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 14, Problem 14.51SP
A rectangular hollow shape carries loads as shown. Calculate the maximum value of P if the allowable stresses are
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Chapter 14 Solutions
Applied Statics and Strength of Materials (6th Edition)
Ch. 14 - Calculate the section modulus for: (a) a 6 -in-by-...Ch. 14 - Calculate the section modulus (with respect to the...Ch. 14 - Prob. 14.3PCh. 14 - Rework Problem 14.3 changing the orientation of...Ch. 14 - Assume that the timber member (a) of Problem 14.2...Ch. 14 - The structural steel built-up member (b) of...Ch. 14 - A round steel rod, 25 mm in diameter, is subjected...Ch. 14 - A square steel bar, 38 mm on each side, is used as...Ch. 14 - Calculate the moment strength for a W36302...Ch. 14 - Calculate the allowable bending moment for a solid...
Ch. 14 - The beams of cross sections shown are subjected to...Ch. 14 - A solid rectangular simply supported timber beam 6...Ch. 14 - A W1430 supports the loads shown. Calculate the...Ch. 14 - If the allowable shear stress is 100 MPa,...Ch. 14 - A steel pin 112 in diameter is subjected to a...Ch. 14 - A timber power-line pole is 10 in. in diameter at...Ch. 14 - Calculate the value of S and Z and the shape...Ch. 14 - For beams that have cross sections as shown for...Ch. 14 - Calculate the maximum load P that the beam shown...Ch. 14 - A 412 (S4S) hem-fir timber beam carries a...Ch. 14 - A simply supported W1636 A992 steel beam carries a...Ch. 14 - A W250115 steel wide-flange section supports a...Ch. 14 - Assume that the floor joist dimensions of Example...Ch. 14 - Calculate the allowable superimposed uniformly...Ch. 14 - A 3 -in.-by- 12 -in. (S4S) scaffold timber plank...Ch. 14 - For the following computer problems, any...Ch. 14 - For the following computer problems, any...Ch. 14 - For the following computer problems, any...Ch. 14 - Calculate the section modulus with respect to the...Ch. 14 - The timber box section (a) of Problem 14.29 is...Ch. 14 - A timber beam is subjected to a maximum bending...Ch. 14 - Rework Problem 14.31 assuming that the beam is...Ch. 14 - A 12 -in.-diameter steel rod projects 2 ft...Ch. 14 - Calculate the maximum bending stress in a W530101...Ch. 14 - A cantilever cast-iron beam is 6 ft long and has a...Ch. 14 - 14.36 Calculate the moment strength for a...Ch. 14 - A W813 steel wide-flange beam on a 20 -ft span is...Ch. 14 - A simply supported beam with a cruciform cross...Ch. 14 - A rectangular beam 100 mm in width and 250 mm in...Ch. 14 - The timber box section (a) of Problem 14.29 is...Ch. 14 - For the I-shaped timber beam shown, calculate the...Ch. 14 - 14.42 A steel wide-flange beam is oriented so that...Ch. 14 - A W1045steel wide-flange beam supports a uniformly...Ch. 14 - 14.44 A steel wide-flange section is subjected to...Ch. 14 - A W30108 steel wide-flange beam is simply...Ch. 14 - A W612 is strengthened with a 34 -in.-by- 34 -in....Ch. 14 - Four wood boards 1 in. by 6 in. in cross section...Ch. 14 - A lintel consists of two 8 -in.-by- 12 in. steel...Ch. 14 - A 50 -mm-by- 300 -mm scaffold timber plank, placed...Ch. 14 - A laminated wood beam is built up by gluing...Ch. 14 - A rectangular hollow shape carries loads as shown....Ch. 14 - For the beam shown, calculate the maximum tensile...Ch. 14 - 14.53 A box beam is built up of four -in.-by--in....Ch. 14 - 14.54 Find the value of the loads P that can be...Ch. 14 - 14.55 Solve Problem 14.54 assuming that the timber...Ch. 14 - Calculate the values of S and Z and the shape...Ch. 14 - 14.57 A is supported on simple supports on a -ft...
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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
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