The stress tensor at a point in the xi system is given by 17 0 0...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The stress tensor at a point in the xi system is given by 17 0 0 -23 28 0 28 10 σij = 0 i. Find the principal stresses 01, 02 and 03 ii. Find the maximum shearing stress at the point by drawing the three associated Mohr's circles. iii. By defining an appropriate transformation tensor relating the principal axes to the axes associated with the maximum shear, verify results of (ii) analytically by using []=[A] JA] iv. Obtain the transformation tensor relating the principal axes x;* to the coordinate axes xi. v. Locate in Mohr's space the locus of (ON, Os) for normals in directed in x₁ direction, X2 direction and x3 direction. Locate in Mohr's space the locus of (ON, OS) for normal n = (e₁ - 2e2+ e3) / √6, where e; are the unit vectors in the direction of x₁. The stress tensor at a point in the xi system is given by 17 0 0 -23 28 0 28 10 σij = 0 i. Find the principal stresses 01, 02 and 03 ii. Find the maximum shearing stress at the point by drawing the three associated Mohr's circles. iii. By defining an appropriate transformation tensor relating the principal axes to the axes associated with the maximum shear, verify results of (ii) analytically by using []=[A] JA] iv. Obtain the transformation tensor relating the principal axes x;* to the coordinate axes xi. v. Locate in Mohr's space the locus of (ON, Os) for normals in directed in x₁ direction, X2 direction and x3 direction. Locate in Mohr's space the locus of (ON, OS) for normal n = (e₁ - 2e2+ e3) / √6, where e; are the unit vectors in the direction of x₁.
Expert Answer:
Answer rating: 100% (QA)
SOLUTION i The principal stresses are the eigenvalues of the stress tensor and they represent the maximum and minimum stresses in the material To find the principal stresses we need to diagonalize the ... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these finance questions
-
A company that manufactures baseball gloves is contemplating whether to increase its advertising budget by $3 million for next year. If the expanded advertising campaign is successful, the company...
-
A two-dimensional state of stress at a point in a loaded material in the direction defmed by the x-y coordinate system is defined by three components of stress xx yy, and xy. The stresses at the...
-
Bank A has increased its leverage from 2016 to 2017 as shown below. Assume the bank invests in plain loans which yield an annual interest of 5% in both years. The annual interest paid on liabilities...
-
1. Should organizations work to create jobs that are satisfying to individual employees? 2. Are there any potential drawbacks to the job crafting approach? If so, how can they be minimized?
-
Sales revenue totals (in dollars) by day of the week are contained in the data file Stordata. repare a cross table that contains the days of the week as rows and the four sales quartile intervals as...
-
A train is comprised of an engine car of inertia \(M\), and 3 more cars of inertias \(m_{1}, m_{2}\), and \(m_{3}\), respectively. The acceleration of the train is \(a\). Friction can be ignored. (a)...
-
Value-added, nonvalue-added costs. The Marino Repair Shop repairs and services machine tools. A summary of its costs (by activity) for 2011 is as follows: a. Materials and labor for servicing machine...
-
When an object is placed at the focus of a concave mirror, the image formed is (i) at infinity (ii) real and inverted, and (iii) highly magnified (or highly enlarged) M E A D C B P F At infinity N
-
What four environmental conditions that increase user demand for relevant and reliable information?
-
Cullumber Corporation's December 31, 2025, trial balance includes the following accounts: Investment in Starling Common Stock, $62.000; Retained Earnings, $137,000; Treasury Stock, $5,000;...
-
Discuss your experience of learning about your classmates and how it impacted your understanding of people from other backgrounds. In your second post, reflect on what you learned in this course and...
-
Dan Kirner, a South Dakota farmer has signed a contract in January 2019 to sell an equivalent of US$200,000 worth of beef to Isetan in Japan. The beef will be delivered in March 2019, however, Isetan...
-
Find M to three decimal places for the definite integral, using the indicated value of n. 3 1 Sdx, X 1 -dx, n = 8
-
Your organization needs some specialized equipment for the next project. The project is anticipated to last one year. Salvage rate on the equipment is 25 cents on the dollar. When the project is...
-
8. Twenty years ago, a US dollar bought 1.69 Australian dollar; this year, a US dollar buys 1.39 Australian dollar. Given that total inflation over this period was 25 percent in the U.S. and 15...
-
FIFO and LIFO Costs Under Perpetual Inventory System The following units of an item were available for sale during the year: Beginning inventory 22 units at $46 Sale 11 units at $69 First purchase 28...
-
Flicker, Inc., a closely held corporation, acquired a passive activity this year. Gross income from operations of the activity was $160,000. Operating expenses, not including depreciation, were...
-
During 2012, Palo Fiero purchases the following property for use in his manufacturing business: Palo uses the accelerated depreciation method under MACRS, if available, and does not make the election...
-
Carl and Jenny adopt a Russian orphan. The adoption takes 2 years and two trips to Russia and is final in 2012. They pay $6,000 in 2011 and $7,500 in 2012 of qualified adoption expenses, and have AGI...
-
Clarita is a single taxpayer with two dependent children, ages 10 and 12. Clarita pays $3,000 in qualified child care expenses during the year. If her adjusted gross income (all from wages) for the...
-
Let us consider a call option with maturity \(T=1\) year and strike price \(\$ 11\). The current price of the stock share is \(\$ 10\), and the riskfree interest rate is \(10 \%\). The two possible...
-
Let us consider the PDE with terminal condition In order to apply the representation theorem, we observe that \(r=0\), \((x t)=\), and , so that the underlying stochastic process boils down to a...
-
Let us consider the same setting as Example 13.4: \(S_{0}=K=50\), \(r=01, \quad=04\), and time-to-maturity is \(T=5/12\) (here we take \(t=0)\). The calculation is as follows: This exact result may...
Study smarter with the SolutionInn App