Strain Rosette

Strain Rosette for Strain Measurement

A wire strain gage can effectively measure strain in only one direction. To determine the three independent components of plane strain, three linearly independent strain measures are needed, i.e., three strain gages positioned in a rosette-like layout. Consider a strain rosette attached on the surface with an angle afrom the x-axis. The rosette itself contains three strain gages with the internal angles b and g, as illustrated on the right. Suppose that the strain measured from these three strain gages are ea, eb, and ec, respectively. The following coordinate transformation equation is used to convert the longitudinal strain from each strain gage into strain expressed in the x-y coordinates, Applying this equation to each of the three strain gages results in the following system of equations, These equations are then used to solve for the three unknowns, ex, ey, and exy. Note: 1. The above formulas use the strain measure exy as opposed to the engineering shear strain gxy,. To use gxy, the above equations should be adjusted accordingly.   2. The free surface on which the strain rosette is attached is actually in a state of plane stress, while the formulas used above are for plane strain. However, the normal direction of the free surface is indeed a principal axis for strain. Therefore, the strain transform in the free surface plane can be applied.

Special Cases of Strain Rosette Layouts

Case 1: 45º strain rosette aligned with the x-y axes, i.e., a = 0º, b = g = 45º. Case 2: 60º strain rosette, the middle of which is aligned with the y-axis, i.e., a = 30º, b = g = 60º.

Regarding Assignment 2

As most of the regular students had submitted the assignment 2

Rotating Ring ( fig, derivation, applications)
Rotating Disc  ( fig, derivation, applications)

The back loggers who are registered in the course ME 213, may also send their assignments soft copy having above topics on azeem.zhcet@gmail.com  upto 19 Nov 2014.

Make up Test: BE

The Make up test of EME-213 is sheduled on 13 Nov 2014, THURSDAY (12:00 -1:00 PM) in the drawing hall

Syllabus for Make up: Topics Covered in the Class uptill 8 Nov 2014 in both the classes (of Mr. Khwaja Zaheer uddin & M Azeem )

Make up Test: BTech

The Make up test of ME-213 is sheduled on 13 Nov 2014, THURSDAY (12:00 -1:00 PM) in the drawing hall

Syllabus for Make up Topics Covered in the Class uptill 8 Nov 2014 in both the classes (of Mr. Najeeb ur Rahman & M Azeem )

Stress Transformation: Lecture (important Figures)

https://drive.google.com/file/d/0B0hvU4t2vA-CU1NrMkpxdmJSQUE/view?usp=sharing

Regarding Make up Test of ME-213

Those Students who need to appear in the Make-Up Test for ME-213, may kindly discuss the schedule with me till Saturday (8/11/14) so that It may not have any clash with other Make Up Test Schedule. Otherwise it will be notified at any day in the upcoming week.

Please inform the back log students who are in the III, IV, V year of graduation and appearing in this Course.

Stress Transformation: Plane Stress

Plane State of Stress

A class of common engineering problems involving stresses in a thin plate or on the free surface of a structural element, such as the surfaces of thin-walled pressure vessels under external or internal pressure, the free surfaces of shafts in torsion and beams under transverse load, have one principal stress that is much smaller than the other two. By assuming that this small principal stress is zero, the three-dimensional stress state can be reduced to two dimensions. Since the remaining two principal stresses lie in a plane, these simplified 2D problems are called plane stressproblems. Assume that the negligible principal stress is oriented in the z-direction. To reduce the 3D stress matrix to the 2D plane stress matrix, remove all components with z subscripts to get, where txy = tyx for static equilibrium. The sign convention for positive stress components in plane stress is illustrated in the above figure on the 2D element.

Coordinate Transformations

The coordinate directions chosen to analyze a structure are usually based on the shape of the structure. As a result, the direct and shear stress components are associated with these directions. For example, to analyze a bar one almost always directs one of the coordinate directions along the bar's axis. Nonetheless, stresses in directions that do not line up with the original coordinate set are also important. For example, the failure plane of a brittle shaft under torsion is often at a 45° angle with respect to the shaft's axis. Stress transformation formulas are required to analyze these stresses. The transformation of stresses with respect to the {x,y,z} coordinates to the stresses with respect to {x',y',z'} is performed via the equations, where q is the rotation angle between the two coordinate sets (positive in the counterclockwise direction). This angle along with the stresses for the {x',y',z'} coordinates are shown in the figure below,