CALCS PROC024
FAILURE CRITERIA

NOTATION

fxstress-axial,parallel to x axis
fyy
fsstress-shear, in xy plane
f1stress-principal, parallel to axis one
f2two
fsmaxstress-shear, pseudo max

APPLICATION

Stress Analysis

OUTPUT

Failure Stresses

SEE ALSO

other porcs & progs

THEORY

Strength of Materials Theory

GUIDANCE

The graphical representation of the 2D stress system is shown in the figure.
Failure is predicted when the point determined by the principal stresses lies on or outside the corresponding failure boundary:
1.Max Principal Stress is represented by the square boundary ABCD
2.Max Shear Stress is AEFCGHA
3.Strain Energy Theory is ihe ellipse thru the points E F G & H
4.Shear Strain Energy Theory is the ellipse similar to (3)
5.Principal Strain is JKLMJ

INPUT FORMAT

LET Nm=:Nk=:fx=:fy=:fs=:PROC024

EXAMPLE

Call Statement

LET Nm=1:Nk=1:fx=2.1:fy=1.5:fs=.7:PROC024

Output

PROC024 FAILURE CRITERIA, Rev 220399
PRINCIPAL STRESSES,
f1= (fx+fy)/2+SQR((fx-fy)^2/4+fs^2)= 2.562
f2= (fx+fy)/2-SQR((fx-fy)^2/4+fs^2)= 1.038
fsmax= SQR(((fx-fy)/2)^2+fs^2)= 0.7616
UF= fsmax/(Ks(Nk)*Fy(Nm))= 0.5599
RANKINE,
fR= f1= 2.562
TRESCA,
fT= ((f1-f2)/2)= 0.7616
VON MISES,
fVM= (f1^2+f2^2-f1*f2)= 4.98
COULOMB-MOHR,
fCM= (f1+f2)= 3.6
EQUIVALENT,
fE= SQR(fx^2+fy^2+ABS(fx*fy)+3*fs^2)= 3.359
UF= FNmax(fR,fT,fVM,fCM,fE)/(Kd(Nk)*Fy(Nm))= 2.1242.124
END024