Homework Answers
your E value is so high (it seems to unrealistic ) but if it is correct then provided solution is correct....thank you
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Question 1 (10 marks) Consider the bar element shown in Figure 1. Cross sectional area A...
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.
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...
Figure < 1 of 1 Consider, for instance, a bar of initial length L and cross-sectional...
Figure < 1 of 1 Consider, for instance, a bar of initial length L and cross-sectional area A stressed by a force of magnitude F. As a result, the bar stretches by AL (Figure 1) Let us define two new terms: • Tensile stress is the ratio of the stretching force to the cross-sectional area: stress = 5 • Tensile strain is the ratio of the elongation of the rod to the initial length of the bar strain= 41 It...
for 60,000 the 1D bar shown with an elastic modulus of 200 GPa, cross-sectional area of...
for 60,000 the 1D bar shown with an elastic modulus of 200 GPa, cross-sectional area of 12.5x10 m2, and length of 1.5 m. determine the following e(x) dx d. σ(x) o (x) dx a) Theoretical axial displacement equation based on ö(x) dx E F(x) dx EA |zE
1. A wire 2.0 m long and cross sectional area of 10-6 m2 is stretched 1.0...
1. A wire 2.0 m long and cross sectional area of 10-6 m2 is stretched 1.0 mm by a force of 50.0 N. Calculate: (a) The stress. (5.0 x 107 N/m2 ) (b) The strain. (5.0 x 10-4 ) (c) Young’s modulus of elasticity. (1.0 x 1011 N/m2) (d) The energy stored in the wire. (0.025 J)
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....
Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below.
Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that the bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 3 are fixed Element 1 has Young's Modulus of 300 Pa, length of 1 m and cross-sectional area of 1 m2. Element 2 has Young's Modulus of 200 Pa, length of 2...
The A992 steel rod is subjected to the loading shown. If the cross-sectional area of the...
The A992 steel rod is
subjected to the loading shown. If the cross-sectional area of the
rod is 100 mm2. Neglect the size of the couplings at B and C. The
elastic modulus and yield stress of A992 steel is 200 GPa and 345
MPa respectively. Determine the displacement of B and A with
respect to point D. (Preserve 2 significant digits after the
decimal point.)
QUESTION 1 The 1992 steel rod is subjected to the loading shown. If the...
Consider the bar shown below which is made of two different materials with different cross sectional...
Consider the bar shown below which is made of two different materials with different cross sectional areas. An axial force P 200x103 N is applied at the intersection point. Both ends of the bar are fixed 300 mm> 400 mm Aluminum A 2400 mm2 E 70 x 10 N/2 E2-200 x 109 N/m2 Steel A,-600 mm2 1. 2. 3. Find the axial displacements at X, -140 mm and X2 -440 mm Find the stress at X' = 140 mm and...
3. 2090] Consider a uniform bar of Young's modulus E, cross-sectional area A, moment of inertia d...
3. 2090] Consider a uniform bar of Young's modulus E, cross-sectional area A, moment of inertia density p, length L, with an attached end mass, m, connected to a rigid wall via a linear spring of spring constant, k, see Figure. Let the longitudinal vibration of the bar be Wa.f). (a) [4] Write down the boundary conditions. m E, p Boundary condition at x 0 Boundary condition at x L (b) [81 Derive the equation for the natural frequency (c)...
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.
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...
Figure < 1 of 1 Consider, for instance, a bar of initial length L and cross-sectional area A stressed by a force of magnitude F. As a result, the bar stretches by AL (Figure 1) Let us define two new terms: • Tensile stress is the ratio of the stretching force to the cross-sectional area: stress = 5 • Tensile strain is the ratio of the elongation of the rod to the initial length of the bar strain= 41 It...
for 60,000 the 1D bar shown with an elastic modulus of 200 GPa, cross-sectional area of 12.5x10 m2, and length of 1.5 m. determine the following e(x) dx d. σ(x) o (x) dx a) Theoretical axial displacement equation based on ö(x) dx E F(x) dx EA |zE
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....
Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that the bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 3 are fixed Element 1 has Young's Modulus of 300 Pa, length of 1 m and cross-sectional area of 1 m2. Element 2 has Young's Modulus of 200 Pa, length of 2...
The A992 steel rod is
subjected to the loading shown. If the cross-sectional area of the
rod is 100 mm2. Neglect the size of the couplings at B and C. The
elastic modulus and yield stress of A992 steel is 200 GPa and 345
MPa respectively. Determine the displacement of B and A with
respect to point D. (Preserve 2 significant digits after the
decimal point.)
QUESTION 1 The 1992 steel rod is subjected to the loading shown. If the...
Consider the bar shown below which is made of two different materials with different cross sectional areas. An axial force P 200x103 N is applied at the intersection point. Both ends of the bar are fixed 300 mm> 400 mm Aluminum A 2400 mm2 E 70 x 10 N/2 E2-200 x 109 N/m2 Steel A,-600 mm2 1. 2. 3. Find the axial displacements at X, -140 mm and X2 -440 mm Find the stress at X' = 140 mm and...
3. 2090] Consider a uniform bar of Young's modulus E, cross-sectional area A, moment of inertia density p, length L, with an attached end mass, m, connected to a rigid wall via a linear spring of spring constant, k, see Figure. Let the longitudinal vibration of the bar be Wa.f). (a) [4] Write down the boundary conditions. m E, p Boundary condition at x 0 Boundary condition at x L (b) [81 Derive the equation for the natural frequency (c)...
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