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 41E
Use the finite element method to determine the nodal displacements in the plane truss shown in figure (a). The temperature of element 2 is 200°C above the reference temperature, that is,
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Statics of rigid bodies
*Solve the following problems completely: Show your complete solution and drawing:
Analyse the statically determinate bar illustrated below by expressing the loading as a single function using Macaulay brackets and the Dirac delta, integrating to find th
axial force and integrating again to find the displacements, applying the boundary conditions appropriately. Find the axial force in the bar at point A and the displaceme
at point B. The cross section of the bar is constant with EA = 18000 kN. a = 4 m, b = 2 m, c = 2 m and d = 4 m. w1 = 12 kN/m, w2 = 17 kN/m,, P1 = 12 kN and P2 =
19kN.
a
W1
L/2
W2
Multiple Choice Answers
Multiple Choice Answer: Axial force at point A (kN, tension positive):
a. 3.31
b. 31.97
c. 37.33
d. 31
Multiple Choice Answer: Displacement at point B (mm, positive to right):
a. 0.0061
b. 0.0395
c. 0.0193
d. 0.0261
Axial force at point A (kN, tension positive):
Displacement at point B (mm, positive to right):
L/2
P1
P2
(type in your multiple choice answer, e.g. a, b, c or d)
(type in your multiple choice answer, e.g. a, b, c or d)
For the cantilever plane truss in the figure above, use MATLAB to determine:
1)Nodal displacements
2)Reaction Forces
3)Element Strains and Stresses
Assuming that both supports are going to be fixed and the values of E = 70 GPa and A = 0.003125
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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- Helparrow_forward(Solid Mechanics) This finite element model is composed of 4 linear bar elements, each with a cross section of 10 mm² and material properties (E = 6 GPa, v=0.3). A weight of 200 N is applied and the nodes are named as shown below. (1) Compute the reaction forces. (2) What are the reaction forces when the weight is tripled to be 600 N? Find the solution without repeating the FEA. Explain why you can get the quick answer.arrow_forwardThe dimensions are of the graph are d1 = 7 cm , L1 = 6 m , d2 = 4.2 cm , and L2 = 5 m with applied loads F1 = 130 kN and F2 = 60 kN . The modulus of elasticity is E = 80 GPa . Use the following steps to find the deflection at point D. Point B is halfway between points A and C. What is the reaction force at A? Let a positive reaction force be to the right.arrow_forward
- Problem 2 Consider a plate formed by a homogeneous material with Young's modulus E, and Poisson's ratio v. The plate has total thickness h, the reference plane is located at the center of the plate, and N and Ny are applied at z = -h/2. Find the stiffness matrix of the plate.arrow_forwardParvinbhaiarrow_forwardis my entered value correct ? please correct me if I'm mistakenarrow_forward
- Dont Copy from chegg need step wise step and correct answers only Use Finite Elemental method Assemble element stiffness matrix for the member of plane frame shown in Figure is oriented at angle 30° to the x-axis. Take E= 200 GPa, I=4 × 106 m* and A = 4 × 10-³m². ,if it 5m 30arrow_forward3. 2 ft 1106 2 ft B ww Cord AB is 2 ft long, the force P = 76 lb, the angle 0 = 56 degrees and the spring's stiffness is k = 56 Ib/ft.arrow_forwardx=8arrow_forward
- Find the global stiffness matrix, displacement at node 1&2, reaction forces at 1&4, and force in spring for the following figure shown below. k1=90 N/mm, k2=1800 N/mm, k3=80 N/mm, P=600 N and u1=u4=0arrow_forwardFor 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.arrow_forwardPlease include plot/diagram in your solution. Strictly don't use chatgpt.arrow_forward
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