For a dynamics load case, it is unlikely that the local forces of the adjacent elements will add up to the restraint load. This is due to the following reasons:

1) All loads are reported as positive. Therefore, if one element load is positive, and the other is negative, the sum of the two reported (positive) element loads will of course not equal the restraint load.

Example: Element load #1 = 500; Element load #2 = -300; Restraint load = 200. Reported values are 500, 300, and 200 respectively. Of course, 500 + 300 does not equal 200!!

2) Reported results are the sum of a large number of modal, pseudostatic, and missing mass results, which are summed either using the SRSS or absolute methods. Therefore, in the above example, the user may be able to determine what happened, but any relationship is lost as the summation becomes more intricate.
<table>
<tr>
<th>Example:</th> <th>Element Load #1 </th><th>Element Load #2</th><th>Restraint Load</th>
</tr>
<tr>
<td>Mode #1</td> <td align="center">500</td><td align="center">-300</td><td align="center"> 200</td>
</tr>
<tr>
<td>Mode #2</td><td align="center"> 400</td> <td align="center"> 200</td> <td align="center">600</td>
</tr>
<tr>
<td>Missing Mass</td><td align="center">200</td><td align="center">-200 </td><td align="center">0</td>
</tr>
<tr><td> </td><td> </td><td> </td><td> </td>
</tr>

<tr>
<td>SRSS Totals</td><td align="center">671</td><td align="center"> 412 </td><td align="center">632</td>
</tr>
<tr>
<td>ABS Totals</td> <td align="center">1100</td><td align="center">700</td> <td align="center"> 800</td>
</tr>
</table>

Obviously, 671 + 412 does not equal 632, and 1100 + 700 does not equal 800!! (And we can't see any other apparent relationship.)

3) Dynamic models are constructed of discrete mass points, not as continuous elements. Therefore there are no body loads in dynamic analysis, only point loads. Therefore, the free-body diagram for the restraint includes not just the loads from each adjacent element, but also the force due to the acceleration times the mass of the restrained node (this force usually goes directly into the restraint, not into the adjacent elements). (The contribution of this mass point can be decreased if the user creates a finer mesh of mass points, i.e., so less mass goes directly into the restraints.)
<table>
<tr>
<th>Example:</th> <th>(Element Load #1)</th> <th>(Element Load #2)</th> <th>(Mass Point x Acceleration)</th> <th> (Restraint Load)</th>
</tr>

<tr>
<td>Mode #1</td> <td align="center">500</td> <td align="center">-300</td> <td align="center">50</td> <td align="center">250</td>
</tr>

<tr>
<td>Mode #2</td> <td align="center">400</td> <td align="center">200</td> <td align="center"> -20</td> <td align="center">180</td>
</tr>

<tr>
<td>Missing Mass</td> <td align="center">200</td> <td align="center">-200</td> <td align="center">1000</td> <td align="center">1000</td>
</tr>

<tr>
<td>SRSS Totals</td> <td align="center">671</td> <td align="center">412</td> <td align="center"> (not reported)</td> <td align="center">1046</td>
</tr>

<tr>
<td>ABS Totals</td> <td align="center">1100</td> <td align="center">700</td> <td align="center">(not reported)</td> <td align="center">1430</td>
</tr>
</table>

Obviously, 671 + 412 does not equal 1046, and 1100 + 700 does not equal 1430!! (And again there isn't any apparent relationship.) Note that the bulk of the Mass Point contribution will often show up (on the restraint) as the missing mass contribution, since it is rigidly restrained. (That explains why the greatest contributor to your restraint was missing mass, but the greatest contributor to your element was due to a mode.)

Due to summation methods as demonstrated above, the Response Spectrum method will never give "exact" results. Rather, the intent of the Response Spectrum method is to provide probabilistic results: i.e., probabilistically the largest element load, probabilistically the largest restraint load, probabilistically the highest stress, probabilistically the largest displacement, etc.

As far as you particular problem (calculating the load on the skewed snubber) is concerned, I don't see a problem. Your component loads are FX=1096, FZ=566. Therefore, adding these vectorially, your resultant load can be found as SQRT(1096x1096+566x566)=1234. The line of action of the snubber is confirmed by calculating ARCSIN(566/1234)=27.3 degrees.


------------------
Regards,
Richard Ay (COADE, Inc.)



[This message has been edited by rich_ay (edited February 04, 2000).]