1. Optimization Study of Beam with Sudden Profile Change Jan HlaváčekJune, 2002

2. Assessment span L = 4 m steel S235 f y = 235 MPa uniformly distributed load- deadg = 10 kN/m (extreme values) - liveq = 8 kN/m [mm]

3. Response ‘S’ - Variables g = 10 kN/m ∙ g var dead, extreme [kN/m] q = 8 kN/m ∙ q var live, extreme [kN/m] 8.18 10.00 0.00 8.00

4. Response ‘S’ – Bending Moment M x = ½ ∙ (g+q) ∙ (L∙x - x 2 ) g+q

5. Resistance ‘R’ - Profiles Profile 1Profile 2 beam centernear support [mm]

6. Resistance ‘R’ - Variables f y = f y,var yield stress [MPa] W = W nom ∙W var section modulus [m 3 ] 200 395 95% 105%

7. Resistance ‘R’ M R1 = f y ∙ W 1 M R2 = f y ∙ W 2 g+q M R1

8. Profile 1 Assessment (beam center) Failure Probability P f = 0.000053 < P f,lim = 0.000070... profile 1 satisfies MRMR MSMS MRMR MSMS SF = R - S

9. Profile 2 Assessment - Optimization x[m]prob. Pf[0] 0,900,0000000 0,950,0000000 1,000,0000270 1,050,0001297 1,100,0004193 1,200,0018979 1,400,0104442 1,600,0280406 P f,lim = 0.0000700

10. Profile 2 Assessment (x = 1 m) Failure Probability P f = 0.000027 < P f,lim = 0.000070... profile 2 (x=1) satisfies MRMR MSMS MRMR MSMS SF = R - S

11. Résumé MR1MR1 MR2MR2 M S (x)

12. Additional Study G 1 +Q 1 G 2 +Q 2 g+q MRMR M R1 MSMS MSMS M R2

13. Optimization Study of Beam with Sudden Profile Change Jan HlaváčekJune, 2002