"Geometry"
'<img style="height:237pt; width:204pt; float:right;" src="./T-stub_geometry.png" alt="T-stub_geometry.png">
'Web plate thickness'
t_w = 20mm
'Flange plate thickness'
t = 20mm
'Plate width'
b = 200mm
'Plate height'
h = 220mm
'Fillet weld throat thickness'
a = 10mm
'Bolt to edge distance'
e = 50mm
m = (h - 2*e)/2 - t_w/2 - sqrt(2)*a*0.8
n = min(1.25*m; e)
'Bolt head or nut diameter'
d_w = 38mm
e_w = d_w/4
'Bolt tensile stress area'
A_s = 353mm^2
"Material"
'Plate yield strength'
f_y = 355MPa
'Bolt ultimate strength'
f_ub = 800MPa
"Partial safety factors"
γ_M0 = 1.0
γ_M2 = 1.25
"Bolt tensile resistance"
'EN 1993-1-8 – Table 3.4'
k_2 = 0.9
F_t,Rd = k_2*f_ub*A_s/γ_M2
"Yield lines"
'<img style="height:143pt; width:120pt; float:right;" src="./circular_patterns.png" alt="circular_patterns.png">
'Circular'
l_eff,cp = min(2*π*m; π*m + 2*e)
'Non-circular'
'<img style="height:141pt; width:129pt; float:right;" src="./non-circular_patterns.png" alt="non-circular_patterns.png">
l_eff,nc = min(4*m + 1.25*e; b)
l_eff,1 = min(l_eff,cp; l_eff,nc)
l_eff,2 = l_eff,nc
"T-stub resistance"
'EN 1993-1-8 – Table 6.2'
'Plastic bending strength of plate for mode 1'
M_pl1_Rd = 0.25*l_eff,1*t^2*f_y/γ_M0
'Plastic bending strength of plate for mode 2'
M_pl2_Rd = 0.25*l_eff,2*t^2*f_y/γ_M0
'T-stub resistances'
F_T,1,Rd = (8*n - 2*e_w)*M_pl1_Rd/(2*m*n - e_w*(m + n))
F_T,2,Rd = (2*M_pl2_Rd + n*2*F_t,Rd)/(m + n)
F_T,3,Rd = 2*F_t,Rd
F_T,Rd = min(F_T,1,Rd; F_T,2,Rd; F_T,3,Rd)
Mode = if(F_T,Rd ≡ F_T,1,Rd; 1; if(F_T,Rd ≡ F_T,2,Rd; 2; 3))

 