I-BEAM DESIGN CALCULATOR

I-BEAM DESIGN CALCULATOR (AISC 360-22)

INPUT DATA

Member Geometry (I-Section)

L = ft   Member Length

d = in   Section Depth

b_f = in   Flange Width

t_f = in   Flange Thickness

t_w = in   Web Thickness

Material Properties (ASTM A992)

E = ksi   Elastic Modulus

F_y = ksi   Yield Strength

F_u = ksi   Ultimate Tensile Strength

Axial Loads (Tension Positive, Compression Negative)

N_D = kips   Dead Load Axial Force

N_L = kips   Live Load Axial Force

Bending Loads

w_D = klf   Dead Load (Uniformly Distributed)

w_L = klf   Live Load (Uniformly Distributed)

P_D = kips   Dead Load (Point Load at Midspan)

P_L = kips   Live Load (Point Load at Midspan)

End Restraints

K_x =   Effective Length Factor (Strong Axis)

K_y =   Effective Length Factor (Weak Axis)

LOAD COMBINATIONS (AISC 360-22)

LRFD Load Factors:

w_u = 1.2·w_D + 1.6·w_L = 2.60 klf   Factored Distributed Load

P_u = 1.2·P_D + 1.6·P_L = 44.00 kips   Factored Point Load

N_u = 1.2·N_D + 1.6·N_L = 0.00 kips   Factored Axial Force

ASD Load Factors:

w_a = w_D + w_L = 1.50 klf   Allowable Distributed Load

P_a = P_D + P_L = 30.00 kips   Allowable Point Load

N_a = N_D + N_L = 0.00 kips   Allowable Axial Force

ACTIONS

M_max = w·L²/8 + P·L/4 = 136.25 kip-ft   Maximum Design Moment

V_max = w·L/2 + P/2 = 30.50 kips   Maximum Design Shear

SECTION PROPERTIES

h_w = d − 2·t_f = 11 in

A_g = 2·b_f·t_f + h_w·t_w = 12.30 in²   Gross Area

I_x = 257.4 in⁴   Second Moment of Area (strong axis)

I_y = 21.3 in⁴   Second Moment of Area (weak axis)

S_x = 42.9 in³   Elastic Section Modulus (strong axis)

Z_x = 48.2 in³   Plastic Section Modulus (strong axis)

r_x = 4.58 in   Radius of gyration (strong axis)

r_y = 1.32 in   Radius of gyration (weak axis)

DESIGN CHECKS (AISC 360-22)

Tension Strength (Chapter D)

A_g = 12.30 in²

P_n = F_y·A_g = 615.0 kips   Nominal Tension Capacity

φ_t = 0.90   Resistance Factor (LRFD)

φ_tP_n = 553.5 kips   Design Tension Strength (LRFD)

P_n/Ω_t = 368.6 kips   Allowable Tension Strength (ASD)

Tension Check: Tension_ratio = |N|·φ_tP_n⁻¹ = 0.000

Compression Strength (Chapter E)

L_c,x = K_x·L·12 = 240 in   Effective Length (Strong Axis)

L_c,y = K_y·L·12 = 240 in   Effective Length (Weak Axis)

r_min = min(r_x, r_y) = 1.32 in   Minimum Radius of Gyration

λ = L_c/r_min = 181.8   Slenderness Parameter

F_e = π²·E/λ² = 0.87 ksi   Euler Buckling Stress

F_cr = 0.877·F_e = 0.76 ksi   Critical Buckling Stress

P_n = F_cr·A_g = 9.3 kips   Nominal Compression Capacity

φ_cP_n = 8.4 kips   Design Compression Strength (LRFD)

P_n/Ω_c = 5.6 kips   Allowable Compression Strength (ASD)

Compression Check: Compression_ratio = |N|·φ_cP_{n⁻¹ = 0.000}

Bending Strength (Chapter F)

M_n = F_y·Z_x = 200.8 kip-ft   Nominal Moment Capacity

φ_b = 0.90   Resistance Factor (LRFD)

φ_bM_n = 150.6 kip-ft   Design Moment Strength (LRFD)

Bending Check: Bending_ratio = M_max/(φ_bM_n) = 0.904

Combined Axial and Bending (Chapter H)

P_u/(φ_cP_n) = 0.000

M_u/(φ_bM_n) = 0.904

Interaction Check: Interaction_ratio = P_u/(φ_cP_n) + M_u/(φ_bM_n) = 0.904

Shear Strength (Chapter G)

A_w = d·t_w = 3.60 in²   Web Area

V_n = 0.6·F_y·A_w = 108.0 kips   Nominal Shear Strength

φ_vV_n = 97.2 kips   Design Shear Strength (LRFD)

Shear Check: Shear_ratio = V_max/(φ_vV_n) = 0.314

Deflection Check (Serviceability)

δ_max = 5·w_L·L⁴/(384·E·I_x) + P_L·L³/(48·E·I_x) = 0.89 in

δ_limit = L/360 = 0.67 in

Deflection Check: Deflection_ratio = δ_max/δ_limit = 1.33

Compact Section Check (AISC Section B4)

λ_p = 0.38·√(E/F_y) = 10.8   Limiting λ for compact flange

λ_f = (b_f/2)/t_f = 8.00   Flange slenderness

λ_pw = 3.76·√(E/F_y) = 107.1   Limiting λ for compact web

λ_w = h_w/t_w = 36.7   Web slenderness

Section Classification: Compact

RESULTS