1 Analysis of Stress and Strain Review - Torsional shaft - Axially loaded Bar Questions (1) Is there any general method to determine stresses on any arbitrary plane at one point if the stresses at this point along some planes are known (2) For a general loaded member how many planes on which stresses are known are required to determine the stresses at any plane at one point 2 Analysis of Stress and Strain State of stress at one point Stress element
Use a cube to represent stress element. It is infinitesimal in size.
(xyz) axes are parallel to the edges of the element
faces of the element are designated by the directions of their
Normal stresses tension - compression.
Shear stresses the directions associated with its subscripts are
plus-plus or minus-minus
- the directions associated with its subscripts are
plus-minus or minus-plus
3 Plane Stress Definition Only x and y faces are subjected to stresses and all stresses are parallel to the x and y axes. Stresses on inclined planes 4 Transformation Equations angle between x1 and x axes measured counterclockwise 5 Plane Stress Special Cases Uniaxial Stress Pure Shear Biaxial Stress 6 Plane Stress Example 1 A plane-stress condition exists at a point on the surface of a loaded structure where the stresses have the magnitudes and directions shown on the stress element of the following figure. Determine the stresses acting on an element that is oriented at a clockwise angle of 15o with respect to the original element. 7 Principal Stresses Principal stresses maximum and minimum normal stresses. Principal planes the planes on which the principal stresses act 8 Principal Stresses Shear stress on the principal planes 9 Principal Stresses Example 2 Find principal stresses of an element which is in pure shear. 10 Maximum Shear Stresses 11 Plane Stress Example 3 Find the principal stresses and maximum shear stresses and show them on a sketch of a properly oriented element. 12 Mohrs Circile For Plane Stress Equations of Mohrs Circle Transformation equations 13 Two Forms of Mohrs Circle 14 Construction of Mohrs Circle 15 Applications of Mohrs Circle
Stresses on inclined element
Principal stresses and maximum shear stresses
16 Applications of Mohrs Circle Example An element in plane stress at the surface of a large machine is subjected to stresses Using Mohrs circle determine the following quantities (a) the stresses acting on an element inclined at an angle of 40o (b) the principal stresses and (c) the maximum shear stress. 17 Plane Strain Definition Only x and y faces are subjected to strains and all strains are parallel to the x and y axes. Note Plane stress and plane strain do not occur simultaneously. 18 Plane Strain Transformation Equations Principal Strains 19 Measurement of Strain Electrical Resistance Strain Gages Principle length changes electrical resistance change Measurement of Principal Strains need three gages! Why How 20 Hookes Law For Plane Stress Assumptions - - 21 Hookes Law For Plane Stress Example A 450 strain rosette consists of three strain gages arranged to measure strain in two perpendicular directions and also at a 450 angle between them as shown in the Following figure. The rosette is bounded to the surface before it is loaded. It is measured that the strains in three gages (ABC) are 0.0003 0.0001 and 0.00011 respectively. Find principal stresses at this point. 22 Strain Energy Density Strain Energy
PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.
You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!
For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!