Introduction To Finite Element Analysis And Design
2nd Edition
ISBN: 9781119078722
Author: Kim, Nam H., Sankar, Bhavani V., KUMAR, Ashok V., Author.
Publisher: John Wiley & Sons,
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Chapter 1, Problem 31E
Two bars are connected as shown in the figure. Assume all joints are frictionless pin joints. At node 2, a vertical spring is connected as shown. Both bars are of length L and have the same properties: Young’s modulus = L and area of cross section = A. The spring stiffness = k.
a. Set up the stiffness matrices for the two truss elements and the spring element.
b. Assemble the stiffness matrices to form the global stiffness matrix.
c. Compute the deflections at node 2, if a force
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Q: For the spring system shown in the accompanying figure, determine the
displacement of each node. Start by identifying the size of the global matrix.
Write down elemental stiffness matrices, and show the position of each
elemental matrix in the global matrix. Apply the boundary conditions and
loads. Solve the set of linear equations.
Also, compute the reaction forces.
k2 = 9 lb
k1 = 20b
in
20 lb
k,=5 lb
ww
lb
in
kz = 5 lb
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ks = 9
in
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k6 = 9 in
50 lb
k4 = 20 lb
kg = 20 b
in
in
For the spring system shown in the above figure, determine the displacement of each node. In the figure, the unit for the stiffness k is pound (lb) per inch. The left side of the system is fixed to a rigid wall, while the right side is displaced 0.5 inch to the right. Put a node between the rigid wall on the left and spring 1. Use the element method to establish the element stiffness matrix and then the global stiffness matrix. Apply the boundary conditions and theloads (by modifying the appropriate rows of the matrix and load vector). Solve the set of linear equations either by hand or using Matlab, Mathcad or Maple.
- For the spring system given in Figure 1,
Create the element matrices as well as the global stiffness and force matrix, note that k=1.
Figure 1
Chapter 1 Solutions
Introduction To Finite Element Analysis And Design
Ch. 1 - Answer the following descriptive questions a....Ch. 1 - Calculate the displacement at node 2 and reaction...Ch. 1 - Repeat problem 2 by changing node numbers; that...Ch. 1 - Three rigid bodies, 2,3, and 4, are connected by...Ch. 1 - Three rigid bodies, 2,3, and 4, are connected by...Ch. 1 - Consider the spring-rigid body system described in...Ch. 1 - Four rigid bodies, 1, 2, 3, and 4, are connected...Ch. 1 - Determine the nodal displacements, element forces,...Ch. 1 - In the structure shown, rigid blocks are connected...Ch. 1 - The spring-mass system shown in the figure is in...
Ch. 1 - A structure is composed of two one-dimensional bar...Ch. 1 - Two rigid masses, 1 and 2, are connected by three...Ch. 1 - Use the finite element method to determine the...Ch. 1 - Consider a tapered bar of circular cross section....Ch. 1 - The stepped bar shown in the figure is subjected...Ch. 1 - Using the direct stiffness matrix method, find the...Ch. 1 - A stepped bar is clamped at one end and subjected...Ch. 1 - A stepped bar is clamped at both ends. A force of ...Ch. 1 - Repeat problem 18 for the stepped bar shown in the...Ch. 1 - The finite element equation for the uniaxial bar...Ch. 1 - The truss structure shown in the figure supports a...Ch. 1 - The properties of the two elements of a plane...Ch. 1 - For a two-dimensional truss structure as shown in...Ch. 1 - The 2D truss shown in the figure is assembled to...Ch. 1 - For a two-dimensional truss structure as shown in...Ch. 1 - The truss shown in the figure supports force Fat...Ch. 1 - Prob. 27ECh. 1 - In the finite element model of a plane truss in...Ch. 1 - Use the finite element method to solve the plane...Ch. 1 - The plane truss shown in the figure has two...Ch. 1 - Two bars are connected as shown in the figure....Ch. 1 - The truss structure shown in the figure supports...Ch. 1 - It is desired to use the finite element method to...Ch. 1 - Determine the member force and axial stress in...Ch. 1 - Determine the normal stress in each member of the...Ch. 1 - The space truss shown has four members. Determine...Ch. 1 - The uniaxial bar shown below can be modeled as a...Ch. 1 - In the structure shown below, the temperature of...Ch. 1 - Prob. 39ECh. 1 - The three-bar truss problem in figure 1.23 is...Ch. 1 - Use the finite element method to determine the...Ch. 1 - Repeat problem 41 for the new configuration with...Ch. 1 - Repeat problem 42 with an external force added to...Ch. 1 - The properties of the members of the truss in the...Ch. 1 - Repeat problem 44 for the truss on the right side...Ch. 1 - The truss shown in the figure supports the force ....Ch. 1 - The finite element method as used to solve the...Ch. 1 - Prob. 48E
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- Alert for not submit AI generated answer. I need unique and correct answer. Don't try to copy from anywhere. Do not give answer in image formet and hand writingarrow_forwardLearning Goal: To solve for the support reactions of a frame. The frame shown in (Figure 1) is supported by a pin at A and a pin at D. The two members are connected by a pin at C. The dimensions are H₁ = 1.1 m, H₂ = 1.3 m, and L = 1 m. The applied force P = 11 kN acts at the midpoint of BC, and the distributed load has intensity w = 1.3 kN/m. Figure H1 B A P O W H₂arrow_forwardA simple structure is to be built to hold load at C as shown in Figure Q5. Body ABC is pin joint at wall A is regarded as a rigid body and is pin supported to rod BD at B. The respective dimensions are as shown in the figure. A support unit is to be connected by pin between point B and point D or point D' at the wall. a) Compare and analyze the two positions for the support unit not to fail by buckling when maximum load F is applied at C. Which position is the better choice between D and D' ? b) If load F is in opposite direction, what is the maximum load F that can be applied. (Properties of rod BD, E= 200GPA, G=77 GPa, v=0.3, o, = 250 MPa ) A 1.6m В 1.4m C 0.9m F 10mm 4mm D 0.8m 9. 15mm mm D' Crossection of Hollow Rod BD or BD'. ( 10mm x 15mm and 4mm x 9mm) Figure 05arrow_forward
- A. The frame shown in Figure I is hinged to rigid supports at A and E. Find the values of: 1. Force components of Hinge A 2. Force components of Hinge B 3. Force in Member BC 4. Force in Member BD 크 트 A 5' 3' P = 600 15 FIGURE 1 DA 3' 3' Barrow_forwardSolve the complex truss below by the method of substitution. See component reactions at the supports . bar force on member ab bar force on member bc bar force on member cd bar force on member de bar force on member ef bar force on member fa bar force on member ad bar force on member be bar force on member cfarrow_forwardA sign hangs from a wall, as shown. The upper left corner is supported by a pin joint, firmly attached to the wall. The upper right corner is supported by a rope. The rope is at a 30° angle from the horizontal. The pin joint is at the same height as the point where the sign attaches to the rope. The sign has a mass of 20kg. It is 2m long and the center-of- mass is 1m from the wall. a) Consider torques about the pin joint. Draw the line-of-action and lever-arm for both the tension force and the weight force. 1m c) What is the tension in the rope? mg b) What is the magnitude of the torque produced by the weight force about the pin joint? d) What are the reaction (support) forces at the pin joint? Write your answer as a vector. Y₁ 30° 2m -Xarrow_forward
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