First let us consider say Octahedron of unit edge length
The vertices of the regular octahedron with its centre at origin will be as below. let us enter these in excel worksheet as Dynamic tables
click on the any cell in the table created and go to design tab and enter the table name -in this case as Octahedroncoordinates
Below this Create another Dynamic table with same table headings and enter the formulae as shown in the below images in all three column cells
Enter the vertice names in such order that it all the edges are connected. the x y and z co ordinate values appear automatically.
Select the x and y co ordinate columns in the table and insert a scattered chart
Only the x-y co ordinates are plotted & z dimension is not visible when seen from x-y plane unless the object is rotated about y axis and x axis.
To rotate about the axes we need to make use of transformation matrices
To obtain one resultant of all the three matrices first multitpy(matrix mautiplication)
[Z] * [X]; then multiply the product with the [Y] matrix
ie., [[Z] * [X]] * [Y] = R =Resultant Matrix
Create the final dynamic table with SUMPRODUCT formula as below:
Now drag the Table so that table size becomes equal to previous table’s size.
To rotate the solid we need to change the angle on which the transformation matrix is dependant, let us make it say 30 degree about z axis, 30 Deg about X axis and 5 Degree about Y axis
The graph changes to
you can change the angles as you like depending on the view you want to see.
Similarly rest of the Platonic solids can be represented
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Please click here to the download the excel file.
Let us consider this example below:
For the initial stress element shown, draw the mohr’s circle and also determine the principle stresses and the maximum shear stress
First enter the stress details in the excel sheet considering the sign conventions.
Plot the points (σ along x-axis & τ along y-axis). The two end points of the Diametre are:
Distance of this point from the origin will be average of the normal stresses.
These three points are to be tabulated in the same excel sheet as below:
Select this table and insert the scattered graph (Insert →Scatter→Scatter with Straight lines and Markers)
Radius will be the hypotenuse of the triangle as in the figure below:
Calculate Radius of the Mohr circle in any cell with the formula
We need Calculate Cartesian co ordinates of the points of the Circle whose Radius is ‘R’ & with ( (σx+σy)/2, 0) as origin( for 0 – 360 degree)
First create a table
(σ , τ) = ((σx+σy)/2 + Radius x Cos(angle in radians) , Radius x Sin(angle in radians))
Then complete the table till 360 degrees
Select the Chart (in which already the Diametre is plotted )→Right click →select data →add series →select all the Cartesian co-ordinates of the circle from the table
Create a Table just below the σ –τ table
SERIES NAME |
X axis |
Y axis |
Max Normal stess |
σ_{avg }+ R |
0 |
Min Normal stess |
σ_{avg }– R |
0 |
Max clockwise Shear Stress | +INDEX(all σ values, MATCH(Cell containing +R, all τ values,0)) |
+R |
Max anti-clockwise Shear Stress | +INDEX(all σ values, MATCH(Cell containing -R, all τ values,0)) |
-R |
Add series and give the series name, x values & y values
Format these max/ min stresses points by right clicking on the points and formatting marker properties
Now the Mohr’s circle is complete.Do a little bit of formatting the Mohr Circle looks like this:
you can download this by clicking on the link below:
Excel_MohrCircle_sadakchapobserver
(Note: every time when the stress values are changed , the formed circle may not be a perfect circle so the chart needs to be re-sized each time when the values are changed)
did you find this post useful? please don’t forget to leave your comments and suggestions. thank you
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