矩形 b=50, h=100 mm, M=5×10⁶ N·mm → σ_max = 60 MPa I = b·h³/12 = 4.1667×10⁶ mm⁴。c = 50 mm。Z = 83333.33 mm³。σ_max = M/Z = 60 MPa。{"result":"Rectangle b=50 mm, h=100 mm, M=5000000 N·mm. I = b·h³/12 = 4166666.6667 mm⁴, c = h/2 = 50 mm, Z = I/c = 83333.3333 mm³. σ_max = M/Z = 60 MPa.","metadata":{"input":{"shape":"rectangle","M":5000000,"b":50,"h":100},"result":{"shape":"rectangle","stress":60,"stressUnit":"MPa","inertia":4166666.6667,"sectionModulus":83333.3333,"c":50}}}
实心圆 D=100 mm, M=5×10⁶ N·mm → σ_max ≈ 50.93 MPa I = π·D⁴/64 ≈ 4.9087×10⁶ mm⁴。c = 50 mm。Z ≈ 98174.77 mm³。σ_max ≈ 50.93 MPa。{"result":"Solid circle D=100 mm, M=5000000 N·mm. I = π·D⁴/64 = 4908738.5212 mm⁴, c = D/2 = 50 mm, Z = π·D³/32 = 98174.7704 mm³. σ_max = M/Z = 50.9296 MPa.","metadata":{"input":{"shape":"circle","M":5000000,"D":100},"result":{"shape":"circle","stress":50.9296,"stressUnit":"MPa","inertia":4908738.5212,"sectionModulus":98174.7704,"c":50}}}