Page 318 - Marine Structural Design
P. 318
294 Part I1 Ultimate Strength
where m, is a bending moment and the subscript "p" indicates the filly plastic value for the
corresponding force component. The time history of the displacement at the impact point is
shown in Figure 14.2 (d). The results obtained, by using only one element, are depicted by the
solid line. It is easily observed that even one element is sufficient to obtain reasonably
accurate results.
EXAMPLE 14.2: Rectangular Portal Frame Subjected to Impact Loads
The rectangular portal frame shown in Figure 14.3(a) is subjected to concentrated pulse loads
as shown in Figure 14.3(b).
In a MARC FEM analysis, the frame is modeled using 32 elements (element type 16) as
shown in Figure 14.3(c). The element is a curved, two-dimensional, rectangular, cross-section
beam-column element. Integration points for the evaluation of element stiffhess are the same
as in EXAMPLE 14.1. Only normal stresses due to axial forces and bending moments are
considered in the plastic analysis.
The plastic yield condition used in the present analysis is taken as:
(M,/M, Y + F,/F, - 1 = 0 (14.22)
where f' is an axial force.
The time history of displacements located at the impact points along the load direction is
plotted in Figure 14.3(d). Again, it is observed that the present method is quite accurate when
using only one element for each structural member.
