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 8E
Determine the nodal displacements, element forces, and reaction forces using the direct stiffness method for the two-bar truss shown in the figure.
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A truss is subjected to a 10 Kips of vertical load at G, a 30 Kips of vertical load at F and a 10 Kips of vertical load at E as shown in the figure.
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(a) Forces in members AG and AB using the method of joints,
(b) Forces in members FC and FE using the method of sections.
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Chapter
Problem
CH3
4P
For the bar assemblages shown in Figure P3-4,
determine the nodal displacements, the forces in
each element, and the reactions. Use the direct
stiffness method for the problem.
2 5,000 1b 10,00ю iь з
E = 30 x 10* psi
A = 4.0 in?
30 in.
- 30 in. –
-30 in -
Figure P3-4
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Calculate
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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- -11 A rubber cube R of a side L = 3 in. and cross- sectional area A = 9 in2 is compressed inside a steel cube S by a force F = 5 lb that applies uniformly distributed pressure to the rubber. Assume E 0.3ksi and,, = 0.45. (a) Calculate the lateral pressure between the rubber and steel (disregard friction between the rubber and the steel, and assume that the steel block is rigid when compared to the rubber). (b) Calculate the change in volume of the rubber.arrow_forwardRepeat 1.3-9 but use the method of sections go find member forces in AC and BD.arrow_forwardFor the bar assemblages shown in Figure P3-3, determine the nodal displacements, the forces in each element, and the reactions. Use the direct stiffness method for the problem. 16,000 Ib 2 E - 30 x 10 psi A = 2.0 in? 20 in. 50 in. Figure P3-3arrow_forward
- THE ORIGINAL QUESTION IS: For the beam shown, find the reactions at the supports and plot the shear-force and bending-moment diagrams. Label the diagrams properly and provide values at all key points. THE QUESTION THAT NEEDS TO BE ANSWERED IS: Repeat problem 3-5 using singularity functions exclusively (including reactions).arrow_forwardFor the truss shown in Figure 4, where a load of 6kN is applied at point D, calculate: i) the force in member AB, using the method of sections and taking moments about point G. Sketch the position of the section cut. ii) the force in members BG and FG 6 kN A 2.4 m B 2.4 m C 2.4 m D 2 m E 5 m F H. Figure 4: Loaded Trussarrow_forwardLabel the nodes and the elements in the figure with appropriate node and element numbers. Compute the local stiffness matrix and load vector for each element Assemble the global stiffness matrix and load vector. State the boundary conditions, apply them, and solve the reduced system to obtain the DOF solution Compute reactions at the supports Evaluate the slope occurring at the midpoint of the right portion of the beam.arrow_forward
- 1 (a)The bar shown in Figure 1(a) has a mass of 15 kg and is subjected to a couple moment of M = 70 Nm and a force P = (200M) N applied to the end of the bar. The spring has unstretched length of 0.4 m and remain in the vertical position due to roller guide at B. Note; Use your last three digit of matrix number to determine the value of force P as follows; Example of matrix number, CD180002 M= (0+0+2) = 2 Therefore, P = 200M = 200+2 = 202 N Draw the free body diagram of the bar to account for all the forces that act on it. (i) (ii) Determine the total work done by all the forces acting on the bar when it has rotated downward from 0 = 0° to 0 = 90°.arrow_forwardThe force P3 to make it to equilibrium in kN is The Stress in section 1 in N/mm2 is The Compressive Stress in section 2 in N/mm2 is The stress in section 3 in N/mm2 is The total change in length in x10-3 mm isarrow_forwardplease i need the solution with full stepsarrow_forward
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