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 2, Problem 21E
A tapered bar with circular cross section is fixed at
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3) For the given plate subjected to two point forces,
calculate the nodal displacements and the moments at points A and B. (Note that A is the mid-point of
the finite element)
E = 30000 MPa
h = 0.14 m
v = 0.20
2 m
2 m
50 kN
2 m
50 kN
A
B
50 kN
50 kN
2 m
50
Cross-section along
the symmetry axis
A bar ABC of length L consists of two parts of equal lengths but
different diameters. Segment AB has diameter d1= 100 mm while
segment BC has diameter dz = 60 mm. Both segments have length
L/2 = 0.6 m. A longitudinal hole of diameter d is drilled through
segment AB for one-half of its length (distance L/4= 0.3 m). The bar
is made of plastic having modulus of elasticity E = 4.0 GPa.
Compressive loads P= 110 kN act at the ends of the bar. If the
shortening of the bar is limited to 8.0 mm, what is the maximum
allowable diameter dmax (mm) of the hole?
dmax
d2
4.
2
(a)
The 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.
Chapter 2 Solutions
Introduction To Finite Element Analysis And Design
Ch. 2 - Answer the following descriptive questions.
a....Ch. 2 - Use the Galerkin method to solve the following...Ch. 2 - Solve the differential equation in problem 2 using...Ch. 2 - Prob. 4ECh. 2 - Using the Galerkin method, solve the following...Ch. 2 - A one-dimensional heat conduction problem can be...Ch. 2 - Solve the one-dimensional heat conduction problem...Ch. 2 - Prob. 8ECh. 2 - Solve the differential equation in problem 8 for...Ch. 2 - Prob. 10E
Ch. 2 - Prob. 11ECh. 2 - Prob. 12ECh. 2 - Using the Galerkin method, calculate the...Ch. 2 - The boundary-value problem for a clamped-clamped...Ch. 2 - The boundary-value problem for a cantilevered beam...Ch. 2 - Prob. 16ECh. 2 - Consider a finite element with three nodes, as...Ch. 2 - A vertical rod of elastic material is fixed at...Ch. 2 - A bar in the figure is under the uniformly...Ch. 2 - Prob. 20ECh. 2 - A tapered bar with circular cross section is fixed...Ch. 2 - The stepped bar shown in the figure is subjected...Ch. 2 - A bar shown in the figure is modeled using three...Ch. 2 - Consider the tapered bar in problem 17. Use the...Ch. 2 - Consider the tapered bar in problem 21. Use the...Ch. 2 - Consider the uniform bar in the figure. Axial load...Ch. 2 - Determine shape functions of a bar element shown...Ch. 2 - Consider a finite element with three nodes, as...
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- A bar ABC of length L consists of two parts of equal lengths but different diameters. Segment AB has a diameter d 1 = 100 mm and segment BC has a diameter d 2 = 60 mm. Both segments have a length L / 2 = 0.6 m. A longitudinal hole of diameter d is drilled through segment AB in the middle of its length (distance L / 4 = 0.3 m). The bar is made of plastic with a modulus of elasticity. E = 4.0 GPa. Compressive loads P = 110 kN act at the ends of the bar. (a) If the shortening of the bar is limited to 8.0 mm, what is the maximum allowable diameter d max of the hole? (See figure part a.) (b) Now, if d max is set to d 2/2, at what distance b from the end C must the load P be applied to limit the shortening of the bar to 8.0 mm? (See Figure part b.) (C) Finally, if the loads P are applied at the ends and d max = d 2/2, what is the allowable length x of the hole if shortening is limited to 8.0 mm? (See figure part c.)arrow_forwardConsider a two-component rod fixed at the left end. The first component (on the left, positioned from z=0 to z=L/2) is a solid rod with a shear modulus of G and radius c1. The second component (on the right, positioned from z=L/2 to z=L) is a hollow pipe fixed to component 1 at z=L/2 with the same shear modulus and outer radius c1, but with an inner radius of c2. A torque of 6To is applied at z=L/2, and a torque of -2To is applied at z=L. What value of c2 is required to make the maximum shear stress equivalent in each component? What is the angle of twist at the free end at z=L?arrow_forwardQ4arrow_forward
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