# Tsai-Wu Criterion

The Tsai-Wu theory defines the ply failure index as below:

${F}_{index}=\left(\frac{1}{{X}_{T}}-\frac{1}{{X}_{C}}\right){\text{σ}}_{1}+\left(\frac{1}{{Y}_{T}}-\frac{1}{{Y}_{C}}\right){\text{σ}}_{2}+\frac{{\text{σ}}_{1}^{2}}{{X}_{T}{X}_{C}}+\frac{{\text{σ}}_{2}^{2}}{{Y}_{T}{Y}_{C}}+\frac{{\text{τ}}_{12}^{2}}{{S}^{2}}+2{F}_{12}{\text{σ}}_{1}{\text{σ}}_{2}$

Where:
• $Xt,Xc$ are the maximum allowable stresses in the 1-direction in tension and compression,
• $Yt,Yc$ are the maximum allowable stresses in the 2-direction in tension and compression,
• $S$ is the allowable in-plane shear stress
• ${F}_{12}$ is a factor to be determined experimentally

## Syntax

TsaiWuFT(tensor,xt,xc,yt,yc,s,f12,sets,plies,elems,parts,props,pool_name,layer_index,opt_str)

## Arguments

tensor
Stress table
xt
Allowable tensile stress in ply material direction 1
xc
Allowable compressive stress in ply material direction 1
yt
Allowable tensile stress in ply material direction 2
yc
Allowable compressive stress in ply material direction 2
f12
F12 experimental factor
s
Allowable in-plane shear stress
sets
Set table (D=NULL)
plies
Ply table (D=NULL)
elems
Element table (D)
parts
Part table (D)
props
Property table (D)
pool_name
Pool name (D=@current_pool)
layer_index
Layer index (D=@current_slice_index)
opt_str
This is an optional argument, which can passed if needed (D=option).

## Tsai-Wu Reserve Factor

Considering the above expression for the Failure Index if we set:

$\text{A}=\frac{{\text{σ}}_{1}^{2}}{{X}_{\text{T}}{\text{X}}_{\text{C}}}+\frac{{\text{σ}}_{2}^{2}}{{Y}_{\text{T}}{\text{Y}}_{\text{C}}}+\frac{{\text{τ}}_{12}^{2}}{{S}^{2}}+2{F}_{12}{\sigma }_{1}{\sigma }_{2}$

$B=\left(\frac{1}{{X}_{T}}-\frac{1}{{X}_{C}}\right){\sigma }_{1}+\left(\frac{1}{{Y}_{T}}-\frac{1}{{Y}_{C}}\right){\sigma }_{2}$

Being $k$ a given factor of safety, then the reserve factor formula can be evaluated as below:

${\text{RF}}_{Tsai-Wu}=\frac{-B±\sqrt{{B}^{2}-4AC}}{2ak}$

### Syntax

TsaiWuRF(tensor,xt,xc,yt,yc,s,f12,FoS,sets,plies,elems,parts,props,pool_name,layer_index,opt_str)

### Arguments

tensor
Stress table
xt
Allowable tensile stress in ply material direction 1
xc
Allowable compressive stress in ply material direction 1
yt
Allowable tensile stress in ply material direction 2
yc
Allowable compressive stress in ply material direction 2
f12
F12 experimental factor
FoS
Factor of Safety (D=1.0)
s
Allowable in-plane shear stress
sets
Set table (D=NULL)
plies
Ply table (D=NULL)
elems
Element table (D)
parts
Part table (D)
props
Property table (D)
pool_name
Pool name (D=@current_pool)
layer_index
Layer index (D=@current_slice_index)
opt_str
This is an optional argument, which can passed if needed (D=option).