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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Textbook Question
Chapter 1, Problem 9E
In the structure shown, rigid blocks are connected by linear springs. Imagine that only horizontal displacements are allowed. Write the global equilibrium equations
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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
in
ks = 9
in
lb
k6 = 9 in
50 lb
k4 = 20 lb
kg = 20 b
in
in
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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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- Beam AB has a pin support at A and a roller support at B Joint B is also restrained by a linearly elastic rotational spring with stiffness kR, which provides a resisting moment MBdue to rotation at B. Member AB has flexural rigidity EI. A moment M0acts counterclockwise at B. Use the method of superposition to solve for all reactions. Find an expression for joint rotation Ain terms of spring stiffness kR. What is Awhen kR 0? What is Awhen kR— ? What is Awhen kR= 6EI/L?arrow_forwardA uniform bar AB of weight W = 25 N is supported by two springs, as shown in the figure. The spring on the left has a stiffness k[= 300 N/m and natural length Lt=250 mm. The corresponding quantities for the spring on the right are k2= 400 N/m and L^ = 200 mm. The distance between the springs is L = 350 mm, and the spring on the right is suspended from a support that is a distance it = SO mm below the point of support for the spring on the left. Neglect the weight of the springs. (a) At what distance x from the left-hand spring (figure part a) should a load P = 18 N be placed in order to bring the bar to a horizontal position? (b) If P is now removed, what new value of k{is required so that the bar (figure part a) will hang in a horizontal position underweight If? (c) If P is removed and kt= 300 N/m. what distance b should spring ktbe moved to the right so that the bar (figure part a) will hang in a horizontal position under weight II"? (d) If the spring on the left is now replaced by two springs in series (kt= 300 N/m, kt) with overall natural length Lt= 250 mm (see figure part b). what value of k; is required so that the bar will hang in a horizontal position under weight IF?arrow_forwardThe device shown in the figure consists of a prismatic rigid pointer ABC supported by a uniform translational spring of stiffness k = 950 N/m. The spring is positioned a distance P = 165 nun from the pinned end A of the pointer. The device is adjusted so that, when there is no load P, the pointer reads zero on the angular scale. (a) If the load P = 11 N, al what distance .v should the load be placed so that the pointer will read ?? = 2.5° on the scale (see figure part a)? (b) Repeal part (a) if a rotational spring E1= kb-6 is added al A (see figure part b). (c) Lel.x = 7b/8.What is P maxif 0 cannot exceed 2"? Include spring krin your analysis. (d) Now, if the weight of the pointer ABC is known to be W =3N and the weight or the spring is Ws= 2.75 N, what initial angular position (Left in degrees) of the pointer will result in a zero reading on the angular scale once the pointer is released from rest? Assume P = kr=0. (e) If the pointer is rotated lo a vertical position (see figure part c), find the required load P applied at mid-height of the pointer that will result in a pointer reading of 0 = 2.5" on the scale. Consider the weight of the pointer W. in your analysis.arrow_forward
- Repeat 1.3-9 but use the method of sections go find member forces in AC and BD.arrow_forwardK1 For the spring shown above, kl=100 N/mm, k2-200N/mm, k3-100N/mm, P-500N, ul-u3-0 Find: 1. The global stiffness matrix 2. Displacements of nodes 2 and 3arrow_forwardThe figure below shows a beam supported by a spring while subjected to a horizontal force f. The spring has a natural unstretched length 7 and stiffness constant k. The total length of the beam is 3L, the force acts at 2L (see figure). The spring sits on vertical slider, such that it remains horizontal at all times. 7 2L (a) Find the equilibrium values of the angle 0 as a function of the parameters: k,L,1, and f. (b) Let 1 = L and f = 4kL. Determine the stability of the solution at 0 = 0 and interpret the result. (c) Using the other stationary value for the angle, verify that the moment of the applied force and the spring about the pivot (bottom left) sum to zero.arrow_forward
- Member AB (helical spring) and Member AC (axial rod) are carrying a weight at point A. Member AB has the following properties: R = 90 mm, n -4 turns, G- 70 GPa, d- 30 mm, and Talow = 105 MPa while Member AC has the following properties: L= 2.A- 500 mm?, E = 200 GPa, and a low- 30 MPa. Determine the maximum safe %3D value of W (in N). Use simplified formula for the helical spring. A 60°arrow_forwardb) A steel column AB is fixed at its base and is braced at its top by cables as shown in Figure Q4 (b). This column has moment of inertia of l= 113 x 10° mm and ly36.6 x 10° mm". If the length of column is 8 m, examine the allowable load, P that can be resisted by this column before it either begins to buckle or yields. Take modulus of elasticity, E = 200 GPa, yield stress, a, = 250 MPa, and factor of safety, F.S= 2.0. Given the cross-sectional area of this column is 12,700 mm. If the applied load P exceeded the allowable load, suggest TWO (2) methods of strengthening for this column. (CO2-PO2)(C6) !!arrow_forwardis my entered value correct ? please correct me if I'm mistakenarrow_forward
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