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

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]

Response ‘S’ - Variables g = 10 kN/m ∙ g var dead, extreme [kN/m] q = 8 kN/m ∙ q var live, extreme [kN/m]

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

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

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

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

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

Profile 2 Assessment - Optimization x[m]prob. Pf[0] 0,900, ,950, ,000, ,050, ,100, ,200, ,400, ,600, P f,lim =

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

Résumé MR1MR1 MR2MR2 M S (x)

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

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