Applied Statics and Strength of Materials (6th Edition)
6th Edition
ISBN: 9780133840544
Author: George F. Limbrunner, Craig D'Allaird, Leonard Spiegel
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 1, Problem 1.10P
One side of a triangular lot is 100 ft and the angle opposite this side is 55°. Another angle is 63°. Sketch the shape of the lot and determine how much fencing is needed to enclose it.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Spur gears
Note : Exam is open notes &tables / Answer all questions.
Q.1. The press shown for Figure.1 has a rated load
of 22 kN. The twin screws have double start Acme
threads, a diameter of 50 mm, and a pitch of 6 mm.
Coefficients of friction are 0.05 for the threads and
0.08 for the collar bearings. Collar diameters are 90
mm. The gears have an efficiency of 95 percent and a
speed ratio of 60:1. A slip clutch, on the motor shaft,
prevents overloading. The full-load motor speed is
1720 rev/min.
(a) When the motor is turned on, how fast will the
press head move? (Vm= , Vser. =
)
(5M)
(b) What should be the horsepower rating of the
motor? (TR=, Tc= Pser. =
"
Bronze
bushings
Foot
Motor
Bearings
watt, Pm= watt, Pm= h.p.) (20M)
2['s
Fig.1
Worm
Collar
bearing
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.
An 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.
Chapter 1 Solutions
Applied Statics and Strength of Materials (6th Edition)
Ch. 1 - Prob. 1.1PCh. 1 - In the right triangle ABC shown, c = 25 ft and...Ch. 1 - Determine the length of side a and the meausre of...Ch. 1 - A 28-ft-long ladder leaning against a wall makes...Ch. 1 - Two legs of a right triangle are 6 ft and 10 ft....Ch. 1 - In the roof truss shown determine the lengths of...Ch. 1 - A level scaffold s to be supported at the center...Ch. 1 - A wanderer hikes due east for 2 mi, then southeast...Ch. 1 - Freehand sketch the following triangles and solve...Ch. 1 - One side of a triangular lot is 100 ft and the...
Ch. 1 - A box containing 8 shock absorbers and 10 brake...Ch. 1 - Prob. 1.12PCh. 1 - Express 0.015 ton (a) in pounds (lb) and (b) in...Ch. 1 - Express 5 mi (a) in yards (yd) and (b) in feet...Ch. 1 - Express 60 miles per hour (mph) in units of feet...Ch. 1 - Find the number of square rods in one acre.Ch. 1 - A reservoir contains an estimated 125 billion...Ch. 1 - Convert the following: a. 27 ft 734 in. to...Ch. 1 - 1.19 A water system of 2 in (inside diameter)...Ch. 1 - The soil pressure under a concrete footing is...Ch. 1 - Using Table 1 , establish your height in...Ch. 1 - The dimensions on a baseball field are as follows:...Ch. 1 - Convert the following quantities from U.S....Ch. 1 - Convert the following quantities to SI units of...Ch. 1 - Convert the following quantities to SI units of...Ch. 1 - Convert the following quantities to the designated...Ch. 1 - 1.27 Rework Problem 1.19 using an inside pipe...Ch. 1 - A spherical tank has a radius of 27 in. Find the...Ch. 1 - 1.29 A ladder rests against a vertical wall at a...Ch. 1 - A surveyor measures a zenith angle of 70° 03’20”...Ch. 1 - The tower of a tower crane casts a shadow (on...Ch. 1 - 1.32 From the top of a 30-ft building, the angle...Ch. 1 - Two planes, starting from airport X, fly for 2 hr,...Ch. 1 - Rework Problem 1.31 assuming that the ground...Ch. 1 - An Egyptian pyramid has a square base and...Ch. 1 - Two observation towers A and B are located 300 ft...Ch. 1 - Two people fishing from rowboats on a lake are 100...Ch. 1 - What is the average speed in miles per hour (mph)...Ch. 1 - The volume flow of a river is expressed as 5000...Ch. 1 - A 55-gal drum filled with sand weighs 816 lb. The...Ch. 1 - The total area to be occupied by a building and a...Ch. 1 - An electronic distance measurement device (EDM) is...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Problem 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_forwardProblem 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_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 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_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L
International Edition---engineering Mechanics: St...
Mechanical Engineering
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:CENGAGE L
moment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY