(3)
Equation (3) gives limit moment about 11% higher than equation (2) regardless of h. One notable point is that the above solutions depend only on bend factor(h), not on r/t and R/r. Equations (1-3) are applicable only for the pure in-plane bending moment and the effect of internal pressure is not taken in to account. Also these analytical solutions consider constant wall thickness along the contour of the pipe bend cross section. However, the most of the pipe bends are made using a forming process and as a result, have wall thickness variation along the surfaces of the pipe bend cross section. The pipe wall is thinner than nominal on the convex side and is thicker on the concave one. Considering the most practical case, this study is …show more content…
Figure 9 shows the effect of ovality on the plastic limit moment for the pipe bend attached to a significantly long straight pipe, for different values of h. It shows that the effect of ovality on the limit moment could be significant for in plane bending moment case. The case of ovality induced in the manufacturing process is 4% for which the value of limit moment reduces 6.7% in the bend region as compared with the existing finite element solution without shape imperfection. The results suggest that the effect of the attachment on finite element limit solution can be significant for in-plane bending case. Careful examination suggested interesting plastic yielding patterns for inlet pigtail pipe bends with the attached straight pipes. For smaller r/t ratio, an intrados region of the pipe bends yields first and then the yielding region spreads to a part of the attached straight pipe. Accordingly piping system can hold more loads, at the higher load, the crown region of the pipe bend finally yields and the load reaches its limit value, which corresponds to the limit moment. Such a phenomenon occurs for smaller value of r/t and also for smaller value of h. When the bend factor (h) increases and the load carrying capacity of inlet pigtail pipe bend also
Equation (3) gives limit moment about 11% higher than equation (2) regardless of h. One notable point is that the above solutions depend only on bend factor(h), not on r/t and R/r. Equations (1-3) are applicable only for the pure in-plane bending moment and the effect of internal pressure is not taken in to account. Also these analytical solutions consider constant wall thickness along the contour of the pipe bend cross section. However, the most of the pipe bends are made using a forming process and as a result, have wall thickness variation along the surfaces of the pipe bend cross section. The pipe wall is thinner than nominal on the convex side and is thicker on the concave one. Considering the most practical case, this study is …show more content…
Figure 9 shows the effect of ovality on the plastic limit moment for the pipe bend attached to a significantly long straight pipe, for different values of h. It shows that the effect of ovality on the limit moment could be significant for in plane bending moment case. The case of ovality induced in the manufacturing process is 4% for which the value of limit moment reduces 6.7% in the bend region as compared with the existing finite element solution without shape imperfection. The results suggest that the effect of the attachment on finite element limit solution can be significant for in-plane bending case. Careful examination suggested interesting plastic yielding patterns for inlet pigtail pipe bends with the attached straight pipes. For smaller r/t ratio, an intrados region of the pipe bends yields first and then the yielding region spreads to a part of the attached straight pipe. Accordingly piping system can hold more loads, at the higher load, the crown region of the pipe bend finally yields and the load reaches its limit value, which corresponds to the limit moment. Such a phenomenon occurs for smaller value of r/t and also for smaller value of h. When the bend factor (h) increases and the load carrying capacity of inlet pigtail pipe bend also