- A Short Column With Rectangular Cross Section Of Dimensions B And H Is Subjected To Normal Force F And Biaxial Bending 1 (155.21 KiB) Viewed 32 times
A short column with rectangular cross-section of dimensions b and h, is subjected to normal force F and biaxial bending moments M₁ and M₂. According to the elasticplastic constitutive law, the limit state function takes the following form Mean G(x) = 1- The RBDO is applied to minimize the cross-section area of the column under the target reliability pr = 3. The design variables are the means cross-section breadth and depth: band Uh. The initial design point is: dº = {0.5, 0.5). The random variables are the yield stress fy, the applied bending moments M₁ and M2, the applied normal force F, the breadth b and the depth h of the cross-section. Different coefficients of variation of h and b are applied: 0.05 and 0.1. Additionally, all the random variables are normally distributed. Table 1 lists the distributional type and parameters. F(kN) M₁(kN.m) M2(kN.m) (Mpa) h 125 COV 2500 0.2 4M₁ 4M₂ F2 bh² fy b²hfy (bhfy)² 250 0.3 Distributions Normal Normal s.t. : 0.3 min A = bfh fb.ph { 40 μh A physical constraint (side constraint) is considered for the cross-section aspect. The RBDO problem is written as: Objective function h*b* Reliability index B b Normal Normal Normal Normal Pr [G(X) ≤0] ≤ PT 0.5 ≤ Mb/ph≤2 μb 0.1 0.05/ 0.1 0.05/0.1 Presenting your results with the following table and attaching your soure codes. Cov 0.05 Cov -0.10