Welding: Principles and Applications (MindTap Course List)
8th Edition
ISBN: 9781305494695
Author: Larry Jeffus
Publisher: Cengage Learning
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Chapter 26, Problem 28R
How do ferrite and cementite work together to form a strong ductile steel?
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Chapter 26 Solutions
Welding: Principles and Applications (MindTap Course List)
Ch. 26 - What gives metals their desirable properties?Ch. 26 - What is heat?Ch. 26 - What are the basic units of measure for heat?Ch. 26 - What is sensible heat?Ch. 26 - Prob. 5RCh. 26 - What does the color of light given off from a hot...Ch. 26 - Prob. 7RCh. 26 - In steel-making, what is ore combined with in the...Ch. 26 - Prob. 9RCh. 26 - What is an alloy?
Ch. 26 - Using Figure 26-18, answer the following...Ch. 26 - What is a eutectic composition?Ch. 26 - Using Table 26-3, what are the lowest and highest...Ch. 26 - Approximately how many degrees wide is the...Ch. 26 - Referring to Figure 26-20, what color would...Ch. 26 - Referring to Figure 26-20, what is the approximate...Ch. 26 - Prob. 17RCh. 26 - Referring to Figure 26-20, above what temperature...Ch. 26 - Prob. 19RCh. 26 - What is known as the critical temperature of...Ch. 26 - Can a metal have all the mechanical properties at...Ch. 26 - What other properties can a metal's hardness...Ch. 26 - Which property, brittleness or ductility, will let...Ch. 26 - What is toughness?Ch. 26 - What are the common types of strength...Ch. 26 - Prob. 26RCh. 26 - What are the three steps in precipitation...Ch. 26 - How do ferrite and cementite work together to form...Ch. 26 - Why is brine quenching faster than water...Ch. 26 - What can be done to speed up the quenching rate in...Ch. 26 - Why is the formation of martensite a problem when...Ch. 26 - How can the effects of cold working be removed?Ch. 26 - Prob. 33RCh. 26 - Referring to Figure 26-20, what would the preheat...Ch. 26 - Why must the stress-relieving temperature be kept...Ch. 26 - What properties can annealing produce in metals?Ch. 26 - How long does it take the weld metal to go through...Ch. 26 - What are some sources of hydrogen that can...Ch. 26 - How can nitrogen get into an SMA weld?Ch. 26 - What are some of the problems that oxygen can...Ch. 26 - When do cold cracks develop?Ch. 26 - What is carbide precipitation?
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- Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.arrow_forwardAn aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.arrow_forwardProblem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forward
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