Applied Statics and Strength of Materials (6th Edition)
6th Edition
ISBN: 9780133840544
Author: George F. Limbrunner, Craig D'Allaird, Leonard Spiegel
Publisher: PEARSON
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Chapter 11, Problem 11.61SP
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Chapter 11 Solutions
Applied Statics and Strength of Materials (6th Edition)
Ch. 11 - Prob. 11.1PCh. 11 - A rectangular ASTM A36 steel bar 2 in. by 6 in. in...Ch. 11 - Calculate Poisson’s ratio for a cast iron that has...Ch. 11 - Modulus of elasticity, modulus of rigidity, and...Ch. 11 - Compute all the dimensional changes for the steel...Ch. 11 - A surveyor’s steel tape is exactly 100ft long...Ch. 11 - An aluminum wire is stretched between two rigid...Ch. 11 - Prob. 11.8PCh. 11 - A concrete roadway pavement is placed in 60ftlong...Ch. 11 - Prob. 11.10P
Ch. 11 - A 4in. -by- 8in . short wood post is reinforced on...Ch. 11 - A short post. 150mm by 150mm , of Douglas fir, is...Ch. 11 - The cables of a power line are copper-coated steel...Ch. 11 - Prob. 11.14PCh. 11 - For the short column shown, assuming that lateral...Ch. 11 - A 1.0 -in.-diameter hole is drilled on the...Ch. 11 - Prob. 11.17PCh. 11 - A long, flat steel bar 4 in. wide and 38 thick is...Ch. 11 - A long, flat steel bar 5 in. wide and 38 thick has...Ch. 11 - 11.20 An aluminum specimen of circular cross...Ch. 11 - Prob. 11.21PCh. 11 - Prob. 11.22PCh. 11 - 11.23 A concrete cylinder, -in, in diameter, was...Ch. 11 - Prob. 11.24PCh. 11 - For the element of Problem 11.24: a. Locate the...Ch. 11 - Prob. 11.26CPCh. 11 - Prob. 11.27CPCh. 11 - Prob. 11.28CPCh. 11 - Prob. 11.29CPCh. 11 - A 50 -mm-diameter ASTM A36 steel rod is subjected...Ch. 11 - A 4 -ft-long square ASTM A36 steel bar, 2 in. by 2...Ch. 11 - A concrete test cylinder is 150 mm in diameter and...Ch. 11 - A 14 -in.-long steel rod, 112 in diameter, was...Ch. 11 - Determine the change in the diameter of an ASTM...Ch. 11 - 11.35 The steel bar shown in Figure 11.3 (see...Ch. 11 - Compute the change in the thickness of the ASTM...Ch. 11 - The steel rails of a railroad track are laid in...Ch. 11 - A rolled brass rod and a steel rod are secured to...Ch. 11 - 11.39 A -m-long steel member is set snugly between...Ch. 11 - 11.40 The distance between two fixed points on a...Ch. 11 - A steel truss is loaded as shown. The...Ch. 11 - 11.42 For the truss of Problem 5.25, the members...Ch. 11 - A surveyor’s steel tape has a cross-sectional area...Ch. 11 - A 1 -in.-diameter ASTM A36 steel tie rod, 30 ft...Ch. 11 - 11.45 A copper wire is held taut between two...Ch. 11 - 11.46 A horizontal steel member is anchored at...Ch. 11 - 11.47 Three vertical steel wires are loaded as...Ch. 11 - 11.48 Assume for Problem 11.47 that the same load...Ch. 11 - The rod shown is firmly attached to rigid...Ch. 11 - 11.50 A structural steel bar mm in width and mm...Ch. 11 - A redwood timber member having a 16 -in.-square...Ch. 11 - A steel pipe has an outside diameter of 12 in. and...Ch. 11 - A short 14 -in.-square concrete pier is reinforced...Ch. 11 - An ASTM A36 steel rod, 375.06 mm long and having a...Ch. 11 - An aluminum rod with an area of 1.5in.2 and an...Ch. 11 - A solid brass cylinder with a cross-sectional area...Ch. 11 - Three 14 in.-diameter wires are symmetrically...Ch. 11 - Rework Problem 11.57 with outer wires of aluminum,...Ch. 11 - Three rods support a weight, as shown. The...Ch. 11 - A flat steel bar 4 in. wide and 12 thick must be...Ch. 11 - A 19 -mm-diameter hole is drilled on the...Ch. 11 - A flat bar is 38 thick and has a centrally located...Ch. 11 - A long, flat steel bar 125 mm wide and 10 mm thick...Ch. 11 - 11.64 A short -in.-diameter compression member is...Ch. 11 - Prob. 11.65SPCh. 11 - 11.66 A rectangular block of wood, in. by in. in...Ch. 11 - 11.67 A -mm-diameter rod is subjected to an axial...Ch. 11 - The rectangular plate shown is subjected to a...Ch. 11 - A wood block, subjected to a tensile load, fails...Ch. 11 - Prob. 11.70SPCh. 11 - A shaft in a speed-reduction mechanism is loaded...Ch. 11 - An axially loaded 50 -mm-by- 75 -mm steel bar has...
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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
- Problem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forwardI need part all parts please in detail (including f)arrow_forward
- Problem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forwardB5 Please help on the attached question.arrow_forward
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