For the hollow elliptical section in Example 9.5, explicitly show that the given stress function (9.6.1) will
Question:
For the hollow elliptical section in Example 9.5, explicitly show that the given stress function (9.6.1) will yield the constant value specified by (9.6.2) on the inner boundary. Next using the methods from Example 9.1, show that the general torque relation (9.3.31) will also produce the result (9.6.3). Finally verify the maximum shear stress relation (9.6.4).
Data from example 9.5
Equation 9.6.1
Equation 9.6.2
Equation 9.3.31
Equation 9.6.3
Equation 9.6.4
Transcribed Image Text:
Consider the torsion of a bar with a hollow elliptical section as shown in Fig. 9.15. The inner boundary is simply a scaled ellipse similar to that of the outer boundary. Using the solid section solution from Example 9.1, it can be shown that the contour lines, or lines of constant shear stress, coincide with such a scaled concentric ellipse (see Exercise 9.10). The shear stress will then be tangent to the inner boundary contour and no stress will then act on the lateral surface of a cylinder with inner ellipse section. Therefore, the solution to the hollow section can be found by simply removing the inner core from the solid solution developed in Example 9. 1, and this results in the same stress distribution in the remaining material. Thus, the stress function solution for the hollow case is given by (-) ab a a + b (9.6.1)
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 75% (4 reviews)
General stress function for elliptical problem K 21 1 Kabu...View the full answer
Answered By
Somshukla Chakraborty
I have a teaching experience of more than 4 years by now in diverse subjects like History,Geography,Political Science,Sociology,Business Enterprise,Economics,Environmental Management etc.I teach students from classes 9-12 and undergraduate students.I boards I handle are IB,IGCSE, state boards,ICSE, CBSE.I am passionate about teaching.Full satisfaction of the students is my main goal.
I have completed my graduation and master's in history from Jadavpur University Kolkata,India in 2012 and I have completed my B.Ed from the same University in 2013. I have taught in a reputed school of Kolkata (subjects-History,Geography,Civics,Political Science) from 2014-2016.I worked as a guest lecturer of history in a college of Kolkata for 2 years teaching students of 1st ,2nd and 3rd year. I taught Ancient and Modern Indian history there.I have taught in another school in Mohali,Punjab teaching students from classes 9-12.Presently I am working as an online tutor with concept tutors,Bangalore,India(Carve Niche Pvt.Ltd.) for the last 1year and also have been appointed as an online history tutor by Course Hero(California,U.S) and Vidyalai.com(Chennai,India).
4.00+
2+ Reviews
10+ Question Solved
Related Book For
Elasticity Theory Applications And Numerics
ISBN: 9780128159873
4th Edition
Authors: Martin H. Sadd Ph.D.
Question Posted:
Students also viewed these Engineering questions
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
-
The Chicago Omni Hotel is a 750-room luxury hotel offering guests the finest facilities in downtown Chicago. The hotel is organized into four departments: lodging, dining, catering, and retail...
-
In Figure a 3.2 kg box of running shoes slides on a horizontal frictionless table and collides with a 2.0 kg box of ballet slippers initially at rest on the edge of the table, at height h = 0.40 m....
-
Assume that the company can eliminate an office for every 200 virtual workdays (regardless of who is not there).Add another conclusion, Savings in real estate costs per year, and enter the formula...
-
13. Why do controls need to be timely and economical? Employee Mon. Tues. Wed. Thurs. Fri. Total Variance Brown 10 28 39 42 16 135 115 Lee 48 51 58 43 49 249 1 Mendoza 65 72 56 83 61 337 87 Smith 53...
-
Change in Estimate Assume that Bloomer Company purchased a new machine on January 1, 2010, for $80,000. The machine has an estimated useful life of nine years and a residual value of $8,000. Bloomer...
-
Fellar Corp. has identified the following information: $36,080 19,000 Activity cost pools Materials handling Machine maintenance Cost drivers Number of material moves Number of machine hours 880...
-
The illustrated uniform composite circular rod is composed of a solid inner core with shear modulus 1 and a different outer core material of modulus 2 . The two materials are assumed to be...
-
For the keyway section of Exercise 9.23, show that resultant stresses on the shaft and keyway boundaries are given by: Determine the maximum values of these stresses, and show that for b the maximum...
-
Parallel current-carrying wires exert magnetic forces on each other. What about perpendicular wires? Imagine two such wires oriented perpendicular to each other and almost touching. Does a magnetic...
-
(a)The local police station found that the speed of vehicles travelling around the suburb in the 60 km/hour zone varies uniformly between 55 km/hour and 62 km/hour. What is the probability that the...
-
Consider the following fixed-point iteration: xn+1 = g(xn), where [f(x)] 2 g(x) = x (x + f(x)) f(x)* (a) What is the order of convergence for the method? (e.g. what is p?). Hint: Show that the method...
-
Problem 1. In a study of infant birth weight and maternal factors, the newborn babies were categorized as being either small size for gestational age (N=201) or normal size (N=2089). The following...
-
Max 1 page allowed] Consider a DRAM chip of capacity 256 KB and each memory location contains 8 bits. The memory chip is organized in matrix form with equal number of rows and column for each memory...
-
find the dimensions of a notman window of perimeter 3 9 ft that will admit the greatest possible amount of light. Round answer to two decimal places
-
A function with a positive, increasing derivative. Draw graph of functions with the above properties.
-
AB CORPORATION ISSUED THE FOLLOWING 850 COMMON STOCKS PAR VALUE P100 750 PARTICIPATING PREFERRED STOCKS PAR VALUE P100 AT 3% AB CORPORATION DECLARED P100,000.00 DIVIDEND IN 2022.
-
The disk in a computer hard drive spins at 7200 rpm (Figure P8.3). At the radius of 30 mm, a stream of data is magnetically written on the disk, and the spacing between data bits is 25 m. Determine...
-
The lengths of the two links in the industrial robot are AB = 22 in. and BC = 18 in. (Figure P8.4). The angle between the two links is held constant at 40 as the robots arm rotates about base A at...
-
For the industrial robot in Problem P8.4, assume that the robot arm stops rotating about base A. However, the link BC begins to rotate about joint B. If link BC rotates 90 in 0.2 s, calculate the...
-
Long-term liabilities are shown in two places in the business firm's balance sheet depending upon when the long-term liabilities are scheduled for payment. True False
-
Julio is single with 1 withholding allowance. He earned $1,025.00 during the most recent semimonthly pay period. He needs to decide between contributing 3% and $30 to his 401(k) plan. If he chooses...
-
Acquirer firm plans to launch a takeover of Target firm. The manager of Acquirer indicates that the deal will increase the free cash flow of the combined business by $13.6m per year forever. The beta...
Study smarter with the SolutionInn App