SMA Backup Structure Tube Loads

William N. Davis , SAO Central Engineering

February 3, 1998

This memo documents results of tube loads and simplified bond stress calculations for the SMA Reflector Backup Structure (BUS) tube end fittings. Resultant tube loads are presented for combined loadings due to  gravity, wind, and thermal conditions. Two sets of data are presented, one with the backup structure nodes pinned as a true truss, and the other with full fixity at the tube ends. This was done to bound the tube loads in consideration of possible moment carrying capability of the tube ends.  The maximum axial forces and recommended proof loads for each tube cross section are summarized in Table 1.
 

Discussion:

The SMA BUS model was run for gravity, wind loadings, and a uniform thermal soak of 25^oC. The model was also modified to include the effects of full fixity at the tube ends, and run for both configurations.

Eccentricities for CFRP tube connections to nodes were assumed to be 1.61mm for all tube sizes.

Axial assembly loads are based on the axial stiffness of each tube type and an assembly mismatch of .0005", which is as close as the tubes are able to be shimmed during assembly. No assembly load is considered for the dash-27 tubes, which are the first set of tubes to be installed.

The maximum axial loads from all load combinations for each tube type are listed in Table 1. A proof load of 1.5 times the maximum combined load is recommended. Philippe Raffin has also calculated proof  loads with a separate model. They are very similar but not exactly the same as those calculated here due to various modeling differences. The larger of the two values is taken as the recommended proof load. 


Maximum loads for each tube type for the individual load cases are summarized in Tables 2 and 3,  for the fully fixed and pinned tube end conditions respectively.

The load cases are then combined as follows:  (gravity) +/- (56m/sec wind) +/- (25^oC)  at the 5 degree and zenith elevations. Maximum axial loads and bending moments from these combinations are then added to assembly loads and additional moments due to eccentricities based on worst case offsets are calculated for each rod type and summarized in Tables 4-5 for the fully fixed tube joints, and Tables 6-7 for the pinned tube joints.

Results of simplified calculations of bond stresses at the tube ends and tube inside diameter locations for axial and bending loads also included in Tables 4-7. Average bond stresses are calculated based on the assumption that the axial force and bending moment are shared by the bond area at the tube end and the tube's inside wall. The amount of load in each portion of the bond is estimated by the following equations, based on relative stiffness of the two areas, and substantiated by a detailed model of several  bond geometries.
 

     Where R_o and R_i are the tube outside and inside radii (in.),
     and L is the length of the end fitting bonded to the inside surface of the tube (in.).
     F_end is the fraction of the load carried by the bond at the tube end
     F_side is the portion carried by the bond on the inside diameter of the tube (lb.).

List of Tables

Table 1 - Maximum tube loads and recommended proof loads

Table 2 - Maximum tube loads by loadcase, full fixity at truss nodes
Table 3 - Maximum tube loads by loadcase, pinned at truss nodes

Table 4 - Max of combinations at 5^o elevation, full fixity at truss nodes
Table 5 - Max of combinations at 90^o elevation, full fixity at truss nodes

Table 6 - Max of combinations at 5^o elevation, pinned at truss nodes
Table 7 - Max of combinations at 90^o elevation, pinned at truss node