RHS DESIGN CALCULATOR (AISC 360-22)

INPUT DATA

Member Geometry (RHS-Section)

L = ft   Member Length

b = in   Section Width (Outer)

h = in   Section Height (Outer)

t = in   Wall Thickness

Material Properties (ASTM A500 Grade C)

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 (x-axis)

K_y =   Effective Length Factor (y-axis)

K_z =   Effective Length Factor (torsional)

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

b_i = b − 2·t = 7 in   Inner Width

h_i = h − 2·t = 11 in   Inner Height

A_g = b·h − b_i·h_i = 12.25 in²   Gross Area

I_x = 269.4 in⁴   Second Moment of Area (strong axis)

I_y = 131.5 in⁴   Second Moment of Area (weak axis)

S_x = 44.9 in³   Elastic Section Modulus (x-axis)

S_y = 32.9 in³   Elastic Section Modulus (y-axis)

Z_x = 57.3 in³   Plastic Section Modulus (x-axis)

r_x = 4.69 in   Radius of gyration (x-axis)

r_y = 3.28 in   Radius of gyration (y-axis)

J = 455.1 in⁴   Torsional Constant

DESIGN CHECKS (AISC 360-22)

Tension Strength (Chapter D)

A_g = 12.25 in²

P_n = F_y·A_g = 612.5 kips   Nominal Tension Capacity

φ_t = 0.90   Resistance Factor (LRFD)

φ_tP_n = 551.3 kips   Design Tension Strength (LRFD)

P_n/Ω_t = 366.8 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 (x-axis)

L_c,y = K_y·L·12 = 240 in   Effective Length (y-axis)

L_c,z = K_z·L·12 = 240 in   Effective Length (torsional)

r_min = min(r_x, r_y) = 3.28 in   Minimum Radius of Gyration

λ = L_c/r_min = 73.2   Slenderness Parameter

F_e = π²·E/λ² = 5.35 ksi   Euler Buckling Stress

F_cr = 0.877·F_e = 4.69 ksi   Critical Buckling Stress

P_n = F_cr·A_g = 57.5 kips   Nominal Compression Capacity

φ_cP_n = 51.8 kips   Design Compression Strength (LRFD)

P_n/Ω_c = 34.4 kips   Allowable Compression Strength (ASD)

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

Bending Strength (Chapter F)

M_n,x = F_y·Z_x = 238.8 kip-ft   Nominal Moment Capacity (x-axis)

φ_b = 0.90   Resistance Factor (LRFD)

φ_bM_n,x = 179.1 kip-ft   Design Moment Strength (LRFD)

Bending Check: Bending_ratio = M_max/(φ_bM_n,x) = 0.761

Combined Axial and Bending (Chapter H)

P_u/(φ_cP_n) = 0.000

M_u/(φ_bM_n) = 0.761

Interaction Check: Interaction_ratio = P_u/(φ_cP_n) + M_u/(φ_bM_n) = 0.761

Shear Strength (Chapter G)

A_v,x = 2·(h−2·t)·t = 11.00 in²   Shear Area (x-axis)

V_n,x = 0.6·F_y·A_{v,x = 330.0 kips}   Nominal Shear Strength (x-axis)

φ_vV_n,x = 297.0 kips   Design Shear Strength (LRFD)

Shear Check: Shear_ratio = V_max/(φ_vV_n,x) = 0.103

Deflection Check (Serviceability)

δ_max = 5·w_L·L⁴/(384·E·I_x) + P_L·L³/(48·E·I_x) = 0.78 in

δ_limit = L/360 = 0.67 in

Deflection Check: Deflection_ratio = δ_max/δ_limit = 1.16

Compact Section Check (AISC Section B4)

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

λ_f = (b/t) = 16.00   Flange slenderness

λ_pw = 2.42·√(E/F_y) = 68.9   Limiting λ for compact web

λ_w = (h−2·t)/t = 22.00   Web slenderness

Section Classification: Compact

RESULTS