矩形 b=50, h=100 mm → W = 83333.33 mm³ I = b·h³/12 = 4166666.67 mm⁴。c = 50 mm。W = I/c = 83333.33 mm³。A = 5000 mm²,r = 28.87 mm。{"result":"Rectangle b=50 mm, h=100 mm. I = b·h³/12 = 4166666.6667 mm⁴, c = h/2 = 50 mm, W = I/c = 83333.3333 mm³. Area A = 5000 mm², radius of gyration r = 28.8675 mm.","metadata":{"input":{"shape":"rectangle","b":50,"h":100},"result":{"shape":"rectangle","area":5000,"inertia":4166666.6667,"sectionModulus":83333.3333,"distance_c":50,"radiusOfGyration":28.8675,"units":{"dims":"mm","area":"mm²","inertia":"mm⁴","sectionModulus":"mm³","radiusOfGyration":"mm"}}}}
空心管 Do=100, Di=80 mm → W = 57962.38 mm³ I = π(Do⁴−Di⁴)/64 ≈ 2898119.22 mm⁴。c = 50 mm。W = 57962.38 mm³。A ≈ 2827.43 mm²,r ≈ 32.02 mm。{"result":"Hollow circle Do=100 mm, Di=80 mm. I = π(Do⁴−Di⁴)/64 = 2898119.2229 mm⁴, c = Do/2 = 50 mm, W = I/c = 57962.3845 mm³. Area A = 2827.4334 mm², radius of gyration r = 32.0156 mm.","metadata":{"input":{"shape":"hollow","Do":100,"Di":80},"result":{"shape":"hollow","area":2827.4334,"inertia":2898119.2229,"sectionModulus":57962.3845,"distance_c":50,"radiusOfGyration":32.0156,"units":{"dims":"mm","area":"mm²","inertia":"mm⁴","sectionModulus":"mm³","radiusOfGyration":"mm"}}}}