STAINLESS STEEL I BEAM-COLUMN DESIGN (SCI P291)

INPUT DATA

Member Geometry

L = m   Member Length

d = mm   Section Depth

b = mm   Flange Width

t_f = mm   Flange Thickness

t_w = mm   Web Thickness

Material Properties (Austenitic Grade 1.4301)

E = MPa   Elastic Modulus

f_y = MPa   0.2% Proof Stress

f_u = MPa   Ultimate Tensile Strength

γ_m0 =   Partial safety factor (cross-section)

γ_m1 =   Partial safety factor (buckling)

n =   Strain hardening exponent

Loading

G_k = kN/m   Dead Load (UDL)

Q_k = kN/m   Live Load (UDL)

N_ed = kN   Axial Force (Ten. +ve, Comp. -ve)

End Restraints

K_x =   Effective Length Factor (Major Axis)

K_y =   Effective Length Factor (Minor Axis)

LOAD COMBINATIONS

w_fact = 1.4·G_k + 1.6·Q_k = 10.26 kN/m   Factored Load

w_service = Q_k = 6.00 kN/m   Unfactored Live Load (for deflection)

ACTIONS

M_ed = w_fact·L²/8 = 11.54 kNm   Design Bending Moment

V_ed = w_fact·L/2 = 15.39 kN   Design Shear Force

SECTION PROPERTIES

h_w = d − 2·t_f = 180 mm

A = 2·b·t_f + h_w·t_w = 2900 mm²   Gross Area

I_x = 20496667 mm⁴   Second Moment of Area (major axis)

I_y = 1668542 mm⁴   Second Moment of Area (minor axis)

W_el,x = 204967 mm³   Elastic Section Modulus (major)

W_el,y = 33371 mm³   Elastic Section Modulus (minor)

W_pl,x = 230500 mm³   Plastic Section Modulus (major)

W_pl,y = 26125 mm³   Plastic Section Modulus (minor)

r_x = 84.07 mm   Radius of gyration (major)

r_y = 23.99 mm   Radius of gyration (minor)

DESIGN CHECKS

Cross-section Classification

ε = √(275/f_y) = 1.14

λ_f = (b/2)/t_f = 5.00   Flange slenderness

λ_w = h_w/t_w = 36.00   Web slenderness

Section Class: Compact

Compression Resistance Check (including Buckling)

N_pl = A·f_y = 609 kN   Squash Load

L_e,x = K_x·L = 3.00 m

L_e,y = K_y·L = 1.00 m

N_cr,x = π²·E·I_x/L_e,x² = 4495 kN

N_cr,y = π²·E·I_y/L_e,y² = 3294 kN

N_cr = min(N_cr,x, N_cr,y) = 3294 kN

λ̄ = √(N_pl/N_cr) = 0.43   Non-dimensional slenderness

α = 0.49   Imperfection factor (curve c)

φ = 0.5·(1 + α·(λ̄ − 0.2) + λ̄²) = 0.649

χ = 1/(φ + √(φ² − λ̄²)) = 0.881   Reduction factor

N_b,Rd = χ·A·f_y/γ_m1 = 487.94 kN   Member Buckling Resistance

Compression Check: Compression_Check = |N_ed|/N_b,Rd = 0.021

Bending Resistance

M_c,x = W_pl,x·f_y = 48.41 kNm

M_resistance,x = M_c,x/γ_m0 = 44.00 kNm

Bending Check: Bending_ratio = M_ed/M_resistance,x = 0.807

Combined Bending and Axial Force (Interaction Check)

axial_ratio = |N_ed|/N_b,Rd = 0.021

bending_ratio = M_ed/M_resistance,x = 0.807

Interaction Value (simplified): interaction_value = axial_ratio + bending_ratio = 0.827

Shear Resistance Check

A_v = d·t_w = 1000 mm²

p_v = f_y/(√3·γ_m0) = 110.22 MPa

P_v = A_v·p_v = 110.22 kN

Shear Check: Shear_Check = V_ed/P_v = 0.285

Deflection Check (SLS)

δ_max = 5·w_service·L⁴/(384·E·I_x) = 1.54 mm

δ_limit = L/360 = 8.33 mm

Deflection Check: Deflection_Check = δ_max/δ_limit = 0.185

RESULTS