with a vertical translational spring at A and a pin at B The bar is subjected to a linearly varying distributed load with maximum intensity g Calculate the vertical deformation of the spring if the spring constant is 700 kN/m. (ans: 21.43 mm) 2. A steel cable with a nominal diameter of 25 mm is used in a construction yard to lift a bridge section weighing 38 kN. The cable has an...
X=0 x = 1/2 x= L u U2 Uz (a) Trial solution for a 1-D quadratic elastic bar element can be written as follows: ū(x) = [N]{u} where, [N] = [N1 N2 N3] and {u} u2 13 1 and Ni L2 L2 [N] and {u} are known as interpolation function matrix and nodal displacement, respectively. (272 – 3L + L´), N= = (22- La), Ns = 12 (2=– LE) Derive the expression for element stiffness matrix, (Kelem) and element force...
Bar B of the pin connected system is made of aluminum alloy
(E=105 GPa, A=1200 mm^2) and bar A is made of a hardened carbon
steel (E=210 GPa, A=1200 mm^2). Bar CDE is rigid. When the system
is unloaded, Bars A and B are unstressed.
Determine:
a) The Normal Stress in bars A and B. (5pts)
b) The Shearing Stress in the 20-mm diameter pin E which is in
double shear. (5pts)
c) If the yield stress of the material...
need to solve the mathematical model to prove
that we can get the equations i Q1 a methematically
please use only the weighted resedual and gerkins
methods to prove it
1. A metal bar of length, L = 100 mm, and a constant cross-sectional area of A = 10 mm? is shown in figure Q1. The bar material has an elastic modulus, E = 200,000 N/mm2 with an applied load P at one end. The governing equation for elastostatic problems...
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...
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