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 48E
To determine
To find: Using nodal displacements solve for force and support reaction of the given truss plane.
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A pendulum is made up of a spring with a mass attached to the end. The spring is arranged to lie in a straight line, by wrapping the spring around a massless bar. The equilibrium length of the bar is “l”. Using lagrange’s equations, find the equations of motion.
In a compound helical spring, the inner spring is concentric with the outer spring, but is 9 mm shorter. The outer spring has ten coils of mean diameter 24 mm, and the wire diameter is 3 mm. Find the stiffness of the inner spring if an axial load of 150 N causes the outer spring to compress 18 mm. If the mean coil diameter for the inner spring is 15.94 mm, find the wire diameter of the inner spring when it has eight coils. Both the springs are made of the same material having G = 77 GPa.
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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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- It represents the equilibrium of a sphere of equal weigth as a homogenous and uniform bar whose length is four times the radius of the sphere. Find θ if the rope suspending the sphere. measures the same as the radius of the sphere.arrow_forwardCalculate the maximum force P that can be applied in a phosphor bronze spring having mean diameter of 150 mm and consisting of 24 turns of 10-mm diameter wire when the spring is stretched 180mm. Use G = 42 GPa.arrow_forwardConsider the frame shown in (Figure 1). Suppose that F1 = 890 N . Determine the magnitude of the reaction at pin A. Determine the magnitude of the reaction at pin B. Determine the magnitude of the reaction at pin C on CB.arrow_forward
- (PSD) A precision milling machine, weighing 4500 N, is supported on a rubber mount. The force-deflection relationship of the rubber mount is given by F = 270x + 0.25(x^3). Determine the equivalent linearized spring constant of the rubber mount at its static equilibrium position.arrow_forwardA vertical close-coiled helical compression spring must have a stiffness of 900 N/m under a load of 45 N and the maximum shear stress induced due to this load is to be 120 MPa. With the spring fully compressed the vertical height over the coils is 45 mm. Calculate (a) the wire diameter; (b) the mean coil diameter; and (c) the number of coils (G = 40 GPa)arrow_forwardPhysics for Engineering A uniform bar 3.00 m long is held by ropes at the ends making angle 60.0 and 30.0, respectively, with the horizontal. A weight of 200 N is hung 0.500 m from the left end where the 60.0 rope is attached. Find the tension in the ropes (T1 & T2) and the weight (W) of the bar. (Hint: Formulate three equations for the three unknowns, 2 equations for the 1st condition and 1 equation for the 2nd condition.)arrow_forward
- For the spring assemblages shown in Figures P2–8 through P2–16, determine the nodal displacements, the forces in each element, and the reactions. Use the direct stiffness method for all problems.arrow_forwardA square plate in balance. A square plate with a mass of 16.4 kg is held in balance in the vertical plane by a hinge attached to its right lower corner and by a rope inclined at 30.4 degrees from horizontal fixed at its upper right corner.What is the modulus of the voltage in the rope?arrow_forwardDetermine the possible range for R is the equivalent spring stiffness constant varies from 50 N/m to 500 N/marrow_forward
- Suppose that the assembled stiffness matrix of question 1 (as shown below) is as follows: [K]=108×a-a0-aa+b-b0-bb where a=4.06 N/m and b=2.28 N/m. If the applied force at node 3 is P=210 KN, find the displacement of node 2 in mm?arrow_forwardA 27‑kg sing is attached to the right end of a horizontal beam (the beam's mass m = 7.7 kg). The left end of the beam is mounted into a wall and it's right end is supported by a string which makes an angle θ = 32° with the beam, see the picture below. Find the magnitude of the tension in the string. 1. The tension in the string, T Find the reaction force exerted by the wall on the beam. 2. The x component of the wall's reaction force, Rx = 3. The y component of the wall's reaction force, Ry =arrow_forwardThe inner spring of a compound helical spring is arranged within and concentric with the outer one and is shorter by 9 mm. The outer spring has 10 coils with a mean diameter of 24 mm and a wire diameter of 3 mm. (a) Determine the stiffness of the inner spring when an axial load of 162 N causes the outer spring to compress by 16 mm. If the radial clearance between the springs is 1.5 mm and the inner spring has 8 coils, find its wire diameter. (c) Disregarding the effect of curvature, find the maximum shear stress in each of the spring. Given G = 78 GPa.arrow_forward
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