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1. THEORY
The theory behind the formulas used here can be found in any stress analysis book,
so they will not be repeated here. For stress coordinate transformation there is
a good explanation on the address:
http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/plane_stress.cfm
The formula for the Von Mises stress also can be found in many stress analysis books
and the formula used here is the simplification for plane state of stress.
The notation used is presented on the sketches below:
2. USE
It is quite common to calculate stresses in one coordinate system and transform the
results to a different coordinate system.
This tool performs this transformation and the formulas can be copied to other spreadsheets
to fit specific needs.
As it is common the use of the Von Mises failure criteria, this calculation was also
included here, as the calculation of the principal stresses (zero shear) and the rotation
of the principal axis in relation to the original one.
All calculations here are for a plane state of tension, that is the most common case
of engineering calculations (mainly with Finite Element models of airframes)
This spreadsheet was done to avoid the search of the formulas every time
these operations have to be done.
3. EXAMPLE
http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/plane_stress.cfmhttp://www.efunda.com/formulae/solid_mechanics/mat_mechanics/plane_stress.cfm7/27/2019 Stress Transf Vmises Princ Etk20111006a
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Entering the stress values at the original coordinate system and the rotation angle
the stresses at the rotated system and the Von Mises stress are calculated:
By pressing the button for Principal Axis, a macro is executed and
the principal stresses and the rotation of the principal axis is found.
NOTES: 1. Your spreadsheet program should have calculations set
to "AUTOMATIC" and macros enabled.
2, Principal axis calculations are not performed with formulas
but with the 'Goal-Seek' function of the spreadsheet, searching
the angle that results in zero shear stress.
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1. ENTER DATA ON YELLOW CELLS HERE:
1.1 Initial stress values at coordinate system XY
sx = 201.50 ONLY THE YE
sy = 35.00
txy = 12.00 ALL OTHER V
1.2. Enter the units you want for the stresses (will be transferred to all stress values)
Unit = MPa
1.2. Enter the rotation angle to the new coordinate system (in degrees)
q = 25 degrees
2. THE TRANSFORMATION TO COORDINATE SYSTEM X'Y' IS IMME
Stresses at system XY
sx = 201.50 MPasy = 35.00 MPatxy = 12.00 MPa
Rotation angle (q) = 25.0 degrees
Stresses at system X'Y'
sx' = 180.95 MPasy' = 55.54 MPatxy' = -56.06 MPa
2. THE VON MISES STRESS OF THE STRESS VALUES YOU ENTER
Stress values
sx = 201.50 MPasy = 35.00 MPatxy = 12.00 MPa
The Von Mises stress:
svm = 187.63 MPa
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2. THE STRESSES ON PRINCIPAL AXIS AND THE ANGLE OF THE P
Stress values
sx = 201.72 MPa
sy = 34.78 MPatxy = -10.34 MPa
Rotation angle (q) = 187.6 degrees
above value fot rotation is wrong !! Need to check again
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LOW CELLS HAVE TO BE FILLED !!!
LUES ARE FILLED/CALCULATED
IATE. BELOW BLOCK THAT MAY BE COPIED TO REPORTS
D IS CALCULATED. BELOW BLOCK THAT MAY BE COPIED TO REP
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INCIPAL AXIS TO THE SYSTEM XY IS CALCULATED BY PRESSING
CALCULATION NOT DONE OR PROBLEM WITH INPUT DATA
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RTS
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THE BUTTON
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