Frame Model Geometry

3 DRIP SHIELD FRAME MODEL

A drip shield frame model was developed in the program SAP2000 (Computers and Structures, Inc., 2004) to perform a sensitivity study of input parameters that potentially affect the drip shield response. The frame model is suitable for sensitivity analysis because modifications of geometry and loading conditions are straightforward and little computational effort is required for running the analyses. Using a rather simplified structural model is justified, given the large uncertainties of several drip shield parameters and loading conditions, which overcome the precision obtained with complex finite element models.

In this chapter, the methodology to evaluate the strength capacity of the drip shield is presented for the baseline model. This model considers most of the expected system

parameters and static loading conditions of the drip shield and is the reference system for the sensitivity study of Chapter 4. To demonstrate that the frame model is capable of reproducing the response of the drip shield finite element model, the output parameters of both models are compared for several loading configurations.

3.1 Frame Model Description

The drip shield frame model is based on the U.S. Department of Energy (DOE) drip shield drawings discussed in Chapter 2 (Bechtel SAIC Company, LLC, 2004a). The elastic behavior of the drip shield frame model is based on beam–column elements. The nonlinear behavior is included by means of concentrated plasticity at the end of the beam–column elements where zero-length nonlinear rotational springs are incorporated. In addition, the structural analyses include geometric nonlinearities due to P-Delta effects that take place when gravity loads act on the deformed drip shield configurations.

The drip shield failure criterion is the onset of structural instability, which is reached by

monotonically increasing the static loads until a minute loading increase results in unbounded displacements (Ibarra, 2003). Drip shield collapse is associated with the maximum gravity load that is applied at the onset of structural instability (known as vertical load-carrying capacity).

The interaction of the drip shield bulkhead and waste package due to large vertical crown deformations may also be assumed as a drip shield failure. Before the onset of drip shield structural instability, however, the drip shield crown deflection is not enough to cause drip shield waste package contact. Contact of the drip shield walls and the waste package is not automatically assumed as drip shield failure.

3.1.1 Frame Model Geometry

The unidimensional beam–column elements of the drip shield frame model represent both the Titanium Grade 24 frame components and the equivalent cross section of the Titanium

Grade 7 plates, based on their stiffness contribution. This stiffness contribution is simplified by adopting an equivalent width obtained from calibrating the drip shield frame model with elastic SAP2000 and ABAQUS finite element models (Appendix A). Frame model calibration is based on the comparison of eigenvalues and displacements. The equivalent widths for the different drip shield sections are listed on Table 3-1.

Table 3-1. Bending Strength Capacity of Average Cross Sections Used in the

Center 105 230 15.0 45.7 105.1 151.0 2.30 3.31 1.44

Transition 110 230 27.7 61.8 123.3 191.9 2.00 3.11 1.56

Corner 135 230 27.7 86.0 172.4 264.3 2.00 3.07 1.53

Column Sections

C1 (base) 45.36 450 15.0 15.0 21.5 36.4 1.43 2.42 1.70

C2 50.69 441 15.0 18.6 27.0 45.0 1.45 2.42 1.67

C3 56.02 431 15.0 22.3 33.1 54.2 1.49 2.44 1.64

C4 61.35 418 15.0 25.9 39.7 66.8 1.53 2.58 1.68

C5 66.67 404 15.0 29.5 46.8 74.3 1.59 2.52 1.59

C6 72.00 387 15.0 32.8 54.0 85.0 1.64 2.59 1.57

C7 77.33 367 15.0 35.8 59.7 96.0 1.67 2.68 1.61

C8 86.25 345 15.0 38.4 65.5 107.2 1.70 2.79 1.64

C9 87.98 320 15.0 40.5 71.3 118.6 1.76 2.93 1.66

C10 93.31 282 27.7 46.7 83.8 138.9 1.80 2.98 1.66

C11 98.64 248 27.7 47.4 89.6 149.7 1.89 3.16 1.67

C12 (top) 101.3 230 27.7 47.2 91.8 154.7 1.94 3.27 1.69

* 1 mm = 0.0394 in

† 1 kN-m = 0. 737 k-ft

The node and element discretization of the drip shield frame model is presented in Figure 3-1.

The model prevents out-of-plane deformations, and its base assumes pin restraints (see Section 3.1.4). The drip shield columns and some of the bulkhead sections are nonprismatic components (i.e., the cross section varies along the length of the element). Figure 3-2a presents the variable cross section for support beams (columns). The 15-mm [0.6-in]-thick Titanium Grade 7 plate corresponds to the drip shield shell, whereas the 12.7-mm [0.5-in]-thick Titanium Grade 7 plate is an external support plate included in the top column sections

(Figures 2-2 and 2-3). Figure 3-2b shows the cross section for the bulkhead component, where the 12.7-mm [0.5-in]-thick Titanium Grade 7 plate is an internal support plate only included in the sections adjacent to the drip shield corner (Figures 2-2 and 2-3).

3-3

(a) (b)

Figure 3-1. Discretization of Drip Shield Frame Model: (a) Node Labels and (b) Element Labels

To account for the variable cross section in the frame model, the columns were discretized in 12 prismatic elements (constant section), each having the average cross section of the corresponding longitudinal segment.¹ SAP2000 (Computers and Structures, Inc., 2004) is capable of evaluating nonprismatic sections, but the use of prismatic sections is preferred because nonlinear inelastic springs must be connected to prismatic elements in series. The simplification is acceptable because the cross section variation with length is smooth along the support beams (3.5-percent slope). For the bulkhead, however, two nonprismatic beams were included close to the corners of the drip shield because of the significant variation of the bulkhead depth in this region (Figure 2-5). In the joints where a nonprismatic member is connected to a prismatic one, the nonlinear spring was included only in the latter element. In the joints where nonprismatic elements should be connected, an auxiliary prismatic element of very small length was introduced in between the joints to accommodate the nonlinear spring (elements 15 and 32 of the frame model, Figure 3-1).

________________________

1The elements at the top of the columns (12 and 35 in Figure 3-1b) are larger than the rest of the elements because these elements have contant cross section.

b_E = variable

15 mm Variable

(27.7 bottom to 86.3 top)

76 mm

Ti-7 (External Plate)

Ti-24 “Support Beam”

(Column)

Ti-7 (Shell)

12.7 mm

138 mm bE = 230 mm

38 mm

20 mm

Variable

(90 mm center to 120 mm corner) Ti-7 (Internal

Plate) Ti-24 Bulkhead

15 mm Ti-7 (Shell)

12.7 mm (a)

(b)

Figure 3-2. Cross Sections for Drip Shield Frame Model: (a) Support Beams Columns and (b) Bulkhead (Beams) [1 mm = 0.039 in]

3-5